JP2008176084A - Particle behavior analyzer and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To obtain higher efficiency in parallelization, regarding a particle behavior simulation to process interactions between particles by a plurality of computers. <P>SOLUTION: Close distance force such as mechanical contact force and sticking force to be analyzed while taking notice of the interaction between particles at a short distance is processed following a region segmentation method (S302 to S316), electromagnetic interaction force and electrostatic interaction force to be analyzed while taking notice of interactions between the particles at a short distance and particles at a long distance are processed following a force segmentation method (S318 to S328). Particularly, the long distance force is computed for every prescribed number of times to the computation of short distance force (S316). <P>COPYRIGHT: (C)2008,JPO&INPIT

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 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.

  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). -3, patent documents 1 and 2).

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 JP 2005-122354 A 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 Documents 1 and 2 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, when calculating long-distance forces such as magnetic interaction force and Coulomb force by applying the domain-division parallelization method, it is necessary to communicate with all other processors in addition to nearby regions. Efficiency is reduced. Also, in principle, communication is possible if the area size is increased and divided so as to cover a certain range (cut-off distance) exerted by long-range force by limiting the points that must be considered up to the infinity point. While the amount can be reduced, the number of particles to be calculated per node increases, the load increases, and the calculation system decreases.

  For this reason, in the analysis of a region where particles are densely packed in a relatively narrow region as in the electrophotographic development process, the number of divisions is small, in other words, the number of nodes cannot be increased and the calculation time cannot be shortened.

  As a mechanism for solving such a problem, Patent Document 2 proposes a calculation method that does not reduce parallelization efficiency even when a long-distance force is calculated by a region division method.

  An object of the present invention is to provide a mechanism capable of obtaining higher parallelization efficiency in a particle behavior simulation in which interparticle interactions are processed by a plurality of computers.

  According to the first aspect of the present invention, the short-distance force, which is an interaction force for performing an analysis focusing on the interaction with particles close to each other among the acting forces acting on the particles, is determined according to the region division method. A division processing unit that divides a processing target particle according to a force division method and a division processing for a long-distance force that is an interaction force that performs an analysis focusing on an interaction between a particle having a short distance and a particle having a long distance A data processing unit provided in each network-connected computing device that calculates a near-distance force according to a region division method and a long-distance force according to a force division method for a divided portion allocated by a division process by a unit; A particle behavior analysis device characterized by analyzing the behavior of particles in consideration of the interaction force with other substances acting on the particles. .

  The invention described in claim 2 is characterized in that, in the invention described in claim 1, the data processing unit calculates the long distance force every predetermined number of times for the calculation of the short distance force.

  The invention according to claim 3 is the invention according to claim 1, and further, based on the type of acting force acting on the particles and the type of particles, the calculation load in the data processing unit provided in each calculation device is increased. An analysis load distribution processing unit is further provided that divides the processing target element by the region division method or the force division method so as to be uniform.

  The invention according to claim 4 is the invention according to claim 3, wherein the analysis load distribution processing unit divides the processing target region according to the region division method so that the number of particles belonging to each divided portion is equal. The division direction is determined so that

  The invention according to claim 5 is an interaction force that analyzes any one of a plurality of network-connected computing devices focusing on the interaction with a particle having a short distance among the acting force acting on the particle. For near-distance forces, the region to be processed is divided according to the region division method, and analysis focusing on the interaction between particles that are close and those that are far away is performed. This is a program that enables particle behavior analysis considering interaction force with other substances acting on particles by functioning as a division processing unit that divides the particles to be processed according to the law. is there.

  In the invention according to claim 6, each of a plurality of network-connected computing devices performs analysis focusing on the interaction between the allocated divided portions and the particles having a short distance among the acting forces acting on the particles. The near-distance force, which is the interaction force to be performed, is calculated according to the domain division method, and the analysis is performed focusing on the interaction between the particles with a close distance and the particles with a long distance. By being made to function as a data processing unit that calculates in accordance with the law, it is a program that enables particle behavior analysis in consideration of interaction force with other substances acting on particles.

  According to the first aspect of the present invention, the short-distance force is calculated by the region division method having a communication load smaller than that of the force division method, and the long-distance force is calculated by the force division method capable of higher resolution than the region division method. As a result, the overall processing time and accuracy can be balanced without reducing parallelization efficiency.

  According to the second aspect of the present invention, high parallelization efficiency can be obtained even when the force division method having a larger communication volume than the region division method is used in combination.

  According to the third aspect of the present invention, it is possible to ensure equalization of load distribution, to suppress generation of dead time waiting until calculation of all other processors is completed, and to analyze processing time Can be reliably shortened. If the type of particles to be analyzed and the force to be analyzed are different, even if they are distributed evenly focusing on “number”, the calculation load is not distributed evenly. However, the types of particles to be analyzed and the actions to be analyzed This is because by dividing based on the force, it is possible to distribute the load so that the processing time of the analysis process is as equal as possible, and to ensure equalization of load distribution.

  According to the fourth aspect of the present invention, even under conditions where the number of particles varies depending on the dividing direction, the load distribution can be equalized by appropriately setting the dividing direction and evenly distributing the number of particles. It can be done reliably.

  According to the invention described in claim 5, the mechanism of the division processing unit of the particle behavior analysis apparatus that performs the processing that balances the overall processing time and accuracy without reducing the parallelization efficiency is achieved using a computer. realizable.

  According to the sixth aspect of the present invention, the mechanism of the data processing unit of the particle behavior analysis apparatus that performs the processing that balances the overall processing time and accuracy without reducing the parallelization efficiency is achieved using a computer. realizable.

  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 transporting the developer 102 to the opposite portion of the photoreceptor 130 and causing the toner particles 102b to fly to the photoreceptor 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.

  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.

  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, 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.

  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 photoreceptor 130.

  The developing roller 140 is provided so as to face the photoconductor 130, and the inner toner particles 102 b and the external additive 102 c of the developer 102 adsorbed on the developing roller 140 are charged and adsorbed on the photoconductor 130. The At this time, an electrostatic latent image is formed on the surface of the photosensitive member 130 according to a recorded image, and the toner particles 102b and the external additive 102c are formed on the electrostatic latent image formed on the photosensitive member 130. Adsorbed according to the image.

  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. At this time, the powder additive fluidity, charging property, transfer property, or cleaning property is secured by using the external additive 102c. The carrier particles 102a after the development processing and the toner particles 102b and the external additive 102c that have not been ejected to the photoreceptor 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 and the external additive 102c fly to the surface of the photoreceptor 130 by electrostatic force. To do. The flying toner particles 102b and the external additive 102c 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.

  In addition, 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 apparatus 100. Become.

<Particle behavior analysis system; basic>
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 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, 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 computer system (also referred to as a processor; in FIG. 1, the particle behavior analysis apparatus 202) includes a division processing unit 250 that assigns each divided portion.

  The division processing unit 250 determines the relationship between the interparticle distance and the interaction force (distance dependency of the interaction force) so that the parallelization efficiency is higher than the application of only the force division method or the application of the region division method. Considering this, it is assumed that the force division method and the region division method (SD) are combined. For example, whether the interaction force to be analyzed is an interaction force that should be focused only on the interaction with a particle at a short distance (referred to as a short distance force), or a particle at a distance as well as a particle at a close distance The division processing method to be applied is determined depending on whether the interaction force needs to be paid attention to (the long-distance force). Then, a force matrix is set according to the determined division method, and analysis target particles are assigned to each force matrix. These processes in the division processing unit 250 will be described in detail later.

  At this time, it is preferable that the division processing unit 250 also considers that the calculation load at each node is approximately 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 data communication with other processors in charge of processing related to other divided parts as necessary, and the divided division parts in charge are divided into areas, force division methods, and the like. The particle behavior analysis by

<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 or the like 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, or a semiconductor memory controller. 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 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 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 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 that performs a part of the functional portion 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 and the analysis load distribution processing unit 908e 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 a little, but in that case, analysis of the interaction force with the particles that should be focused on may be omitted. There is concern about a decrease in accuracy.

  Considering the relationship with the interaction force from the viewpoint of these interparticle distance types, in order to make the calculation time (calculation load) in each processor equal, in the division method depending on the distance of the target particle Combined with two types of splitting methods, specializing only in short-range forces, and performing splitting methods that do not depend on the distance of the target particle, but only in calculating far-distance forces. It is thought that it is effective to use the method.

  Although details will be described later, in this embodiment, an example in which the region division method is applied as an example of a division method that depends on the distance of the target particle and the force division method is applied as a division method that does not depend on the distance of the target particle. Explained.

<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. Since nine processors calculate 18 particles in parallel, each processor arranged in the 3 × 3 force matrix first focuses on two particles, and each of the other particles targeted for each particle of interest. 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 100 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 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.

<Partitioned parallel processing; basic (number of processors M)>
7 and 8 are diagrams for explaining parallel processing to which the region division method is applied. Here, FIG. 7 is a flowchart showing an example of the area division parallel processing procedure. FIG. 8 is a diagram illustrating an example of a division matrix when the region division method is applied.

  Here, FIG. 7 shows an area division parallel processing procedure for the developer 102 (specifically, the carrier particles 102a and the toner particles 102b) used in the electrophotographic method. For the interaction (contact force), a detailed procedure (parallel processing example 2 in electrophotographic simulation) for performing analysis processing using a region dividing method that divides an analysis target region that is a processing target element into a plurality of regions is shown.

  The processing procedure of the second example makes it possible to consider a plurality of types of particles at the same time or to consider a plurality of types of particles at the same time and to apply dynamic load balancing even when the region division method is applied. By adopting this concept, calculation processing time in each processor is equalized.

  For example, first, after reading calculation conditions such as various physical parameters necessary for the calculation and initial arrangement of particles (S202), a particle density calculation process for calculating the state of particle density in the analysis target region is performed (S204). Next, an effective distance of interaction is set (S206), and a mesh size L is set (S208).

  By setting the mesh size L after setting the effective distance of interaction, the mesh size L can be set in consideration of the effective interaction distance. In addition, since the effective distance setting process of the interaction in step S208 is performed, a calculation flow in which the mesh size L can be determined in consideration of the density of particles and the minimum and maximum values of the effective distance of the interaction. Therefore, a more optimal mesh size L can be obtained.

  The effective distance of the interaction is the maximum particle size of the particle to be calculated in contact, and when acting up to infinity in the mathematical expression like electrostatic interaction, the cut-off distance is necessary if necessary. Can be set, and the effective distance can be used. Note that the effective distance setting method may be appropriately determined according to the calculation target or the purpose of analysis, and various known methods can be employed.

  Thereafter, a mesh is generated (S210), and the types of particles present in each cell and the types of acting forces that need to be analyzed for the particle types are examined (S212). Then, it is determined whether or not the balance of the sum of the calculation times determined by the combination of the acting force and the particle type to be analyzed is within a predetermined range (S214).

  FIG. 8 shows a state in which particles are assigned to each node so that the number and types of particles are equal when 18 particles are calculated in parallel by nine processors.

  Here, it is not necessary to actually measure the calculation time when determining whether or not “the balance of the sum of the calculation times determined by the combination of the acting force and the particle type to be analyzed is within a predetermined range”. For example, for a combination of particle type and action force, a table that specifies the action force to be analyzed and the calculation time of each action force is prepared, and analysis calculations for all particles in each currently set cell are performed. The total processing time should be obtained. Since it is not necessary to actually measure a calculation time different from the parameter handled in the normal behavior analysis process, the process is not complicated.

  Regardless of the particle type, the calculation time may be defined for each acting force for items that need to be analyzed, but the calculation time may be defined for each particle type and each acting force. For example, when magnetic toner particles 102b and carrier particles 102a are to be analyzed, there are subtle differences in the electrostatic interaction to be analyzed. There is an effect of prescribing.

  Ultimately, it is only necessary to determine the degree of balance so that the calculation time of the processor in charge of each cell is as uniform as possible, and it is not necessary to strictly calculate the total calculation time of each cell. A weight of calculation time may be set for the combination, and the sum may be determined. In addition, although weight may be prescribed | regulated for every particle | grain type and every action force about the item which requires an analysis, you may prescribe | regulate weight only according to every action force.

  If the balance degree is within the predetermined range, the particle behavior calculation is started for each divided cell immediately (S214-YES). If the balance degree is not within the predetermined range (S214-NO), the process returns to step S208. The mesh size L is reset so that the degree of balance is improved (S208). It is not essential to equalize the number of particles in each cell, and the mesh size L may be reset so that the degree of balance falls within a predetermined range.

  In the particle behavior calculation for each cell, for example, as a candidate for determining contact with the target particle, a particle in a cell in the vicinity of the cell in which the target particle exists is selected (S216), and electrostatic interaction acting on each particle is selected. Interactions such as action, magnetic interaction, mechanical interaction (contact force), or adhesion force are calculated and integrated (S218).

  Next, the completion of calculation of all particles is checked (S220). If not completed, the process returns to step S216 (S220-NO), and if completed (S220-YES), the equation of motion of each particle is calculated. Solve, calculate acceleration, velocity, and displacement (S222), and update each particle position (S224).

  At this time, the data processing unit 230, with respect to particles that exist in the vicinity of the cell boundary and are in contact with particles in other cells, the position information of the particles is used as the processor (node) of the adjacent cell related to the interaction matrix. (S225).

  Next, it is checked whether it is the final time step (S226). If the final time step has not been reached (S226-NO), the time step is updated (S228), and the process proceeds to step S212 for checking the particles in the cell. To do. On the other hand, if the final time step has been reached, the calculation is terminated (S226-YES).

  By such processing, regardless of whether or not the number of particles contained in each cell is equal, the balance of the combination of the particle types existing in each cell and the action force that needs to be analyzed for the particle types is predetermined. Since the region size can be set so as to be within the range, the difference in calculation time for each region (cell) can be reduced, and as a result, higher parallelization performance can be reliably achieved.

<< Combined processing of force division method and region division method >>
When calculating the interaction of multiple particles such as long-range force and short-range force, the analysis process time can be shortened by using the particle behavior analysis process that uses the force-division method without using the domain-division method.

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

  Therefore, in the present embodiment, not only short distance forces such as contact force and adhesion force between particles but also long distance forces such as magnetic interaction force and Coulomb force are calculated. The following mechanism is further adopted in order to ensure higher parallelization efficiency than before when acting force is processed in parallel by a plurality of computers.

  The principle is as follows. First, as can be seen from the description of the force splitting method described above, in force splitting, particle information held by each node is communicated in the matrix row and column directions, so communication is performed regardless of the interparticle distance when calculating the interaction force. It involves processing. In other words, even when the distance between particles is large or small, their interaction force is obtained. As an advantage, not only long-distance forces such as magnetic interaction force and Coulomb force, but also short-distance forces such as contact force and adhesion force between particles, processing focused on all particles. Is made. When calculating the contact force or the interaction force of the adhesive force, if the distance is long, the calculation is attempted even when the calculation can be omitted.

  On the other hand, in the area division method, since the target area is divided and only the particles in the divided area are processed for each divided area, the interaction with the particles existing in the vicinity of the other divided areas is performed. Consider power. In other words, in the region division method, the interaction force is obtained for particles having a relatively small distance between particles, but particles having a relatively large distance between particles that belong to other divided regions are not analyzed.

  Although it is possible to adopt a mechanism that considers the interaction force with the particles in the adjacent divided regions, even in that case, as indicated by hatched lines or diagonal grids for node 5 (# 5) in FIG. It can be seen that the amount of communication can be reduced by simply communicating.

  Concerning things that should take into account long-range forces such as magnetic interaction force and Coulomb force, it is feared that the accuracy will be inferior if the cut-off distance is set and attention is paid only to particles that are relatively close. Since communication processing for obtaining the interaction force with the particles can be omitted, there is an advantage that the communication load is less than that of the force division method.

  Based on these considerations, the region division method is used to calculate the interaction force (short-range force) that only needs to focus on the interaction with particles that are close to each other. When calculating the interaction force (far-distance force) that needs to pay attention to the interaction with the particles, if the combination process adopting force splitting method is used, the communication load is reduced and the distance dependence of each interaction force It is considered that an appropriate analysis can be performed taking into account the above.

  Therefore, in this embodiment, the force division method is applied to the calculation of the long distance force (for example, Coulomb force or magnetic force), and the region division method is applied to the calculation of the short distance force (for example, mechanical contact force or adhesion force). The applied algorithm. This will be specifically described below.

<Processing procedure>
FIG. 9 is a flowchart illustrating an example of a procedure of a process combining the force dividing method and the region dividing method (hereinafter also simply referred to as a combined process).

  First, the division processing unit 250 determines the cell size according to the region division method in the same manner as steps S202 to S210 in FIG. 7 so that the calculation time (calculation load) in each processor in charge of each cell becomes equal. As an example, particles are assigned to each node so that the number of particles and the number of particle types are the same (S302).

  Although an example of this will be described later, the size (division size) of the division region (cell) in the region division method is not calculated by applying the force division method to the analysis of the long distance force and applying the region division method. Therefore, it is not necessary to consider the cut-off distance, and an arbitrary size that does not depend on the long distance force may be set.

  In addition, the size of the divided region in the region dividing method may be changed to a size according to the position so that the number of particles is equal. Note that the division processing unit 250 that also functions as the analysis load distribution processing unit considers that the number of particles is equal in the division direction in order to equalize the calculation load in each divided region. Good. The case will be described later.

  Next, for each divided region (cell), the data processing unit 230 calculates a short-range force such as a mechanical contact force and an adhesion force among a plurality of types of multi-particle interaction forces. In this case, the data processing unit 230 first identifies and lists particles existing near the boundary of the cell that each node is responsible for (S304). That is, as in step S216, as a candidate for contact determination with the focused particle, a particle in a cell near the cell where the focused particle exists is selected. Then, it is determined whether or not particles existing in the vicinity of the cell boundary are in contact with other particles existing in other cells in the vicinity of the boundary (S306).

  The data processing unit 230 has a short-range force (between particles in the cell that the node is in charge of and between particles in the vicinity of the cell boundary based on the determination result of step S306 and in contact with particles existing in other cells. For example, mechanical contact force and adhesion force are calculated (S308).

  Next, the data processing unit 230 checks the end of the calculation of all particles (S310), and if the calculation of the short-range force for all the processing target particles is not completed, the process returns to step S304 (S310-NO). ), If completed (S310-YES), each interaction such as mechanical contact force and adhesion force (the long distance force uses the same value until it is updated, that is, the long distance force does not change) The motion equation of each particle is solved to calculate acceleration, velocity, and displacement (S312), and the position coordinates of each particle are updated (S314).

  When the calculation of the short distance force for all the particles to be processed is completed (S310-YES), the data processing unit 230 uses each interaction such as the mechanical contact force and the adhesion force to calculate the equation of motion of each particle. And the position coordinates are calculated (S314). At this time, it is assumed that there is no change in the long-distance force.

  At this time, the data processing unit 230 updates the position information of the particles in each cell, and for the particles existing in the vicinity of the cell boundary and in contact with the particles of other cells, the position information of the particles is The calculation information is updated (S316) by sending (communication) to the node (processor) in charge of the adjacent cell related to the action matrix.

  In this way, for each divided area, the short distance force is calculated for the target area and the immediate vicinity of another adjacent area as a target, and the communication processing time with other nodes is reduced, thereby reducing the total calculation time. As shown in FIG. 8, when attention is paid to the node 5 (# 5), communication with other nodes is necessary because each region is in the vicinity of the boundary existing in the region adjacent to the region handled by the node 5. The amount of communication can be reduced by communicating only when the particles are in contact with each other.

  Thereafter, the process returns to step S304 until the predetermined calculation step is reached, and the same processing is repeated for the short-range force (S317-NO).

  Here, the “predetermined calculation step” means, for example, that the magnetic interaction force is about 1000 times and the electrostatic interaction force is about 100 times. These 1000 times and 100 times are only examples. Long-range forces such as electromagnetic interaction force and electrostatic interaction force work as powers of distance, so even a slight positional variation at each step when calculating short-range force has little effect on the overall particle behavior analysis. . The number of “predetermined calculation steps” may be set based on the point that it may be thinned out appropriately within a range that does not hinder the whole particle behavior analysis.

  When the predetermined calculation step is reached (S317-YES), the division processing unit 250 assigns particles so that the processing load at each node becomes equal according to the force division method (S318). The data processing unit 230 calculates a long distance force such as a magnetic interaction force or an electrostatic interaction force (Coulomb force) among a plurality of types of interaction forces among many-body particles according to a force division method. At this time, first, the long-range force among the multiple types of multi-particle interaction forces is distributed to specific processors that require communication in the row direction and the column direction centering on themselves in the force matrix. (S320). At this time, a plurality of types of multi-particle interactions are calculated using different force matrices.

  Next, it communicates between specific processors, and for each long-range force such as magnetic interaction and electrostatic interaction, the interactions in the row direction in the force matrix are added together, that is, all the interactions calculated in a distributed manner A total sum SUM_Total of forces (here, only long-distance forces) is obtained (S322). The total sum value SUM_Total for the long-distance force collectively represents a plurality of interactions such as electrostatic force and magnetic force.

  Next, using the total sum value SUM_Total collectively represented for the long-distance force and the short-distance force previously obtained, the equation of motion of each particle is solved to calculate the position coordinates (S324). 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 (S326).

  Thereafter, the process returns to step S304 and the same processing is repeated until a predetermined calculation step is reached (S328). 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).

  As described above, in the combined processing of the region division method and the force division method according to the present embodiment, first, a short-distance force such as a mechanical contact force or an adhesion force is analyzed according to the region division method, and then electromagnetic waves are generated at a predetermined timing. It is characterized by analyzing long-range forces such as static interaction force and electrostatic interaction force according to force splitting method. In particular, the short distance force is calculated at each step, but the long distance force is characterized in that it is calculated every predetermined number of times for the short distance force analysis.

<Case 1: About division size>
FIG. 10 is a diagram for explaining an example of a method for determining a division size by the region division method in the combined processing.

  When the analysis using the domain division method is performed also for the long distance force, as shown in FIG. 10A, the range of the long distance force is limited to a certain range, and the limited cut-off distance Lcut is covered. In general, a method of dividing the image by increasing the region size is used. In this case, the processing target area is divided into rectangular areas each having a size of 1 / √2 times in the vertical and horizontal directions so as to form a circumscribed circle having the cutoff distance Lcut as a radius with respect to the cutoff distance Lcut.

  However, in the combined method of the present embodiment, since the analysis using the force division method is performed for the long distance force, the region division method does not need to consider the long distance force, and the region focuses only on the short distance force analysis. Just set the size.

  Here, in setting the region size focusing only on the short-range force analysis, as shown in FIG. 10B, it is sufficient to divide the region so that at least the analysis target particle is completely included. 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 does not need to take into account long-range force analysis, so it is not necessary to consider the cut-off distance for long-range force analysis and can be set to any size that does not differ from long-range force. What is necessary is just to set the size according to a position so that each particle | grain number of may become equal. The short-distance force is analyzed separately from the region splitting method, and the long-distance force is analyzed separately from the force splitting method. Can be divided into

<Case 2: About division direction>
FIG. 11 is a diagram for explaining an example of a method for determining a division direction by the region division method in the combined processing. Here, an example is shown in the case of analysis of the development region in the vicinity of the photoreceptor 130 in the development apparatus 100 shown in FIG.

  As shown in FIG. 1B, the developing roll 140 of the developing device 100 is in the form of a roll disposed to face the photoreceptor 130, and the carrier particles 102a are sequentially attracted to the outer surface by magnetic force. And form a head. The toner particles 102b are transported to the photosensitive member 130 side by the adhesion action with the carrier particles 102a and are attracted to the latent image portion of the photosensitive member 130, whereby the photosensitive member 130 is developed.

  Therefore, as shown in FIG. 11 (A), if the region is divided into concentric circles and the same radius step with respect to the developing roll 140, the number of particles to be analyzed differs for each region. It is virtually impossible to determine the region size to be uniform. 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, when attention is paid to the longitudinal direction of the developing roll 140, the formation of the carrier particles 102a may be considered to be almost the same, and the behavior of the toner particles 102b is determined by the amount of adsorption of the toner particles 102b to the photoreceptor 130. It can be considered that it is almost the same except for.

  Therefore, as shown in FIG. 11B, development is performed on a concentric surface having a certain radial distance (including the outer peripheral surface of the developing roll 140 itself) except for the region where the toner particles 102b are attracted to the photosensitive member 130. If the roll 140 is divided into slices at a constant division pitch in the longitudinal direction, the particle types and the number of particles in each divided region (cell) can be made substantially uniform, and the calculation load can be equalized. it is conceivable that.

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 the flowchart which showed an example of the area division | segmentation parallelization processing procedure. It is a figure which shows an example of the division | segmentation matrix in the case of applying a region division method. It is a flowchart which shows an example of the procedure of the process (henceforth only a combined use process) which combined the force division method and the area | region division method. It is a figure explaining an example of the determination method of the division size by the area | region division method in combined processing. It is a figure explaining an example of the determination method of the division direction by the area | region division method in combined use processing.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 100 ... Development apparatus, 101 ... Storage container, 101a ... Opening part, 102 ... Developer, 102a ... Carrier particle, 102b ... Toner particle, 102c ... External additive, 130 ... Photoconductor, 140 ... Development roll, 142 ... Magnet, DESCRIPTION OF SYMBOLS 150 ... Restriction blade, 160 ... 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 230, data processing unit, 232 ... data receiving unit, 234 ... numerical value calculation processing unit, 236 ... output data processing unit, 240 ... information presentation unit, 250 ... division processing unit (also: analysis load distribution processing unit)

Claims (6)

Among the acting forces acting on the particles, for the short-distance force, which is an interaction force that performs an analysis focusing on the interaction with particles close to each other, the region to be processed is divided according to the region division method, For a long-distance force that is an interaction force that performs an analysis focusing on the interaction with a distant particle, a division processing unit that divides the processing target particle according to a force division method,
Provided in each network-connected computing device that calculates a near-distance force according to the region division method and a long-distance force according to the force division method for the divided portion allocated by the division process by the division processing unit. A data processing unit,
A particle behavior analysis apparatus characterized in that the behavior of the particle is analyzed in consideration of an interaction force with another substance acting on the particle. The particle behavior analysis apparatus according to claim 1, wherein the data processing unit calculates the long distance force every predetermined number of times for the calculation of the short distance force. Based on the type of acting force acting on the particles and the type of the particles, the region segmentation method or the element to be processed is set so that the calculation load in the data processing unit provided in each calculation device is equalized. The particle behavior analysis apparatus according to claim 1, further comprising an analysis load distribution processing unit that divides by a force division method. The analysis load distribution processing unit, when dividing the processing target region according to the region dividing method, determines the dividing direction so that the number of particles belonging to each divided portion is equal. The particle behavior analysis apparatus according to 1. For any one of a plurality of network-connected computing devices, an analysis is performed in which an analysis focusing on an interaction with a particle having a short distance among the acting forces acting on the particle. The processing target region is divided according to the division method, and the analysis target particle is analyzed according to the force division method for the long-distance force, which is an interaction force that performs an analysis focusing on the interaction between the particles having a short distance and the particles having a long distance. Function as a split processing unit,
A program enabling analysis of behavior of the particles in consideration of interaction force with other substances acting on the particles. Short-distance force, which is an interaction force that analyzes each of a plurality of network-connected computing devices, focusing on the interaction with particles that are close to each other, among the acting forces that act on the particles for the assigned divided parts As a data processing unit that calculates the distance force, which is an interaction force that performs an analysis focusing on the interaction between particles with a close distance and particles with a long distance, according to the force division method Let
A program enabling analysis of behavior of the particles in consideration of interaction force with other substances acting on the particles.

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