JP2010198399A - Particle behavior analyzing device and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To shorten analytical processing time of long-range interaction force in a particle behavior analyzing device. <P>SOLUTION: A lookup table in which an interparticle range in each fixed interval is made to correspond to long-range interaction force applied to a pair of particles in each interparticle range is prepared (S110). An interparticle range r is calculated (S120), and after processing of contact force, a pair of particles to be used for calculating the long-range interaction force are selected, and a long-range force of the interparticle range r is specified by referring to the lookup table (S152). Since the long-range force is specified by using the lookup table, processing time can be shortened as compared with usual calculation of the long-range force. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a particle behavior analysis apparatus and a program.

  Patent Document 1 proposes a mechanism relating to behavioral simulation of particles such as powder and granules. Patent Documents 2 and 3 propose a mechanism that uses a lookup table in simulation processing.

JP 2007-193152 A Japanese Patent Laid-Open No. 08-185545 Japanese Patent Application Laid-Open No. 06-083980

  Patent Document 1 proposes a mechanism for performing particle behavior analysis processing according to a force division parallel algorithm by parallel processing of a plurality of processors. Specifically, a plurality of computing devices are connected to a network so that particle behavior analysis can be realized at high speed while considering a plurality of types of interparticle interactions. For example, each particle's magnetic force, electrostatic force, and contact force interaction between each particle was calculated using a separate force matrix, distributed to specific processors, and calculated by communicating between specific processors. The sum of interaction forces is obtained, and the position coordinate is calculated by solving the equation of motion of each particle. And the position coordinate of each particle | grain is communicated to a specific processor, and calculation information is updated. Such a process is similarly repeated until a predetermined calculation step is reached.

  Patent Document 2 discloses a mechanism for displaying detailed and quantitative interference information such as approach and collision between objects in robot simulation. When the object surface for which interference information is to be displayed is used as the projection surface and the object for which interference information is to be calculated is used as the projection object, the interference information is displayed from the object surface for which interference information is to be displayed. Find the distance image to the object you want to calculate. Then, the distance image is converted into a texture image with reference to a lookup table, and the obtained texture image is texture-mapped on the object surface on which interference information is to be displayed when drawing a scene, and the interference information is displayed as a texture. Let

  Japanese Patent Application Laid-Open No. 2004-228561 discloses a mechanism that can favorably preserve highlights in color simulation and can be applied well between the same color system and between chromatic and achromatic colors. For example, a lightness-lightness conversion lookup table, a saturation-saturation conversion lookup table, and a lightness-saturation conversion lookup table are created. Calculating a weighting coefficient corresponding to the look-up table for saturation-saturation conversion and a look-up table for lightness-saturation conversion, and calculating the changed saturation based on the weighting coefficients corresponding to both look-up tables; By obtaining the lightness after change based on the lightness-lightness conversion lookup table, the hue specified as the change color is adopted to change the color of the color change target region.

  An object of this invention is to provide the structure which can perform the analysis process regarding long-distance interaction force in a short time rather than the case where this invention is not applied.

  The invention according to claim 1 is a storage unit that stores correspondence information in which each inter-particle distance is associated with a long-range interaction force acting on a particle pair at each inter-particle distance; A particle behavior analysis device comprising: a particle behavior calculation unit that calculates a particle behavior by specifying a long-range interaction force at a distance between a pair of particles with reference to information stored in the storage unit It is.

  The invention according to claim 2 is the invention according to claim 1, wherein when there are a plurality of types of long-range interaction forces to be analyzed, the storage unit determines the distance between the particles and the distance between the particles. Correspondence information in which a total value of long-range interaction forces acting on particle pairs at a distance is associated is stored.

  According to a third aspect of the present invention, in the first or second aspect of the present invention, when there are a plurality of types of particles to be analyzed, the storage unit is configured according to a combination of particle types constituting the particle pair. The correspondence information is stored.

  The invention according to claim 4 is the invention according to any one of claims 1 to 3, wherein the storage unit stores the correspondence information with respect to an interparticle distance equal to or greater than a predetermined threshold value. The particle behavior calculation unit calculates a long-range interaction force when the interparticle distance of the particle pair to be analyzed is less than the threshold value, and stores the memory when the interparticle distance of the particle pair to be analyzed is equal to or greater than the threshold value. The long-range interaction force is specified with reference to the information stored in the section.

  The invention according to claim 5 is the area division according to any one of claims 1 to 4, wherein the analysis target area is divided into a plurality of areas and a number indicating the position of each area is given. The storage unit and the particle behavior calculation unit substitute a difference in the number of each region where each particle of the particle pair to be analyzed exists as the interparticle distance.

  The invention according to claim 6 is the invention according to claim 5, wherein the storage unit stores the correspondence information with respect to either a positive value or a negative value of a difference in the number of the area, When the sign of the difference in the number of the region of the particle pair to be analyzed is different from the sign of the difference in the correspondence information stored in the storage unit, the particle behavior calculation unit is referred to from the storage unit. The sign of the correspondence information is inverted and used.

  The invention according to claim 7 includes a correspondence information generation unit that generates the correspondence information in an analysis process and stores the correspondence information in the storage unit in the invention according to any one of claims 1 to 6, In the analysis process, when the long-range interaction force is not stored in the arrangement position of the storage unit corresponding to the interparticle distance of the particle pair to be analyzed in the analysis process, the correspondence information generation unit corresponds to the interparticle distance. The long-range interaction force calculated by the particle behavior calculation unit is stored in the array position of the storage unit corresponding to the inter-particle distance.

  The invention according to claim 8 is the invention according to claim 7, wherein when the storage capacity becomes insufficient, the storage unit discards the reference frequency less.

  In the invention according to claim 9, the long-range interaction force in the inter-particle distance of the particle pair to be analyzed includes the inter-particle distance, the long-distance interaction force acting on the particle pair in each inter-particle distance, Is a program that causes the electronic computer to function as a particle behavior calculation unit that calculates the behavior of particles by specifying with reference to the correspondence information stored in the storage unit that stores the correspondence information that associates.

  According to the first and ninth aspects of the present invention, it is possible to perform analysis processing related to the long-distance interaction force in a shorter time than when the inventions according to the first and ninth aspects are not applied.

  According to the second aspect of the present invention, when there are a plurality of types of long-distance interaction forces required for analysis, the analysis process for the long-distance interaction force is shorter than when the invention according to the second aspect is not applied. You can do it in time.

  According to the invention described in claim 3, when there are a plurality of types of particles to be analyzed, it is possible to appropriately specify the long-range interaction force corresponding to each combination as compared with the case where the invention according to claim 3 is not applied. can do.

  According to the invention described in claim 4, it is possible to balance the analysis accuracy and the analysis processing time as compared with the case where the invention according to claim 4 is not applied.

  According to the fifth aspect of the present invention, the analysis process relating to the long-distance interaction force can be performed in a shorter time than when the invention according to the fifth aspect is not applied.

  According to the invention described in claim 6, the amount of correspondence information stored in the storage unit can be reduced as compared with the case where the invention according to claim 6 is not applied.

  According to the seventh aspect of the present invention, it is possible to prevent waste of storing correspondence information that is not referred to during analysis processing in the storage unit, compared to the case where the invention according to the seventh aspect is not applied.

  According to the eighth aspect of the present invention, it is possible to avoid the adverse effects caused by the shortage of storage capacity, compared with the case where the invention according to the eighth aspect is not applied.

1 is a diagram illustrating a configuration example of an electrophotographic image forming apparatus. It is a block diagram which shows the structural example of a particle behavior analysis system. It is a figure explaining 1st Embodiment of a main particle behavior analysis apparatus. It is a figure explaining 1st Embodiment of a secondary particle behavior analysis apparatus. It is a flowchart which shows the process sequence of the particle behavior analysis method of the comparative example with respect to the particle behavior analysis method of the 1st example of 1st Embodiment. It is a flowchart which shows the process sequence of the particle behavior analysis method of the 1st example of 1st Embodiment. It is a figure explaining an example (the 1) of the look-up table used in the 1st example of 1st Embodiment. It is a figure explaining an example (the 2) of the look-up table used in the 1st example of 1st Embodiment. It is a figure explaining contrast with the particle behavior analysis method of a comparative example and the 1st example of a 1st embodiment. In the 2nd example of 1st Embodiment, it is a figure explaining the area | region which refers to a look-up table. It is a flowchart which shows the process sequence of the particle behavior analysis method of the 2nd example of 1st Embodiment. It is a figure explaining 2nd Embodiment of a main particle behavior analysis apparatus. It is a figure explaining 2nd Embodiment of a secondary particle behavior analyzer. It is a flowchart which shows the process sequence of the particle | grain behavior analysis method of the 1st example of 2nd Embodiment. It is a figure explaining the production | generation method of the look-up table in 2nd Embodiment. It is a flowchart which shows the process sequence of the particle | grain behavior analysis method of the 2nd example of 2nd Embodiment. It is a flowchart which shows the process sequence of the particle behavior analysis method of the 3rd example of 2nd Embodiment. It is a figure explaining the effect | action of the 3rd example of 2nd Embodiment. It is a figure explaining 3rd Embodiment of a main particle behavior analysis apparatus. It is a figure explaining 3rd Embodiment of a secondary particle behavior analysis apparatus. It is a flowchart which shows the process sequence of the particle behavior analysis method of the 1st example of 3rd Embodiment. It is a flowchart which shows the process sequence of the contact determination process in 3rd Embodiment. It is a figure explaining an example of the look-up table used by the 1st example of 3rd Embodiment. It is a figure explaining contrast with the particle behavior analysis method of the 1st example of a comparative example and a 1st embodiment, and the 1st example of a 3rd embodiment. It is a flowchart which shows the process sequence of the particle | grain behavior analysis method of the 2nd example of 3rd Embodiment. It is a figure explaining the area | region which refers to a look-up table in the 2nd example of 3rd Embodiment. It is a flowchart which shows the process sequence of the particle behavior analysis method of the 3rd example (the 1) of 3rd Embodiment. It is a flowchart which shows the process sequence of the particle | grain behavior analysis method of the 3rd example (the 2) of 3rd Embodiment. It is a figure explaining an example of the look-up table used in the 3rd example of 3rd Embodiment. It is a figure explaining the feature point of the 3rd example of a 3rd embodiment. It is a flowchart which shows the process sequence of the particle behavior analysis method of the 4th example (the 1) of 3rd Embodiment. It is a flowchart which shows the process sequence of the particle behavior analysis method of the 4th example (the 2) of 3rd Embodiment. It is a flowchart which shows the process sequence of the particle behavior analysis method of the 4th example (the 3) of 3rd Embodiment. It is a figure explaining the production | generation method of the look-up table in the 4th example of 3rd Embodiment.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In the following, a particle behavior analysis device will be described as an example as a specific example to which the information processing device is applied. As an apparatus in which particles to be analyzed by the particle behavior analysis apparatus exist, an image forming apparatus such as a printer apparatus, a facsimile apparatus, or a multifunction machine having these functions will be described as an example.

  In relation to the analysis target particles, attention is paid to developer behavior analysis in a developing device of an electrophotographic image forming apparatus using only toner particles or a developer composed of carrier particles and toner particles. However, this is only an example, and the apparatus in which the particles to be analyzed exist is not limited to the image forming apparatus.

<Outline of image forming apparatus>
FIG. 1 is a diagram illustrating a configuration example of an electrophotographic image forming apparatus such as a printing apparatus (printer) or a copying apparatus (copier). As shown in the figure, the image forming apparatus 1 includes a charging device 20 including a DC power source 22, an AC bias power source 24, and a charging unit 26 arranged around the photoreceptor 10, a laser light source 32, and a polygon. An exposure device 30 having a mirror 34 and a motor 36, a developing device 40 having a stirring mechanism (not shown), a transfer device 50 having a transfer power source 52 and a transfer unit 54, a cleaning device 60 having a blade mechanism, and paper And a fixing device 70 provided with a roll mechanism disposed at a predetermined position on the downstream side on the conveyance path.

  The developing device 40 is filled with developer particles 102. In the figure, one developer particle 102 is indicated by one circle for convenience. Actually, the developer particle 102 is, for example, a two-component system containing carrier particles composed of magnetic materials having different physical properties and particle sizes and non-magnetic toner particles (for example, toner particles of each color) as main components. It is. The pair of carrier particles and toner particles forms a magnetic powder as a whole. The toner particles are adsorbed to the carrier particles by electrostatic force. In general, the particle size of the carrier particles is larger than the particle size of the toner particles. Note that magnetic toner may be used as the toner particles.

  In addition to the carrier particles and toner particles described above, the developer 102 has a particle diameter (average particle diameter of about 1 to 50 nanometers) to ensure powder flowability, chargeability, transferability, or cleaning properties. Meter) small substances (external additives) are mixed. Examples of the external additive include titanium oxide and silica containing silicone oil.

  The developing device 40 includes a developing roll 140 (also referred to as a mag roll, a magnet roller, or a magnetic transport roller), which is an example of a carrying roll carrying the developer particles 102 on the surface, in the storage container 101, and a peripheral surface having an opening 101a. Prepare to stick out a little. A predetermined number of magnets 142 are arranged in the developing roll 140 at predetermined intervals along the inner periphery.

  Further, the developing device 40 includes a regulating blade 150 (trimming blade block) that functions as a height regulating member or a layer forming member in the vicinity of the developing roll 140, and the developer particles 102 formed along the magnetic force lines of the magnet 142. The height of the magnetic brush (heading) is regulated.

  The developing roll 140 rotates together with the photoconductor 10 rotated in the direction of arrow X, and the rotational movement direction of the surface on the side facing the photoconductor 10 rotates in the same direction as the movement direction X of the photoconductor 10 (arrow Y direction). Is done. The photosensitive member 10 may be driven to rotate in the direction opposite to the moving direction X.

  The developer particles 102 are conveyed to the developing roll 140 side while being agitated and frictionally charged by an agitating and conveying roll (not shown) having an agitating function. The amount of adsorption of the developer particles 102 to the developing roll 140 is regulated by the regulating blade 150, and the developer particles 102 adhere to the periphery of the developing roll 140 at a certain height. The carrier particles constitute a magnetic brush by a magnetic field from a magnet 142 built in the developing roll 140. The toner particles are transported together with the carrier particles to a portion facing the photoreceptor 10.

  When the image forming apparatus 1 is configured as a copying apparatus, the charging device 20 generates a charging potential (initial potential) by superimposing the AC bias voltage from the AC bias power source 24 on the DC voltage from the DC power source 22, and this charging. The surface of the photoconductor 10 is charged to a uniform surface potential with an electric potential.

  Thereafter, a polygon mirror which is driven by a motor 36 to rotate a laser beam emitted from a laser light source 32 provided on the exposure device 30 on the surface of the photosensitive member 10 in accordance with image data obtained by scanning the original with a reading device (not shown). By scanning at 34, the surface of the photoconductor 10 is exposed to form an electrostatic latent image having a latent image potential.

  Subsequently, the developing device 40 forms the toner particles in the developer particles 102 on the surface of the photoconductor 10 while mixing the developer particles 102 such as output color toner particles and carrier particles in a stirring mechanism (not shown). A toner image is formed on the surface of the photoconductor 10 by being superimposed on the electrostatic latent image. As a result, the latent image formed on the surface of the photoconductor 10 is developed. The carrier particles after the development processing and the toner particles that have not been ejected to the photoconductor 10 are collected in the storage container 101.

  Thereafter, the transfer device 50 transfers the toner image formed on the surface of the photoreceptor 10 onto the printing paper conveyed from the outside. A predetermined range in which the photoconductor 10 and the transfer unit 54 face each other is referred to as a transfer region.

  The transferred sheet is conveyed to the fixing device 70 side, and the fixing device 70 fixes the toner image onto a printing sheet as a transfer body by heating, melting and pressing. The fixed paper is discharged out of the image forming apparatus 1 by a discharge device (not shown).

  On the other hand, the cleaning device 60 removes residual toner remaining on the surface of the photoreceptor 10 after being transferred by the transfer device 50. Although the residual potential remains on the surface of the photoreceptor 10 after cleaning, it is used in the next electrophotographic process after the initial potential is applied by the charging device 20.

  In the case where the image forming apparatus 1 for color image formation is configured, as a configuration of a main part related to image formation, for example, the toner image of the photoconductor 10 is directly applied to a sheet by a transfer device 50 on a sheet as a transfer body. For example, a plurality of engines corresponding to output colors of K (black), Y (yellow), M (magenta), and C (cyan) are inlined in the order of K → Y → M → C, for example. The K, Y, M, and C images are processed in parallel (simultaneously) by four engines, that is, the photosensitive member 10 is placed on the intermediate transfer belt one color at a time according to the arrangement position. The toner image may be transferred (particularly referred to as primary transfer), and then the toner image on the intermediate transfer belt may be transferred onto the paper (particularly referred to as secondary transfer). .

  In such an electrophotographic process, charging of the photoconductor 10, exposure of a scanned original image, development, that is, toner superimposition on the photoconductor 10, toner transfer to a sheet and toner fixing, and cleaning of the photoconductor 10 are performed. Become. In the electrophotographic process, for example, by applying a powder behavior analysis simulation in each process such as stirring, development, and transfer, an image to be formed is predicted and evaluated without actually performing an image forming experiment. Analysis of the behavior of carrier particles and toner particles is an important factor for the development of the electrophotographic apparatus main body and the developing apparatus 40.

  For example, in the analysis of the developing device 40, an agitation process, a development process, and the like are analyzed. For example, a predetermined range region on the stirring and conveying roll side of the regulating blade 150 is referred to as a layer formation region, and in the particle behavior analysis for the developer particles 102, the effects of a magnetic field and a gravitational field are taken into consideration. A predetermined range region that is agitated and conveyed by the agitating / conveying roll is referred to as an agitating / conveying region, and the action of the gravitational field is considered in the particle behavior analysis of the developer particles 102.

  A predetermined range area in which the developer particles 102 between the stirring conveyance area and the layer forming area are magnetically attracted to the developing roll 140 is referred to as a pickup area. In the particle behavior analysis of the developer particles 102, magnetic field and gravity are used. Consider field effects.

  A region where the peripheral edges of the photoconductor 10 and the developing roll 140 face each other and a developing action is performed is referred to as a developing nip region. In the particle behavior analysis of the developer particles 102, the effects of an electric field, a magnetic field, and a gravitational field are considered. A predetermined range area in which the developer particles 102 are collected is referred to as a pick-off area, and in the particle behavior analysis for the developer particles 102, the effects of a magnetic field and a gravitational field are considered.

  The surface of the photoconductor 10 is charged according to the recorded image, and the toner particles fly to the surface of the photoconductor 10 by electrostatic force. The flying toner particles adhere to the surface of the photoconductor 10, and a toner image corresponding to the recorded image is formed. At this time, the image quality of the recorded image depends on how the toner particles are attracted to the photoreceptor 10. Since the toner particles are conveyed to the photoconductor 10 by the carrier particles, how the toner particles are adsorbed to the photoconductor 10 is determined by the carrier particles in the developing nip region between the developing roll 140 and the photoconductor 10 and It is determined by the behavior of the toner particles.

  Further, in the transfer process in the transfer device 50, while changing condition parameters in the transfer process such as the surface roughness of the photoreceptor, the speed difference between the transfer bodies such as the photoreceptor / intermediate transfer belt and paper, and the contact width of the transfer body, By repeating the powder behavior analysis simulation, the image quality formed is evaluated while reproducing the transfer process. Incidentally, in the particle behavior analysis for the transfer process, an electric field and a gravitational field acting on the developer particles 102 (particularly toner particles) are considered.

<Particle behavior analysis system>
FIG. 2 is a block diagram illustrating a configuration example of the particle behavior analysis system. In the particle behavior analysis system, when analyzing each interaction, parallel processing using many processors tends to saturate the parallel processing efficiency. As a countermeasure, analysis is performed using various division methods such as particle division, force division, and region division. In the following description, unless otherwise specified, it is assumed that the particle behavior analysis using the force splitting method is performed. The mechanism itself for performing the particle behavior analysis using the force splitting method may be the same as that described in Patent Document 1, and the description thereof is omitted here.

  The particle behavior analysis system 200A is configured by connecting a plurality of particle behavior analysis devices 202 each having a particle behavior analysis function to a network. Each particle behavior analysis apparatus 202 has a single core with a core portion (so-called CPU portion) that performs calculation processing in one housing (on a semiconductor substrate).

  Each particle behavior analysis apparatus 202 transmits main processing data to each other via the network 209 and can execute the particle behavior analysis processing in parallel, and the particle behavior analysis system 200A is practical. It is configured as a parallel computing device (cluster computer). The network 209 is managed by a network management device 208 whose communication state has a routing function.

  As an example, each particle behavior analysis device 202 may be configured by the same as a general electronic computer. In the illustrated example, one of the particle behavior analysis devices 202 constituting the particle behavior analysis system 200A functions as a main particle behavior analysis device 202a having a function of a calculation management node that controls the whole. ing. The remaining particle behavior analysis device 202 is connected to the main particle behavior analysis device 202a as a sub particle behavior analysis device 202b controlled by the main particle behavior analysis device 202a.

  Here, although the details of the secondary particle behavior analysis apparatus 202b of this embodiment will be described later, each secondary particle behavior analysis apparatus 202b for each row direction in the force matrix (force matrix) used when applying the force splitting method. For the representative node (representative secondary particle behavior analysis device 202b_1) having a function unit (row direction processing result output processing unit) that collectively outputs the analysis results obtained by the above (for the other general nodes ( And a general secondary particle behavior analyzer 202b_2).

  In the figure, for convenience, one network line is drawn from the network management device 208, and the main particle behavior analysis device 202a and the secondary particle behavior analysis device 202b are connected to the network line. Each particle behavior analysis device 202 is connected to an individual port provided in the network management device 208, and communication between the particle behavior analysis devices 202 is performed via the network management device 208. .

  Connected to the main particle behavior analysis device 202a are an instruction input device 210 such as a keyboard and a mouse for performing various operations for particle behavior analysis processing, and a display device 212 for presenting the processing results as image information to the operator. Has been.

  By adopting such a basic system configuration, when performing particle behavior analysis processing for a system with multiple types of multi-particle interactions, each particle's magnetic interaction, electrostatic interaction, or mechanical interaction For each interaction such as an action (contact force; contact force between a wall or the like and contact between particles), a behavior analysis is executed by parallel processing by applying a predetermined division method. The mechanical interaction is, for example, a contact force between a wall or other object and particles, or a contact force due to contact between particles. The wall (wall surface) serves as a motion boundary of the analysis region when analyzing the behavior of the analysis target particle.

  For example, for carrier particles, the magnetic force is mainly calculated using a magnetic field analysis method based on the Maxwell equation, and for the toner particles, electrostatic field analysis mainly focusing on Coulomb force is performed. The contact force of the toner particles is calculated from the contact amount of the particles, and finally, the equation of motion is solved by combining the acting forces to predict the behavior of the developer particles 102 with high accuracy.

  In particular, in the present embodiment, when each interaction analysis is performed in each particle behavior analysis apparatus 202, a region decomposition method (SD) or a particle decomposition method (PD: Particle Decomposition Method or RD: Replicated Data Method) is used. By using a force division method (algorithm using a force matrix) instead, the amount of calculation data communication among all the processors (each particle behavior analysis device 202 of the present embodiment) is reduced. By reducing the amount of communication of calculation data, the parallelization performance of the program when using multiple processors is improved, and the calculation time is greatly shortened.

  In the basic configuration of the particle behavior analysis system 200A shown in FIG. 2, the configuration of a practical parallel computer (cluster computer) is shown, but this is only an example. Although not shown in the figure, as shown in FIG. 3 of Patent Document 1, a plurality of particle behavior analysis devices each having a particle behavior analysis function are connected to each other via a first network and configured as a parallel computing device. The plurality of particle behavior analysis systems may be further connected by another second network. In this case, each particle behavior analysis system can transmit main processing data to each other via an external network (second network), and can execute different particle behavior analysis processing for different objects in parallel. The particle behavior analysis system of a modified example is configured as a grid-type computing device formed by connecting a virtual parallel computing device over a network. Moreover, it is good also as what has the multi-core which accommodated the several core part (what is called CPU part) in one housing | casing (semiconductor chip).

  In addition, here, in order to increase the efficiency when outputting the analysis result to which the force splitting method is applied as a file, the secondary particle behavior analysis device 202b, the representative secondary particle behavior analysis device 202b_1, and other general secondary particle behavior analysis devices are used. 202b_2, but this is not essential.

<Particle Behavior Analysis Device: First Embodiment>
3 to 3A are block diagrams illustrating a configuration example of the first embodiment of the particle behavior analysis apparatus 202. Here, FIG. 3 shows a main particle behavior analysis apparatus 202a (including a representative secondary particle behavior analysis apparatus 202b_1 of a representative node) having a function of a calculation management node. FIG. 3A shows a general secondary particle behavior analysis apparatus 202b_2 having a function of a general node other than the representative node.

  In the first embodiment, the lookup table is stored in the data storage unit 238 in advance before the analysis of the object behavior, and the distance between the objects that appears during the analysis is determined based on the value stored in the lookup table. It is characterized in that it refers to the long-range interaction force.

  Therefore, as shown in FIG. 3, the particle behavior analysis device 202 of the first embodiment is the same as the main particle behavior analysis device 202 a, the data input unit 220, the data processing unit 230, the information presentation unit 240, and the moving particle determination unit 260. , An LUT acquisition unit 280 is provided. The data input part 220, the information presentation part 240, and the LUT acquisition part 280 are provided in the part corresponded to the calculation management node of the main particle behavior analysis apparatus 202a. The data input unit 220 takes in data to be processed using the instruction input device 210 or the like. The data processing unit 230 performs a particle behavior analysis process. The information presentation unit 240 presents the processing result to the operator using the display device 212 or the like.

  Further, the particle behavior analysis device 202 includes a division processing unit 250 in a portion corresponding to the calculation management node of the main particle behavior analysis device 202a. When the processing unit 250 divides the processing target element by the force division method, each of the calculation systems (also referred to as a processor; in FIG. 1, the particle behavior analysis device 202) is configured by a calculation device and performs particle behavior analysis by the force division method. Assign each segment to.

  The data input unit 220 receives commands and data input by an operator via the keyboard and mouse constituting the instruction input device 210, and passes the data necessary for the data processing unit 230 and the division processing unit 250, respectively. .

  The division processing unit 250 is set to use a vertical N / horizontal N force matrix, and assigns analysis target particles to each force matrix. It should be noted that the division processing unit 250 may consider that the calculation load at each node is substantially equal. For example, when the processing target element is divided by a predetermined division method, the calculation time (calculation time per step) in the same range time in each calculation system (particle behavior analysis system 200) configured by a plurality of calculation devices, respectively. ) Are equal to each other, an analysis load distribution processing unit that distributes analysis target elements is provided. The analysis load distribution processing unit may be configured to be shared by the division processing unit 250 (denoted as an analysis load distribution processing unit 250a), or may be provided as a functional element different from the division processing unit 250.

  The analysis load distribution processing unit 250a configures the developer 102 when considering a plurality of types of interparticle interactions such as electrostatic interaction, magnetic interaction, mechanical interaction (contact force), or adhesion force. Even when multiple types of particles with different physical properties (carrier particles, toner particles, external additives in this example) are to be analyzed, the calculation time difference between each numerical computation processing unit (particle behavior calculation unit) during parallel analysis processing In order to surely reduce the difference, the dividing process for distributing the analysis target elements is performed in consideration of the difference in the acting force and the particle type of the analysis target.

  The analysis load distribution processing unit 250a also takes into account the processing performance (calculation capability) of each particle behavior analysis device 202 constituting the particle behavior analysis system 200 and each particle behavior analysis system 200 constituting the particle behavior analysis system 201. Therefore, it is better to allocate the analysis target elements. Then, the analysis load distribution processing unit 250a assigns the division charge region and the division charge particle (group) to a calculation system (particle behavior analysis system 200) configured by a plurality of calculation devices (particle behavior analysis device 202). The data processing unit 230 performs data communication with each of other numerical calculation processing units in charge of processing related to the other divided portions, and performs particle behavior analysis by the force division method for the divided divided portions. Do.

  When processing data using the force splitting method, consider the relationship between the interparticle distance and the interaction force (distance dependence of the interaction force), and analyze multiple component particle systems with multiple particle types to be analyzed. A cutoff may be set. For example, when the interaction force to be analyzed is an interaction force that should be focused only on the interaction with particles close to each other (referred to as short-range force or short-range force), the cut-off is set small and the distance is close When the interaction force needs to be paid attention not only to the particles but also to the particles at a distance, the cut-off is set large.

  The data processing unit 230 performs a particle behavior analysis process described later based on the data input from the data input unit 220. More specifically, the data processing unit 230 includes a data receiving unit 232, a numerical operation processing unit 234 (particle behavior calculation unit), an output data processing unit 236, and a data storage unit 238.

  The data storage unit 238 is a device that stores parameter table data for calculating the interaction, and is connected to the numerical operation processing unit 234 via a memory bus. Here, the data storage unit 238 includes a temporary storage unit 238 a and an external storage device 238 b provided for each particle behavior analysis device 202.

  The temporary storage unit 238a is a so-called cache memory built on the same semiconductor substrate as the CPU. The external storage device 238b is an external semiconductor storage medium (for example, having a capacity of several hundred MB to several GB) also called a so-called main memory, and a hard disk device (HDD) having a larger capacity (several hundred GB or more) than the main memory. ) Etc. As is well known, the CPU access is faster in the cache memory than in the main memory.

  The data processing unit 230 is included in the secondary particle behavior analysis apparatus 202b. Here, when the main particle behavior analysis device 202a corresponds to a representative node, as shown in the figure, the secondary particle behavior analysis device 202b includes a representative secondary particle behavior analysis device 202b_1. On the other hand, when the main particle behavior analyzer 202a does not correspond to the representative node, the general subparticle behavior analyzer 202b_2 is used instead of the representative subparticle behavior analyzer 202b_1.

  The data receiving unit 232 stores the data input from the data input unit 220 in the external storage device 238b, and supplies data necessary for numerical calculation to the numerical operation processing unit 234. The external storage device 238b stores, for example, data on the configuration of the developing device 40 to be analyzed, the coordinates of the developer particles 102, physical property values, and the like.

  The numerical arithmetic processing unit 234 performs input / output (memory access) of data (information) to and from the data storage unit 238 in accordance with the determined division method for the divided portion assigned by the division processing by the division processing unit 250. It functions as a particle behavior calculator that performs calculations.

  As shown in FIG. 3, the particle behavior analysis apparatus 202 further includes a row direction processing result output processing unit 290 in the portion of the representative secondary particle behavior analysis apparatus 202b_1. The row direction processing result output processing unit 290 acquires each analysis result from the output data processing unit 236 of each general secondary particle behavior analysis apparatus 202b_2 on the same row to which it belongs. Then, the row direction processing result output processing unit 290 includes the analysis results from its own output data processing unit 236 and collectively outputs each analysis result of the row to the information presenting unit 240 of the calculation management node.

  As shown in FIG. 3A, the general secondary particle behavior analysis apparatus 202b_2 does not include the row direction processing result output processing unit 290 in the representative secondary particle behavior analysis apparatus 202b_1. The output data processing unit 236 transfers each analysis result to the row direction processing result output processing unit 290 of the representative secondary particle behavior analysis apparatus 202b_1 on the same row to which the output data processing unit 236 belongs.

  Based on the supplied data, each numerical arithmetic processing unit 234 performs magnetic interaction, electrostatic interaction, or mechanical interaction on developer particles 102 (specifically, carrier particles, toner particles, etc.) that are examples of particles. Analyze particle behavior considering multiple interactions such as action (contact force) at the same time by applying force splitting method. The numerical arithmetic processing unit 234 supplies the output file of the analysis result to the output data processing unit 236 at a predetermined timing.

  For example, first, the main particle behavior analysis device 202a specifies the number (the number of processors) of the particle behavior analysis devices 202 constituting the particle behavior analysis system 200 that can be used for the particle behavior analysis processing at the present time. Thereafter, various physical parameters necessary for the calculation, initial arrangement of particles, and calculation conditions such as the number of analysis target particles that are particularly necessary in the force division method are read. Then, the identified particle behavior analysis devices 202 (processors) are arranged in a matrix according to the force division method, and the analysis target particles (carrier particles and toner particles constituting the developer 102) are assigned.

  Next, a plurality of types of interaction forces between many-body particles are calculated by being distributed to specific processors (other numerical calculation processing units 234). At this time, a plurality of types of interaction between many-body particles are calculated using different force matrices. For example, the magnetic interaction with the partner particle in the assigned matrix is analyzed using the force matrix for the magnetic interaction analysis. Next, communication is performed between specific processors via the output data processing unit 236, and the total value of the magnetic interaction forces calculated in a distributed manner is obtained for the magnetic interaction.

  Similarly, the electrostatic interaction with the partner particle in the assigned matrix is analyzed using the force matrix for the electrostatic interaction analysis. Next, communication is performed between the specific processors via the output data processing unit 236, and the total value of the electrostatic interaction forces calculated in a distributed manner is obtained for the electrostatic interaction.

  Further, the mechanical interaction (contact force) with the partner particle in the assigned matrix is analyzed using the force matrix for analyzing the mechanical interaction. Next, communication is performed between specific processors via the output data processing unit 236, and a total value of mechanical interaction forces calculated in a distributed manner is obtained for the mechanical interaction.

  Furthermore, the sum total value calculated | required about each of a magnetic interaction, an electrostatic interaction, and a mechanical interaction (contact force) is added, and a total sum value is calculated | required. Next, using the total sum of the magnetic interaction, electrostatic interaction, and mechanical interaction (contact force), the equation of motion of each particle is solved and the position coordinates are calculated. Then, the position coordinates of each particle obtained in this way are sent to a specific processor (numerical calculation processing unit 234) related to the interaction matrix, and the calculation information is updated. Thereafter, the same processing is repeated until a predetermined calculation step is reached.

  The output data processing unit 236 outputs the calculation result output from the numerical operation processing unit 234 for each predetermined calculation step in addition to the exchange of calculation data at each calculation step between the numerical operation processing units 234. From the particle behavior analysis device 202 (numerical calculation processing unit 234) determined in advance (in this example, the force splitting method in the row direction) and passed to the information presentation unit 240. The information presentation unit 240 aggregates data from each particle behavior analysis device 202, converts it into display data, and supplies it to the display device 212. The display device 212 displays a processing result image based on the display data supplied from the information presentation unit 240. The behavior prediction of the developer particle 102 is visualized and displayed on the display device 212 so that the behavior of the developer particle 102 that is actually difficult to confirm can be visually grasped.

  Note that the processor not only functions as the numerical operation processing unit 234 but also can realize functions provided by a general CPU such as other general arithmetic processing functions and control functions. The secondary particle behavior analysis apparatus 202b has a configuration similar to that of a general electronic computer (computer) as a mechanism for allowing the CPU to function as each functional unit by program processing, and a computer system is constructed. .

  In the present embodiment, the mechanism for analyzing the behavior of particles is not limited to being configured by a hardware processing circuit, but may be realized by software using a computer (computer) based on a program code that realizes the function. Is possible. Therefore, a program suitable for realizing the mechanism according to the present embodiment by software using an electronic computer (computer) or a computer-readable recording medium (storage medium) storing this program is extracted as an invention. By adopting a mechanism that is executed by software, the processing procedure and the like can be easily changed without changing hardware.

  A series of particle behavior analysis processing can be realized not only by hardware or software alone but also by a combined configuration of both. When executing processing by software, a program showing the processing procedure is installed (installed) in a storage medium in a computer embedded in hardware and executed, or a general-purpose electronic computer capable of executing various types of processing is used. Incorporate and execute the program.

  A program for causing a computer to execute the particle behavior analysis processing function is distributed through a recording medium such as a CD-ROM. Alternatively, this program may be stored in the FD instead of the CD-ROM. In addition, an MO drive may be provided to store the program in the MO, or the program may be stored in another recording medium such as a nonvolatile semiconductor memory card such as a flash memory.

  The program constituting the software is not limited to being provided via a recording medium, but may be provided via a wired or wireless communication network. For example, the program may be obtained by downloading or updating from another server via a network such as the Internet. The program is provided as a file describing a program code that realizes the function of performing particle behavior analysis processing. In this case, the program is not limited to being provided as a batch program file, and the hardware configuration of a system configured by a computer Depending on the case, it may be provided as an individual program module.

  For example, the computer system includes a central control unit 910 in which a processor core functions, a ROM (Read Only Memory) that is a read-only storage unit, or a RAM (Random Access Memory) that is a memory that can be read and written as needed. A storage unit 912, an operation unit 914, and other peripheral members not shown. The ROM stores a control program for the particle behavior analysis processing function. The operation unit 914 is a user interface for accepting an operation by a user.

  As a control system of the computer system, an external recording medium such as a memory card, which is not shown, can be inserted and removed, and can be connected to a communication network such as the Internet. For this purpose, the control system includes a memory reading unit 920 that reads information on a portable recording medium and a communication I / F 922 as a communication interface unit with the outside in addition to the central control unit 910 and the storage unit 912. It is good to make it. By providing the memory reading unit 920, a program can be installed or updated from an external recording medium. By providing the communication I / F 922, the program can be installed or updated via the communication network.

  Note that the specific means of each unit (including functional blocks) of the information processing apparatus for realizing the particle behavior analysis processing of the present embodiment is hardware, software, communication means, a combination thereof, or other means. This is well known to those skilled in the art. Moreover, the functional blocks may be combined and integrated into one functional block. Also, software that causes a computer to execute program processing can be distributed and installed according to the combination.

  Although not shown, when the secondary particle behavior analysis device 202b has a system configuration that cannot be divided into the representative secondary particle behavior analysis device 202b_1 and the other general secondary particle behavior analysis device 202b_2, the row direction processing result output processing unit 290 is removed. Then, the output data processing unit 236 of each secondary particle behavior analysis apparatus 202b performs file output processing separately, or performs data communication in order to collect file output data in any one node (processor). The output data processing unit 236 of one node performs file output processing as a representative.

  The data processing unit 230 (numerical calculation processing unit 234) of each processor applies a particle behavior analysis method to which an individual element method for tracking the behavior of individual particles based on the equation of motion is applied. The individual element method is a method of simulating powder behavior with high accuracy by tracking the behavior of individual particles constituting the powder every moment based on the equation of motion. The image forming apparatus 1 shown in FIG. 1 adopting an electrophotographic process can be applied to various powder behavior simulations including carrier and toner particles.

  However, in the particle behavior calculation algorithm based on the individual element method, the force (mechanical contact force, electromagnetic far-distance force, etc.) received by the particle is calculated every minute and the particle coordinates are updated according to the equation of motion. However, a huge number of particles must be considered in order to reproduce the actual powder process. In general methods, the analysis load increases with the square of the number of particles. Therefore, if the number of particles increases, the amount of calculation becomes enormous, and even though the performance of the computer is improved, it is equivalent to the actual system. It is often difficult to perform calculations with a number of particles. It is difficult to perform large-scale analysis with realistic calculation time.

  Therefore, in the particle behavior analysis method, for the purpose of shortening the calculation time, it has been proposed to use a plurality of electronic computers in which programs are installed and to perform distributed processing by parallelizing each program. Each computer performs behavior analysis by the individual element method.

  Also in this embodiment, when applying the individual element method, a region division method, a force division method, a particle division method, a method that arbitrarily combines them, or a plurality of computers that apply any of the other division methods. Adopt parallel processing method. The region division method is a method in which an analysis region (calculation target region) that is a processing target element is divided and all particles existing in the region are allocated to each processor for each divided region. The particle division method is a method of dividing a calculation target particle, which is a processing target element, by a predetermined number and assigning it to each processor. The force division method is a method using an algorithm using a force matrix.

  The division processing unit 250 divides the analysis target region into a plurality of regions instead of collectively setting the entire analysis target device, and further divides the analysis target region into a plurality of regions, It is preferable to apply a particle division method or a force division method. For example, when analyzing the entire developing device 40, the analysis may be performed separately for the agitating and conveying area, the pickup area, the layer forming area, the developing nip area, and the pick-off area.

  In addition, in the individual element method, regardless of whether or not various division methods are applied, not only short-range interaction force (also referred to as short-range force: contact force as a typical example) but also long-range interaction force ( Calculation of the distance force (also referred to as long-distance force) is also required, which further increases the calculation load. For example, in an electrophotographic process, the electromagnetic long-range interaction force acting on carrier particles and toner particles must be considered.

  A hard sphere that simplifies the calculation method of the mechanical contact force and the cut-off method that ignores the long-range force such as magnetic force between particles that exceed a certain distance as a method of reducing the calculation load of the long-range force There are models. However, these methods increase the calculation speed and increase the calculation efficiency, but on the other hand, there is a problem that the analysis accuracy is deteriorated and the reliability of the analysis result is lowered. For example, in the magnetic force cut-off method, the magnetic interaction force between long-distance objects is ignored, and thus the accuracy of analysis is unavoidable.

  Therefore, in order to simulate the powder behavior with high accuracy under conditions that are closer to the actual system, a high-speed method for calculating long-distance force that combines calculation speed (calculation efficiency) and analysis accuracy (reliability of analysis results). Development is required.

  In this embodiment, regardless of whether or not the division method is applied and what the division method is, even in the same analysis system and processing step, for each particle, a long-range force analysis method is dynamically applied. Take a different approach. The basic idea is to reduce the calculation load of the long-distance force acting on the object in the discrete element method (in other words, to increase the processing speed), and use a look-up table (LUT). This is achieved by omitting the calculation of distance force. Focusing on the interparticle distance as a physical quantity that changes from time to time, it is determined whether to look up the lookup table based on the interparticle distance.

  In order to achieve such a mechanism, in the particle behavior analysis apparatus 202 of the first embodiment, first, the calculation management node portion of the main particle behavior analysis apparatus 202a includes the LUT acquisition unit 280, and further, the secondary particle behavior analysis apparatus 202b. This part includes a moving particle determination unit 260.

  The LUT acquisition unit 280 acquires a long-range interaction force lookup table, and stores the acquired lookup table information in the data storage unit 238 of each secondary particle behavior analysis apparatus 202b. Specifically, as shown in FIG. 3, the LUT acquisition unit 280 includes an LUT generation unit 282 (corresponding information generation unit) that creates a lookup table in which long-distance interaction forces according to the distance between objects are associated with each other. Assume that any one of the LUT accepting unit 286 (corresponding information accepting unit) that accepts a look-up table created externally in advance is included. The look-up table associates the long-distance force at the inter-particle distance r_n for each inter-particle distance r_n at a constant interval, and the numerical calculation processing unit 234 has a long-distance force at the inter-particle distance r not in the array. Is identified by a technique such as substitution or interpolation based on the long-distance force at the inter-particle distance r_n in the array.

  When there are a plurality of types of long-range interaction forces to be calculated, the LUT acquisition unit 280 also prepares a plurality of lookup tables according to the types. For example, when focusing on carrier particles and toner particles, the magnetic force is calculated using a magnetic field analysis method based on the Maxwell equation for carrier particles, and the electrostatic field analysis is performed for toner particles focusing on Coulomb force. . Therefore, a Coulomb force lookup table and a magnetic force lookup table are prepared separately. As another method, when there are a plurality of long-range interaction forces to be calculated, the total value of each interaction force may be stored in the lookup table as a long-range interaction force.

  Based on the calculation result of the behavior of each particle by the numerical calculation processing unit 234, the moving particle determination unit 260 determines a particle whose movement amount exceeds a predetermined threshold value, and sends the determination result to the numerical calculation processing unit 234. Notice.

  The moving particle determination unit 260 includes a moving particle identification unit 262 and a threshold setting reception unit 266. The threshold setting accepting unit 266 accepts designation of a threshold from the operator and notifies the moving particle specifying unit 262 of the information. The threshold value setting reception unit 266 is provided not in each of the secondary particle behavior analysis devices 202b but in the calculation management node portion so as to notify the information on the specified threshold to the moving particle specifying unit 262 of each secondary particle behavior analysis device 202b. May be.

  The moving particle specifying unit 262 compares the calculation result of the moving amount from the numerical calculation processing unit 234 with the threshold value specified via the threshold setting receiving unit 266 for each particle, and the interparticle distance (for example, the center distance). For particles that do not exceed the threshold, the long-range force is obtained based on a long-range force calculation method that has been generally used in the individual element method. On the other hand, for particles whose interparticle distance exceeds a threshold value, a long distance force corresponding to the obtained interparticle distance is read with reference to a lookup table, and the read value is used as a long distance force in this step. . By setting the threshold value to zero, virtually all particles that are not in contact with other substances (other particles or walls) can be found by referring to the lookup table and corresponding to the calculated interparticle distance. The long distance force to be read is read out, and the read value is used as the long distance force in this step.

  In other words, the numerical calculation processing unit 234 determines whether the particles are in contact with each processing step and for each particle depending on whether or not the particle is in contact with each other and whether or not the interparticle distance exceeds a threshold value (excluding zero). Switches whether or not to refer to the lookup table for the distance force. By referring to the lookup table, the far-field force calculation is omitted in that step. Since the long-distance force is obtained by referring to the lookup table without performing the calculation, the processing efficiency is improved as compared with the normal calculation of the long-distance force (that is, the analysis processing time is shortened).

  Hereinafter, the mechanism of this embodiment will be specifically described.

<Particle Behavior Analysis Processing: First Example of First Embodiment>
4 to 5C are diagrams for explaining a particle behavior analysis method of the first example in the particle behavior analysis device 202 of the first embodiment. Here, FIG. 4 is a flowchart showing a processing procedure of the particle behavior analysis method of the comparative example with respect to the particle behavior analysis method of the first example of the first embodiment. It may be considered that there is no difference from the basic flowchart of the discrete element method (DEM). FIG. 5 is a flowchart illustrating a processing procedure of the particle behavior analysis method of the first example of the first embodiment for reducing the calculation load of the long-distance force between particles. 5A to 5B are diagrams illustrating an example of a lookup table used in the first example of the first embodiment (also in the second embodiment). FIG. 5C is a diagram illustrating a comparison between the comparative example and the particle behavior analysis method of the first example of the first embodiment.

  The first example of the first embodiment shown in FIG. 5 is to reduce the calculation load of the long-distance force acting on the object in the discrete element method (in other words, to speed up the processing), using a long-distance force using a lookup table. This method is realized by omitting the calculation. This is the most basic of all the embodiments that are common to other embodiments described later. In FIG. 5, as an example, attention is paid to a distance (for example, a distance between centers) of a particle (an example of an object) as a physical quantity that changes every moment, and a lookup table is referred to based on the distance between particles. In the first example, the moving particle determination unit 260 does not need to include the threshold setting reception unit 266.

  First, as shown in FIG. 4, in the comparative example, the numerical operation processing unit 234 takes in data necessary for numerical calculation from the data receiving unit 232. Among them, there are initial coordinate data (data of particle arrangement positions) of the developer particles 102. The numerical calculation processing unit 234 identifies the initial particle arrangement (S100). Then, corresponding to the distance between the objects, a short distance force (here, contact force) and a long distance force (for example, magnetic force and Coulomb force) are specified. That is, first, in the contact determination process (S121) of each particle pair, the inter-particle distance is obtained based on the coordinate data of the particle (S124), and the contact determination of each particle pair is further performed (S126). The contact force is not calculated for the particle pair that is not determined to be in contact (S126-NO), and the contact force is calculated for the particle pair that is determined to be in contact to obtain the contact force. (S126-YES, S128). For example, highly accurate contact force calculation is performed based on a viscoelastic model generally used conventionally in the individual element method.

  Thereafter, a particle pair (object pair) for calculating a long-distance interaction force is selected, and a long-distance force is strictly calculated by a method generally used in the conventional individual element method (S150). The direction in which the force acts is specified, the sign is adjusted according to the specified direction (S180), and then the particle coordinates are updated based on the contact force and the long-distance force (S190).

  It should be noted that the calculation of the long distance force is not necessarily performed. For example, a long-range force is calculated in the particle behavior analysis in the image forming apparatus 1 that performs image formation by an electrophotographic process, but a long-range force calculation is not required in the analysis of the deposition behavior of glass beads from a hopper. .

  Thereafter, the process returns to step S124 until the calculation step satisfying the file output condition is reached, and the same processing is repeated (S194-NO). When the calculation step that satisfies the file output condition is reached (S194-YES), an output process is performed (S196). Here, “output processing” means, for example, file output of analysis results. Note that this file output is not necessarily executed.

  Thereafter, the process returns to step S124 until the calculation step satisfying the end condition is reached, and the same processing is repeated (S198-NO). Here, the “calculation step that satisfies the end condition” may be performed until all the particles to be analyzed are in a generally stable position.

  On the other hand, in the first example of the first embodiment, as shown in FIG. 5, before analyzing the object behavior, the interparticle distance and the Coulomb force or magnetic force at the interparticle distance are calculated for each interparticle distance. A long-distance interaction force look-up table in which a long-distance force such as force is associated is prepared in advance (S110).

  When preparing the lookup table based on the idea of the interparticle distance alone, if the distance between the target particle and the other particle is the same, the other particle is the first, second, third, Regardless of where in the fourth quadrant, the far-distance forces are the same and there is no distinction of the direction of action.

  For example, even if the LUT generation unit 282 creates a lookup table in which the far-distance force F [r] corresponding to the distance r between the objects at regular intervals (for example, 1 mm step) is created and stored in the data storage unit 238. Alternatively, the LUT accepting unit 286 may accept a lookup table created externally in advance and store it in the data storage unit 238.

  As a configuration of the lookup table, for example, when there are a plurality of types of long-distance forces F [r] to be calculated, such as magnetic force Fp [r] and Coulomb force Fq [r], FIG. As shown, a lookup table LUT_1 for the magnetic force Fp [r] and a lookup table LUT_2 for the Coulomb force Fq [r] are prepared for each type. Note that the look-up table LUT_3 is a look-up table in which the magnetic force Fp [r] and the Coulomb force Fq [r] are gathered with respect to the interparticle distance r, but this should be substantially calculated. When there are a plurality of types of long-range interaction forces, this corresponds to a case where a plurality of lookup tables are prepared according to the types.

  As another method, as shown in FIG. 5B, the total value (Fp [r] + Fq [r]) of each interaction force (for example, magnetic force Fp [r] and Coulomb force Fq [r]) is set to a long distance. You may make it prepare the lookup table LUT_4 made into interaction force (total interaction force Fsum [r]). Compared with the case where each is prepared separately, the number of arrays required for the lookup table is reduced, so that the number of memories required for the lookup table is small, and the number of lookup table references is also reduced. Memory reduction and faster processing are achieved.

  In addition, when there are a plurality of particle types to be analyzed, such as developer particles 102 including carrier particles, toner particles, and external additives, a lookup table is provided for each combination of particle types constituting the particle pair. It is good to prepare several. This is because even if the long-distance force is the same type and the inter-particle distance is the same, the long-distance force differs if the combination particle type is different. For example, regarding magnetic force Fp [r], Coulomb force Fq [r], and total interaction force Fsum [r], a pair of toner particles and toner particles, a pair of toner particles and external additives, a pair of carrier particles and carrier particles A lookup table is prepared separately for each carrier particle / external additive pair and each external additive / external additive pair. For magnetic force Fp [r], there is no need to have a look-up table for a pair of toner particles and toner particle, and for Coulomb force Fq [r], a pair of carrier particles and carrier particles.

  As in the comparative example, after processing related to contact force, a particle pair (object pair) for calculating the long-range interaction force is selected. Here, in the first embodiment, unlike the comparative example, the inter-particle distance is matched with a long-distance force lookup table stored in the data storage unit 238, and the corresponding long-distance force (magnetic force Fp [ r], Coulomb force Fq [r] and total interaction force Fsum [r]). That is, the long-range interaction force corresponding to the interparticle distance calculated in step S124 is referred from the lookup table (S152).

  In the analysis, when there are multiple types of long-range interaction forces to be calculated and different lookup tables are used, for each long-range interaction force, the long-range interaction force corresponding to the interparticle distance is used. The applied force is referenced from each lookup table. For example, in the previous example, the magnetic force Fp [r] is referred to the lookup table LUT_1 for the magnetic force Fp [r], and the Coulomb force Fq [r] is referred to the lookup table LUT_2 for the Coulomb force Fq [r]. Refer to Alternatively, the lookup table LUT_3 is referred to for both the magnetic force Fp [r] and the Coulomb force Fq [r]. Then, the magnetic force Fp [r] and the Coulomb force Fq [r] are added to specify the long distance force at the interparticle distance.

  In addition, when there are multiple types of long-range interaction forces to be calculated in the analysis, when a lookup table is prepared in which the total value of multiple long-range interaction forces is the long-range interaction force total value Reads out the total value corresponding to the interparticle distance, and reflects a plurality of long-range interaction forces in the object behavior by referring to the lookup table once. For example, in the previous example, the lookup table LUT_4 for the total interaction force Fsum [r] obtained by adding the magnetic force Fp [r] and the Coulomb force Fq [r] is referred to.

  Here, when the object corresponding to the actual inter-particle distance r does not exist in the look-up table array, the closest one is read and substituted, or two adjacent values are read and the long-distance force is calculated by interpolation. May be calculated. The interpolation calculation may be a simple average or a weighted average related to a distance difference. As a weighted average expression, for example, when two adjacent values are Fq [x] and Fq [x + 1], Fq [r] = (1−x / r) × Fq [x] + x / r × The first expression Fq [x + 1] or Fq [r] = {1− (x / r) ^ 2} × Fq [x] + {(x / r) ^ 2} × Fq [x + 1] An expression can be considered. Among these, the weighted average is the method with the best analysis accuracy. Interpolation calculation has a smaller calculation load than the case where exact calculation of long-distance force is performed by a method generally used conventionally in the individual element method.

  After referring to the long-distance force corresponding to the interparticle distance from the lookup table, the direction in which the long-distance force acts is specified and the sign is adjusted according to the specified direction (S180), and then the contact force and the long-distance The particle coordinates are updated based on the force (S190).

  Since the long-distance force itself at the interparticle distance is a positive value, it is the same value as long as the interparticle distance is the same regardless of the position where the other particle exists with respect to one particle (target particle). In the behavior calculation, the long-distance force acts on the value referenced from the lookup table by referring to the mutual particle coordinates, that is, referring to the position where the other particle is present with respect to the target particle. Identify the direction.

  Specifically, the reference standard when referring to the look-up table is the interparticle distance (which is always a positive value), and the x and y directions are used to determine the action direction of the referenced far-field force. The sign of the difference between the coordinates (which can be positive or negative) is used. When the other particle is in the first quadrant, the action direction in the x direction is “+” and the action direction in the y direction is “+”, and when the other particle is in the second quadrant, the action direction in the x direction is “−”. ", The direction of action in the y direction is" + ", and when the other particle is in the third quadrant, the direction of action in the x direction is"-", the direction of action in the y direction is"-", and the other particle is When in the fourth quadrant, the action direction in the x direction is “+” and the action direction in the y direction is “−”.

  FIG. 5 shows the detailed procedure of this code adjustment. The long-distance force referred from the lookup table is divided into a long-distance force component in the x direction and a long-distance force component in the y direction based on the particle coordinate relationship. Then, it is determined whether or not the difference value of the coordinate in the x direction is positive (S182). If it is negative, the sign of the long-distance force in the x direction is reversed (S182-NO, S184). Similarly, it is determined whether or not the difference value of the coordinate in the y direction is positive (S186). If it is negative, the sign of the long-distance force in the y direction is reversed (S186-NO, S188).

  As described above, in the first example of the first embodiment, the long-distance force corresponding to the interparticle distance is specified with reference to the look-up table. The processing efficiency is improved rather than calculating. In the case of thinning out the calculation of the long-distance force at that step, the analysis accuracy decreases. However, in the first example of the first embodiment, the identification of the long-distance force at that step is not thinned out. Such analysis accuracy is not lowered. Thus, according to the processing method of the first embodiment, both processing speed and analysis accuracy are achieved. The processing efficiency of the entire analysis system is increased while maintaining the analysis accuracy. The analysis processing time as a whole is shortened without reducing the reliability of the analysis result.

  FIG. 5C shows calculation times (standardized values) under certain analysis conditions for the comparative example and the first example of the first embodiment. Here, the normalized value means that the comparative example is “1” for each of the total calculation time, the long-distance force calculation time, and the interparticle distance calculation time.

  For example, when the volume of the first particle is q1 and the volume of the second particle is q2, the Coulomb force Fq [r] is defined by “K × q1 × q2 ÷ r ÷ r”. When a comparative example for calculating a long-distance force is applied and a target calculation is actually executed, the calculation of the Coulomb force Fq [r] includes “real number multiplied by 2 + real number divided by 2 = 4.24 sec. / M times "calculation time was required. On the other hand, when the first example of the first embodiment that specifies the long-distance force with reference to the lookup table is applied and processing is performed on the same thing as the comparative example, “array search + value The processing time of “assignment = 0 to 3.1 sec / M times” is sufficient. Compared to the comparative example, the processing time (calculation time) of the method of the first example of the first embodiment is shortened.

  In the first example of the first embodiment, the calculation time varies because the time required for the array search differs depending on which position of the array in the lookup table is stored.

  In order to arrange the interparticle distance r in the lookup table, a method of arranging the smaller interparticle distance r on the upper side of the array as shown in FIGS. 5A and 5B, and an upper side of the array (not shown). Any of the methods of arranging the one having the larger inter-particle distance r may be adopted. When performing a sequence search from the upper side of the sequence, in the former case, the time required for the sequence search increases as the actual interparticle distance r increases, and in the latter case, the sequence search increases as the actual interparticle distance r decreases. It takes a long time to complete. When performing a sequence search from the lower side of the sequence, in the former case, the time required for the sequence search increases as the actual interparticle distance r decreases, and in the latter case, the sequence search increases as the actual interparticle distance r increases. It takes a long time to complete. As a modified example, by preparing lookup tables for both arrays and referring to both lookup tables in order from the upper side (or the lower side) at the same time, the time required for the overall array search is substantially halved. It is possible.

<Particle behavior analysis processing: second example of the first embodiment>
6A to 6A are diagrams for explaining a particle behavior analysis method of the second example in the particle behavior analysis device 202 of the first embodiment. Here, FIG. 6 is a diagram illustrating an area that refers to a lookup table in the second example. FIG. 6A is a flowchart illustrating a processing procedure of the particle behavior analysis method of the second example of the first embodiment.

  The second example of the first embodiment balances the analysis accuracy and the analysis processing time. As shown in FIG. 6, when the particle pair is closer than the threshold Th1 (for example, r3), a comparative example is provided. In the same way as the above, the long-range interaction force is calculated, and the lookup table is referred only to the identification of the long-range interaction force when the long-distance interaction force exceeds the threshold Th1 (or more). Incidentally, as in the first example, when there are a plurality of types of long-distance forces F [r] to be calculated, such as magnetic force Fp [r and Coulomb force Fq [r], Separately, a lookup table is prepared, or a lookup table of the total interaction force Fsum [r] of their total value (Fp [r] + Fq [r]) is prepared. Furthermore, when there are a plurality of particle types to be analyzed, such as developer particles 102 including carrier particles, toner particles, and external additives, a lookup table is also provided for each combination of particle types constituting the particle pair. Prepare several.

  Hereinafter, the flowchart shown in FIG. 6A will be described focusing on differences from the first example. Similar to the first example, after the processing related to the contact force, first, the moving particle determination unit 260 compares the interparticle distance calculated in step S124 with the threshold Th1 specified by the threshold setting reception unit 266 (S130). ), And notifies the numerical calculation processing unit 234 of the result. If the interparticle distance is less than the threshold value Th1, the numerical calculation processing unit 234 performs the exact calculation of the far-distance force by the method generally used in the past by the individual element method as in the comparative example (S130-). YES, S150). On the other hand, when the interparticle distance exceeds the threshold Th1 (or above), the numerical calculation processing unit 234 looks for the long-range interaction force corresponding to the interparticle distance calculated in step S124, as in the first example. Refer to the up table (S130-NO, S152).

  In the second example of the first embodiment, when the interparticle distance r is less than the threshold Th1, the far distance force is actually calculated strictly without referring to the look-up table. Therefore, as shown in FIG. When r is less than the threshold Th1, the arrangement of the lookup table is not necessary.

  The method of the second example of the first embodiment compares the interparticle distance with the threshold value Th1, and specifies the long distance force with reference to the lookup table according to the comparison result, or calculates the long distance force strictly. I'm trying to switch between them. For this reason, the long-range interaction force that acts between particles that are relatively close to each other has better analysis accuracy than the first example that uses the reference values from the lookup table for the entire region. This is because there is no difference in accuracy when an object corresponding to the actual inter-particle distance r exists in the look-up table array, but when the corresponding object does not exist in the look-up table array, the closest one is read out. This is caused by substituting, or reading out two adjacent values and calculating a long-distance force by interpolation calculation. Since the long-distance force is generally inversely proportional to the square of the distance difference, even if the weighted average is calculated using the second equation weighted by the square of the distance, an error that cannot be ignored can occur in the long-distance interaction force. Because there is. That is, in the technique of the second example of the first embodiment, a region where the error between the actual distance and the distance stored on the lookup table has a large influence on the interaction force calculation is strictly determined. The long-range force is calculated and the decrease in accuracy is suppressed.

<Particle Behavior Analysis Device: Second Embodiment>
7 to 7A are block diagrams illustrating a configuration example of the second embodiment of the particle behavior analysis apparatus 202. Here, FIG. 7 shows a main particle behavior analysis apparatus 202a (including a representative secondary particle behavior analysis apparatus 202b_1 of a representative node) having a function of a calculation management node. FIG. 7A shows a general secondary particle behavior analysis apparatus 202b_2 having a function of a general node other than the representative node.

  The second embodiment does not store the look-up table in the data storage unit 238 in advance before analyzing the object behavior, but for a particle pair (object pair) that appears as an interparticle distance for the first time during the analysis. Calculates the long-range interaction force and stores the value in the lookup table. For the inter-particle distance that appears after the second time during the analysis, the long-range interaction force is calculated from the value stored in the lookup table. It is characterized in that it refers to. The waste of storing the correspondence information that is not referred to in the analysis processing in the data storage unit 238 is avoided, and as a result, the number of arrays required for the lookup table is small.

  Here, “inter-particle distance first appearing during analysis” and “inter-particle distance appearing second or later during analysis” constitute a lookup table with an array of inter-particle distances r_n at constant intervals. Consider. That is, consider that a lookup table based on a typical distance is used. Hereinafter, considering this point, the description will focus on the differences from the first embodiment.

  As shown in FIGS. 7 to 7A, the particle behavior analysis apparatus 202 of the second embodiment is different from the first embodiment in that the LUT generation unit 282 is provided in the portion of the secondary particle behavior analysis apparatus 202b. This takes into account the generation of a lookup table based on the analysis result of each secondary particle behavior analysis apparatus 202b. By the way, when a long distance force for a certain interparticle distance r is specified by any of the secondary particle behavior analysis devices 202b, the information is notified to the other secondary particle behavior analysis devices 202b, so that each You may comprise so that the information of a lookup table may be made common. Further, as in the first embodiment, the LUT generation unit 282 is configured to be included in the calculation management node portion of the primary particle behavior analysis device 202a, and the particles that first appear during the analysis in each secondary particle behavior analysis device 202b. The distance information may be notified to the LUT generation unit 282 so that the LUT generation unit 282 generates a lookup table. Further, the numerical operation processing unit 234 may function as the function of the LUT generation unit 282.

<Particle Behavior Analysis Processing: First Example of Second Embodiment>
8 to 8A are diagrams for explaining a particle behavior analysis method of the first example in the particle behavior analysis device 202 of the second embodiment. Here, FIG. 8 is a flowchart showing a processing procedure of the particle behavior analysis method of the first example of the second embodiment for reducing the calculation load of the long-distance force between particles. FIG. 8A is a diagram for explaining a lookup table generation method according to the second embodiment.

  In the second embodiment, since the lookup table is generated in the analysis process, there is no step S110 in the first embodiment, and the interparticle distance appears for the first time during the analysis after the processing related to the contact force. It is determined whether or not. In determining whether or not the interparticle distance appears for the first time during the analysis, as shown in FIG. 8A, for each interparticle distance r_n_n at a constant interval, the far-distance force at the interparticle distance r_n is associated. In order to construct the attached lookup table, the following determination process is performed. “N” in the interparticle distance r_n corresponds to 1 to z in FIG. 5A and the like, and r_0 is zero. In the following description, it is assumed that there is an LUT generation unit 282 in addition to the numerical operation processing unit 234, focusing on the differences from the first example of the first embodiment.

  First, the numerical calculation processing unit 234 determines whether or not the interparticle distance r exceeds r_1 / 2 (S132). When the interparticle distance r is equal to or less than r_1 / 2, the numerical computation processing unit 234 calculates the long-range interaction force corresponding to the interparticle distance calculated in step S124, as in the first example of the first embodiment. Reference is made from the lookup table (S132-NO, S152). Incidentally, in this case, when the long distance force at the interparticle distance r_1 does not yet exist in the lookup table, the numerical calculation processing unit 234 calculates the long distance force at the interparticle distance r (≦ r_1 / 2). (S150).

  When the interparticle distance r exceeds r_1 / 2, information on the interparticle distance r is notified to the LUT generation unit 282 to instruct generation of a lookup table. The LUT generation unit 282 specifies n satisfying (r_n−r_n−1) / 2 <r ≦ (r_n + r_n + 1) / 2 in order to associate the interparticle distance r with the interparticle distance r_n in the lookup table array. (S133) Further, it is determined whether or not a long distance force at the interparticle distance r_n exists in the lookup table (S134).

  When the long distance force at the interparticle distance r_n exists in the lookup table, the LUT generation unit 282 notifies the numerical calculation processing unit 234 to that effect. Similar to the first example of the first embodiment, the numerical calculation processing unit 234 refers to the long-range interaction force corresponding to the interparticle distance calculated in step S124 from the lookup table (S134-YES, S152).

  When the long distance force at the interparticle distance r_n does not exist in the lookup table (S134-NO), the LUT generation unit 282 calculates the long distance force at the interparticle distance r and the interparticle distance r_n by the numerical calculation processing unit 234. To instruct. The numerical computation processing unit 234 calculates the long-range interaction force at the interparticle distance r or the interparticle distance r_n, sets the value as the long-range interaction force, and notifies the LUT generation unit 282 (S135). The LUT generation unit 282 stores the long-range interaction force notified from the numerical calculation processing unit 234 in the array of interparticle distances r_n in the lookup table (S138).

  Here, rather than calculating the long distance force at the interparticle distance r and storing the value in the array of the interparticle distance r_n in the lookup table, the long distance force at the interparticle distance r_n is calculated and the value is calculated. Is preferably stored in the array of interparticle distances r_n in the lookup table. That is, when a long-distance interaction force lookup table corresponding to the inter-particle distance r at that time is not created, the conventional method using the inter-particle distance r_n in the lookup table array as the inter-particle distance. It is preferable to calculate the long-range interaction force and store the value as a lookup table. As shown in FIG. 8A (2), when the long-range force is calculated based on the actual (at that time) interparticle distance r itself, in the worst case, (r_n−r_n−1) / 2 <r ≦ (R_n + r_n + 1) / 2 in order to avoid representing a long-distance force at an interparticle distance r_n at an interparticle distance r (r_a is nearer to r_a and r_b is farther away) corresponding to both ends of (r_n + r_n + 1) / 2. is there. As the physical property value of particles other than the interparticle distance, the value at that time is used, but the interparticle distance r_n corresponding to the array of the lookup table is used for the interparticle distance, so that a more appropriate lookup table can be obtained. is there.

  Incidentally, considering the accuracy of the long distance force at the interparticle distance r at that time, even if the long distance force at the interparticle distance r_n is stored in the array of interparticle distances r_n in the lookup table, the far distance at that time is stored. Regarding the distance, it is conceivable that the far-distance force at the interparticle distance r_n at that time is also calculated and the value is taken as the far-distance force. However, in this case, it is not preferable because the calculation of the long-distance force is required twice and the calculation load increases. In order to avoid this calculation load, when a long-distance interaction force lookup table corresponding to r_n-1 or r_n + 1 is created, the lookup table including the far-distance force at r_n created here is used. You may make it refer similarly to the 1st example of 1st Embodiment. In other words, by using a long distance force corresponding to r_n-1 or r_n + 1, or by performing an interpolation calculation using each long distance force at r_n-1, r_n, r_n + 1, the interparticle distance r It is to specify the long-distance force. When the interpolation calculation is performed, it is not necessary to reduce the accuracy of the long-distance force compared to the case where the long-distance force corresponding to r_n-1 or r_n + 1 is substituted.

  The method of the first example of the second embodiment completes the lookup table in the analysis process, so that a memory for the interparticle distance r that does not appear in the analysis process becomes unnecessary. The number of arrays required for the lookup table is small, and the number of memories required for analysis is expected to be reduced. That is, when the inter-particle distance r that does not appear in the analysis process is predicted in advance, the memory prepared in the lookup table may be reduced accordingly.

<Particle Behavior Analysis Processing: Second Example of Second Embodiment>
FIG. 9 is a flowchart showing a processing procedure of the particle behavior analysis method of the second example in the particle behavior analysis device 202 of the second embodiment. In the second example of the second embodiment, the mechanism of the first example of the second embodiment is applied to the second example of the first embodiment. Although a detailed description is omitted, in the second example of the second embodiment, when the interparticle distance r is less than the threshold Th1, the far-distance force is actually strictly calculated without referring to the lookup table. As shown, when the interparticle distance r is less than the threshold value Th1, the arrangement of the lookup table is not necessary. Therefore, the mechanism of the first example of the second embodiment is applied when the interparticle distance r is equal to or greater than the threshold Th1.

<Particle Behavior Analysis Processing: Third Example of Second Embodiment>
10A to 10A are diagrams for explaining a third example particle behavior analysis method in the particle behavior analysis apparatus 202 according to the second embodiment. Here, FIG. 10 is a flowchart showing a processing procedure of the particle behavior analysis method of the third example of the second embodiment. FIG. 10A is a diagram for explaining the operation. FIG. 10 shows an application example of the second embodiment to the first example, but the third example is similarly applied to the second example of the second embodiment.

  The third example of the second embodiment is to prevent the harmful effects associated with memory reduction while reducing the number of memories prepared in the lookup table. In the first example of the second embodiment, it has been described that the number of arrangements required for the lookup table is small. However, when the inter-particle distance r that does not appear in the assumption appears in the analysis process, the memory is insufficient. There is a risk of bankruptcy.

  Therefore, in the third example, when the memory capacity is insufficient, the infrequently used one is discarded. Specifically, when the lookup table is referenced, the reference time point information (for example, the number of steps at the reference time point) and the cumulative reference number up to that point are associated with the referenced array value (interparticle distance r_n). Further, when storing the array value in the lookup table (S153), information at that time (for example, the number of steps at the time of storage) is also stored (S139). When it becomes necessary to store the array values in the lookup table and the memory necessary for creating the lookup table reaches a specified amount (S136-YES), the old array values and the degree of reference are small. The memory value for the array value is discarded (S137) and replaced with the latest one (S138).

  For example, as shown in FIG. 10A, in the case where the position of the aggregate of particles is greatly different between the first half, the middle and the second half in the analysis process, the behavior of the particles as a whole is large, but the movement in the first half and the second half is large. Assume that the movement is small. In this case, in the first half and the latter half, the appearance frequency of the large interparticle distance r is high and the small interparticle distance r is small, and when the memory is insufficient, the memory value of the small interparticle distance r is small. Should be discarded. On the other hand, in the middle stage, when the appearance frequency of the small interparticle distance r is high and the appearance frequency of the large interparticle distance r is low, and the memory is insufficient, the memory value of the small interparticle distance r and small reference degree is discarded. Good.

<Particle Behavior Analysis Device: Third Embodiment>
FIGS. 11A to 11A are block diagrams illustrating a configuration example of the third embodiment of the particle behavior analysis apparatus 202. Here, FIG. 11 shows a main particle behavior analysis apparatus 202a (including a representative secondary particle behavior analysis apparatus 202b_1 of a representative node) having a function of a calculation management node. FIG. 11A shows a general secondary particle behavior analysis apparatus 202b_2 having a function of a general node other than the representative node.

  In the third embodiment, the analysis target region is divided into a plurality of regions (referred to as subdivided cells), and numbers indicating the positions of the respective regions are assigned in order, and the interparticle distance r is substituted by the difference between the subdivided cell numbers. It is characterized by In other words, the range in which the particles to be analyzed for long-distance force exist is divided into subdivided cells. By specifying, the rough position of the analysis target particle is specified. And the difference of the subdivision cell number in which each analysis object particle | grain of the particle pair which calculates long-distance interaction force exists is made into the substitute value of the distance r between particles. Correspondingly, the look-up table also corresponds to the difference between the subdivided cell numbers.

  For this reason, the particle behavior analysis apparatus 202 according to the third embodiment does not include the LUT reception unit 286 and includes the region division unit 264. In the figure, an example in which the moving particle determination unit 260 includes the region division unit 264 is shown, but this is only an example. The area dividing unit 264 divides the range where the particles to be analyzed for the long-distance force exist into small divided cells, and assigns a number that defines the position to each small divided cell. When the coordinate position of the analysis target particle is notified from the numerical calculation processing unit 234, the region division unit 264 specifies the subdivision cell number where the analysis target particle exists and notifies the numerical calculation processing unit 234 of the information. . The numerical calculation processing unit 234 obtains a difference between the subdivided cell numbers in which each analysis target particle of the particle pair for calculating the long-range interaction force is present, and refers to the lookup table based on the difference. Here, when the cell number in the x direction of the particle of interest in the particle pair is xa, the cell number in the y direction is ya, the cell number in the x direction of the other particle is xb, and the cell number in the y direction is yb, The difference between the small divided cell numbers in the x direction is defined as xb-xa, and the difference in the y direction between the small divided cell numbers is defined as yb-ya.

<Particle Behavior Analysis Processing: First Example of Third Embodiment>
12 to 12C are diagrams for explaining a particle behavior analysis method of the first example in the particle behavior analysis device 202 of the third embodiment. Here, FIG. 12 is a flowchart showing a processing procedure of the particle behavior analysis method of the first example of the third embodiment for reducing the calculation load of the long-distance force between particles. FIG. 12A is a flowchart illustrating a processing procedure of contact determination processing according to the third embodiment. Step numbers are shown in the 300s, and steps similar to or similar to those in the first embodiment are assigned numbers in the 10s and 1s as in the first embodiment. FIG. 12B is a diagram illustrating an example of a lookup table used in the first example of the third embodiment. FIG. 12C is a diagram illustrating a comparison between the particle behavior analysis method of the comparative example and the first example of the first embodiment and the first example of the third embodiment.

  The first example of the third embodiment is a modification of the first example of the first embodiment. Hereinafter, the description will be focused on differences from the first example of the first embodiment.

  In the first example of the third embodiment, as shown in FIG. 12, before analyzing the object behavior, the region dividing unit 264 sets the range in which the particles to be analyzed for the long-distance force exist as small divided cells. Divide and assign a number for defining the position to each subdivided cell (S302). The size of the subdivided cell may be arbitrary as long as it exceeds the diameter of the maximum particle, for example, approximately the same as the maximum size of all the particles to be analyzed or several times the size. If the size of the subdivided cell is larger than the maximum particle diameter, all the particles that may come into contact with the target particle are included in the adjacent cells, and the number of cells to be searched at the time of touch determination can be reduced. This is because the calculation speed is advantageous.

  Correspondingly, as shown in FIG. 12B, the LUT acquisition unit 280 associates long-distance forces such as Coulomb force and magnetic force in the difference between the cell number difference and the subdivision cell number for each cell number difference. A long-distance interaction force lookup table is prepared in advance (S310).

  Basically, when the target particle of the particle pair is placed at the origin in the x and y directions, the difference in the x direction (xb−xa) and the difference in the y direction (yb−ya) of the subdivided cell numbers are A look-up table for the long-distance force F [x] [y] when the other particle is in each of the first to fourth quadrants is prepared. As will be described later, the direction in which the long-distance force acts differs depending on the quadrant in which the other particle is present with respect to the particle of interest, so that the x-distance long-distance force Fx [x] [y] and y acting on the particle of interest It is divided by the long distance force Fy [x] [y] in the direction.

  Incidentally, as in the first embodiment, there are a plurality of long-distance forces F [x] [y] to be calculated, such as a magnetic force Fp [x] [y] and a Coulomb force Fq [x] [y]. If there are types, a lookup table is prepared for each type, or the total interaction force Fsum [x of their total values (Fp [x] [y] + Fq [x] [y]) ] [Y] lookup table is prepared. Furthermore, when there are a plurality of particle types to be analyzed, such as developer particles 102 including carrier particles, toner particles, and external additives, a lookup table is also provided for each combination of particle types constituting the particle pair. Prepare several. In FIG. 12B, the coulomb force Fqx [x] [y] in the x direction acting on the target particle and the coulomb force Fqy [x] [y] in the y direction are collectively shown as Fq [x] [y].

  When x in the long-distance force Fx [x] [y] is positive, it indicates that the position of the cell in which other particles exist is on the right side of the cell in which the target particle exists, and Fx [ When x in [x] [y] is negative, it indicates that the position of the cell in which other particles exist is on the left side of the position of the cell in which the target particle exists. When y in Fy [x] [y] is positive, it indicates that the position of the cell in which the other particle exists is above the position of the cell in which the target particle exists, and Fy [x] [y] When y in y is negative, it indicates that the position of the cell in which other particles are present is lower than the position of the cell in which the target particle is present.

  That is, when x is positive and y is positive, the other particle is in the first quadrant, and when x is negative and y is positive, the other particle is in the second quadrant, When x is negative and y is negative, the other particle is in the third quadrant, and when x is positive and y is negative, the other particle is in the fourth quadrant. When the absolute values of x and y are the same, the long-distance force Fx [x] [y] acting on the target particle in the x direction is the opposite direction when x is positive and when x is negative (that is, Similarly, the far-distance force Fy [x] [y] in the y direction acting on the particle of interest is the opposite direction (ie, the sign is different) when y is positive and when y is negative. Vice versa).

  When the region division unit 264 receives the notification of the coordinate position of the analysis target particle from the numerical calculation processing unit 234, the region division unit 264 stores the analysis target particle in the small division cell in order to obtain a rough position of the analysis target particle. The subdivision cell number in which the analysis target particle exists is specified, and the information is notified to the numerical calculation processing unit 234 (S316). The numerical calculation processing unit 234 obtains the difference between the subdivided cell numbers in which each analysis target particle of the particle pair for calculating the long-range interaction force and the absolute value thereof are obtained (S320), and further determines the contact determination of each particle pair ( (See FIG. 12A) (S321).

  In the contact determination process, the numerical calculation processing unit 234 first determines whether or not the absolute value of the difference between the subdivided cell numbers is 1 or less (S322). When the absolute value of the difference between the sub-divided cell numbers exceeds 1 (S322-NO), there is no possibility of contact, so contact force calculation is unnecessary. When the absolute value of the difference between the subdivided cell numbers is 1 or less (S322—YES), there is a possibility of contact, so the same processing as in steps S124 to S128 is performed. That is, the numerical calculation processing unit 234 obtains a distance between particles based on the coordinate data of particles (S324), and further performs contact determination of each particle pair (S326). The contact force is not calculated for the particle pair that is not determined to be in contact (S326-NO), and the contact force is calculated for the particle pair that is determined to be in contact to obtain the contact force. (S326-YES, S328).

  After that, the difference between the subdivided cell numbers is matched with the long-distance force lookup table stored in the data storage unit 238, and the corresponding long-distance force (magnetic force Fp [x] [y] and Coulomb force Fq [ x] [y] and the total interaction force Fsum [x] [y]). That is, the long-distance interaction force corresponding to the difference of the subdivision cell numbers obtained in step S320 is referred from the lookup table (S352).

  In the processing of the first example of the third embodiment, the numerical calculation processing unit 234 refers to the lookup table corresponding to the difference of the subdivided cell numbers, so that it is not necessary to calculate the interparticle distance. Compared with the first and second embodiments, the analysis process can be further speeded up.

  FIG. 12C shows calculation times (standardized values) under certain analysis conditions for the comparative example, the first example of the first embodiment, and the first example of the third embodiment. In the first example of the third embodiment, since the difference between the subdivided cell numbers in which the respective particles are stored is used as a substitute value for the interparticle distance, the analysis processing time is shortened compared to the case where the interparticle distance is used. Is done.

  For example, assuming a three-dimensional space, the interparticle distance r is defined by equation (1). Note that x, y, and z represent particle coordinates, and the subscripts A and B represent particles.

  When a comparative example using the interparticle distance is applied and the actual calculation is executed, the calculation of the interparticle distance r is “3 times real number subtraction + 3 times real number multiplication + square root = 9.01 sec / M”. Time "was required. On the other hand, when the third embodiment using the difference between the subdivided cell numbers is applied and processing is performed on the same thing as the comparative example, “integer subtraction 3 times = 0.81 sec / M times” Processing time was enough. Compared to the comparative example and the first example of the first embodiment, the method of the first example of the third embodiment has a shorter processing time for specifying the interparticle distance.

<Particle Behavior Analysis Processing: Second Example of Third Embodiment>
FIGS. 13 to 13A are diagrams for explaining a particle behavior analysis method of the second example in the particle behavior analysis device 202 of the third embodiment. Here, FIG. 13 is a flowchart showing a processing procedure of the particle behavior analysis method of the second example of the third embodiment. FIG. 13A is a diagram illustrating an area that refers to a lookup table in the second example.

  The second example of the third embodiment is obtained by applying the mechanism of the first example of the third embodiment to the second example of the first embodiment. Hereinafter, the flowchart shown in FIG. 13 will be described by focusing on the differences from the first example.

  Similar to the first example, after performing the process related to the contact force, the moving particle determination unit 260 first sets the absolute value of the difference between the small divided cell numbers calculated in step S320 to the threshold value specified by the threshold setting reception unit 266. The result is compared with Th2 (for example, 10) (S330), and the result is notified to the numerical calculation processing unit 234. If the absolute value of the difference between the sub-divided cell numbers is equal to or smaller than the threshold value Th2, the numerical calculation processing unit 234 performs a rigorous calculation of the far-distance force by a method generally used conventionally in the individual element method (S330- YES, S350). On the other hand, when the absolute value of the difference between the subdivided cell numbers exceeds the threshold value Th2, the numerical calculation processing unit 234 performs the long-distance mutual processing corresponding to the subdivided cell number difference calculated in step S320 as in the first example. The acting force is referred from the lookup table (S330-NO, S352).

  Here, in comparing the absolute value of the difference between the subdivided cell numbers and the threshold Th2, the following two methods can be representatively taken when focusing on the two dimensions in the x direction and the y direction. The first method is the method shown in FIG. 13A, where the absolute value of the difference between the subdivision cell numbers in the x and y directions is expressed as “the absolute value of the difference between the subdivision cell numbers in the x direction + the subdivision cell number in the y direction”. The absolute value of the difference ”is set, and the absolute value of the difference between the small divided cell numbers in the x and y directions is compared with the threshold Th2.

  In the second method, although not shown, the absolute value of the difference between the subdivision cell numbers in the x direction is compared with the threshold Th2, and the absolute value of the difference between the subdivision cell numbers in the y direction is compared with the threshold Th2. When the absolute value of the difference between the subdivision cell numbers exceeds the threshold Th2 in both the direction and the y direction, the long-distance mutual correspondence corresponding to the subdivision cell number difference calculated in step S320 is performed as in the first example. The applied force is referred from the lookup table.

  In the second example of the third embodiment, when the absolute value of the difference between the subdivided cell numbers is equal to or smaller than the threshold Th2, the far-distance force is actually strictly calculated without referring to the lookup table. When the absolute value of the difference between the subdivided cell numbers is less than the threshold value Th2, the arrangement of the lookup table is not necessary.

<Particle Behavior Analysis Processing: Third Example of Third Embodiment>
14 to 14C are diagrams for explaining a particle behavior analysis method of the third example in the particle behavior analysis device 202 of the third embodiment. Here, FIG. 14 to FIG. 14A are flowcharts showing the processing procedure of the particle behavior analysis method of the third example of the third embodiment. “No. 1” shown in FIG. 14 is an application example to the first example of the third embodiment, and “No. 2” shown in FIG. 14A is an application to the second example of the third embodiment. It is an example. FIG. 14B is a diagram illustrating an example of a lookup table used in the third example of the third embodiment. FIG. 14C is a diagram for explaining the feature point of the third example of the third embodiment, and shows the case of “No. 1” shown in FIG. 14 which is an application example to the first example of the third embodiment. ing.

  In the third example of the third embodiment, a lookup table is prepared only for either positive or negative x (or y) of subdivided cell number differences, and analysis is performed for each of the x direction and the y direction. It is determined whether or not the sign of the difference x (or y) of the subdivided cell number of the target particle pair is the same as the sign of the look-up table. use. This is because, in the lookup table used in the first example, when the absolute values of x and y are the same, the long-distance force in the x direction (or y direction) acting on the target particle is positive in x (or y). Attention is focused on the fact that the direction is opposite (that is, the sign is reversed) when x (or y) is negative. Hereinafter, FIG. 14 will be described as a representative, focusing on the differences from the first example and the second example.

  When the target particle of the particle pair is placed at the origin in the x direction and the y direction, the LUT acquisition unit 280 makes a difference between the subdivision cell numbers in the x direction (xb−xa) and a difference in the y direction (yb−ya). When the other particle is present in any of the first to fourth quadrants, a long-range interaction force lookup that associates a long-distance force such as a Coulomb force or a magnetic force in the difference of the subdivided cell numbers A table is prepared in advance (S311). FIG. 14B shows a look-up table when the other particle is in the first quadrant. Incidentally, in this example, it is not necessary to store the x direction and the y direction separately as in “part 1”, and the x direction and the y direction may be stored together as in “part 2”.

  After performing the process related to the contact force, the numerical calculation processing unit 234 refers to the long-distance interaction force corresponding to the difference between the subdivision cell numbers calculated in step S320 from the lookup table, similarly to the first example (S352). ). Further, the numerical computation processing unit 234 compares the quadrant in which the other particle with respect to the target particle in the particle pair exists and the quadrant employed in the look-up table array (the first quadrant in this example). (S354). In other words, the code of the difference in the x direction of the subdivision cell number and the code of the difference in the x direction of the subdivision cell number employed in the look-up table array are compared, and the difference in the y direction of the subdivision cell number is compared. Is compared with the sign of the difference in the y direction of the subdivision cell numbers employed in the look-up table array.

  When the quadrant used in the array of the lookup table is different from the quadrant in which the other particle with respect to the target particle in the particle pair is present (S354-NO), the numerical operation processing unit 234 determines from the lookup table. The read value is acquired as a correct long-distance force by changing the sign in the x direction and / or y direction according to the difference in quadrant (S356). In other words, when only the code in the x direction is different, the code is changed only for the x direction, and when only the code in the y direction is different, the code is changed only for the y direction, and the codes in the x direction and the y direction are different. Changes the sign for the x and y directions.

  For example, as shown in FIG. 14C, since particle # 1 (difference is [7] [5]) exists in the first quadrant, there is no need to change the signs in the x and y directions, and particle # 2 (difference is [-3] [4]) is in the second quadrant, so only the sign in the x direction is changed to negative, and particle # 3 (difference is [-6] [-6]) is in the third quadrant. The sign in the x direction and the y direction are changed to negative, and since the particle # 4 (difference is [4] [−2]) exists in the fourth quadrant, only the sign in the y direction is changed to negative.

  In the third example of the third embodiment, compared to the first example and the second example of the third embodiment, the arrangement amount of the lookup table is ¼, and the number of necessary memories is reduced.

<Modification>
The idea of the third example of the third embodiment can be applied even when the interparticle distance is used instead of the small divided cell. In this case, instead of calculating only the distance between particles, the coordinates in the x and y directions are subtracted (without taking absolute values) to determine in which quadrant the other particle is present from the particle of interest. The same idea can be applied.

  In other words, in the first embodiment, a lookup table is prepared based only on the interparticle distance, but the lookup table is divided into x and y directions based on the interparticle distance and the position where the other particle is present with respect to the target particle. May be. By doing so, the concept of the lookup table is substantially similar to that of the third embodiment. In that case, the method of the third embodiment (first example) in which values are prepared individually for all quadrants (that is, taking the action direction into consideration) and values are prepared for one quadrant, and the direction is specified after reference. Any of the methods of the third embodiment (third example) can be adopted.

  When the method of the third embodiment (third example) is adopted, the reference standard for referring to the table is the distance between objects (which is always a positive value), and determines the action direction of the referenced long-distance force. The sign of the difference between the coordinates in the x and y directions (which can be positive or negative) is used. That is, the inter-object distance corresponds to the absolute value of the cell number difference, and the coordinate difference between the x and y directions corresponds to the cell number difference.

<Particle Behavior Analysis Processing: Fourth Example of Third Embodiment>
FIGS. 15 to 15C are diagrams illustrating a particle behavior analysis method of the fourth example in the particle behavior analysis device 202 of the third embodiment. Here, FIG. 15 to FIG. 15B are flowcharts showing a processing procedure of the particle behavior analysis method of the fourth example of the third embodiment for reducing the calculation load of the long-distance force between particles. FIG. 15C is a diagram illustrating a lookup table generation method according to the fourth example of the third embodiment.

  The fourth example of the third embodiment applies the mechanism of the second embodiment that generates a lookup table during analysis to the mechanism of the third embodiment, and “part 1” shown in FIG. The first example of the third embodiment, “No. 2” shown in FIG. 15A is the second example of the third embodiment, and “No. 3” shown in FIG. 15B is the third example of the third embodiment (comparison processing with the threshold Th2). It is shown in an application example.

  Although the illustration of the configuration example of the particle behavior analysis device 202 is omitted, in the configuration of the third embodiment including the region dividing unit 264, for example, the LUT generation unit 282 is used as the secondary particle behavior analysis device as in the second embodiment. What is necessary is just to comprise so that it may be provided in 202b side.

  Hereinafter, FIG. 15B will be described as a representative, focusing on the differences from the first example, the second example, and the third example. Incidentally, the case where the lookup table is stored as a value in the first quadrant will be described.

  In the fourth example of the third embodiment, as in the second embodiment, the subdivision that appears for the first time during the analysis is not performed before the object behavior is analyzed in advance in the data storage unit 238 of the lookup table. For particle pairs (object pairs) that are cell number differences, the long-range interaction force is calculated and the value is stored in the lookup table, and the difference between the subdivided cell numbers that appears the second time or later during the analysis Is characterized by referring to the long-range interaction force from the value stored in the lookup table.

  For this reason, in the fourth example of the third embodiment, the lookup table is generated in the analysis process, so there is no step S310 in the first example, the second example, or step S311 in the third example, and the process related to the contact force It is determined whether or not the interparticle distance appears for the first time during the analysis.

  After the process related to the contact force and the comparison process with the threshold value Th2, the numerical calculation processing unit 234 determines that the subdivision cell number is different when the absolute value of the difference x, y between the subdivision cell numbers exceeds the threshold value Th2 (S330-NO). The difference x, y information is notified to the LUT generation unit 282 to instruct the generation of the lookup table. The LUT generation unit 282 determines whether or not a long-distance force for the difference x, y between the subdivision cell numbers exists in the lookup table (S334). In this example, since the lookup table is created in any one of the first to fourth quadrants, the determination may be made based on whether or not the absolute values of the differences x and y of the subdivided cell numbers are the same.

  When the long-distance force F [x] [y] corresponding to the subdivision cell number difference x, y exists in the lookup table, the LUT generation unit 282 notifies the numerical calculation processing unit 234 to that effect. Similar to the first to third examples of the third embodiment, the numerical calculation processing unit 234 performs the long-distance force F [x] [y] corresponding to the subdivision cell number differences x and y calculated in step S320. Is referenced from the lookup table (S334-YES, S352).

  When the long-distance force F [x] [y] corresponding to the difference between the subdivided cell numbers does not exist in the lookup table (S334-NO), the LUT generation unit 282 performs the far-distance with the subdivided cell number differences x and y. The numerical force calculation processing unit 234 is instructed to calculate the distance force. The numerical calculation processing unit 234 calculates the long-distance force F [x] [y] at the difference x, y between the subdivision cell numbers, sets the value as the long-distance interaction force, and notifies the LUT generation unit 282 (S335). The LUT generation unit 282 uses the far-distance force F [x] [y] notified from the numerical calculation processing unit 234 as the array position value (Fq [x] [ y]) is stored (S338).

  At this time, in “No. 3”, the LUT generation unit 282 adjusts the sign of Fq [x] [y] in consideration of which of the first to fourth quadrants the lookup table is created (S337). . For example, for the first quadrant, the x direction is a “positive” value and the y direction is also “positive”. For the second quadrant, the x direction is a “negative” value and the y direction is “positive”. For the third quadrant, the x direction is “negative” and the y direction is “negative”, and for the fourth quadrant, the x direction is “positive” and the y direction is “negative”. Value. In “No. 1” and “No. 2”, this sign adjustment is unnecessary.

  Here, the far-field force at the center-to-center distance of each particle is calculated as a substitute value for the inter-particle distance r, and the far-field force F [x] of the difference x, y between the subdivision cell numbers in the lookup table is calculated. Rather than storing it as [y], it calculates the long-distance force at the distance between the barycentric coordinates of the subdivided cells in which each particle is stored (the distance between the centers of the cells), and calculates the value in the lookup table It is preferable to store the far-distance force F [x] [y] as the difference between the divided cell numbers. That is, if the long-distance interaction force lookup table corresponding to the difference in the subdivision cell number at that time has not been created, the cell centers defining the subdivision cell number difference in the look-up table array It is preferable to calculate the long-range interaction force by a conventional method using the distance between the particles as a distance between particles and store the value as a lookup table.

  As shown in FIG. 15C, in the third embodiment, basically, the interparticle distance is not calculated, and the subdivided cell number in which the analysis target particle (the center thereof) exists is specified, thereby identifying the analysis target particle. In the worst case, if the far-field force is calculated based on the point where the approximate position is specified and the actual (current) inter-particle distance r itself, the particles corresponding to both ends of the cell (closer or farther) This is to avoid representing the long-distance force due to the difference between the subdivision cell numbers in the inter-distance. As the physical property value of the particle other than the interparticle distance, the value at that time is used, but regarding the interparticle distance corresponding to the difference in the subdivided cell numbers, the cell corresponding to the subdivided cell number difference in the lookup table array is used. By using the distance between the centers, a more appropriate lookup table is obtained.

  As in the second embodiment, the fourth example method of the third embodiment completes the look-up table in the analysis process, so that it is not necessary to have a memory for subdivided cell number differences that do not appear in the analysis process. Become. The number of arrays required for the lookup table is small, and the number of memories required for analysis is expected to be reduced. That is, if a difference in subdivided cell numbers that does not appear in the analysis process is predicted in advance, the memory prepared in the lookup table may be reduced accordingly.

  As can be inferred from the description in the third example of the second embodiment, in the fourth example of the third embodiment, the number of arrays required for the lookup table is small, but this does not appear in the assumption. If the difference between the subdivided cell numbers appears in the analysis process, there is a risk of failure due to insufficient memory. In order to deal with this, although not shown in the figure, a mechanism that eliminates the possibility of failure due to a memory shortage may be applied as in the third example of the second embodiment.

  As mentioned above, although this invention was demonstrated using embodiment, the technical scope of this invention is not limited to the range as described in the said embodiment. Various changes or improvements can be added to the above-described embodiment without departing from the gist of the invention, and embodiments to which such changes or improvements are added are also included in the technical scope of the present invention.

  Further, the above embodiments do not limit the invention according to the claims (claims), and all combinations of features described in the embodiments are not necessarily essential to the solution means of the invention. Absent. The embodiments described above include inventions at various stages, and various inventions can be extracted by appropriately combining a plurality of disclosed constituent elements. Even if some constituent requirements are deleted from all the constituent requirements shown in the embodiment, as long as an effect is obtained, a configuration from which these some constituent requirements are deleted can be extracted as an invention.

  For example, in the above-described embodiment, a particle behavior analysis apparatus is described as an example to which the information processing apparatus is applied. As an apparatus in which the analysis target particle exists, a developer including only toner particles or carrier particles and toner particles is used. Although an example of an electrophotographic image forming apparatus using the above has been described, this is only an example.

  Further, the particle behavior analysis is not limited to application to a stirring process or a developing process in the developing device of the image forming apparatus. For example, the present invention may be applied to a transfer process in an electrophotographic transfer device and a cleaning process in a cleaning device. Moreover, you may apply similarly to the simulation of the system which handles all particle | grains (powder) irrespective of a particle | grain kind and action force. Other than the electrophotographic method, the present invention may be applied to rock fall simulation of rocks, powder flow simulation in a hopper, powder flow simulation in a pharmaceutical preparation device, and the like.

  DESCRIPTION OF SYMBOLS 1 ... Image forming apparatus, 20 ... Charging apparatus, 30 ... Exposure apparatus, 40 ... Developing apparatus, 50 ... Transfer apparatus, 60 ... Cleaning apparatus, 70 ... Fixing apparatus, 102 ... Developer particle, 200 ... Particle behavior analysis system, 202 ... Particle behavior analysis device, 202a ... Main particle behavior analysis device, 202b ... Subparticle behavior analysis device, 208 ... Network management device, 209 ... Network, 210 ... Instruction input device, 212 ... Display device, 220 ... Data input unit, 230 ... Data processing unit, 232 ... Data receiving unit, 234 ... Numerical calculation processing unit (particle behavior calculation unit), 236 ... Output data processing unit, 238 ... Data storage unit, 240 ... Information presentation unit, 250 ... Division processing unit, 250a ... Analysis load distribution processing unit, 260 ... Moving particle determination unit, 262 ... Moving particle specifying unit, 264 ... Area dividing unit, 266 ... Threshold setting receiving unit 280 ... LUT acquiring unit, 282 ... LUT generation unit, 286 ... LUT reception unit, 290 ... line direction processing result output processing unit

Claims (9)

A storage unit that stores correspondence information in which each inter-particle distance is associated with a long-range interaction force acting on a particle pair at each inter-particle distance;
A particle behavior calculation unit that calculates the behavior of the particles by specifying the long-range interaction force in the interparticle distance of the particle pair to be analyzed with reference to the information stored in the storage unit; and
Particle behavior analysis device equipped with. When there are a plurality of types of long-range interaction forces to be analyzed, the storage unit corresponds to each inter-particle distance and a total value of long-range interaction forces acting on particle pairs at the inter-particle distance. The particle behavior analysis device according to claim 1, wherein the attached correspondence information is stored. The particle behavior analysis apparatus according to claim 1, wherein the storage unit stores the correspondence information separately for each combination of particle types constituting the particle pair when there are a plurality of types of particles to be analyzed. The storage unit stores the correspondence information regarding a distance between particles that is equal to or greater than a predetermined threshold,
The particle behavior calculation unit calculates a long-range interaction force when the interparticle distance of the particle pair to be analyzed is less than the threshold value, and stores the memory when the interparticle distance of the particle pair to be analyzed is equal to or greater than the threshold value. The particle behavior analysis device according to any one of claims 1 to 3, wherein a long-range interaction force is specified with reference to information stored in the unit. A region dividing unit that divides the analysis target region into a plurality of regions and gives a number indicating the position of each region,
The storage unit and the particle behavior calculation unit substitute the difference in the number of each region in which each particle of the particle pair to be analyzed exists as the interparticle distance, according to any one of claims 1 to 4. Particle behavior analyzer. The storage unit stores the correspondence information regarding one of a positive value and a negative value of a difference in the number of the area,
When the sign of the difference in the number of the region of the particle pair to be analyzed is different from the sign of the difference in the correspondence information stored in the storage unit, the particle behavior calculation unit refers to the storage unit. The particle behavior analysis apparatus according to claim 5, wherein the sign of the correspondence information is inverted and used. A correspondence information generation unit that generates the correspondence information in an analysis process and stores the correspondence information in the storage unit;
In the analysis process, when the long-range interaction force is not stored in the arrangement position of the storage unit corresponding to the interparticle distance of the particle pair to be analyzed in the analysis process, the correspondence information generation unit corresponds to the interparticle distance. The particle behavior analysis apparatus according to any one of claims 1 to 6, wherein the long-range interaction force calculated by the particle behavior calculation unit is stored in an array position of the storage unit corresponding to the inter-particle distance. . The particle behavior analysis device according to claim 7, wherein when the storage capacity becomes insufficient, the storage unit discards those having a low reference frequency. Stores correspondence information in which the long-range interaction force at the inter-particle distance of the particle pair to be analyzed is associated with each inter-particle distance and the long-range interaction force acting on the particle pair at each inter-particle distance. A program that causes an electronic computer to function as a particle behavior calculator that calculates the behavior of particles by specifying the corresponding information stored in the storage unit.

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