JP4967646B2 - Particle behavior analyzer, program - Google Patents

Description

  The present invention relates to a particle behavior analysis apparatus and a program. More specifically, for example, a state in which a plurality of particles are mixed in a color material (powder, developer) used in an image forming apparatus such as a printer device, a facsimile device, or a multifunction device having these functions. 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 giving an electrostatic charge and irradiating a light image on this photoconductive insulator by various means, and then the formed latent image is formed with a magnetic powder using a 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.

  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.

  Therefore, as a conventional particle behavior simulation method, for the purpose of shortening the calculation time, a plurality of electronic computers in which programs are installed are used, and distributed processing by parallel operation of each program is proposed (for example, Patent Document 1). See).

JP 2000-003352 A

  In the mechanism described in Patent Document 1, a molecular dynamics calculation device that simulates the motion of a large number of particles in an n-dimensional space using a parallel computer having a plurality of processors has been proposed, and the number of adjacent regions is three. ^ N-1 ("^" indicates a power; 3 to the nth power minus 1) is divided into a smaller number of local regions, thereby reducing communication time and speeding up the overall calculation process. I am trying. The idea is to divide the calculation area space into parallel processors and divide the calculation area space by a polyhedron that is closer to a sphere, thereby reducing the number of transfer partners that exchange particle data near the boundary. , Try to reduce the number of communication activations.

  An object of the present invention is to provide a mechanism capable of improving the calculation speed improvement ratio of the parallel processing by an approach different from the mechanism described in Patent Document 1 when considering the interaction between particles. .

  The invention according to claim 1 divides the particles by a force division method using a force matrix, and assigns each divided portion to each computing device, and other processing units provided in each computing device. While performing data communication with the computing device, the behavior of the particles is determined in consideration of the interaction force with the other substances acting on the particles with respect to the divided portions allocated by the force dividing method. The division processing unit is set to use an expanded force matrix such that N ^ 2 <M <(N + 1) ^ 2 for the number M of computing devices. In addition, a particle behavior analysis device characterized by allocating a substantial computing device as a substitute device for (N + 1) ^ 2-M computing device portions in the expanded force matrix. It is.

  According to a second aspect of the present invention, in the first aspect of the present invention, the division processing unit is configured such that the number M of computing devices does not satisfy the relationship of N ^ 2 and N · (N + 1) + 1 ≦ M When the relationship of ≦ (N + 1) ^ 2-1 is satisfied, the division is performed so that the vertical (N + 1) / horizontal (N + 1) force matrix is used, and the calculation that should not be handled by a computing device that does not actually exist is performed. As for the portion, the particle information is distributed so that a substantial computing device existing in the (N + 1) th row is in charge as an alternative device.

  According to a third aspect of the present invention, in the second aspect of the present invention, the division processing unit distributes the particle information evenly when there are a plurality of substantial calculation devices in the (N + 1) th row. It is characterized by.

  In the invention according to claim 4, when the particles are divided by the force division method using the force matrix and each divided portion is assigned to each calculation device, the number M of the calculation devices does not satisfy the relationship of N ^ 2. When the relationship of N · (N + 1) + 1 ≦ M ≦ (N + 1) ^ 2-1 is satisfied, the division is performed so that the vertical (N + 1) / horizontal (N + 1) force matrix is used. As for the calculation part that should be handled by a non-existing computing device, data between the other computing devices and the procedure for distributing the particle information so that the actual computing device is in charge in the (N + 1) th row A feature of performing a procedure of analyzing the behavior of the particles in consideration of the interaction force with other substances acting on the particles with respect to the divided portions assigned by the force division method while performing communication. Grain Is a program for behavior analysis.

  According to the first aspect of the present invention, the amount of communication among all the computing devices is reduced by performing analysis using a force division method that is an algorithm using a force matrix instead of a region division method or a particle division method. Can do. Reducing the amount of communication can improve the parallelization performance of the program when many computing devices are used, and can greatly reduce the computation time.

  In addition, the conventional limitation that the number M of calculation devices in the particle behavior analysis to which the force splitting method is applied must satisfy the relationship of N ^ 2 is eliminated, and when N ^ 2 <M <(N + 1) ^ 2, Particle behavior analysis can be performed by parallel processing using a vertical (N + 1) and horizontal (N + 1) force matrix. Even in the number of computing devices other than N ^ 2, the speed can be increased by applying the force division parallelization method. As a result, the speed improvement ratio of the calculation speed is higher than when parallel processing is performed with N ^ 2 calculation devices.

  Further, as an additional effect, even when some of the computing devices of the parallel computing system composed of n ^ 2 computing devices using a vertical n and horizontal n force matrix malfunction, Instead of switching to an operation using a vertical (n-1) / horizontal (n-1) force matrix that is compatible with (n-1) ^ 2 computing devices below the rank, the forces of vertical n and horizontal n Since the matrix can be continuously used and the computing device operable at that time can be operated, it is possible to operate with the minimum degradation in computing performance.

  According to the second aspect of the present invention, in the case of extending to a vertical (N + 1) / horizontal (N + 1) force matrix, particle behavior analysis to which a force division method is actually applied cannot be realized. N ^ 2 + 1 ≦ M The range of ≦ N · (N + 1) can be excluded.

  As an additional effect, even when some of the computing devices of the parallel computing system composed of n ^ 2 computing devices using the vertical n and horizontal n force matrix malfunction, When the number of remaining computing devices operable at the time satisfies the relationship of (n−1) · n + 1 ≦ M ≦ n ^ 2-1, the number of computing apparatuses adapted to (n−1) ^ 2 computing devices below one rank Instead of switching to the operation using the vertical (n-1) / horizontal (n-1) force matrix, all calculations that can be performed at that time are continued using the vertical n / horizontal n force matrix. Since the system can be operated to operate, it can be operated with minimal degradation in computing performance.

  According to the third aspect of the present invention, it is possible to reduce the unbalance (unbalance) of the calculation load between the alternative device and another calculation device.

  According to the fourth aspect of the present invention, the mechanism of the particle behavior analysis apparatus capable of improving the calculation speed improvement ratio of the parallel processing can be realized using a computer.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

<Overview of development device>
FIG. 1 is a diagram illustrating a configuration example of a developing device 100 used in an image forming apparatus such as a printing apparatus (printer) or a copying apparatus (copier).

  As shown in FIG. 1A, the developing device 100 is disposed so as to face the photoreceptor 130 and fills the inside of the storage container 101 with the developer 102. The storage container 101 is formed with an opening 101a for allowing the developer 102 to fly to the photosensitive member 130 side.

  As shown in FIG. 1B, the developer 102 is a two-component system configured to include carrier particles 102a and toner particles 102b (for example, black toner particles) having different physical properties and particle sizes. . A magnetic powder is formed as a whole by a pair of carrier particles 102a and toner particles 102b. 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.

  Inside 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 the developer 102 on its surface, has a peripheral surface slightly protruding from the opening 101a. I have. 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 100 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 102 formed along the magnetic force lines of the magnet 142. The height of the head is regulated.

  Further, the storage container 101 is provided with a pair of stirring and conveying rolls 160 (respectively 160a and 160b) for stirring the developer 102 and conveying it 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 102 to the developing roll 140 side while being agitated by the rotating operation.

  The developing roll 140 rotates together with the photosensitive member 130 rotated in the direction of arrow X so that the rotational movement direction of the surface on the side facing the photosensitive member 130 is the same as the moving direction X of the photosensitive member 130 (arrow Y direction). Is done. The photosensitive member 130 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 and the toner particles 102b are stirred and frictionally charged by the stirring and transporting roll 160 having a stirring function, and are transported to the developing roll 140 side. Adhere to.

  The toner particles 102b 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 are transported together with the carrier particles 102a to a portion facing the photoreceptor 130.

  The developing roller 140 is provided to face the photoconductor 130, and the toner particles 102 b of the developer 102 adsorbed to the developing roller 140 are charged and are adsorbed to the photoconductor 130. At this time, an electrostatic latent image is formed on the surface of the photosensitive member 130 according to the recorded image, and the toner particles 102b are attracted according to the electrostatic latent image formed on the photosensitive member 130. Is done.

  That is, the developing roller 140 causes the toner particles 102b carried on the developing roller 140 to fly to the photosensitive member 130 via the carrier particles 102a, and develops the latent image formed on the surface of the photosensitive member 130. ing. The carrier particles 102a after the development processing and the toner particles 102b that have not jumped to the photosensitive member 130 are collected in the storage container 101.

  Here, as shown in FIG. 1B, the surface of the photoreceptor 130 is charged according to the recorded image, and the toner particles 102b fly to the surface of the photoreceptor 130 by electrostatic force. The flying toner particles 102b adhere to the surface of the photoreceptor 130, 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 130.

  Since the toner particles 102b are conveyed to the photoconductor 130 by the carrier particles 102a, the toner particles 102b are adsorbed to the photoconductor 130 by the carrier in the developing gap between the developing roll 140 and the photoconductor 130. 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 factor for the development of the electrophotographic apparatus main body and the developing apparatus 100.

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

  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. 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 related to the configuration of the developing device 100 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, when the processing target element is divided into the parts corresponding to the calculation management node of the main particle behavior analysis apparatus 202a by the force division method, each of the particle behaviors by the force division method is configured by a calculation apparatus. Each computer system (also referred to as a processor; in FIG. 1, the particle behavior analyzer 202 in FIG. 1) is provided with a division processing unit 250 that assigns each divided part.

  The division processing unit 250 is not a vertical N / horizontal N force matrix so that N ^ 2 <M <(N + 1) ^ 2 with respect to the number of processors M, but not vertical (N + 1) / horizontal (N + 1). The extended force matrix is set to be used, and for the (N + 1) ^ 2-M non-existent processor parts in the expanded force matrix, the actual processor is used as an alternative processor (alternative device). assign.

  In addition, when the division processing unit 250 is expanded to a force matrix of vertical (N + 1) and horizontal (N + 1), particle behavior analysis to which the force division method is applied cannot actually be realized. N ^ 2 + 1 to N · (N + 1) In order to exclude the range of N), only when the relationship of N ^ 2 is not satisfied and the relationship of N. (N + 1) +1 to (N + 1) ^ 2-1 is satisfied, the vertical (N + 1) / horizontal (N + 1) ), And for the calculation part that should be handled by a processor that does not actually exist, the particle processor is responsible for the real processor in the (N + 1) th row. Distribute information.

  These processes in the division processing unit 250 will be described in detail later.

<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 force-division parallelization algorithm using a force matrix 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 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 function that takes into account two or more types of interaction forces using a force-division parallelization algorithm, the program that configures the software is built into dedicated hardware. System on a chip (SOC) that implements a desired system by mounting functions such as a built-in computer (such as an embedded microcomputer) or a CPU (Central Processing Unit), a logic circuit, and a storage device on one chip. System on chip) or a general-purpose personal computer capable of executing various functions by installing various programs is installed from a recording medium.

  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 in which a program code of software that realizes a particle behavior analysis processing function that considers multiple types of interaction forces using a force-division parallelization method is supplied to a system or apparatus, and the system or apparatus The same effect as the case where the computer (or CPU or MPU) is configured by the hardware processing circuit is also achieved by reading and executing the program code stored in the storage medium. 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, not only the function of performing the particle behavior analysis process considering the multiple types of interaction force using the force division parallelization method is realized, but also the program code instruction Based on the above, the OS (Operating Systems; basic software) running on the computer performs part or all of the actual processing, and considers multiple types of interaction forces using the force-division parallelization method. The function of performing the particle behavior analysis process may be realized.

  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.

  Note that the program is provided as a file that describes the program code that implements the function of performing particle behavior analysis processing that takes into account multiple types of interaction forces using the force-division parallelization method. However, the program may be provided as an individual program module 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 “nonvolatile 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 that takes into account a plurality of types of interaction forces using a force-division parallelization 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. FD and CD-ROM as examples of recording media have some or all of the functions for realizing particle behavior analysis processing functions that take into account multiple types of interaction forces using the force-division parallelization method. It 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 according to the particle behavior analysis program, stores the processing result in a storage device such as a 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 combination of dedicated hardware that performs processing of each functional unit shown in FIG. A particle behavior analysis system 200 or a particle behavior analysis device 202 that performs a particle behavior analysis process considering the above may be configured.

  For example, instead of performing all the processing of each functional part for particle behavior analysis processing that considers multiple types of interaction forces using the force division parallelization method, a part of these functional parts is dedicated. A processing circuit 908 performed by 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 that takes into account a plurality of types of interaction forces using the force-division parallelization method, the data processing unit 230 shown in FIG. A data receiving unit 908a corresponding to the data receiving unit 232, a numerical operation processing unit 908b corresponding to the numerical operation processing unit 234, an 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.

<Force division parallel processing; basic (number of processors M = N ^ 2)>
5 to 12 are diagrams for explaining the parallelization processing of the force division method (algorithm using a force matrix) applied in the particle behavior analysis processing of the present embodiment. Here, FIG. 5 is a flowchart showing an example of a force-division parallel processing procedure.

  FIG. 6 is a diagram illustrating a method of assigning analysis target particles to each node. FIG. 7 to FIG. 9 are diagrams for explaining calculation targets of the interaction force at each node with respect to magnetic interaction, electrostatic interaction, and mechanical interaction (contact force).

  FIG. 10 is a diagram for explaining the interaction force addition processing (particularly in the row direction of the force matrix) obtained at each node. FIG. 11 is a diagram for explaining another specific processor that needs to communicate the interaction forces calculated in the row direction and the column direction. FIG. 12 is a diagram summarizing the communication target processor when the force matrix in the force division method is used, focusing on the node 6. In the force matrix, all the particles are assumed to be carrier particles 102a and are represented by the interaction of magnetic force.

  In the present embodiment, when each particle behavior analysis apparatus 202 analyzes each interaction, the analysis is performed using a force division method (algorithm using a force matrix) instead of a region division method or a particle division method. The amount of communication between processors is reduced. By reducing the amount of communication, the parallelization performance of the program when using multiple processors is improved, and the calculation time is shortened.

  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 = 4 and the total number of processors M is 16 (= 4 ^ 2). In this case, each processor is arranged in a force matrix of 4 rows and 4 columns. Although the details will be described later, the mechanism of this embodiment is characterized in that the restriction of 2 ^ N is relaxed so that the force division method can be applied even with the number of processors M other than N ^ 2. .

  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). ).

  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 (a total of 16 from 0 to 15 in this example).

  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 relaxes the restriction on the number of processors M (M = N ^ 2) as a process unique to the present embodiment. After executing the process (S106), the process proceeds to step S108.

  For example, the example shown in FIG. 6 shows a force matrix when 32 particles are calculated in parallel by 16 processors. The vertical direction is a substantial processor, which indicates its own node N (processor number) and the target particle, and the horizontal direction indicates the communication partner node N (processor number) and the target particle.

  Since 32 particles are calculated in parallel by 16 processors, each processor arranged in a force matrix of 4 rows and 4 columns first focuses on two particles, and other particles targeted for each particle of interest. Will be analyzed. For example, when focusing on the node 6, first, the 12th and 13th particles are set as the target particles.

  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, although the details will be described later, for a plurality of types of multi-particle interactions, calculation is performed using different force matrices.

  For example, the magnetic interaction is analyzed using a force matrix for analyzing the magnetic interaction shown in FIG. Further, the electrostatic interaction is analyzed using a force matrix for analyzing the electrostatic interaction shown in FIG. Further, the contact force is analyzed using a force matrix for analyzing the mechanical interaction (contact force) shown in FIG.

  Here, each force matrix for each interaction shown in FIGS. 7 to 9 is characterized in that the particle numbers handled are different. By calculating each type of many-body particle interaction using a separate force matrix, each force matrix calculates only the minimum number of particles required for the 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, among 32 analysis target particles, particle numbers 0 to 15 are carrier particles 102a (indicated by “C” to the right of the particle numbers in FIGS. 7 to 9), and particle numbers 16 to 31 are toners. It is assumed that the particle 102b (shown with “T” to the right of the particle number in FIGS. 7 to 9). 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 the magnetic force is as FIG. 7 including only the carrier particles 102a, the force matrix of the electrostatic force is as FIG. 8 including only the toner particles 102b, and the force matrix of the contact force is the carrier particles 102a and the toner particles 102b. 9 including the above, respectively. The number of particles in charge of each processor is set to “2” in the force matrix for contact force (FIG. 9), but the force matrix for magnetic interaction (FIG. 7) and the force matrix for electrostatic interaction (FIG. 9). In FIG. 8), “4” is used instead of “2”.

  In this way, by using each separate force matrix, only the minimum required 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 magnetic force, only the calculation for 16 carrier particles 102a is performed, so that the total calculation time is shortened compared with the case of calculating all 32 particles.

  For example, as can be seen from FIG. 6 (or FIG. 9), the force splitting method has a feature in the way of combining the partner particles when obtaining the interaction force. As shown in association with an index “−” indicating an interaction calculation between the particle number in the row direction and the particle number in the column direction (partially omitted), each of the particle numbers 8 to 15 The interaction between each of the particle numbers 4, 5, 12, 13, 20, 21, 28, and 29 is analyzed.

  Here, each particle calculates the sum of the acting forces from other particles acting on itself. For this reason, for particle numbers 12 and 13, the 12th particle requires the 13th interaction force and the 13th particle requires the 12th interaction force. However, since the magnitudes of the interaction forces of 12 and 13 and 13 and 12 are the same, the calculation may be performed once.

  In addition, “12-12” and “13-13” can be taken in combination, but this means self-interaction, and in this embodiment, the analysis is unnecessary.

  Next, it communicates between specific processors and for each interaction, such as magnetic interaction, electrostatic interaction, or mechanical interaction (contact force), adds the row-wise interactions in the force matrix, 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, as shown in FIG. 10, when attention is paid to node 6, the interaction values at nodes 4, 5, and 7 are sent to node 6, and summation calculation is performed at node 6. Thereby, the sum total value of the interaction force of the particles 12 and 13 in charge of the node 6 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, as shown in FIG. 11, when attention is paid to the node 6, the position coordinates of the particles 12 and 13 assigned to the node 6 that are updated by calculating from the total value of the interaction force are related to the interaction matrix. To nodes 4, 5, 7 in the direction and nodes 2, 10, 14 in the column direction. This is because only the nodes 4, 5, 7 in the row direction and the nodes 2, 10, 14 in the column direction need information on the particles 12, 13 that the node 6 is responsible for. Therefore, the node 6 performs communication only with these six 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 FIGS. The behavioral analysis is performed by simultaneously considering a plurality of 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, mechanical contact, etc., in the developer 102 (specifically, carrier particles 102a and toner particles 102b) accommodated in the developing device 100 of the image forming apparatus 1 A behavior analysis is performed on particles having various types of multi-particle interaction using a force matrix (interparticle interaction rule) shown in FIG. 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 the electromagnetic effect and the rubbing from the carrier particles 102a after the toner particles 102b are electrodeposited on the photoreceptor 130, and the amount of toner particles 102b contributing to the development from the carrier particles 102a, You may analyze the flying to the photoreceptor 130 etc., and also 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.

<Force division parallel processing; Restriction relaxation method>
FIG. 13 is a flowchart for explaining the details of the technique that relaxes the limitation on the number of processors M in the force division method employed in the present embodiment, that is, step S106 of FIG.

  As described above, the basic principle of the force division method is that the number of processors M needs to satisfy the relationship of N ^ 2, and the particles to be processed are arranged in a square force matrix of N rows and N columns. It is assumed that. In other words, the force division method can be applied only when the number of processors M satisfies the relationship of N ^ 2.

  For example, a force matrix is configured by a combination of 3 × 3 by using 9 processors so that 3 ^ 2 (= 9). In addition, a force matrix is configured by a combination of 4 × 4 by using 16 processors so that 4 ^ 2 (= 16). In addition, a force matrix is configured by a combination of 5 × 5 by using 25 processors so that 5 ^ 2 (= 25).

  However, in the mechanism of the force division method with such limitations, as a matter of course, parallel processing using the force division method cannot be performed with the number of processors M other than N ^ 2. Therefore, when the number of processors M is within the range of N ^ 2 to (N + 1) ^ 2-1, a force matrix of vertical N and horizontal N is used regardless of the number of processors M. In effect, only the N ^ 2nd processor is used, and the N ^ 2 + 1 to (N + 1) ^ 2-1th processors are not used.

  As a result, for example, when the particle behavior analysis device 202 of a part (for example, one) of the parallel computer system goes down, one class lower (N−1) ^ 2 than the previous N ^ 2. Therefore, the particle behavior analysis system 200 must be configured with the number M of processors in order to cope with it, and the calculation performance is greatly reduced. Further, in practice, the remaining operable particle behavior analysis apparatus 202 (for N ^ 2-1- (N-1) ^ 2) must be in a non-operating state, resulting in waste.

  For example, when N = 5 and 25 particle behavior analyzers 202 constitute the particle behavior analysis system 200, when one particle behavior analyzer 202 goes down, N = 4 and 16 particle behaviors. It is necessary to reconfigure and operate the particle behavior analysis system 200 with the analysis device 202. The computation must be performed by 16 processors, and the parallel processing capacity is reduced accordingly, and 5 ^ 2-4 ^ 2-1 = 8 particle behavior analyzers 202 must be put into a non-operating state, which is wasteful. Will occur.

  Similarly, when the particle behavior analysis system 200 is configured with 16 particle behavior analysis devices 202 with N = 4, when one particle behavior analysis device 202 goes down, N = 3 and nine particles It is necessary to reconfigure and operate the particle behavior analysis system 200 with the behavior analysis device 202. The calculation must be performed by 9 processors, and the parallel processing capacity is reduced accordingly, and 4 ^ 2-3 ^ 2-1 = 6 particle behavior analyzers 202 must be put into a non-operating state, which is wasteful. Will occur.

  Therefore, in the present embodiment, a method of relaxing such a limit condition (M = N ^ 2) for the number of processors M is proposed. As shown in FIG. 13, first, the division processing unit 250 specifies the number M of processors that can be used at that time (S210). Then, an expanded force matrix is created so that N ^ 2 <M <(N + 1) ^ 2 for the number of processors M (S211). In this case, the expanded force matrix is a vertical (N + 1) / horizontal (N + 1) force matrix.

  Specifically, it is determined whether or not the number M of usable processors satisfies a relationship of N · (N + 1) + 1 ≦ M ≦ (N + 1) ^ 2-1 (S212).

  When the number of processors M does not satisfy the relationship of N · (N + 1) + 1 ≦ M ≦ (N + 1) ^ 2-1 (S212-NO), that is, when N ^ 2 + 1 ≦ M ≦ N · (N + 1), division processing is performed. The unit 250 assumes that the extension method of the present embodiment is not applicable, and uses a force matrix of vertical N and horizontal N so as to apply the force division method with N one class lower than N + 1 as in the past. It will be decided (S214).

  Here, N · (N + 1) + 1 ≦ M ≦ (N + 1) ^ 2-1 is excluded (S212-NO, S214), and the force matrix is a square matrix due to the algorithm of the force division parallelization method. It is necessary. That is, in the force matrix, when no substantial processor is arranged in the (N + 1) th row and a square matrix cannot be obtained substantially, the extension processing of the present embodiment is practically not applicable.

  On the other hand, when the number of processors M satisfies the relationship of N · (N + 1) + 1 ≦ M ≦ (N + 1) ^ 2-1 (S212—YES), the division processing unit 250 uses the vertical (N + 1) / horizontal (N + 1) force. A matrix is used (S216). At this time, a processor that does not actually exist in the expanded force matrix is set as a dummy (S218).

  For example, when the number of processors M is in the range of 2 · 3 + 1 (= 7) to 3 ^ 2−1 (= 8), a force matrix of 3 in length and 3 in width is used. The extension processing of this embodiment cannot be applied to the 5 and 6 processors corresponding to N ^ 2 + 1 to N · (N + 1), which have a matrix configuration of 2 × 3.

  When the number of processors M is in the range of 3 · 4 + 1 (= 13) to 4 ^ 2−1 (= 15), a force matrix of 4 × 4 is used. The expansion processing of this embodiment cannot be applied to 10-12 processors corresponding to N ^ 2 + 1 to N · (N + 1), which have a matrix configuration of 3 × 4.

  When the number of processors M is in the range of 4 · 5 + 1 (= 21) to 5 ^ 2−1 (= 24), a force matrix of 5 × 5 is used. The expansion processing of this embodiment cannot be applied to 17 to 20 processors corresponding to N ^ 2 + 1 to N · (N + 1) having a matrix configuration of 4 × 5.

  Further, in the case of applying such an extension process, the division processing unit 250, for (N + 1) ^ 2-M dummy processor parts in the extended vertical (N + 1) / horizontal (N + 1) force matrix, Assign a processor as an alternative processor. In other words, regarding the calculation part that (N + 1) ^ 2-M dummy processors that do not actually exist are supposed to be in charge of the particles, the actual processor in the (N + 1) th row is in charge as an alternative processor. Information is distributed (S220). An actual processor existing in the (N + 1) th row is also referred to as an additional matrix processor. At this time, when there are a plurality of actual processors in the (N + 1) th row, it is preferable to distribute them equally to all the processors.

  Specifically, for the computation part in charge of the intangible processor, the data (particle information) is copied (duplicated) to the actual processor so that the actual processor executes the calculation process on behalf of the processor. . Subsequent parallel calculations may be performed according to a normal force-division parallelization method.

  In this way, in the present embodiment, the number of processors other than the limit (N ^ 2) that can be used in the conventional force division method is used by using the expanded vertical (N + 1) / horizontal (N + 1) force matrix. N + 1) +1 to (N + 1) ^ 2-1 also performs force-division parallel processing. Hereinafter, a description will be given using specific examples.

<Force division parallel processing; restriction relaxation example 1>
FIG. 14 is a diagram for explaining a first example (limitation relaxation example 1) of a technique for relaxing the restriction on the number of processors M (M = N ^ 2) when the force division method is applied. In this restriction relaxation example 1, in the case of N = 2 in N · (N + 1) +1 to (N + 1) ^ 2-1, that is, the number of processors M is 4 (when N = 2) and 9 (when N = 3). In the case of 2 · 3 + 1 (= 7) within the range of the processor and within the range to which the extension processing of this embodiment can be applied.

  In this case, as can be seen from the above description, first, the division processing unit 250 is set to use an expanded force matrix of 3 vertical and 3 horizontal as shown in FIG. Since the number of processors M is “7”, the division processing unit 250 assumes that the seventh processor is present at the node 6 in the third row in the expanded force matrix of 3 × 3. And particle numbers 12 and 13 are assigned. Further, the division processing unit 250 does not assign particle numbers to the remaining nodes 7 and 8 (indicated by “none” in the figure), and sets them as dummy processors without substance.

  Further, the division processing unit 250, regarding the calculation portion that should be handled by the dummy processors of the nodes 7 and 8 that do not actually exist, the processor of the substantial node 6 (# of the additional matrix) that exists in the third row. (6 processors) are assigned.

  For example, the calculation part A (in the # 7 node interaction matrix) that the original node 7 (an example of an intangible processor) takes charge of and the calculation part B that the original node 8 (an example of an intangible processor) takes charge of With respect to (in the # 8 node interaction matrix), the substantial processor of the node 6 once copies (duplicates) data (particle information) necessary for the calculation to the memory. Thereafter, in accordance with the normal force-division parallelization method, the node 6 (an example of a substantial processor) executes the calculation of the physical quantity of interaction on behalf of the node 6. In the figure, the dotted lines of the nodes 7 and 8 of the # 6 interaction matrix indicate the position of the copy data on the memory (= position on the data array).

  For example, as shown in FIG. 14, when attention is paid to the node 2, the position coordinates of the particles 4 and 5 in charge of the node 2 in charge of the node 2 updated from the total value of the interaction forces are updated. , 5 (that is, a processor related to the communication), the nodes 0 and 1 in the row direction related to the interaction matrix, and the node 6 and the node 6 that substitutes the nodes 5 and 8 in the column direction. The calculation part B may be sent to the person in charge).

  Although not shown in the drawing, when attention is paid to the node 5, the position coordinates of the particles 10 and 11 in charge of the node 5 in charge of the updated node 5 calculated from the total value of the interaction forces are related to the row direction related to the interaction matrix. Nodes 3 and 4 and node 2 and node 8 in the column direction may be sent to node 6 (in charge of calculation part B).

  Further, although omitted from the drawing, when attention is paid to the node 1, the position coordinates of the particles 2 and 3 in charge of the node 1 that are updated by calculating from the total value of the interaction force are changed in the row direction related to the interaction matrix. The nodes 0 and 2 and the node 4 and the node 7 in the column direction may be sent to the node 6 (in charge of the calculation part A). When attention is paid to the node 4, the position coordinates of the particles 8 and 9 assigned to the node 4 updated by calculating from the total value of the interaction force are changed to the nodes 3 and 5 in the row direction related to the interaction matrix. What is necessary is just to send to the node 6 (in charge of the calculation part A) acting as the node 1 and the node 7 of the column direction.

  In response to this, the node 6 acting as the calculation part A of the node 7 analyzes the interaction between each of the particle numbers 12 and 13 and each of the particle numbers 2, 3, 8, and 9. The node 6 acting as the calculation part B of the node 8 analyzes the interaction between each of the particle numbers 12 and 13 and each of the particle numbers 4, 5, 10, and 11.

<Force division parallel processing; restriction relaxation example 2>
FIG. 15 is a diagram for explaining a second example (limitation relaxation example 2) of a technique for relaxing the restriction on the number of processors M (M = N ^ 2) when the force division method is applied. In this example of relaxed restriction, in the case of N = 2 in N · (N + 1) +1 to (N + 1) ^ 2-1, that is, the number of processors M is 4 (when N = 2) and 9 (N = 3). In the case of 2) 3 + 2 = 3 ^ 2-1 (= 8), which is within the range of the processor and within the range to which the extension processing of this embodiment can be applied.

  In this case, as can be understood from the above description, first, the division processing unit 250 is set to use an expanded force matrix of 3 vertical and 3 horizontal as shown in FIG. Since the number M of processors is “8”, the division processing unit 250 assumes that the seventh processor is present at the node 6 in the third row in the expanded force matrix of 3 × 3. The particle numbers 12 and 13 are allocated, and the eighth processor is allocated as an entity to the node 7 and the particle numbers 14 and 15 are allocated. Further, the division processing unit 250 does not assign a particle number to the remaining node 8 (indicated by “none” in the figure), and sets it as an innocent dummy processor.

  In addition, the division processing unit 250, regarding the calculation part that should be handled by the dummy node 8 processor that does not actually exist, the processor (additional matrix) of the substantial nodes 6 and 7 existing in the third row. The data (particle information) are distributed so that the # 6 and # 7 processors) are equally responsible.

  For example, for the two calculation parts A and B (in the # 8 node interaction matrix) that the original node 8 is in charge of, the actual processors of the nodes 6 and 7 temporarily copy the values necessary for the calculation to the memory. (Duplicate). Thereafter, the physical quantity of the interaction is calculated according to the normal force division parallelization method.

  For example, as shown in FIG. 15, when attention is paid to the node 2, the position coordinates of the particles 4 and 5 in charge of the node 2 that are updated by calculating from the total value of the interaction force are related to the interaction matrix. It may be sent to the nodes 6 and 6 (in charge of the calculation part A) and the node 7 (in charge of the calculation part B) acting as the nodes 0 and 1 in the direction and the nodes 5 and 8 in the column direction. In the figure, the dotted line of the node 8 portion of the interaction matrix of # 6 and # 7 indicates the position of the copy data on the memory (= position on the data array).

  Although not shown in the drawing, when attention is paid to the node 5, the position coordinates of the particles 10 and 11 in charge of the node 5 in charge of the updated node 5 calculated from the total value of the interaction forces are related to the row direction related to the interaction matrix. Nodes 3 and 4 and node 2 and node 8 in the column direction may be sent to node 6 (in charge of calculation part A) and node 7 (in charge of calculation part B).

  In response to this, the node 6 acting as the calculation part A of the node 8 analyzes the interaction between each of the particle numbers 12 and 13 and each of the particle numbers 4, 5, 10, and 11. The node 7 acting as the calculation part B of the node 8 analyzes the interaction between each of the particle numbers 14 and 15 and each of the particle numbers 4, 5, 10, and 11.

  In principle, data is copied so that either one of the actual nodes 6 and 7 functions as an alternative processor that performs all the processing of the two calculation parts A and B of the node 8 ( However, in this case, an unbalance (unbalance) of the calculation load between the alternative processor and another processor becomes large, which is not preferable.

<Force division parallel processing; restriction relaxation example 3>
FIG. 16 is a diagram for explaining a third example (limitation relaxation example 3) of a technique for relaxing the restriction on the number of processors M (M = N ^ 2) when the force division method is applied. In this restriction relaxation example 3, N = (N + 1) +1 to (N + 1) ^ 2-1 where N = 3, that is, the number of processors M is 9 (when N = 3) and 16 (N = 4). When) it is within the range of the processor and within the range to which the expansion processing of this embodiment can be applied.

  In this case, as can be seen from the above description, 13 to 15 processors can be supported. In the figure, the number of processors M is 4 ^ 2-2 (= 14).

  In this case, as can be understood from the above description, first, the division processing unit 250 is set to use an expanded force matrix of 4 × 4 as shown in FIG. Since the number of processors M is “14”, the division processing unit 250 assumes that the 13th processor is present at the node 12 in the 4th row in the expanded force matrix of 4 × 4. The particle numbers 24 and 25 are allocated, and the fourteenth processor is allocated to the node 13 as an entity, and the particle numbers 26 and 27 are allocated. Further, the division processing unit 250 does not assign a particle number to the remaining nodes 14 and 15 (indicated by “none” in the drawing), and sets it as an innocent dummy processor.

  In addition, regarding the calculation portion that should be handled by the dummy nodes 14 and 15 that do not actually exist, the division processing unit 250 is the processor of the actual nodes 12 and 13 (in the fourth row). The additional matrix # 12, 13 processor) is assigned to be equally responsible.

  For example, for the two calculation parts A and B (in the # 14 node interaction matrix) that the original node 14 is in charge of, the processor of the actual nodes 12 and 13 temporarily copies the values necessary for the calculation to the memory. (Duplicate). In addition, for the two calculation parts C and D (in the # 15 node interaction matrix) that the original node 15 is in charge of, the processor of the actual nodes 12 and 13 temporarily copies the values necessary for the calculation to the memory. (Duplicate). Thereafter, the physical quantity of the interaction is calculated according to the normal force division parallelization method.

  For example, as shown in FIG. 16, when attention is paid to the node 6, the position coordinates of the particles 12 and 13 in charge assigned to the node 6 updated from the sum of the interaction forces are related to the interaction matrix. It may be sent to the nodes 12 (in charge of the calculation part A) and the node 13 (in charge of the calculation part B) acting as the direction nodes 4, 5, 7 and the nodes 2, 10 and 14 in the column direction. Although the detailed description is omitted, the same applies to the other nodes 2 and 10 (related to the calculation parts A and B) and the nodes 3, 7, and 11 (related to the calculation parts C and D) related to the proxy processing. In the figure, the dotted lines of the nodes 14 and 15 of the interaction matrix # 12 and # 13 indicate the position of the copy data on the memory (= position on the data array).

  In response to this, the node 12 acting as the calculation part A of the node 14 analyzes the interaction between each of the particle numbers 24 and 25 and each of the particle numbers 4, 5, 12, 13, 20, and 21. To do. The node 13 acting as the calculation part B of the node 14 analyzes the interaction between the particle numbers 26 and 27 and the particle numbers 4, 5, 12, 13, 20, and 21, respectively. Further, the node 12 acting as the calculation part C of the node 15 analyzes the interaction between each of the particle numbers 24 and 25 and each of the particle numbers 6, 7, 14, 15, 22, and 23. The node 13 acting as the calculation part D of the node 15 analyzes the interaction between each of the particle numbers 26 and 27 and each of the particle numbers 6, 7, 14, 15, 22, and 23.

  Note that, in the restriction relaxation example 3 as well, in principle, any one of the actual nodes 12 and 13 performs processing of all the four calculation portions A, B, C, and D of the nodes 14 and 15. It is also possible to copy (duplicate) the values necessary for the calculation to the memory once, but in that case, the calculation load unbalance (unbalance) with other processors will increase. It is not preferable.

  Here, although the case where the number of processors M is 4 ^ 2-2 (= 14) is shown, the remaining number when N = 3 in N · (N + 1) +1 to (N + 1) ^ 2-1 is shown. The extended processing of the present embodiment can also be applied to 13 and 15.

<Force division parallel processing; restriction relaxation example 4>
FIG. 17 is a diagram for explaining a fourth example (limitation relaxation example 4) of a technique for relaxing the limit on the number of processors M (M = N ^ 2) when the force division method is applied. In this restriction relaxation example 4, in the case of N = 4 in N · (N + 1) +1 to (N + 1) ^ 2-1, that is, when the number of processors M is 16 (when N = 4) and 25 (N = 5) When) it is within the range of the processor and within the range to which the expansion processing of this embodiment can be applied.

  In this case, as can be understood from the above description, 21 to 24 processors can be supported. In the figure, the number of processors M is 5 ^ 2-3 (= 22).

  In this case, as can be understood from the above description, first, the division processing unit 250 is set to use an extended force matrix of 5 × 5 as shown in FIG. Since the number M of processors is “22”, the division processing unit 250 assumes that the 21st processor is present at the node 20 in the 5th row in the expanded force matrix of 5 × 5. And assign the particle numbers 40 and 41. Furthermore, the 22nd processor is assigned to the node 21 as an entity, and the particle numbers 42 and 43 are assigned. Further, the division processing unit 250 assigns particle numbers to the remaining nodes 22, 23, and 24 (indicated by “none” in the drawing), and sets them as dummy processors without substance.

  In addition, the division processing unit 250, for the calculation portion that should be handled by the processors of the dummy nodes 22, 23, and 24 that do not actually exist, the actual nodes 20, 21 that exist in the fifth row. Distribution is performed so that processors (# 20 and 21 processors in the additional matrix) are assigned equally.

  For example, for the two calculation parts A and B (in the # 22 node interaction matrix) that the original node 22 is in charge of, the processor of the actual nodes 20 and 21 temporarily copies the values necessary for the calculation to the memory. (Duplicate). In addition, regarding the two calculation parts C and D (in the # 23 node interaction matrix) that the original node 23 is in charge of, the processor of the actual nodes 20 and 21 temporarily copies the values necessary for the calculation to the memory. (Duplicate). Furthermore, for the two calculation parts E and F (in the # 24 node interaction matrix) that the original node 24 is responsible for, the actual processors 20 and 21 once store the values necessary for the calculation in the memory. Copy (duplicate). Thereafter, the physical quantity of the interaction is calculated according to the normal force division parallelization method.

  For example, as shown in FIG. 17, focusing on the node 7, the position coordinates of the particles 14 and 15 in charge of the node 7 in charge of the updated node 7 calculated from the total value of the interaction force are related to the interaction matrix. What is necessary is just to send to the node 20 (responsible for the calculation part A) and the node 21 (responsible for the calculation part B) acting as the nodes 5, 6, 8, 9 in the direction and the nodes 2, 12, 17 and 22 in the column direction. Although detailed explanation is omitted, other nodes 2, 12, 17 (related to calculation parts A and B) and nodes 3, 8, 13, 18 (related to calculation parts C and D) and node 4 related to proxy processing , 9, 14, and 19 (related to calculation parts E and F). In the figure, the dotted lines of the nodes 22, 23 and 24 of the interaction matrix of # 20 and # 21 indicate the position of the copy data on the memory (= position on the data array).

  In response to this, the node 20 acting on behalf of the calculation part A of the node 22 is between each of the particle numbers 40 and 41 and each of the particle numbers 4, 5, 14, 15, 24, 25, 34, and 35. Analyze the interaction. Further, the node 21 acting as the calculation part B of the node 22 performs the interaction between each of the particle numbers 42 and 43 and each of the particle numbers 4, 5, 14, 15, 24, 25, 34, and 35. To analyze.

  Further, the node 20 acting as the calculation part C of the node 23 performs an interaction between each of the particle numbers 40 and 41 and each of the particle numbers 6, 7, 16, 17, 26, 27, 36, and 37. To analyze. Further, the node 21 acting as the calculation part D of the node 23 performs the interaction between each of the particle numbers 42 and 43 and each of the particle numbers 6, 7, 16, 17, 26, 27, 36, and 37. To analyze.

  Further, the node 20 acting as the calculation part E of the node 24 performs an interaction between each of the particle numbers 40 and 41 and each of the particle numbers 8, 9, 18, 19, 28, 29, 38, and 39. To analyze. Further, the node 21 acting as the calculation part F of the node 24 performs an interaction between each of the particle numbers 42 and 43 and each of the particle numbers 8, 9, 18, 19, 28, 29, 38, and 39. To analyze.

  Note that, also in the restriction relaxation example 4, in principle, any one of the actual nodes 20 and 21 has six calculation parts A, B, C, D, and E of the nodes 22, 23, and 24. , F can be temporarily copied (duplicated) to the memory so that all processing of F can be performed, in which case the calculation load is unbalanced (unbalanced) with other processors. (Equilibrium) becomes large, which is not preferable.

  Here, the case where the number of processors M is 5 ^ 2−3 (= 22) is shown, but the remaining number when N = 4 in N · (N + 1) +1 to (N + 1) ^ 2−1 is shown. The extended processing of this embodiment can also be applied to 21, 23, 24.

  Note that, as a specific example of the technique for relaxing the limit on the number of processors M (M = N ^ 2), the case of N = 2 to 4 has been described. However, the extension of the present embodiment is similarly applied to N = 5 or more. Processing can be applied.

<Improvement ratio of parallel processing speed>
18 to 20 are diagrams comparing the speed improvement ratio obtained by the normal force division parallelization method and the speed improvement ratio obtained by the restriction relaxation method (also referred to as extended force division parallelization method) of the present embodiment.

  FIG. 18 is a comparative example in the case of 2 ^ 2 (= 4) <M <3 ^ 2 (= 9), that is, an expansion exceeding four processors in the expansion force division parallelization method of the present embodiment. In this case, in the normal force-division parallelization method, a vertical 2 and horizontal 2 force matrix is applied, and the speed improvement ratio remains at about 4.0 times at the maximum.

  On the other hand, in the extended force division parallelization method of the present embodiment, when the number of processors is M = 5 and 6, a force matrix of 2 × 2 is applied as in the normal force division parallelization method. However, when the number of processors is M = 7, 8, a force matrix of 3 × 3 can be applied, and the speed improvement ratio is improved to about 6 to 7 times. I understand that.

  FIG. 19 shows a comparative example in the case of 3 ^ 3 (= 9) <M <4 ^ 2 (= 16), that is, an expansion exceeding 9 processors in the expansion force division parallelization method of the present embodiment. In this case, in the normal force division parallelization method, a force matrix of 3 in length and 3 in width is applied, and the speed improvement ratio remains at about 8.0 times at the maximum.

  On the other hand, in the extended force division parallelization method of the present embodiment, when the number of processors M = 10 to 12, a force matrix of 3 in length and 3 in width is applied as in the normal force division parallelization method. However, when the number of processors M = 13 to 15, a force matrix of 4 × 4 can be applied, and the speed improvement ratio is improved to about 10 to 11 times. I understand.

FIG. 20 is a comparative example in the case of 4 ^ 4 (= 16) <M <5 ^ 2 (= 25), that is, an expansion exceeding 16 processors in the expansion force division parallelization method of the present embodiment. In this case, in the normal force-division parallelization method, a force matrix of vertical 4 and horizontal 4 is applied, and the speed improvement ratio remains at about 14.0 times at the maximum.
On the other hand, in the extended force division parallelization method of this embodiment, when the number of processors is M = 17 to 20, a force matrix of 4 vertical and 4 horizontal sides is applied as in the normal force division parallelization method. However, when the number of processors M is 21 to 24, a force matrix of 5 × 5 can be applied, and the speed improvement ratio is improved to about 15 to 16 times. I understand.

  In any case, the speed improvement ratio of the calculation speed is higher when parallel processing is performed with (N + 1) ^ 2 computing devices than when parallel processing is performed with N ^ 2 computing devices. It is obvious.

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 a figure explaining the calculation object of the interaction force in each node about a magnetic interaction. It is a figure explaining the calculation object of the interaction force in each node about an electrostatic interaction. It is a figure explaining the calculation object of interaction force in each node about mechanical interaction (contact force). It is a figure explaining the addition process (especially about the row direction of force matrix) of the interaction force calculated | required in each node. It is a figure explaining the other specific processor which needs to communicate the interaction force computed to the row direction and the column direction. It is the figure which summarized the processor of the communication object at the time of using the force matrix in a force division method paying attention to node # 6. It is a flowchart explaining the method (details of step S106 of FIG. 5) which eases the restriction | limiting of the number of processors M in the force division method employ | adopted by this embodiment. It is a figure explaining the restriction relaxation example 1 of a force division method. It is a figure explaining the restriction relaxation example 2 of a force division method. It is a figure explaining the restriction relaxation example 3 of a force division method. It is a figure explaining the restriction relaxation example 4 of a force division method. It is the figure (when exceeding four processors) which compared the speed improvement ratio by the normal force division | segmentation parallelization method and the extended force division | segmentation parallelization method of this embodiment. It is the figure (when 9 processors are exceeded) which compared the speed improvement ratio by the normal force division | segmentation parallelization method and the extended force division | segmentation parallelization method of this embodiment. It is the figure (when exceeding 16 processors) which compared the speed improvement ratio by the normal force division | segmentation parallelization method and the extended force division | segmentation parallelization method of this embodiment.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 100 ... Developing apparatus, 101 ... Storage container, 101a ... Opening part, 102 ... Developer, 102a ... Carrier particle, 102b ... Toner particle, 130 ... Photoconductor, 140 ... Developing roll, 142 ... Magnet, 150 ... Regulating blade, 160 DESCRIPTION OF SYMBOLS ... Agitation conveyance 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 , 232... Data receiving unit, 234... Numerical value calculation processing unit, 236... Output data processing unit, 240.

Claims (4)

A division processing unit that divides the particles by a force division method using a force matrix, and assigns each divided portion to each computing device;
While performing data communication with the other calculation devices provided in the respective calculation devices, the divided portions allocated by the force division method are exchanged with other substances acting on the particles. A data processing unit for analyzing the behavior of the particles in consideration of the interaction force,
The division processing unit is set to use an expanded force matrix so that N ^ 2 <M <(N + 1) ^ 2 with respect to the number M of the computing devices, and further, the expanded force matrix A (N + 1) ^ 2-M piece of the calculation device that does not actually exist is assigned as the substitute calculation device as a substitute device. When the number M of the computing devices does not satisfy the relationship of N ^ 2 and satisfies the relationship of N · (N + 1) + 1 ≦ M ≦ (N + 1) ^ 2-1, the division processing unit performs vertical (N + 1) ) ・ The division is performed so that a lateral (N + 1) force matrix is used. Further, regarding the calculation part that the calculation device that is not actually present is supposed to be in charge, there is an entity existing in the (N + 1) th row. The particle behavior analysis apparatus according to claim 1, wherein the particle information is distributed so that the calculation apparatus is in charge of the substitute apparatus. 3. The particle behavior analysis apparatus according to claim 2, wherein the division processing unit equally distributes the information on the particles when there are a plurality of the actual calculation apparatuses in the N + 1th row. When the particles are divided by a force division method using a force matrix and each divided portion is assigned to each calculation device, the number M of the calculation devices does not satisfy the relationship of N ^ 2, and N · (N + 1) When the relationship of + 1 ≦ M ≦ (N + 1) ^ 2-1 is satisfied, the division is performed so that the vertical (N + 1) / horizontal (N + 1) force matrix is used. Regarding the calculation part that should be in charge, the procedure of distributing the information of the particles so that the actual calculation device in charge in the (N + 1) th row is in charge;
While performing data communication with the other calculation device, the divided portion allocated by the force division method takes into account the interaction force with other substances acting on the particles, and A program for particle behavior analysis, characterized by executing a procedure for analyzing behavior.

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