JP2009075708A - Device and program for analyzing particle behavior - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reduce a calculation load or a communication load in particle behavior simulation for processing an inter-particle interaction by a plurality of computers. <P>SOLUTION: A cycle boundary conditions are introduced to a force division method. An analysis object range is divided to prescribed directions, and one division region is set to a region under consideration, and analysis object particles in the region under consideration are assigned to each data processing part so that the force division method can be applied. A duplicate region is arranged in a prescribed range adjacent to the region under consideration, and prescribed physical property is assigned to the particles of the duplicate region. As for the analysis object particles in the region under consideration which the data processing part itself takes charge in, the force division method is applied to calculate an interaction force between the analysis object particles in the region under consideration which the other data processing part takes charge in and particles in the duplicate region. In a method for applying the cyclic boundary conditions to the region division method, a communication load for acquiring the particle information of the duplicate region is increased, and in a method for applying the cyclic boundary conditions to the force division method, communication for acquiring the particle information of the duplicate region is not required, and a calculation load and a communication load can be reduced. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a particle behavior analysis apparatus and a program. More specifically, the present invention relates to a mechanism for analyzing the behavior of particles exhibiting powder properties by simulation. For example, a state in which one or more kinds of particles are mixed in powder (toner particles, carrier particles, etc.) used in an image forming apparatus such as a printer device, a facsimile device, or a multifunction device having the functions thereof It is related with the structure which analyzes the behavior of the particle in the simulation by simulation.

  For example, when an electrophotographic system is used in an image forming apparatus such as a printer device, a facsimile device, or a multifunction device having these functions, it is generally uniform on a photoconductive insulator such as a photosensitive drum. An electrostatic latent image is formed by applying an electrostatic image by irradiating a light image on this photoconductive insulator by various means, and then using the magnetic powder using the developing device. Development is visualized, and the toner powder image is transferred to a recording medium such as paper and then fixed to obtain a printed matter.

  In such an electrophotographic image forming apparatus, the magnetic powder contained in the container is stirred, conveyed to the magnetic roller, adsorbed to the magnetic roller, and charged according to the recorded image to form a latent image. The behavior such as flight to the existing photoconductor affects the quality of the recorded image. Therefore, analysis of the behavior of the magnetic powder is important for the development of the electrophotographic apparatus main body and the developing apparatus.

  A method called an individual element method or a discrete particle method is widely used for behavior simulation of individual particles in powders and granules (both meaning the aggregate of individual particles). The discrete element method is a method of accurately simulating the behavior of powder by tracking the behavior of individual particles constituting the powder based on the equation of motion. Particle behavior analysis that handles the properties of powder as individual particles is also called particle simulation.

  Regarding behavioral simulation of particles such as powders and granules, a method called individual element method or discrete particle method is widely used. However, in the particle behavior calculation algorithm based on the discrete element method, the analysis load increases approximately by the square of the number of particles. Therefore, if the number of particles increases, the amount of calculation becomes enormous and the performance of the computer improves. However, it is often difficult to perform calculations with the same number of particles as the actual system.

  Thus, as a conventional particle behavior simulation method, a distributed processing using a parallel operation of each program using a plurality of electronic computers installed with a program has been proposed for the purpose of shortening the calculation time (Non-patent Document 1). ~ 5, see Patent Document 1).

STEVE PLIMPTON and BRUCE HENDRICKSON, “A New Parallel Method for Molecular Dynamics Simulation of Macromolecular Systems”, Journal of Computational Chemistry, Vol. 17, No. 3, 1996, p.326-337 Laxmikant Kale, Robert Skeel, Milind Bhandarkar, et al., “NAMD2: Greater Scalability for Parallel Molecular Dynamics”, Journal of Computational Physics, 151, 1999, p.283-312. Takahiro Watanabe, “Development of 3D particle behavior simulator and its application to electrophotography”, Japan hardcopy 2003 Proceedings, 2003, p.269-272 Takashi Enomoto, Hiroyuki Takahashi, Nobuyuki Nakayama, Hiroyuki Kawamoto, “Mechanical properties and shape control of two-component magnetic brush”, Japan Hardcopy 2005 Proceedings, p115-118 Susumu Kikuchi, Yoshiyuki Fukuda, Takashi Hiratsuka, Hiroyuki Kawamoto, “Effect of Carrier Brush Rigidity on Electrophotographic Two-Component Development Method,” Imaging Conference Japan 2006, p251-254 JP-A-5-173787

  For example, Non-Patent Documents 1 and 2 disclose parallel processing methods such as a particle division method, a region division method, and a force division method in the molecular dynamics (MD) method. On the other hand, there are mechanisms described in Non-Patent Document 3 and Patent Document 1 as a mechanism that considers the interaction between multiple types of particles. In these documents, in consideration of calculation cost, communication cost, and memory cost, the region division method shows the highest performance when compared, and an example in which the method is applied to developer particle simulation is disclosed. For example, a proposal has been made in which a region division parallelization method is applied to developer particle simulation.

  On the other hand, Non-Patent Documents 4 and 5 disclose a mechanism for reducing the calculation time, which is a problem of the individual element method, by introducing a periodic boundary condition into the region division method. In this mechanism, the computational load is large in the discrete element method, so the calculation scale is limited, and when considering the magnetic interaction between particles, particles outside the analysis region are near the boundary of the analysis region. The problem is that the magnetic interaction is underestimated due to the absence of.

  An object of the present invention is to provide a mechanism capable of reducing a calculation load and a communication load in a particle behavior simulation in which an interparticle interaction is processed by a plurality of computers, rather than introducing a periodic boundary condition into a region division method.

  According to the first aspect of the present invention, there is provided a division processing unit that assigns analysis target particles within an analysis target range to each of a plurality of network-connected computing devices so that a force division method using a force matrix can be applied. A data processing unit included in each network-connected computing device that calculates a divided portion assigned by the division processing by the division processing unit according to the force division method, and the division processing unit includes the analysis The target range is divided in a predetermined direction, a part of the divided area is set as the attention area, and the analysis target particles in the attention area are provided in the plurality of calculation devices so that the force division method can be applied. Assigning to each of the data processing units, placing a copy area with respect to a predetermined range adjacent to the area of interest, and assigning predetermined physical properties to particles in the copy area, The data processing unit applies the force splitting method, and the analysis target particle in the region of interest for which the data processing unit is responsible and the copy region The particle behavior analysis apparatus is characterized by analyzing the behavior of the particles by calculating the interaction force with the particles.

  According to a second aspect of the present invention, in the first aspect of the present invention, the division processing unit copies the physical properties of the particles in the region of interest and assigns them to the physical properties of the particles in the copied region. .

  According to a third aspect of the present invention, in the first aspect of the present invention, the division processing unit is further divided along a direction orthogonal to a direction along the processing process of the analysis target range. The divided area is set as the attention area.

  According to a fourth aspect of the present invention, in the third aspect of the present invention, the split processing section is further divided along the longitudinal direction of a roll-shaped member that rotates in a direction along the processing process. The divided area is set as the attention area.

  According to a fifth aspect of the present invention, in the fourth aspect of the present invention, the division processing unit sets a divided area at a central portion in the longitudinal direction as the attention area, and the longitudinal direction of the attention area. The copy areas are set on both sides of the image.

  According to a sixth aspect of the present invention, in the fourth aspect of the present invention, the division processing unit sets a divided area at an end portion in the longitudinal direction as the attention area, and the longitudinal direction of the attention area. The copy area is set on the side opposite to the end portion.

  According to a seventh aspect of the present invention, in the first aspect of the invention, the division processing unit divides the analysis target range along a processing process and sets a partial region as the attention region. It is characterized by doing.

  According to an eighth aspect of the present invention, in the seventh aspect of the present invention, the division processing unit further divides the final process by dividing the first process as the copy area along the processing process. A part of the information on the particles in the region is assigned as a corresponding part of the information on the particles in the divided region in the first process, and the remaining information on the particles in the divided region in the first process is assigned according to a predetermined condition. It is characterized by.

  According to a ninth aspect of the present invention, in the first aspect of the present invention, the data processing unit further divides the region of interest and the copy region into cells having a size similar to a particle size, It is associated with the particle number, and the interaction force is calculated by calculating the distance between the cell to which the target particle belongs and the other particles belonging to the cell in the vicinity of the cell to which the target particle belongs.

  The invention according to claim 10 is the invention according to claim 9, wherein the data processing unit is a short-distance force that is an interaction force that performs an analysis focusing on an interaction with a particle having a short distance. The neighborhood set when calculating the interaction force between the particle of interest and the other particles based on whether the interaction force is a long-distance force that performs an analysis focusing on the interaction with a particle at a distance A range of cells is set.

  According to an eleventh aspect of the present invention, in the first aspect of the present invention, the data processing unit interacts according to a distance between the target particle in the target region and another particle in the copy region. It is characterized by setting the frequency of force calculation.

  In the invention according to claim 12, the central processing control unit provided in the electronic computer is connected to a plurality of networks connected so that a force dividing method using a force matrix can be applied to analysis target particles in the analysis target range. A division processing unit assigned to each of the computing devices, and a data processing unit provided in each network-connected computing device that calculates a division portion assigned by the division processing by the division processing unit according to the force division method; And the division processing unit divides the analysis target range in a predetermined direction and sets a part of the divided region as the attention region, and the analysis target particles in the attention region are subjected to the force division. Assigning to each of the data processing units provided in the plurality of computing devices so that the method can be applied, and to a predetermined range adjacent to the region of interest Then, a copy region is arranged, predetermined physical properties are assigned to the particles in the copy region, and the force dividing method is applied by the data processing unit, and the analysis target particles in the region of interest that the user is in charge of The program is characterized in that the behavior of the particle is analyzed by calculating the interaction force between the analysis target particle in the region of interest and the particle in the copy region, which is handled by the data processing unit.

  According to the first aspect of the present invention, in the particle behavior simulation in which the interaction between particles is processed by a plurality of computers, the particle behavior analysis that can reduce the calculation load and the communication load than introducing the periodic boundary condition into the region division method. A device can be realized.

  According to the second aspect of the present invention, it is easy to set the particle physical properties of the copy area.

  According to the third aspect of the present invention, the periodic boundary condition can be introduced into the force division method without being affected by the processing process.

  According to the fourth aspect of the present invention, the periodic boundary condition can be introduced into the force division method without being affected by the field due to the division position.

  According to invention of Claim 5, the behavior of the particle | grains in the center part of the longitudinal direction of a roll member can be analyzed by introduce | transducing a periodic boundary condition into a force division method.

  According to invention of Claim 6, the behavior of the particle | grains in the edge part of the longitudinal direction of a roll member can be analyzed by introduce | transducing a periodic boundary condition into a force division method.

  According to the seventh aspect of the present invention, the behavior of particles along the processing process can be analyzed by introducing a periodic boundary condition into the force splitting method.

  According to the invention described in claim 8, it is possible to perform a more realistic analysis by adjusting the physical properties of the particle information assigned to the copy area in consideration of the behavior of the particles in the process direction.

  According to the ninth aspect of the present invention, the number of target particles for calculating the interaction can be reduced, and as a result, the calculation load can be further reduced.

  According to the invention described in claim 10, based on the difference between the short-range force and the long-range force, the analysis can be performed by appropriately setting the range of the neighboring cells and introducing the periodic boundary condition into the force division method. it can.

  According to the eleventh aspect, the calculation load of the interaction force can be further reduced.

  According to the invention described in claim 12, in the particle behavior simulation in which the interaction between particles is processed by a plurality of computers, a mechanism capable of further reducing the calculation load and the communication load can be realized using a computer.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In the following, 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 of the apparatus in which the analysis target particles exist.

  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 merely an example, and an apparatus to which the mechanism of the present embodiment is applied is not limited to an 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 mirror. 34, 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 a paper transport path. And a fixing device 70 having a roll mechanism arranged at a predetermined position on the wake side.

  When the image forming apparatus 1 is configured as a copying apparatus, first, 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. With this charging potential, the surface of the photoreceptor 10 is charged to a uniform surface potential.

  After that, a polygon mirror 34 that is rotated by a motor 36 with a laser beam emitted from a laser light source 32 provided on the exposure device 30 on the surface of the photoreceptor 10 in accordance with image data obtained by scanning the original with a reading device (not shown). Scanning, the surface of the photoconductor 10 is exposed to form an electrostatic latent image having a desired latent image potential.

  Subsequently, the developing device 40 forms the toner particles in the developer particles 102 on the surface of the photoreceptor 10 while mixing the developer particles 102 including toner particles and carrier particles of a predetermined color 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.

  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, and in the particle behavior analysis regarding the transfer process, it is necessary to consider an electric field and a gravitational field acting on the developer particles 102 (particularly toner particles). .

  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 such an 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. be able to.

  For example, in the transfer process, the powder behavior analysis is performed while changing the condition parameters in the transfer process such as the surface roughness of the photoconductor, the speed difference between the transfer bodies such as the photoconductor / intermediate transfer belt and paper, and the contact width of the transfer body By repeating the simulation, it is possible to evaluate the image quality formed while reproducing the transfer process.

<Overview of development device>
FIG. 1A is a diagram illustrating a configuration example of the developing device 40 used in the image forming apparatus 1. As shown in FIG. 1A (1), the developing device 40 is disposed so as to face the photoconductor 10 and fills the inside of the storage container 101 with developer particles 102. The storage container 101 has an opening 101a for causing the developer particles 102 to fly toward the photoreceptor 10 side.

  As shown in FIG. 1A (2), the developer 102 is a two-component system configured to contain carrier particles 102a and toner particles 102b (for example, black toner particles) having different physical properties and particle sizes. . The pair of carrier particles 102a and toner particles 102b forms a magnetic powder as a whole. That is, the carrier particles 102a are made of a magnetic material and are attracted to the magnet. On the other hand, the toner particles 102b are non-magnetic toner and are powder having a predetermined color. In general, the particle size of the carrier particles 102a is larger than the particle size of the toner particles 102b. As the toner particles 102b, magnetic toner can be used.

  In addition to the above-described carrier particles 102a and toner particles 102b, the developer 102 has a particle size (average particle size of about 1 to about 1) to ensure powder flowability, chargeability, transferability, or cleaning properties. A small substance (external additive 102c) of 50 nanometers is mixed. For example, as the external additive 102c, titanium oxide, silica containing silicone oil, or the like is used.

  In the storage container 101, a developing roll (also referred to as a mag roll, a magnet roller, or a magnetic transport roller) 140, which is an example of a carrying roll that carries developer particles 102 on the surface, slightly protrudes from the opening 101 a. In preparation. A predetermined number of magnets 142 are arranged in the developing roll 140 at predetermined intervals along the inner peripheral edge thereof.

  Further, the developing device 40 is provided with a regulating blade (trimmer bar) 150 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 is regulated. The predetermined range region on the stirring and conveying roll 160b side of the regulating blade 150 is referred to as a layer formation region, and in the particle behavior analysis of the developer particles 102, it is necessary to consider the effects of a magnetic field and a gravitational field.

  In addition, the storage container 101 is provided with a pair of stirring and conveying rolls 160 (respectively referred to as 160a and 160b) for stirring the developer particles 102 and conveying them to the developing roll 140 side. One agitating / conveying roll 160 a is disposed in the back of the storage container 101, and the other agitating / conveying roll 160 b is disposed to face the developing roll 140. The agitating / conveying roll 160 conveys the developer particles 102 to the developing roll 140 side while being agitated by the rotating operation.

  The predetermined range area stirred and conveyed by the agitating and conveying rolls 160a and 160b is referred to as an agitating and conveying area. In the particle behavior analysis of the developer particles 102, it is necessary to consider the action of the gravitational field.

  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.

  A magnet 142 is built in the developing roll 140. The developing roller 140 adsorbs the developer 102 from the stirring and conveying roller 160b by a magnetic force. The developer 102 adsorbed on the developing roll 140 is regulated in the amount of adsorption of the developer 102 by the regulating blade 150.

  That is, the carrier particles 102a, the toner particles 102b, and the external additive 102c are agitated by the agitating / conveying roll 160 having the agitating function and conveyed to the developing roll 140 side while being frictionally charged, and are fixed at a certain height by the regulating blade 150. It adheres to the periphery of the developing roll 140.

  That is, the carrier particles 102a, the toner particles 102b, and the external additive 102c are agitated by the agitating / conveying roll 160 having the agitating function and conveyed to the developing roll 140 side while being frictionally charged, and are fixed at a certain height by the regulating blade 150. It adheres to the periphery of the developing roll 140.

  A predetermined area where the developer particles 102 between the agitating and conveying 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, the action of a magnetic field and a gravitational field Need to be considered.

  The toner particles 102b and the external additive 102c are adsorbed to the carrier particles 102a by electrostatic force. The carrier particles 102 a constitute a magnetic brush by a magnetic field from a magnet 142 built in the developing roll 140. The toner particles 102b and the external additive 102c are conveyed together with the carrier particles 102a to a portion facing the photoconductor 10.

  The developing roll 140 is provided to face the photoconductor 10, and the inner toner particles 102 b and the external additive 102 c of the developer 102 adsorbed to the developing roll 140 are charged and adsorbed to the photoconductor 10. The At this time, the surface of the photoconductor 10 is charged in accordance with the recorded image to form an electrostatic latent image, and the toner particles 102b and the external additive 102c are formed on the electrostatic latent image formed on the photoconductor 10. Adsorbed according to the image.

  That is, the developing roller 140 develops the latent image formed on the surface of the photoconductor 10 by causing the toner particles 102b carried on the developing roller 140 to fly to the photoconductor 10 side via the carrier particles 102a. Yes. At this time, the powder additive fluidity, charging property, transfer property, or cleaning property is secured by using the external additive 102c.

  A predetermined range area 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 area. In the particle behavior analysis of the developer particles 102, the action of an electric field, a magnetic field, and a gravitational field are expressed. It is necessary to consider.

  The carrier particles 102a after the development processing and the toner particles 102b that have not been ejected to the photoreceptor 10 are collected in the storage container 101. The predetermined range area in which the developer particles 102 are collected is referred to as a pick-off area. In the particle behavior analysis of the developer particles 102, it is necessary to consider the effects of a magnetic field and a gravitational field.

  Here, as shown in FIG. 1A (2), the surface of the photoconductor 10 is charged according to the recorded image, and the toner particles 102b and the external additive 102c fly to the surface of the photoconductor 10 by electrostatic force. To do. The flying toner particles 102b and the external additive 102c adhere to the surface of the photoreceptor 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 102b are attracted to the photoreceptor 10.

  Since the toner particles 102b are conveyed to the photoconductor 10 by the carrier particles 102a, how the toner particles 102b are attracted to the photoconductor 10 is determined by the carrier in the developing gap between the developing roll 140 and the photoconductor 10. It is determined by the behavior of the particles 102a and the toner particles 102b. For this reason, analysis of the behavior of the carrier particles 102a and the toner particles 102b is an important element for the development of the electrophotographic apparatus main body and the developing apparatus 40.

  Further, since it affects the powder flowability, charging property, or cleaning property, the analysis of the behavior of the carrier particles 102a and the external additive 102c is also an important factor for the development of the electrophotographic apparatus main body and the developing device 40. Become.

<Particle behavior analysis system; basics>
FIG. 2 is a block diagram showing a basic configuration of a particle behavior analysis system which is a configuration example of the particle behavior analysis device according to the present invention. The particle behavior analysis system 200 having a basic configuration 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 device 202 communicates main processing data to each other via a network 208, and can perform particle behavior analysis processing in parallel. It is configured as a parallel computing device (cluster computer). The network 208 is managed by a network management device 208a whose communication state has a routing function.

  Each particle behavior analysis device 202 is 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 200 functions as a main particle behavior analysis device 202a having a function as a calculation management node that controls the whole. The remaining particle behavior analysis device 202 is connected to the main particle behavior analysis device 202a as a secondary particle behavior analysis device 202b controlled by the main particle behavior analysis device 202a.

  In the figure, for convenience, one network line is drawn from the network management device 208a, 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 208a, and communication between each particle behavior analysis device 202 is performed via the network management device 208a. .

  The main particle behavior analysis device 202a is connected to 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 that presents the processing result as image information to the user. ing.

  By adopting such a basic system configuration, when performing particle behavior analysis on a system with multiple types of multi-particle interactions, each particle's magnetic interaction, electrostatic interaction, or mechanical interaction Analysis of each interaction such as action (contact force; contact force between particles and particles and contact between particles) is performed in parallel processing. 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.

  For example, the carrier particles 102a are subjected to magnetic motion analysis using a magnetic field analysis method based on the Maxwell equation, and the toner particles 102b are subjected to pure mechanical motion analysis and Coulomb force using the particle element method. Electrostatic field analysis focusing on the above is performed, and finally, the flow behavior of the developer 102 is predicted with high accuracy by combining the analysis results.

  In particular, when analyzing each interaction in each particle behavior analysis device 202, if analysis is performed using a force splitting method (algorithm using a force matrix), all the processors (each particle behavior analysis device 202 of the present embodiment) are connected. Can be reduced. If the amount of communication is reduced, the parallelization performance of the program when using multiple processors can be improved, and the calculation time can be greatly shortened. In addition, although details will be described later, the force decomposition method and the domain decomposition method (SD: Spatial Decomposition Method) are considered in consideration of the relationship between the interparticle distance and the interaction force (distance dependency of the interaction force). By using combined processing, parallelization efficiency is further increased.

  In addition, in the basic configuration of the particle behavior analysis system 200 shown in FIG. 2, the configuration of a de facto parallel computer (cluster computer) is shown. A plurality of particle behavior analysis devices having a function are connected by a network in a first network and a plurality of particle behavior analysis systems configured as a parallel computing device are further connected by another second network. It is also good.

  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.

  For example, in each particle behavior analysis system, analysis processing specialized in each interaction such as magnetic interaction, electrostatic interaction, or mechanical interaction (contact force) is performed, and each interaction is individually performed. The analysis process for is executed in parallel. That is, a plurality of types of interactions are analyzed independently and simultaneously using different particle behavior analysis systems.

  Alternatively, analysis processing of each interaction such as magnetic interaction, electrostatic interaction, or mechanical interaction (contact force) is executed in parallel for the carrier particles 102a and the toner particles 102b constituting the developer 102. . For example, the carrier particle 102a having a large influence of the magnetic force is subjected to a particle behavior analysis process specializing in the magnetic force, while the toner particles 102b having a large influence of both the magnetic force and the electrostatic force are particularly affected by the magnetic force and the magnetic force. The particle behavior analysis processing may be performed using a different particle behavior analysis system for each particle type, such as performing particle behavior analysis processing specialized for electrostatic force.

  As described in the basic configuration, each particle behavior analysis system uses force splitting instead of particle splitting when analyzing each interaction. In order to enhance the effect of improving the processing speed, a force-division parallelization method with a small communication amount is adopted even in communication between particle behavior analysis systems configured as parallel computing devices. That is, by adopting such a modified system configuration, each particle behavior analysis system performs an independent particle behavior analysis process, thereby further reducing the processing time compared to the system configuration of the basic configuration.

  Further, the particle behavior analysis system to be used (de facto parallel computing device) may be selected based on the processing capability depending on the degree of calculation load of the interparticle interaction. For example, in a situation where systems of different environments (performance, etc.) coexist, the particle behavior analysis process is efficiently performed using computer resources.

<Particle behavior analyzer; functional block>
FIG. 3 is a block diagram illustrating a configuration example of each particle behavior analysis apparatus 202. Here, the main particle behavior analysis apparatus 202a having the function of the calculation management node is particularly shown.

  In the description of the detailed analysis method described later by the particle behavior analysis device 202, for example, the stirring process of the carrier particles 102a and the toner particles 102b in the electrophotographic process type image forming apparatus 1 or the surface of the photoreceptor 10 is formed. The component particles constituting the developer 102 in a predetermined process such as a development process for superimposing the toner particles 102b on the electrostatic latent image and a transfer process will be described as an analysis target. It can be similarly applied to a simulation of a system that handles all particles (powder) regardless of the kind of particles and the acting force.

  As shown in the figure, a main particle behavior analysis device 202a includes a data input unit 220 that captures processing target data using an instruction input device 210, a data processing unit 230 that performs particle behavior analysis processing, and a processing result display device. And an information presenting unit 240 that presents the user with 212 or the like. The data input unit 220 and the information presentation unit 240 are provided in a portion corresponding to the calculation management node of the main particle behavior analysis apparatus 202a.

  The data input unit 220 receives commands and data input from the user via the keyboard and mouse constituting the instruction input device 210 and passes them to the data processing unit 230.

  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, and an output data processing unit 236. The secondary particle behavior analysis apparatus 202b may be configured by only the data processing unit 230.

  The data receiving unit 232 includes a data storage unit (not shown), stores the data input from the data input unit 220 in the data storage unit, and supplies data necessary for numerical calculation to the numerical operation processing unit 234. To do. The data storage unit of the data receiving unit 232 stores, for example, data relating to the configuration of the developing device 40 to be analyzed and the physical property value of the developer 102.

  Based on the data supplied from the data receiving unit 232, the numerical calculation processing unit 234 performs magnetic interaction and electrostatic interaction on the developer 102 (specifically, the carrier particle 102a and the toner particle 102b) as an example of particles. Alternatively, the particle behavior considering a plurality of interactions at the same time, such as mechanical interaction (contact force), is analyzed by a simulation process using a force splitting method. The numerical operation processing unit 234 supplies the analysis result to the output data processing unit 236.

  The output data processing unit 236 receives the calculation result in the numerical calculation processing unit 234, converts the calculation result in the numerical calculation processing unit 234 into display data, and supplies the display data to the display device 212. The display device 212 displays a processing result image based on the display data supplied from the output data processing unit 236. The behavior prediction of the developer 102 is visualized and displayed on the display device 212 so that the behavior of the developer 102 that is actually difficult to confirm can be visually grasped.

  In addition, as a characteristic part of the present embodiment, in dividing a particle to be analyzed into a part corresponding to a calculation management node of the main particle behavior analysis apparatus 202a by a predetermined division method, each of the calculation apparatuses is configured to perform particle behavior analysis. Each calculation system (also referred to as a processor; in FIG. 1A, particle behavior analysis apparatus 202) includes a division processing unit 250 that assigns each divided portion. The division processing unit 250 sets a force matrix according to the determined division method, 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 dividing the processing target element by a predetermined dividing method, the calculation time (calculation time per step) at the same range time in each calculation system (particle behavior analysis system 200) each constituted by a plurality of calculation devices is calculated. An analysis load distribution processing unit that distributes analysis target elements so as to be equivalent to each other is provided. The analysis load distribution processing unit may be configured to be shared by the division processing unit 250 or may be provided as a functional element different from the division processing unit 250.

  The analysis load distribution processing unit considers a plurality of types of interparticle interactions such as electrostatic interaction, magnetic interaction, mechanical interaction (contact force), or adhesion force, or the physical properties constituting the developer 102. Even when a plurality of different types of particles (carrier particles 102a, toner particles 102b, and external additive 102c in this example) are to be analyzed, the difference in calculation time between processors during parallel analysis processing is surely reduced. A division process for allocating the elements to be analyzed is performed in consideration of the difference in the acting force of the analysis object and the difference in the particle type.

  The analysis load distribution processing unit 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. It is better to allocate analysis target elements.

  Then, the analysis load distribution processing unit assigns the division responsible region and the division responsible particle (group thereof) 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 particle behavior analysis by the force division method for the divided divisions in charge while performing data communication with other processors in charge of processing for other divisions as necessary. 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 cut-off 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.

  Here, the data processing unit 230 and the division processing unit 250 of the present embodiment perform processing in which a periodic boundary condition (details will be described later) is introduced so that the calculation load can be reduced as compared with the application of only the simple force division method. It is characterized in that it is performed.

<Particle behavior analyzer; computer configuration>
FIG. 4 is a block diagram illustrating another configuration example of each particle behavior analysis apparatus 202. Here, a more realistic hardware configuration is shown that is constructed from a microprocessor that executes software for particle behavior analysis using an electronic computer such as a personal computer.

  That is, in this embodiment, a mechanism for analyzing the behavior of particles using a parallel algorithm combining a force division method and a region division method in consideration of two or more kinds of interaction forces is configured by a hardware processing circuit. However, the present invention is not limited to this, and it can be realized in software using an electronic computer (computer) based on a program code that realizes the function.

  Therefore, a program suitable for realizing the mechanism according to the present invention by software using an electronic computer (computer) or a computer-readable storage medium storing this program can be extracted as an invention.

  When a computer executes a particle behavior analysis processing function that considers two or more types of interaction forces using a parallelized algorithm that combines force splitting and domain splitting, a program that configures the software However, a computer (embedded microcomputer, etc.) embedded in dedicated hardware, or a CPU (Central Processing Unit), logic circuit, storage device, and other functions are mounted on a single chip to realize a desired system. It is installed from a recording medium in an SOC (System On a Chip) or a general-purpose personal computer capable of executing various functions by installing various programs.

  The recording medium causes a state change of energy such as magnetism, light, electricity, etc. according to the description contents of the program to the reading device provided in the hardware resource of the computer, and in the form of a signal corresponding to the change. The program description can be transmitted to the reader.

  For example, a magnetic disk (including a flexible disk FD), an optical disk (CD-ROM (Compact Disc-Read Only Memory)), a DVD on which a program is recorded, which is distributed to provide a program to a user separately from a computer. (Including Digital Versatile Disc), magneto-optical disk (including MO (Magneto Optical Disk)), or package media (portable storage medium) made of semiconductor memory, etc. It may be composed of a ROM, a hard disk, or the like in which a program is recorded that is provided to the user.

  The program constituting the software is not limited to being provided via the recording medium without using the recording medium, and may be provided via a wired or wireless communication network.

  For example, a storage medium that records a program code of software that implements a particle behavior analysis processing function that considers multiple types of interaction forces using a parallelization algorithm that combines force splitting and region splitting methods is stored in a system or device. The same effect as in the case where the hardware processing circuit is used can also be achieved by reading and executing the program code stored in the storage medium by the computer (or CPU or MPU) of the system or apparatus supplied. In this case, the program code itself read from the storage medium realizes a particle behavior analysis process function that takes into account a plurality of types of interaction forces using a force-division parallelization method.

  In addition, by executing the program code read by the computer, a function to perform particle behavior analysis processing that takes into account multiple types of interaction forces using a parallelized algorithm that combines force splitting and region splitting is realized. In addition, the OS (Operating Systems; basic software) running on the computer performs part or all of the actual processing based on the instruction of the program code, and the force division method and the region division method are performed by the processing. And a function of performing particle behavior analysis processing in consideration of a plurality of types of interaction forces.

  Further, after the program code read from the storage medium is written in a memory provided in a function expansion card inserted into the computer or a function expansion unit connected to the computer, the function expansion is performed based on the instruction of the program code. The CPU or the like provided in the card or the function expansion unit may perform part or all of the actual processing, and the function of performing the particle behavior analysis processing may be realized by the processing.

  The program is provided as a file that describes the program code that implements the function of performing particle behavior analysis processing considering multiple types of interaction forces using a parallelization algorithm that combines force splitting and region splitting. In this case, the program files are not limited to be provided as a batch program file, but may be provided as individual program modules according to the hardware configuration of a system configured with a computer.

  For example, the computer system 900 reads and records data from a controller unit 901 and a predetermined storage medium such as a hard disk device, a flexible disk (FD) drive, a CD-ROM (Compact Disk ROM) drive, a semiconductor memory controller, or the like. And a recording / reading control unit 902.

  The controller unit 901 includes a CPU (Central Processing Unit) 912, a ROM (Read Only Memory) 913 which is a read-only storage unit, and a RAM (Random Access) which can be written and read at any time and is an example of a volatile storage unit. Memory) 915 and RAM (described as NVRAM) 916 which is an example of a nonvolatile storage unit.

  In the above description, the “volatile storage unit” means a storage unit in which the stored contents are lost when the power of the apparatus is turned off. On the other hand, the “non-volatile storage unit” means a storage unit in a form that keeps stored contents even when the main power supply of the apparatus is turned off. Any memory device can be used as long as it can retain the stored contents. The semiconductor memory device itself is not limited to a nonvolatile memory device, and a backup power supply is provided to make a volatile memory device “nonvolatile”. You may comprise as follows.

  Further, the present invention is not limited to a semiconductor memory element, and may be configured using a medium such as a magnetic disk or an optical disk. For example, a hard disk device can be used as a nonvolatile storage unit. In addition, it is possible to use as a nonvolatile storage unit by adopting a configuration for reading information from a recording medium such as a CD-ROM.

  Further, the computer system 900 includes an instruction input unit 903 as a functional unit that forms a user interface, a display output unit 904 that presents a user with predetermined information such as a guidance screen and a processing result, and each functional unit. And an interface unit (IF unit) 909 that performs an interface function between them.

  Note that an image forming unit 906 that outputs the processing result to a predetermined output medium (for example, printing paper) may be provided so that the analysis processing result is printed out and presented to the user.

  As the instruction input unit 903, for example, an operation key unit 985b of the user interface unit 985 may be used. Alternatively, a keyboard or a mouse may be used.

  The display output unit 904 includes a display control unit 919 and a display device. As the display device, for example, an operation panel unit 985a of the user interface unit 985 may be used. Alternatively, other display units such as CRT (Cathode Ray Tube) or LCD (Liquid Crystal Display) may be used.

  For example, the display control unit 919 displays guidance information, the entire image captured by the image reading unit 905, and the like on the operation panel unit 985a and the display unit. It is also used as a display device for notifying the user of various information. Note that an instruction input unit 903 for inputting predetermined information with a fingertip, a pen, or the like may be configured by using a display unit having a touch panel on the display surface.

  The interface unit 909 includes a system bus 991 that is a transfer path for processing data (including image data) and control data, a printer IF unit 996 that functions as an interface with the image forming unit 906 and other printers, and the like. A communication IF unit 999 is provided to mediate communication data exchange with the network.

  In such a configuration, the CPU 912 controls the entire system via the system bus 991. The ROM 913 stores a control program for the CPU 912 and the like. The RAM 915 is configured by SRAM (Static Random Access Memory) or the like, and stores program control variables, data for various processes, and the like. The RAM 915 includes an area for temporarily storing data obtained by calculation according to a predetermined application program, data obtained from the outside, and the like.

  For example, a program that causes a computer to execute a particle behavior analysis processing function considering a plurality of types of interaction forces by a parallel algorithm combining a force division method and a region division method 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. Furthermore, the program may be downloaded from another server or the like via a network such as the Internet, or may be updated or updated.

  As a recording medium for providing the program, in addition to FD and CD-ROM, optical recording medium such as DVD, magneto-optical recording medium such as MO, tape medium, magnetic recording medium, IC card and miniature card A semiconductor memory such as the above may be used. Some or all of the FD, CD-ROM, etc. as an example of the recording medium when realizing the particle behavior analysis processing function considering a plurality of kinds of interaction forces by combining the force division method and the region division method. Functions may be stored.

  Further, the hard disk device includes an area for storing data for various processes by the control program, and temporarily storing a large amount of data acquired by the device itself or data acquired from the outside.

  With such a configuration, the particle behavior is stored in the RAM 915 from a readable recording medium such as a CD-ROM in which a program for executing a particle behavior analysis method described later is stored in response to an instruction from the operator via the operation key unit 985b. The analysis program is installed, and the particle behavior analysis program is activated by an instruction or automatic processing by the operator via the operation key unit 985b.

  The CPU 912 performs calculation processing according to the particle behavior analysis method described later in accordance with the particle behavior analysis program, stores the processing result in a storage device such as the RAM 915 or a hard disk, and displays the operation panel unit 985a or a display such as a CRT or LCD as necessary. Output to the device.

  Not only the configuration using such a computer, but also a particle behavior analysis process considering a plurality of types of interaction forces by a combination of dedicated hardware that performs the processing of each functional unit shown in FIG. You may comprise the particle behavior analysis system 200 and the particle behavior analysis apparatus 202 to perform.

  For example, instead of performing all the processing of each functional part for particle behavior analysis processing considering multiple types of interaction force using a parallel algorithm combining force division method and region division method, A processing circuit 908 for performing a part of the functional part with dedicated hardware may be provided. Although the mechanism performed by software can flexibly cope with parallel processing and continuous processing, the processing time becomes longer as the processing becomes complicated, so that a reduction in processing speed becomes a problem.

  On the other hand, when constructed with a hardware processing circuit, even if the process is complicated, a reduction in processing speed can be prevented, and an accelerator system capable of achieving high throughput can be constructed.

  For example, in the case of realizing a particle behavior analysis processing function considering a plurality of types of interaction forces by combining the force division method and the region division method, the data processing unit 230 shown in FIG. The data receiving unit 908a corresponding to the data receiving unit 232, the numerical operation processing unit 908b corresponding to the numerical operation processing unit 234, the output data processing unit 908c corresponding to the output data processing unit 236, and the like may be configured by hardware.

  In the case of configuring the main particle behavior analysis apparatus 202a that controls the whole, the division processing unit 908d corresponding to the division processing unit 250 may be configured by hardware.

<Relationship between particle type and interparticle distance and interaction force>
When analyzing the behavior of multiple types of particles with different physical properties on a parallel computer connected by a communication network, analysis calculations that take into account the types of interaction forces acting on the particles, that is, the types of particles and between particles It is important to set the processing in consideration of the distance in order to increase the overall processing efficiency. This is because the interaction force to be noted differs depending on the particle type and the distance between particles, and the degree of influence on the behavior of the particle also varies depending on the type of interaction force.

  For example, from the viewpoint of the particle type, for the non-magnetic toner particle 102b, analytical calculation in consideration of electrostatic interaction, mechanical interaction (contact force), and adhesion force is required, and the magnetic toner particle 102b. With regard to, analysis calculation considering the magnetic interaction force is also required.

  In more detail, the electrostatic interaction needs to be analyzed separately for the force received from the electric field, the Coulomb force between the particles, and the mirror image force of the adhesion force. In addition, by devising the analysis processing, the force received from the electric field and the Coulomb force between the particles can be collectively analyzed in the electric field.

  The degree of influence on the behavior of the non-magnetic toner particles 102b is the largest in electrostatic interaction, and in the following order, mechanical interaction (contact force) and adhesion force. The degree of influence on the behavior of the magnetic toner particles 102b is the largest in the magnetic interaction, and in the following order, the electrostatic interaction, the mechanical interaction (contact force), and the adhesion force.

  On the other hand, regarding the carrier particle 102a, magnetic interaction, electrostatic interaction (focusing on Coulomb force between particles but excluding force received from electric field), mechanical interaction (contact force), and adhesion force are considered. Analytical calculation is required.

  The degree of influence on the behavior of the carrier particle 102a has the largest magnetic interaction, and is in the order of mechanical interaction (contact force), electrostatic interaction, and adhesive force.

  Regardless of the particle type, generally, the interaction calculation load is the largest in terms of magnetic interaction, and in the following order, electrostatic interaction, mechanical interaction (contact force), and adhesion force. .

  Therefore, if the behavior analysis of the non-magnetic toner particles 102b and the behavior analysis of the carrier particles 102a are performed simultaneously by different processors according to the procedure shown in FIG. 3, the toner particles 102b are effectively Since the analysis procedure of the magnetic interaction with the largest calculation load is omitted, there is a great difference in calculation time between processors.

  Here, the relationship between the carrier particles 102a and the toner particles 102b has been described with particular attention. In general, however, the number of particle types N to be analyzed, the number M of types of acting force acting on each particle, Assuming that the total number of acting forces acting on each particle is L, if any particle does not need to be analyzed for any acting force, the condition of M × N> L is satisfied. In this case, since a difference occurs in the calculation time between processors, it is important to take a mechanism for equalizing the calculation time between processors in order to shorten the entire processing time.

  On the other hand, if the behavior analysis of the magnetic toner particles 102b and the behavior analysis of the carrier particles 102a are performed simultaneously, the analysis procedure of the electrostatic interaction regarding the force received from the electric field is practically applied to the carrier particles 102a. Since it will be omitted, there is a slight difference in calculation time between processors.

  Here, the relationship between the carrier particles 102a and the toner particles 102b has been described with particular attention. Generally, however, the number N of particle types to be analyzed, the number M of types of acting force acting on each particle, When the total number of acting forces L is applied, each particle needs to be analyzed for all acting forces. If the details are slightly different, the condition of M × N = L is satisfied, but in actuality, there will be a slight difference in calculation time between processors. In order to shorten the overall processing time, it is important to take a mechanism to make it easier.

  Considering the relationship with the interaction force from the viewpoint of these particle types, it is not necessary to simply equalize the number of assigned particles in order to make the calculation time (calculation load) of each processor equal. It is enough. For example, when assigning particles in order of particle numbers, it is important to consider the calculation load determined by the relationship between the particle type and the interaction force when assigning the particle numbers. As an example, the number of particles targeted by each processor, the number of each particle type, and the distribution ratio are made equal.

  For example, when 6 particles are assigned to one processor during processing related to the carrier particles 102a, the toner particles 102b, and the external additive 102c, the carrier particles 102a → the toner particles 102b → the external additive 102c → the carrier particles 102a → ... (hereinafter the same order) assigning a number to each particle, two carrier particles 102a, two toner particles 102b, and two external additives 102c are reliably assigned to one processor. To be able to

  Alternatively, when three particles are assigned to one processor at the time of processing with respect to the carrier particles 102a and the toner particles 102b (the number thereof is twice that of the carrier particles 102a), the carrier particles 102a → the toner particles 102b → the toner particles 102b → By assigning a number to each particle such as carrier particles 102a →... (Hereinafter the same order), one carrier particle 102a and two toner particles 102b are reliably assigned to one processor. consider.

  Further, from the viewpoint of the distance between particles, the interaction force is an interaction force (near-range force) that only needs to be paid attention to the interaction with particles close to each other, such as mechanical contact force and adhesion force. , It can be roughly divided into interaction forces (far-distance forces) that need to pay attention not only to particles that are close to each other but also to particles that are far away, such as magnetic force and electrostatic force (Coulomb force). .

  If the division method is a method that does not depend on the distance of the target particle (does not consider the distance), the process can be executed for all of the target particles regardless of whether the force is a short distance force or a long distance force. On the other hand, since all the interaction forces are calculated for all target particles, there is a disadvantage that communication steps are increased.

  On the other hand, from the viewpoint of the interparticle distance, if the division method is a method that depends on the distance of the target particle, it is necessary to adjust the analysis target range depending on whether the force is a short distance force or a long distance force. If the analysis target range is narrowed to handle only the short-range force, the processing time can be shortened because the number of particles entering the analysis target range is small and the number of communication steps is small. On the contrary, if the analysis target range is expanded to cope with the long-distance force, the number of particles entering the analysis target range increases and communication steps increase, resulting in a disadvantage that processing time is required. In order to solve this problem in long-distance forces, it may be possible to narrow the analysis target range by using a cutoff, but in that case, the calculation of the interaction force with the particles that should be focused on is omitted. This may cause a decrease in analysis accuracy.

  When considering the relationship with the interaction force from the viewpoint of these interparticle distance species, either the division method without distance dependency is applied, or the division method depending on the distance of the target particle is applied only to the short distance force. A method that combines two types of splitting methods that specializes in calculation processing, and that the splitting method that does not depend on the distance of the target particle performs calculation processing only for the calculation of far-distance forces. Conceivable. In the present embodiment, a method of applying the force division method to both the long distance force and the short distance force is adopted.

<Force division parallel processing; basic (number of processors M = N ^ 2)>
5 and 6 are diagrams for explaining the parallelization processing of the force division method (algorithm using a force matrix). Here, FIG. 5 is a flowchart showing an example of a force-division parallel processing procedure. FIG. 6 is a diagram illustrating an example of a force matrix for explaining a method of assigning analysis target particles to each node when the force division method is applied.

  In FIG. 5, a force-division parallel processing procedure is performed for the developer 102 (specifically, the carrier particles 102a and the toner particles 102b) used in the electrophotographic system, in a magnetic interaction, electrostatic interaction, or mechanical interaction ( A first example (parallel processing example 1 in electrophotographic simulation) of a detailed procedure for analyzing and processing (contact force) using individual force matrices is shown.

  When analyzing each interaction in each particle behavior analysis device 202, if the analysis is performed using a force division method (algorithm using a force matrix), it is possible to reduce the amount of communication among all processors than before. By reducing the amount of communication, the parallelization performance of the program when using multiple processors is improved, and the calculation time is shortened.

  In particular, the processing procedure of the first example is as follows. In the particle behavior analysis system 200 shown in FIG. 2, the developer 102 (specifically, the carrier particles 102a and the toner particles 102b) is subjected to magnetic interaction, electrostatic interaction, and mechanical The interaction (contact force) is analyzed in turn using an individual force matrix. That is, each interaction is analyzed in order by the same parallel computing device.

  First, in the main particle behavior analysis device 202a, the division processing unit 250 includes the number of particle behavior analysis devices 202 constituting the cluster behavior particle behavior analysis system 200 that can be used for the particle behavior analysis processing at present and the particle behavior of the grid configuration. The number of particle behavior analysis systems 200 constituting the analysis system (collectively called the number of processors M) is specified (S102).

  Here, the basic principle of the force division method is that the number of processors M is N ^ 2, and is assumed to be arranged in a square force matrix of N rows and N columns. Here, as an example, it is assumed that N = 3 and the total number of processors M is 9 (= 3 ^ 2). In this case, each processor is arranged in a force matrix of 3 rows and 3 columns.

  Thereafter, the data processing unit 230 reads, via the data input unit 220, calculation conditions such as various physical parameters necessary for the calculation, the initial arrangement of particles, and the number of analysis target particles that are particularly necessary in the force division method (S104). ). FIG. 6 shows a case where a total of 18 particles from No. 1 to No. 18 are calculated in parallel by nine processors.

  Next, the division processing unit 250 determines whether or not the number of processors M specified in step S102 satisfies the relationship of N ^ 2 (S105). When the number of processors M satisfies the relationship of N ^ 2 (S105-YES), the division processing unit 250 arranges each processor specified in step S102 in a matrix form as a square matrix as shown in FIG. Particles (carrier particles 102a and toner particles 102b constituting the developer 102) are assigned (S108). Each numbered processor (each particle behavior analysis device 202 or each particle behavior analysis system 200) is also referred to as a node N (in this example, a total of nine from 0 to 8). When assigning particles to each node, the processing load at each node is made equal.

  On the other hand, when the number of processors M does not satisfy the relationship of N ^ 2 (S105-NO), the division processing unit 250 identifies N that satisfies the square relationship within a range not exceeding the number of processors M, and can be used at that time. In accordance with the number of processors M, the number of processors in the range satisfying N ^ 2 is set (S106).

  For example, when the number of processors M that can be used at that time is N ^ 2 <M, N ^ 2 is used to apply the force division method to N, and N ^ 2 Only one processor is used and the remaining “MN 2” is not used. On the other hand, when the number M of processors that can be used at that time is in a relationship of M <N ^ 2, in order to apply the force division method by “N−1” one step below, the vertical (N−1) / horizontal ( N-1) force matrix is used, only (N-1) ^ 2 processors are used, and the remaining "M- (N-1) ^ 2" is not used.

  In the example shown in FIG. 6, 18 particles are calculated in parallel by 9 processors, so each processor arranged in a 3 × 3 force matrix first focuses on 2 particles, The interaction with other target particles will be analyzed. For example, when attention is paid to node 5 (# 5), firstly, the 11th and 12th particles are set as the particles of interest.

  Next, multiple types of interaction forces between many-body particles are distributed and calculated in processors (especially called specific processors) that require communication in the row and column directions centered on themselves in the force matrix. (S110). At this time, a plurality of types of interaction between many-body particles are calculated using different force matrices.

  Here, each force matrix for each interaction is characterized in that the particle numbers handled are different. By calculating each type of interaction between many-body particles using different force matrices, each force matrix calculates only the minimum number of particles required for interaction calculation, and calculates all particles. The calculation time is shortened compared to the case of doing so. In addition, in anticipation of the time reduction, that is, the reduction of the calculation load, the adjustment may be made in the direction of increasing the number of particles to be analyzed which each processor is in charge of.

  For example, of the 18 analysis target particles, the particle numbers 1 to 9 are carrier particles 102a, and the particle numbers 10 to 18 are toner particles 102b. Further, it is assumed that the interaction force that needs to be analyzed for the carrier particle 102a is a magnetic force and a contact force, and the interaction force that needs to be analyzed for the toner particle 102b is an electrostatic force and a contact force.

  In this case, the force matrix of magnetic force includes only carrier particles 102a, the force matrix of electrostatic force includes only toner particles 102b, and the force matrix of contact force includes carrier particles 102a and toner particles 102b. . The number of particles handled by each processor is set to “2” in the force matrix for contact force, but “1” instead of “2” in the force matrix for magnetic interaction and force matrix for electrostatic interaction. To do.

  In this way, by using different force matrices, only the minimum necessary number of particles is calculated in each matrix, and the calculation time is shortened depending on the matrix. For example, in the force matrix of the magnetic force, only the calculation for the nine carrier particles 102a is performed, so that the total calculation time is shortened compared with the case of calculating all 18 particles.

  Next, it communicates between specific processors, and for each interaction such as magnetic interaction, electrostatic interaction, or mechanical interaction (contact force), the row direction interactions in the force matrix are added together, A total sum SUM_Total of all interaction forces calculated in a distributed manner is obtained (S112). The total sum value SUM_Total collectively represents a plurality of interactions such as electrostatic force, magnetic force, mechanical contact force, or adhesion force.

  For example, paying attention to node 5, the interaction values at nodes 3 and 4 are sent to node 5, and summation calculation is performed at node 5. Thereby, the total value of the interaction force of the particles 11 and 12 in charge of the node 5 is obtained.

  Next, using the total sum value SUM_Total that collectively represents a plurality of interactions, the equation of motion of each particle is solved, and the position coordinates are calculated (S114). Then, the position coordinates of each particle obtained in this way are sent (communication) to a specific processor related to the interaction matrix, and the calculation information is updated (S116).

  For example, paying attention to the node 5, the position coordinates of the particles 11 and 12 in charge of the node 5 that are updated by calculating from the total value of the interaction force are changed to the nodes 3 and 4 in the row direction related to the interaction matrix, and Sent to nodes 2 and 8 in the column direction. This is because only the nodes 3 and 4 in the row direction and the nodes 2 and 8 in the column direction need the information on the particles 11 and 12 that the node 5 is in charge of. Therefore, the node 5 performs communication only with these four nodes, thereby reducing the amount of communication.

  Thereafter, the process returns to step S110 until the predetermined calculation step is reached, and the same processing is repeated (S118). Here, the “predetermined calculation step” may be performed until all the particles to be analyzed are in a state where they are in a generally stable position (a state in which all particles have flowed).

  Thus, when the number of processors M satisfies the relationship of N ^ 2, a processor (each particle behavior analysis device 202 or each particle behavior analysis system) including a CPU as an arithmetic processor, a RAM as a storage medium (memory), or the like. 200) are connected via a network 208 to enable mutual communication to form a parallel computer (cluster computer) or a grid computer, and as shown in FIG. 6, using a force-division parallelization algorithm according to a force matrix, Behavior analysis is performed by simultaneously considering multiple interactions such as magnetic interaction, electrostatic interaction, or mechanical interaction (contact force).

  As in the particle behavior simulation of the electrophotographic development process such as magnetic force, electrostatic force, and mechanical contact in the developer 102 (specifically, carrier particles 102a and toner particles 102b) accommodated in the developing device 40 of the image forming apparatus 1, Behavior analysis is performed on particles having multiple types of interaction between many-body particles using a force matrix (interparticle interaction rule). Not only the behavior of one type of particle, but also the interaction of a two-component developer composed of carrier particles 102a and toner particles 102b may be analyzed.

  For example, the influence of electromagnetic influence and rubbing from the carrier particles 102a after electrodepositing the toner particles 102b on the photosensitive member 10, and the amount of toner particles 102b contributing to development from the carrier particles 102a, You may analyze the flying to the photoconductor 10, etc. Furthermore, you may analyze the influence of the contact force which acts on the toner particle 102b and the carrier particle 102a.

  Further, a high-speed parallel processing algorithm that simultaneously considers electrostatic force, magnetic force, mechanical contact force, adhesion force, and the like necessary for application to developer particle simulation in electrophotography may be realized.

  Each specific processor only needs to communicate with other specific processors in the row and column directions centered on itself associated with the interaction matrix. By increasing the number of specific processors to be used, the amount of communication is reduced, thereby reliably reducing the analysis processing time.

<Introduction of periodic boundary conditions>
When calculating the interaction of multiple particles such as long-distance force and short-distance force, the analysis processing time can be shortened by adopting the particle behavior analysis process using the force division method without using the region division method.

  However, in the particle behavior analysis process using such a force division method, particle information (coordinates) is communicated every step in order to calculate the short distance force, so the communication load is less than when applying region division. It becomes large and high parallelization performance cannot be obtained.

  It is not limited to the force division method that the communication load increases when the division method is applied to perform parallel processing on a plurality of computers. As a general problem in parallel processing, when a plurality of processors are used, the ratio of communication time in the total processing time increases according to the number of parallel processing, and the effect of parallelization becomes saturated.

  On the other hand, in relation to the analysis target area size, regardless of the division method, if the analysis target area size is large, it is considered that the number of analysis target particles in that area will increase. Calculation load increases.

  Here, as a method of reducing the calculation load without reducing the analysis accuracy, there is a method of introducing a periodic boundary condition into the region division method as described in Non-Patent Documents 4 and 5. In the method of introducing the periodic boundary condition, when an analysis is performed assuming a predetermined analysis region, an analysis region (copy region) having a predetermined shape is repeatedly arranged in a two-dimensional direction with respect to the region of interest. As a matter of course, particle motion and magnetic interaction are processed. Specifically, it is assumed that the upper and lower surfaces of the region of interest are normal fixed boundaries and mechanical interaction with the particles occurs, but the side boundary of the region of interest has no mechanical interaction with the particles, and the particles It can pass. However, particles that have moved beyond the region of interest beyond the side boundary are placed in the opposite copy region while maintaining the state of motion at that time. Further, it is assumed that the particles near the side boundary are subjected to magnetic interaction from particles virtually existing outside the region of interest (that is, the copy region).

  The technique of this embodiment is characterized in that the concept of such periodic boundary conditions is introduced into the force division method. The methods described in Non-Patent Documents 4 and 5 are methods that introduce periodic boundary conditions into the region division method, but adopt a method that introduces periodic boundary conditions into the force division method as in this embodiment. In this way, it is possible to enjoy excellent operational effects that cannot be obtained by the methods described in Non-Patent Documents 4 and 5. Although common in terms of introducing periodic boundary conditions, there are significant differences in the effects obtained by the introduction. This point will be described in detail later.

  In addition, when introducing the periodic boundary condition into the force splitting method, the physical property parameter setting of each particle in the copy area to be placed by applying the periodic boundary condition to the attention area is simply copied ( In addition to copying, parameters in a predetermined area (not limited to the attention area) are copied (copied) in consideration of the processing process, and values are corrected and assigned as necessary. This is very different from the methods described in Non-Patent Documents 4 and 5, in which only the method of simply copying (copying) the parameter of the region of interest is disclosed. In this embodiment, a method of simply copying (copying) a parameter of a region of interest and applying a periodic boundary condition is referred to as a simple periodic boundary condition method, and a predetermined region (not limited to the region of interest) in consideration of the processing process. A method of assigning the periodic boundary condition by referring to the parameters is referred to as an extended periodic boundary condition method.

<About the division direction>
FIG. 7 and FIG. 7A are diagrams for explaining an example of a method for determining the division direction in setting the analysis target. Here, an example is given in the case of analysis of the development region in the vicinity of the photoconductor 10 in the development device 40 shown in FIG. 1A.

  First, when focusing on the development process, basically, the carrier particles 102a, the toner particles 102b, and the external additive 102c are transferred from the agitating / conveying area → pickup area → layer formation area → development nip area → pickoff area for reuse. Can be thought of as a circular process.

  For example, as shown in FIG. 1A (2), the developing roll 140 of the developing device 40 is in the form of a roll disposed to face the photoreceptor 10, and the carrier particles 102a are sequentially applied to the outer surface of the developing roll 140 by magnetic force. Adsorb to form a magnetic brush. The toner particles 102b are transported to the photoconductor 10 side by the adhesion action with the carrier particles 102a and are attracted to the latent image portion of the photoconductor 10, whereby the photoconductor 10 is developed.

  Therefore, the direction along the processing process is the X direction, the direction from the developing roll 140 perpendicular to the X direction to the photoreceptor 10 side is the Y direction, and the direction perpendicular to the X direction is the photoreceptor 10 or the developing roll 140 ( As shown in FIG. 7 (1), when the longitudinal direction of each roll is a roll-shaped member that rotates in the direction along the processing process is the Z direction, it is concentric with the developing roll 140 and has the same radius step. When the area is divided in the Y direction, each division area always includes the same processing process, and thus is essentially unaffected by the processing process. Analysis can be performed without being affected by the processing process.

  However, in reality, the number of particles to be analyzed differs depending on the region due to the influence of the magnetic field, electrostatic field, or gravitational field between the developing roll 140 and the photosensitive member 10, so that the calculation load of each node is equalized. It is virtually impossible to determine the region size so that In order to equalize the calculation load of each node while dividing the region concentrically with respect to the developing roll 140, the radius step at the time of division must be changed as appropriate, but the particle behavior must be taken into consideration. Such a thing may be considered difficult.

  On the other hand, paying attention to the longitudinal direction (Y direction) of the developing roll 140, as shown in FIG. 7B, the developing roll 140 is located on a concentric surface having a certain radial distance (including the outer peripheral surface of the developing roll 140 itself). If the image is divided into slices at a constant division pitch in the longitudinal direction (Y direction), the same processing process is always included in each divided region in the longitudinal direction, so that the toner particles are essentially unaffected. Except for the region where 102b is attracted to the photoconductor 10, the influence of the magnetic field, electrostatic field or gravitational field between the developing roll 140 and the photoconductor 10 is the same. That is, at each position in the roll longitudinal direction, the carrier brush 102a may be considered to have substantially the same magnetic brush formation, and the behavior of the toner particles 102b is excluding the amount of toner particles 102b adsorbed to the photoreceptor 10. You may think that it is almost the same. Therefore, it is considered that the particle types and the number of particles in each divided region (cell) divided in the longitudinal direction of the roll can be made substantially uniform, and the calculation load can be made uniform. In a first application example (application example 1) and a second application example (application example 2) which will be described later, a method of dividing the developing roll 140 in the longitudinal direction shown in FIG. 7B is applied.

  On the other hand, when focusing on the development process, there are actually toner particles 102b that are adsorbed to the photoreceptor 10 in the development nip region, but the carrier particles 102a, the toner particles 102b, and the external additive 102c are stirred and conveyed. It can be considered as a circulation process that is reused by transitioning from region → pickup region → layer formation region → development nip region → pickoff region. That is, when applied to the particle behavior analysis of the entire apparatus in the developing device 40, the developer particles 102 (carrier particles 102a, toner particles 102b, and external additive 102c) that are stirred and conveyed from the stirring and conveying region (stirring unit) are magnetic. The pickup area is attracted to the developing roll 140 due to the force, and thereafter, the process proceeds to the layer forming area, the developing nip area, and the pick-off area by the developing roll 140, and finally returns to the stirring and conveying area (stirring unit). In such a case, as shown in FIG. 7A, it is possible to divide along the direction of the processing process (X direction). In a third application example (application example 3), which will be described later, a division method according to the processing process shown in FIG. 7A is applied.

<First application example in developing device (basic)>
8 and 9 are diagrams illustrating a first example (application example 1) of specific processing. Here, FIG. 8 is a diagram illustrating an analysis target region of interest in Application Example 1. FIG. 9 is a diagram for explaining a mechanism for introducing a periodic boundary condition in the force splitting method when performing parallel calculation by the force splitting method algorithm in Application Example 1 (a plan view as seen from the direction A in FIG. 8). ).

  In application example 1 (basic), as a comparison with a modification example of application example 1 described later, in the case where the region to be analyzed is the central portion in the longitudinal direction of the developing roll 140, that is, development at the central portion of the developing roll 140 is performed. This is a case where the behavior of the agent particles 102 is analyzed. In contrast to Application Example 2 to be described later, Application Example 1 is a case where the powder that is an aggregate (developer) of developer particles 102 is an aggregate of one kind of particles, or a developer (powder). ) Is an aggregate of a plurality of types of particles, this is a case where the target particle to be analyzed is one type.

  For example, as shown in FIG. 8, in the developing device 40, when the pickup area and the pick-off area around the developing roll 140 are set as analysis target areas (areas surrounded by dotted lines in the drawing), When analyzing over a wide area, if two types of carrier particles 102a and toner particles 102b are handled, the number of particles becomes enormous and the calculation time increases. Further, when analyzing the performance of pickoff and pickup, the toner particles 102b and the external additive 102c have a lower specific gravity and smaller particle diameter than the carrier particles 102a, and the movement of the carrier particles 102a is dominant. It is conceivable to treat only the particles 102a as analysis target particles.

  As shown in FIG. 8, even if the particle behavior is analyzed with the analysis object as a cross section of the two-dimensional developing device 40, it is sufficiently useful for design support and mechanism analysis, but in order to improve the accuracy, the developing roll 140 is used. It is necessary to analyze the three-dimensional particle behavior in which the space is expanded in the longitudinal direction.

  However, if an attempt is made to analyze the entire region in the longitudinal direction of the developing roll 140 with a discrete element model (discrete element method: DEM) for analyzing the motion of each particle, the number of particles to be analyzed becomes enormous, resulting in an unrealistic calculation time. End up.

  As a solution to this problem, it is conceivable to reduce the calculation time to a practical level by narrowing the calculation area width and setting the narrow area as the attention area. However, simply by narrowing the calculation area width in a predetermined direction, there are no particles (carrier particles 102a in this example) on both sides of the attention area. This does not mean that the analysis accuracy is reduced.

  Therefore, as a method for reducing the calculation load without reducing the analysis accuracy, the application example 1 introduces the simple periodic boundary condition method to the force division method. The basic idea is similar to the method of introducing periodic boundary conditions in the region segmentation method. When analyzing the target analysis target region, a virtual copy region (with the same shape and size as the target region) is virtually created. ) Is repeatedly arranged in the one-dimensional direction, particle motion and magnetic interaction are processed. The one-dimensional direction is because it has periodicity only in the roll longitudinal direction (y direction) and no periodicity in the x direction or z direction.

  In introducing the periodic boundary condition into the force division method, first, the division processing unit 250 divides the analysis target region in a predetermined direction, sets a part of the divided region as the attention region, and analyzes the region within the attention region. The target particles are assigned to each of the data processing units 230 provided in the plurality of calculation devices so that the force division method can be applied, and a copy area is arranged in a predetermined range adjacent to the attention area. It is necessary to assign predetermined physical properties to the particles in the region.

  With respect to the dividing direction when setting the region of interest, for example, the direction along the processing process is the X direction, the direction from the developing roll 140 to the photoconductor 10 side orthogonal to the X direction is the Y direction, and the direction orthogonal to the X direction. The longitudinal direction of the photoconductor 10 and the developing roll 140 is the Z direction, and as shown in FIG. 7A, the region is concentric with the developing roll 140 and divided in the same radial step in the Y direction. It is conceivable that a part of the area is set as an attention area and copy areas are arranged on both sides thereof. In this case, since each divided area always includes the same processing process, it is essentially unaffected by the processing process, but the influence of the magnetic field, electrostatic field, or gravitational field between the developing roll 140 and the photoconductor 10 is not affected. As a result, the number of particles to be analyzed differs for each divided region. Therefore, it is expected that a correct analysis cannot be performed if the physical properties of the particles in the copy area adjacent to the attention area are assigned by copying the physical properties of the particles in the attention area as they are.

  As a solution for this, as estimated from what is shown in FIG. 7 (2), as shown in FIG. 9 (1), the image is divided by paying attention to the longitudinal direction (Y direction) of the developing roll 140. It is conceivable to reduce the calculation time to a practical level by setting the area as the attention area, that is, by narrowing the calculation area width in the longitudinal direction and setting the narrow area as the attention area. In this case, since the same processing process is always included in each divisional area in the longitudinal direction, it is essentially unaffected by the processing process, and is not affected by the magnetic field, electrostatic field, or gravitational field between the developing roll 140 and the photoreceptor 10. It is considered that the dependence on the division position of the field effect can be eliminated.

  However, simply by narrowing the calculation area width in the longitudinal direction, particles (carrier particles 102a in this example) do not exist on both sides of the attention area (both sides in the longitudinal direction of the developing roll 140). It does not mean that only a certain part is taken out (focusing on only a part), and the accuracy of analysis is reduced.

  Therefore, in the application example 1, in order to reduce the calculation load without reducing the analysis accuracy, a simple periodic boundary condition method is introduced into the force splitting method, and a virtual copy region (a shape / Assuming that the size is repeatedly arranged in a one-dimensional direction (in this example, the longitudinal direction of the developing roll 140), particle motion and magnetic interaction are performed.

  Specifically, the upper and lower surfaces of the attention area (both sides in the process direction in this example) are assumed to have a normal fixed boundary and mechanical interaction with the particles, but the side boundary (development roll 140 in this example). The boundary in the longitudinal direction of the carrier particle 102a can pass through. However, the carrier particles 102a that have moved outside the region of interest beyond the side boundary are arranged in the copy region on the opposite side while maintaining the motion state at that time. That is, as shown in FIG. 9 (2), the attention area that is the calculation area is a part of the developing roll 140 (almost the center in the figure), but has the same distribution as the attention area in the longitudinal direction of the developing roll 140. The analysis is performed on the assumption that the carrier particles 102a continue periodically.

  For example, in FIG. 9B, an attention area with a width of 200 μm is set at the center in the longitudinal direction of the developing roll 140, the cutoff distance is 400 μm, and attention is paid to both sides of the attention area by the cutoff distance. The copy area is set with the same size as the area. In this example, two copy areas are set on both sides of the attention area.

  Even when the force splitting method is applied, if the periodic boundary condition is not applied, the magnitude of the magnetic interaction changes depending on the number of particles, that is, the size of the analysis target area. It depends greatly on the region size.

On the other hand, by applying a periodic boundary condition to the force splitting method and adopting a method of copying and assigning the particle physical properties of the region of interest as the particle physical properties of the copy region, the dependence of the accuracy and calculation load on the analysis target region size is reduced (Reduced). Even if the region of interest is set to be narrow (small), the same accuracy (result) as when analysis is performed in a substantially large analysis region can be obtained. Setting the particle property of the copy area is simple because the particle property of the region of interest is copied and assigned.
In addition, there is an advantage that the communication load does not increase even if the periodic boundary condition is applied. Even if analysis is performed by the force splitting method focusing on only a part of the central portion in the longitudinal direction of the developing roll 140 (region of interest), the behavior of the carrier particles 102a in the central portion of each roll in the pickup region → developing nip region → pickoff region It will be possible to calculate with high speed and high accuracy.

  That is, in the method of applying the periodic boundary condition to the region division method, the long distance force (particularly magnetic interaction) from the carrier particles 102a virtually existing outside the attention region is applied to the carrier particles 102a near the boundary of the side surface of the attention region. ) And short-range forces (especially mechanical contact interaction), the communication load for acquiring the particle information in the copy area increases. On the other hand, in the method of applying the periodic boundary condition to the force division method, all particle information acquired at the time of analysis by the force division method for the region of interest can be used as it is as particle information of the copy region. This is because there is no need for communication for acquiring particle information in the copy area. The point where this communication load difference occurs will be described later.

<Modification of First Application Example in Developing Device>
FIG. 9A is a diagram illustrating a modification of the first specific example (application example 1) of specific processing. This modification is a case where the target analysis target region is the end side in the longitudinal direction of the developing roll 140, that is, a case where the behavior of the developer particles 102 at the end of the developing roll 140 is analyzed. In the example shown in FIG. 9A, in consideration of the fact that the developer particles 102 often do not exist at the extreme end in the actual product, the attention area is set slightly inside the extreme end.

  When it is desired to analyze the behavior of the carrier particles 102a at the end portion of the developing roll 140 as described above, as shown in FIG. 9A, one side opposite to the end portion with respect to the region of interest set on the end portion side. It is sufficient to apply the periodic boundary condition only to the above.

  For example, in FIG. 9A, a region of interest having a width of 200 μm is set near the end of the developing roll 140 in the longitudinal direction, the cutoff distance is set to 400 μm, and the region of interest is set to one side of the region of interest by the cutoff distance. A copy area is set with the same size. In this example, two copy areas are set on one side of the attention area.

  Also in this modified example, the behavior of the developer particle 102 (particularly, the carrier particle 102a) is analyzed by applying a periodic boundary condition to the force splitting method and paying attention to only a part of the end portion (the attention region) of the developing roll 140. Therefore, it becomes possible to calculate with high speed and high accuracy.

<Second application example in developing device>
10 to 12B are diagrams illustrating a second example (application example 2) of specific processing. Here, FIG. 10 is a diagram illustrating an analysis target region of interest in Application Example 2. FIG. 11 is a diagram for explaining a mechanism for introducing a periodic boundary condition in the force division method when performing parallel calculation by the force division method algorithm in the application example 2 (a plan view in a state seen from the direction B in FIG. 10). ). FIG. 12 is a diagram for explaining a method for determining a division size (which can also be extended to a cutoff distance) when the cell method used in Application Example 2 is applied. FIG. 12A is a diagram illustrating the two-dimensional cell method. FIG. 12B is a diagram for explaining the three-dimensional cell method.

  In application example 2, as a comparison with application example 1 described above, the powder that is an aggregate (developer) of developer particles 102 is an aggregate of a plurality of types of particles, and a plurality of types of particles are analyzed. This is the case. For example, as shown in FIG. 10, this is an application example to particle behavior analysis in which toner particles 102b are transferred onto the photoconductor 10 to form a toner image in the development nip region. In this case, in the image forming process in which the toner particles 102b are developed on the photoconductor 10, the movement states of both the toner particles 102b and the carrier particles 102a are important and dominant, and therefore the carrier particles 102a and the toner particles 102b in the development nip region. The behavioral analysis is performed in parallel using force division algorithm.

  For example, as shown in FIG. 10, even if the particle behavior is analyzed with a two-dimensional cross section as the analysis target, it is sufficiently useful for design support and mechanism analysis. Particle behavior analysis is required for a three-dimensional development nip region in which a space is extended in the longitudinal direction of the roll 140.

  However, if an attempt is made to analyze the entire area in the longitudinal direction of the developing nip region between the photoreceptor 10 and the developing roll 140 by a discrete element model (discrete element method: DEM) for analyzing the movement of each particle, the number of particles to be analyzed Becomes enormous, resulting in an unrealistic calculation time.

  As a solution to this problem, in application example 2, as in application example 1, first, the simple periodic boundary condition method is introduced into the force division method so as to reduce the calculation load without reducing the analysis accuracy.

  As shown in FIG. 11, the calculation time is reduced to a practical level by narrowing the calculation area width in the longitudinal direction and setting the narrow area as the attention area. At this time, the left and right side surfaces of the attention area (both sides in the process direction in this example) are assumed to be normal fixed boundaries and cause mechanical interaction with the particles. It is assumed that carrier particles 102a and toner particles 102b can pass through the longitudinal boundary of the developing nip region between the rolls 140). However, the carrier particles 102a and the toner particles 102b that have moved out of the region of interest beyond the side boundary are placed in the opposite copy region while maintaining the motion state at that time. That is, as shown in FIG. 11, the attention area that is the calculation area is a part of the development nip area (substantially the central part in the figure), but the carrier particles 102a having the same distribution as the attention area in the longitudinal direction of the development nip area. Assuming that the toner particles 102b are repeated periodically, the analysis is performed.

  For example, in FIG. 11, an attention area having a predetermined width is set at the center in the longitudinal direction of the development nip area, the cut-off distance is set to be the same as the attention area width, and the cut-off distance is set on both sides of the attention area. The copy area is set in the same size as the attention area. In this example, one copy area is set on each side of the attention area.

  Here, in the application example 2, in order to calculate the interaction force between particles at higher speed in the particle behavior analysis, not only the periodic boundary condition but also the cell method is introduced. When the particle sizes of the carrier particles 102a and the toner particles 102b are compared, the toner particles 102b are much smaller than the toner particles 102b, and the total number of particles to be analyzed may be considerably larger than the application example 1. This is because of concern. The cell method can also be introduced in Application Example 1.

<Relationship between division size and cell method>
At the time of particle behavior analysis, as shown in FIG. 12 (1), the range of interaction is limited to a certain range, and the region size is divided so as to cover the limited cutoff distance Lcut. It is common to take it.

  Here, the data processing unit 230 performs an analysis focusing on an interaction with a particle at a long distance, whether it is a short-distance force that performs an analysis focusing on an interaction with a particle at a short distance. Based on whether it is a long-distance force that is an acting force, a range of the neighboring cells that is set when calculating the interaction force between the target particle and the other particles is set (adjusted). Specifically, the data processing unit 230 sets the range (search range) of the neighboring cell set at the time of calculation of the short-range force, which is the interaction force between the target particle and the particle close to the distance, as the particle far from the target particle. The range is set to be smaller than the range (search range) of the neighboring cell set at the time of calculation of the long-distance force that is the interaction force.

  For example, in setting the region size focusing only on the analysis of the short-range force (for example, mechanical interaction force), as shown in FIG. 12 (2), the region is divided so that at least the analysis target particle is completely included. It is enough. This means that the cut-off distance Lcut should be set to the particle radius in effect, and an inscribed circle having the particle radius Lrad is formed with respect to the particle radius Lrad (= cutoff distance Lcut). A rectangular region having a particle diameter Ldia (= 2 · Lrad) in both vertical and horizontal directions can be set to the minimum size.

  On the other hand, the maximum size when setting a region size that focuses only on short-range force analysis need not consider far-distance force analysis, so it is necessary to consider cut-off distance for long-range force analysis It can be of any size that does not exist in the long-range force. In practice, for example, it is preferable to set the size according to the position so that the number of particles in the divided cells is equal.

  As an example, as shown in FIG. 12A, the analysis is performed by setting a search range of 3 × 3 cells expanded by one neighborhood with respect to the minimum size. When calculating the mechanical contact force between particles, as shown in FIG. 12 (1), it is only necessary to search for a cell in which the target particle exists and its neighboring eight cells.

  For example, FIG. 12A (1) is a diagram illustrating a two-dimensional cell method focusing on short-range force analysis. In the cell method, the analysis target area is divided into cells of the same size as the particle size, and the cell number and particle number are first associated with each other so that it can be understood which particle is present in which cell. become. In this example in which the carrier particles 102a and the toner particles 102b are analyzed, the cell is divided into cells having a size similar to the size of the larger one of the carrier particles 102a and the toner particles 102b. Next, when calculating the interaction with the focused particle, the distance between the cell to which the own (targeted particle) belongs and a particle belonging to a cell in the vicinity thereof (for example, 8 cells excluding the center of 3 × 3 minutes) is calculated. The presence / absence of contact (necessity of calculation of mechanical interaction) and the necessity of calculation of magnetic or electrostatic interaction force may be determined.

  In the interaction calculation, the particle of interest usually makes a determination by calculating the total number of particles N and the interparticle distance in order to determine whether or not to perform the interaction calculation. That is, since the calculation is performed with the number of particles N and the total number of particles N, the calculation load is N ^ 2 = N * N. When the number of particles is large, the load for calculating the distance between the target particle and the total number of particles increases (because N * N, so that N can be squared), so the load is reduced by the cell method.

  In the cell method, the determination calculation can be performed only from the target particle and neighboring particles around the target particle from the correspondence relationship between the cell and the particle, so that the calculation load can be greatly reduced. When the number of particles in the vicinity (that is, the number of particles in the search range) is M (M << N), the calculation load is N ^ 2 when the cell method is not applied, whereas FIG. By applying the two-dimensional cell method shown in 1), N * M is obtained, and the calculation load of the interparticle distance that is a hot spot can be reduced.

  On the other hand, when calculating the mechanical contact force between the particles, it is only necessary to search for the cell in which the target particle exists and the neighboring eight cells, but a long distance force (for example, magnetic interaction force or static force). When calculating (electrical interaction force), in order to make a determination including distant particles, as shown in FIG. 12A (2), a two-dimensional cell method focusing on long-distance force analysis is applied. Simply put, it will expand the search area.

  In FIG. 12A (2), the distance between a cell to which the cell belongs and a particle belonging to a cell in the vicinity thereof (for example, 24 cells excluding the center of 5 × 5 minutes) is calculated and determined. As a specific numerical example, when the cell size is 40 μm and the cutoff distance of the magnetic interaction force is 480 μm, 480/40 = 12, so each of the 12 cells up / down / left / right except the center of 13 × 13 minutes You will search for the minutes area.

  In order to simplify the explanation, the two-dimensional cell method is described in FIG. 12A, but in reality, particle behavior analysis is performed on a three-dimensional development nip region in which a space is extended in the longitudinal direction of the photoreceptor 10 and the development roll 140. Therefore, the three-dimensional cell method as shown in FIG. 12B is applied.

  Even in the three-dimensional cell method, the calculation load required for particle contact determination and determination within the cutoff range is reduced. The effect is large when the number of particles is large as compared with the two-dimensional cell method.

  For example, as shown in FIG. 12B (1), the cell size is 40 × 40 × 40 μm. Then, in the same manner as shown in FIGS. 12A (1) and (2), as shown in FIG. 12B (2), a long distance force (for example, a magnetic interaction force or an electrostatic interaction force) and a short distance force. The search range is changed by (mechanical interaction force).

  Although illustration is omitted, in the same way as in the modification to Application Example 1, when the target analysis target region is the end side in the longitudinal direction of the development nip region, the end portion of the target region set on the end side is It is only necessary to apply the periodic boundary condition to one side opposite to.

<Relationship between periodic boundary conditions and communication load>
FIG. 13 is a diagram for explaining the relationship with the communication load when performing the particle behavior analysis by introducing the periodic boundary condition into the region division method or the force division method. FIG. 13 (1) shows a case where the periodic boundary condition is introduced into the region dividing method, and FIG. 13 (2) shows a case where the periodic boundary condition is introduced into the force dividing method. In either case, as in Application Example 2 described above, the behavioral analysis of the carrier particles 102a and the toner particles 102b in the development nip region is performed in parallel using a plurality of computers.

  First, the periodic boundary condition is applied to the longitudinal direction of the developing nip region (in effect, the same as the photosensitive member 10 and the developing roll 140). In addition, as described above, since it is a multi-component particle system, it can be used in combination with a long distance force (for example, magnetic interaction force or electrostatic interaction force) and a short distance force (mechanical interaction force). Set the cut-off (search range).

  Here, as shown in FIG. 13A, when the periodic boundary condition is introduced into the region division method, carrier particles 102a and toner particles 102b in the vicinity of the boundary of the side surface of the attention area are virtually displayed in the copy area outside the attention area. It is analyzed that it receives a long-distance force (magnetic interaction or clonal force) or a short-distance force (contact interaction) from the carrier particles 102a and toner particles 102b that are present. At this time, in the area division method, each Node 1, 2, 3, 4 in charge of each division area for the attention area exchanges particle information each time the interaction is calculated with particles in other division areas. .

  Therefore, for example, when the cut-off 1 is set for the magnetic interaction (for example, the same size as the region of interest), Node 1 requires exchange of particle information handled by Nodes 4, 3 and 2 of the copy region 1, and accordingly Communication load increases. In addition, when the Coulomb force is set to cutoff 2 (for example, 3/4 with respect to the attention area size), Node 1 requires exchange of particle information handled by Nodes 4 and 3 in the copying area 1, and communication for that amount. Load increases.

  Furthermore, since it is necessary to analyze the contact interaction with the copy area, Node 4 requires the particle information handled by Node 1 in the copy area 2 and Node 1 in the copy area 1 is in charge of Node 1 although not shown. Since the exchange of particle information is required, the communication load correspondingly increases.

  On the other hand, as shown in FIG. 13 (2), when the periodic boundary condition is introduced into the force splitting method, first, in the force range splitting method, each Node 1, 2, 3, 4 in charge of each analysis target particle is As shown in Fig. 6, the particle information is exchanged with the node in charge of the particles necessary for the analysis of the interaction, and the copy area is also obtained during the analysis by the force division method for the attention area. All particle information can be used as it is as particle information in the copy area.

  Accordingly, the carrier particles 102a and the toner particles 102b near the boundary of the side surface of the region of interest have a long-distance force (magnetic interaction and clonal force) from the carrier particles 102a and toner particles 102b virtually existing in the copy region outside the region of interest. ) Or near-field forces (contact interaction), it is not necessary to conduct new communication for exchanging particle information in the copy area, and periodic boundary conditions are introduced into the force splitting method. However, the communication load does not increase.

  In the method of introducing the periodic boundary condition into the force splitting method, even if multiple cut-off distances are set for each of the magnetic interaction and the clone force, the calculation load and communication load do not increase. In addition, no new communication is required.

  When introducing periodic boundary conditions into the domain decomposition method, communication for exchanging particle information in adjacent regions to calculate contact force and Coulomb force, and particle information in farther regions to calculate magnetic interaction force However, by introducing the periodic boundary condition into the force division method, it is not necessary to increase the amount of communication even if the periodic boundary condition is introduced.

<Application example of periodic boundary condition + force division method>
FIG. 14 is a diagram for explaining an application example of a technique for introducing a periodic boundary condition into the force division method. In this application example, the data processing unit 230 changes the calculation frequency according to the cut-off distance, that is, the interaction force depends on the distance between the target particle in the target region and other particles in the copy region. It is characterized in that the calculation load is further reduced by setting (adjusting) the calculation frequency. More specifically, the frequency of calculating the interaction force with a distant periodic boundary area (copy region) is reduced. For example, as shown in the figure, the calculation frequency for a relatively large cutoff 1 that is one region or more away from the region of interest is N1, and for a relatively small cutoff 2 within one region of the region of interest. The calculation frequency is N2 (<N1).

  This is a copy region for each particle in the region of interest, and the copy region for each particle in the region of interest is relatively smaller than the acting force of the region of cutoff 2 that is relatively small. Therefore, even if the frequency of calculating the acting force from the cutoff 1 region is reduced, the analysis accuracy is substantially lowered. Based on the idea of not having to.

<Third application example in developing device>
Although illustration is omitted, as a method of setting a region of interest when introducing a periodic boundary condition in the force division method, as in application examples 1 (including modifications thereof) and 2, the photoreceptor 10 and the developing roll 140 may be used. The method is not limited to the method in which the analysis target region is divided in the longitudinal direction and a part thereof is set as the attention region.

  For example, paying attention to the development process, the analysis target area is set (divided) along the processing process, and the attention area is set in a part (for example, so as to include the center of the development nip area). Particle behavior analysis can be performed by force splitting method that introduces conditions. This technique is hereinafter referred to as application example 3.

  When this application example 3 is executed, in the application example 1 (including modifications thereof) and the application example 2 described above, the physical properties of each particle in the copy region arranged by applying the periodic boundary condition to the region of interest. The simple periodic boundary condition method that simply copies (duplicates) the parameters of the region of interest has been introduced as the parameter setting, but the parameters of the predetermined region (not limited to the region of interest) are taken into the copy region in consideration of the processing process. Copy (duplicate) and modify the values as necessary to assign them.

  For example, as shown in FIG. 1A (2) and FIG. 7A, in the development process, it can be considered as a circulation process in which the agitation conveyance area → pickup area → layer formation area → development nip area → pickoff area is transferred and reused. Therefore, if the magnet 142 in the developing roll 140 is considered that the particles near the N2 pole in the pick-off area are connected to the vicinity of the S2 pole in the pick-up area, the particles near the N2 flow from the vicinity of S2. Therefore, it is conceivable to copy (copy) the parameters of the pick-off area to the pickup area.

  At this time, in the developing process, the toner particles 102b are actually attracted to the photoconductor 10 in the developing nip region and toner consumption occurs, and new toner particles 102b are replenished in the pickup region. Further, in the pick-off area, not all of the carrier particles 102a and toner particles 102b fall into the stirring and conveying area (there is a so-called pick-off defect). In addition, since the movement direction in the pick-off area is different from the movement direction in the pickup area, simply copying (copying) the parameters of the pick-off area to the pickup area does not provide an appropriate way of assigning particle information.

  In such a case, the division processing unit 250 uses the divided area in the first process (in this example, the pickup area side) as a copy area, and the divided area in the final process (in this example, the pick-off area side) divided along the processing process. A part of the particle information of (1) is assigned as the corresponding part of the information of the particles in the divided area in the first process, and the remaining information of the particles in the divided area in the first process is assigned according to a predetermined condition.

  For example, the number N2 of carrier particles 102a entering the pickup region is set to the number N1 of carrier particles 102a falling (outing) from the pickoff region. At this time, N1 = N2 may be set, but N1 <N2 may be set in consideration of pick-off failure. Further, in consideration of the toner particles 102b adsorbed to the photoconductor 10 in the development nip region, the number N3 of toner particles 102b entering the pickup region is independent of the number of toner particles 102b falling (exiting) from the pickoff region. A value corresponding to the toner density (ratio to the number of carrier particles 102a per unit volume) is assigned. In addition, the arrangement position, the moving speed, and the moving direction of the carrier particles 102a and the toner particles 102b in the pickup area are not those in the pick-off area but are assigned values determined in advance.

  As described above, the periodic boundary condition can be introduced into the force division method while performing the region division in consideration of the process direction. At this time, the parameter value (particle physical property) of the particle information assigned to the copy area is adjusted in consideration of the behavior of the particles in the process direction, so that a more realistic analysis can be performed. Of course, the advantage of introducing the periodic boundary condition into the force division method can be enjoyed in the same manner as in the first and second application examples.

  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, the particle behavior analysis using the discrete element method and the particle behavior analysis that handles powder as a continuum and analyzes the powder behavior were identified based on a judgment index regarding the number of particles to be analyzed in the analysis target space. A mechanism for applying a method to be used according to the region attribute is not limited to application to the developing device 40. For example, the present invention can be applied to a particle stirring device, a particle conveying device, and the like.

1 is a diagram illustrating a configuration example of an electrophotographic image forming apparatus such as a printing apparatus or a copying apparatus. It is a figure which shows the example of 1 structure of a developing device. It is a block diagram showing one embodiment of a particle behavior analysis system. It is a block diagram which shows the example of 1 structure of a particle behavior analyzer. It is the figure which showed an example of the hardware constitutions in the case of comprising a particle behavior analysis apparatus using an electronic computer. It is the flowchart which showed an example of the force division | segmentation parallel processing procedure. It is a figure explaining the method of assigning analysis object particles to each node. It is FIG. (1) explaining an example of the determination method of the division | segmentation direction in setting an analysis object. It is FIG. (2) explaining an example of the determination method of the division | segmentation direction in setting an analysis object. In application example 1, it is a figure explaining the analysis object field to which attention is paid. In application example 1, it is a figure explaining the mechanism which introduces a periodic boundary condition into a force division method. It is a figure explaining the modification with respect to the application example 1. FIG. In application example 2, it is a figure explaining the analysis object field to which attention is paid. In the application example 2, it is a figure explaining the mechanism which introduce | transduces a periodic boundary condition into a force division | segmentation method. It is a figure explaining the determination method of the division size when applying the cell method used in the example 2 of application. It is a figure explaining the two-dimensional cell method. It is a figure explaining a three-dimensional cell method. It is a figure explaining the relationship with the communication load at the time of introduce | transducing a periodic boundary condition into an area | region division method and a force division method, and performing a particle behavior analysis. It is a figure explaining the application example of the method of introduce | transducing a periodic boundary condition into a force division method.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Image forming apparatus, 10 ... Photoconductor 10, 20 ... Charging device, 30 ... Exposure device, 40 ... Developing device, 50 ... Transfer device, 60 ... Cleaning device, 70 ... Fixing device, 101 ... Storage container, 101a ... Opening Part 102, developer, 102 a carrier particles, 102 b toner particles, 102 c external additive, 130 photoconductor, 140 developing roller, 142 magnet, 150 regulating blade, 160 agitating and conveying roll, 200 Particle behavior analysis system 202 ... Particle behavior analysis device 208 ... Network 208a Network management device 210 ... Instruction input device 212 ... Display device 220 ... Data input unit 230 ... Data processing unit 232 ... Data reception unit 234 ... Numerical calculation processing unit, 236 ... Output data processing unit, 240 ... Information presentation unit, 250 ... Division processing unit (also: Analysis load distribution processing unit)

Claims (12)

A division processing unit that assigns analysis target particles within the analysis target range to each of a plurality of network-connected computing devices so that a force division method using a force matrix can be applied;
A data processing unit provided in each network-connected calculation device that calculates according to the force division method for the divided portion allocated by the division processing by the division processing unit,
The division processing unit divides the analysis target range in a predetermined direction, sets a part of the divided region as a target region, and applies the force splitting method to analysis target particles in the target region. Assigning to each of the data processing units provided in the plurality of computing devices, as well as arranging a copy region for a predetermined range adjacent to the region of interest and assigning predetermined physical properties to particles in the copy region,
The data processing unit applies the force splitting method, and the analysis target particles in the region of interest in which the other data processing unit is responsible and the copy region A particle behavior analysis apparatus characterized in that the behavior of the particles is analyzed by calculating the interaction force with the particles. The particle behavior analysis apparatus according to claim 1, wherein the division processing unit copies the physical properties of the particles in the region of interest and assigns them to the physical properties of the particles in the copy region. The division processing unit is configured to divide along a direction orthogonal to a direction along a processing process of the analysis target range and set a partial region as the attention region. The particle behavior analysis apparatus described. The division processing unit is configured to divide along a longitudinal direction of a roll-shaped member that rotates in a direction along the processing process and set a part of the division region as the attention region. The particle behavior analysis apparatus described. 5. The division processing unit sets a division area at a central portion in the longitudinal direction as the attention area, and sets the copy areas on both sides of the attention area in the longitudinal direction. Particle behavior analyzer. The division processing unit sets a divided region at an end portion in the longitudinal direction as the attention region, and sets the copy region on a side opposite to the end portion in the longitudinal direction of the attention region. The particle behavior analysis apparatus according to claim 4. The particle behavior analysis apparatus according to claim 1, wherein the division processing unit divides the analysis target range along a processing process and sets a part of the divided region as the region of interest. The division processing unit uses the divided area of the first process as the copy area, and part of the particle information of the divided area of the final process divided according to the processing process. The particle behavior analysis apparatus according to claim 7, wherein the information is assigned as a part of the corresponding information, and the remaining information of the particles in the divided region of the first process is assigned according to a predetermined condition. The data processing unit divides the region of interest and the copy region into cells having a size similar to the particle size, associates the cell number with the particle number, and associates the cell to which the particle of interest belongs and the particle of interest. The particle behavior analysis apparatus according to claim 1, wherein the interaction force is calculated by calculating a distance to another particle belonging to a cell in the vicinity of the cell to which the cell belongs. The data processing unit is an interaction force that performs an analysis focusing on an interaction with a particle at a long distance or an interaction force that performs an analysis focusing on an interaction with a particle at a short distance. 10. The particle according to claim 9, wherein a range of the neighboring cells set when calculating an interaction force between the particle of interest and the other particles is set based on whether the force is a certain long-distance force. Behavior analysis device. 2. The particle according to claim 1, wherein the data processing unit sets an interaction force calculation frequency according to a distance between the target particle in the target region and another particle in the copy region. Behavior analysis device. The central processing control unit provided in the electronic computer
A division processing unit that assigns analysis target particles within the analysis target range to each of a plurality of network-connected computing devices so that a force division method using a force matrix can be applied;
For the divided portion assigned by the division processing by the division processing unit, according to the force division method, to function as a data processing unit provided in each network-connected computing device,
The division processing unit divides the analysis target range in a predetermined direction, sets a part of the divided region as a target region, and applies the force splitting method to analysis target particles in the target region. Assigning to each of the data processing units provided in the plurality of computing devices, as well as arranging a copy region for a predetermined range adjacent to the region of interest and assigning predetermined physical properties to particles in the copy region,
By applying the force dividing method by the data processing unit, for the analysis target particle in the attention region for which the data processing unit is responsible, the analysis target particle and the copy region in the attention region for which the other data processing unit is responsible A program characterized by analyzing the behavior of the particles by calculating the interaction force with the particles.