JP2005122354A - Particle behavior computation method and computer readable recording medium storing program for executing its method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a particle behavior computation method, which is a powder behavior computation method based on the discrete element method, and in which a powder behavior computation can be performed at high speed, especially when it is needed to consider two or more interactions between particles, for example, such as developer behavior in a two-component development system in electrophotography, where not only the contact between particles but also electrostatic and magnetic interaction have to be considered, and to provide a computer readable recording medium storing the program for executing the method. <P>SOLUTION: According to the particle behavior computation method, the magnitude of a small area in small area segmenting for selecting particles needed to perform computation of the distance between particles can properly be set in consideration of an effective distance of the interaction, after having determined the effective distance for every two or more interaction depending on the distance between particles, thereby enabling an effective particle behavior computation that is reduced in unnecessary distance computation. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a particle behavior calculation method, and in particular, a powder behavior that needs to consider a plurality of interactions between powders, such as a behavior of a two-component developer in a development process in an electrophotographic image forming process. It relates to computer simulation.

  In recent years, particle behavior simulators based on the individual element method proposed by Cundall et al. Have been widely used for the behavior simulation of particles such as powder and granules. The behavior analysis of the powder using the method has been carried out. This is thought to be due to the dramatic improvement in computer performance and the availability of a large amount of computers having a computing performance equivalent to or higher than that of conventional supercomputers at a low cost.

  On the other hand, in the particle behavior calculation algorithm based on the distinct element method, the calculation amount becomes enormous as the number of particles increases, and the calculation with the same number of particles as in the actual system, even though the performance of the computer is improved. Is often difficult to implement. In the powder behavior analysis method, a method of reducing the number of times of performing contact determination with a wall or a corner and appropriately processing the behavior at the contact with the corner is important. Moreover, the interaction must consider not only the interparticle contact but also electrostatic force and magnetic interaction.

Therefore, as a conventional particle behavior simulation method, Patent Document 1 discloses the adhesion force acting between particles or between a particle and a container wall surface with mixing and stirring of the particles in the container, and the surface roughness of the particle surface and the container wall surface. There has been proposed a method of calculating using this. In addition, as a calculation object in Patent Document 1, charging in a developer of a two-component development system including a carrier and a toner in electrophotography is considered. Further, Patent Document 2 considers not only contact force but also magnetic interaction, and numerically analyzes the behavior of magnetic powder delivery between at least two magnetic transport rollers by combining the particle element method and magnetic field analysis. Thus, a method for predicting the behavior of magnetic powder that can accurately grasp the amount of magnetic powder transported and the stirring rate of magnetic powder has been proposed.
JP 2002-109445 A JP 2003-195642 A

  However, Patent Document 1 does not consider the improvement of the calculation speed, and does not consider the simulation of the mixed state of particles (carrier and toner) having a larger particle size. According to Patent Document 2, a known calculation method is used for a powder behavior simulator that takes into account not only contact force but also magnetic interaction, and functions that improve calculation speed are considered. It has not been.

  The present invention is for solving these problems, and is a powder behavior calculation method based on the individual element method, and in particular, it is necessary to consider a plurality of interactions between particles, for example, two components in electrophotography A particle behavior calculation method capable of performing powder behavior calculation at high speed that requires consideration of not only the contact between particles but also electrostatic and magnetic interactions, such as developer behavior in a development system, and the method An object of the present invention is to provide a computer-readable recording medium storing a program to be executed.

  In order to solve the above problems, according to the particle behavior calculation method of the present invention, an effective distance setting step for determining an effective distance for each interaction acting between particles, a maximum value rmax and a minimum effective interaction distance A small region size setting step for determining the size of the small region in accordance with the value rmin. Therefore, efficient particle behavior calculation with less unnecessary distance calculation can be performed.

  Next, according to the particle behavior calculation method of the present invention, a particle density calculation step for calculating the density of particles in the calculation region, an effective distance setting step for determining an effective distance for each interaction acting between particles, and an interaction A small region size setting step for determining the size of the small region in accordance with the maximum value rmax and minimum value rmin of the effective distance and the density of the particles. Therefore, an efficient particle behavior calculation method with less unnecessary distance calculation can be implemented.

  In addition, according to the particle behavior calculation method of the present invention, an effective distance setting step for determining an effective distance for each interaction acting between particles, and a boundary line or boundary for dividing the entire calculation area into a plurality of partial calculation areas A calculation region dividing step for determining a surface, and a small region size setting step for determining the size of the small region according to the maximum value rmax and the minimum value rmin of the effective distance of interaction for each partial calculation region . Therefore, efficient particle behavior calculation that does not depend on the non-uniformity of the calculation target can be performed.

  Furthermore, according to the particle behavior calculation method of the present invention, a particle density calculation step for calculating the density of particles in the calculation region, an effective distance setting step for determining an effective distance for each interaction acting between the particles, A calculation region dividing step for defining a boundary line or boundary surface that divides the whole into a plurality of partial calculation regions, and for each partial calculation region, depending on the maximum value rmax and minimum value rmin of the effective distance of interaction and the density of the particles And a small region size setting step for determining the size of the small region. Therefore, efficient particle behavior calculation that does not depend on the non-uniformity of the calculation target can be performed.

  Further, according to the particle behavior calculation method of the present invention, an effective distance setting step for determining an effective distance for each interaction acting between particles, and a boundary line or boundary surface that divides the entire calculation region into a plurality of partial calculation regions The calculation area dividing step for determining the particle density, the particle density calculation process for calculating the density of the particles for each partial calculation area, and the maximum effective distance rmax and the minimum value rmin for each partial calculation area according to the particle density And a small region size setting step for determining the size of the small region. Therefore, efficient particle behavior calculation that does not depend on the non-uniformity of the calculation target can be performed.

  Furthermore, according to the particle behavior calculation method of the present invention, a calculation region dividing step for defining a boundary line or a boundary surface that divides the entire calculation region into a plurality of partial calculation regions, and acts between particles for each partial calculation region. An effective distance setting step for determining an effective distance for each interaction, and a small region size setting step for determining the size of the small region according to the maximum value rmax and the minimum value rmin of the effective distance of interaction for each partial calculation region; have. Therefore, efficient particle behavior calculation that does not depend on the non-uniformity of the calculation target can be performed.

  In addition, according to the particle behavior calculation method of the present invention, a calculation region dividing step for defining a boundary line or a boundary surface that divides the entire calculation region into a plurality of partial calculation regions, and acts between particles for each partial calculation region. An effective distance setting step for determining an effective distance for each interaction, a particle density calculation step for calculating the density of particles for each partial calculation region, and a maximum value rmax and a minimum value rmin for the effective distance of interaction for each partial calculation region And a small region size setting step for determining the size of the small region in accordance with the density of the particles. Therefore, it is possible to perform efficient particle behavior calculation that does not depend on the distribution state of particles in the calculation target and the non-uniformity of the calculation target.

  Furthermore, according to the particle behavior calculation method of the present invention, a calculation region dividing step for defining a boundary line or a boundary surface that divides the entire calculation region into a plurality of partial calculation regions, and the number of particles included in each partial calculation region are determined. There are a particle counting step for counting, and a calculation region re-division step for correcting the boundary line or boundary surface according to the number of particles included in each partial calculation region and dividing it again into a plurality of partial calculation regions. Therefore, the entire calculation region can be divided so that the number of particles in each partial calculation region is uniform, and more efficient particle behavior calculation can be performed.

  In addition, since the small area is a square in the case of two dimensions or a cube in the case of three dimensions, it is easy to check the particles contained in each small area. In addition, by appropriately setting the length L of one side of the small region so that the relationship between the maximum value rmax and the minimum value rmin of the effective distance of interaction is rmin ≦ L ≦ rmax, unnecessary distance calculation can be performed. Fewer and efficient particle behavior calculations can be performed.

  Furthermore, by including a step of assigning calculation means for setting the size of the small area for each partial calculation area in the small area size setting step for each partial calculation area, the calculation processing by the assigned calculation means is performed in parallel. By executing it, more efficient particle behavior calculation can be performed.

  Further, the calculation area subdivision step corrects the boundary line or the boundary surface in accordance with the number of particles included in each partial calculation area and / or the calculation time required for each behavior calculation for each partial calculation area, and again includes a plurality of parts. By dividing the calculation area, the calculation time of each partial calculation area can be executed simultaneously, and the particle behavior can be calculated more efficiently.

  Furthermore, as another invention, there is a feature in a computer-readable recording medium storing a program for executing the particle behavior calculation method described above. Therefore, a particle behavior calculation system can be constructed universally without changing an existing system.

  According to the particle behavior calculation method of the present invention, after determining the effective distance for each of the plurality of interactions depending on the interparticle distance, the small region division processing for selecting the particles that need to be subjected to the interparticle distance calculation. The size of the small region can be appropriately set in consideration of the effective distance of interaction, and efficient particle behavior calculation with less unnecessary distance calculation can be performed.

  The particle behavior calculation method of the present invention determines an effective distance for each interaction acting between particles, and has a large number of calculation areas for calculating the behavior of particles according to the maximum value rmax and minimum value rmin of the effective distance of interaction. The size of the small area divided into is determined.

  First, the principle of particle behavior calculation based on the individual element method to which the present invention is applied will be described. This individual element method calculates all the forces acting on each particle forming the powder, The particle behavior is calculated by sequentially solving the equation of motion.

  As the force acting on the particles, in addition to external force such as gravity, contact between the wall and the particles and contact force due to the contact between particles can be considered. The magnitude of the force is calculated according to a contact model as shown in FIG. FIG. 1 (a) is a model of a contact force acting in the normal direction, which is composed of a spring 11 and a dashpot 12. The magnitude of the action force is determined by the normal direction velocity and the contact state of particles. The

  In order to calculate the contact state of each particle, it is necessary to calculate the distance between each particle. When distance calculation is performed between all particles, n (n-1) / 2 distance calculations are required when the number of particles is n, and when the number n of particles increases, the amount of calculation becomes enormous. End up.

  In order to solve such problems, various methods have been proposed and implemented. Among them, there are the following methods as general and efficient methods. The method is a method in which the calculation target area is divided into small areas, and the particles for which the contact determination (distance calculation) is performed are limited to particles existing in the small area where the target particle is present and the small area in the vicinity thereof. is there. This method will be described with reference to FIG. 2. In FIG. 2, the particles 22 included in the small region 24 including the target particle 21 and the region 25 including the surrounding 8 cells are set as target particles for distance calculation. The other particles 23 do not need to perform distance calculation because there is no possibility of contact with the target particle 21. In FIG. 2, since the calculation area is considered in two dimensions, the mesh-divided cells formed by X1 to X5 and Y1 to Y4 with the lattice interval L as the diameter of the target particle are set as small areas. Such a method is a method called a neighborhood cell method or a grid method.

  On the other hand, when calculating the developer behavior in electrophotography, it is necessary to consider an electrostatic force or a magnetic force in addition to the force due to the contact between particles as described above. FIG. 3 shows a case where two particles 31 and 32 having charge amounts Q1 and Q2, respectively, are at a distance r. Although the two particles 31 and 32 are not in contact with each other, a Coulomb force as shown by the following formula acts.

| F1 | = | F2 | = Q1 · Q2 / 4πε ₀ r ²

  Therefore, in the case of performing particle behavior calculation in consideration of interaction between particles other than contact force such as electrostatic acting force, a method of setting the mesh interval L to about the particle interval as in the neighborhood cell method described above. Then there is a problem.

  FIG. 4 shows a case where, for example, an effective distance is determined for the interparticle distance r in the above equation, and the value is set as the mesh interval L. Only the particles in the cell 42 including the particle 41 of interest and the region 43 of the neighboring eight cells are subject to distance calculation, and the other particles 44 and the like do not need to perform distance calculation. This is because the distance between the particle 44 outside the region 43 and the target particle 41 is always larger than the effective distance of the electrostatic force.

  Here, consider that the effective distance of the electrostatic interaction is 8 times the particle diameter d. At this time, when the mesh interval L is set to L = d in the neighborhood cell method, it is sufficient to search for 9 cells when considering only the contact interaction, but the electrostatic interaction (as the effective distance 8d) is performed. When considering, it is necessary to calculate the distance between the particles contained in 289 cells (17 × 17) in the two-dimensional case and 4,913 cells (17 × 17 × 17) in the three-dimensional case. In some cases, the increase in the number of cells that need to be searched may press the memory and increase the calculation time.

  On the other hand, when L = 8d and the effective distance of the electrostatic interaction are matched, the number of cells to be searched is 9 cells in the two-dimensional case and 27 cells in the three-dimensional case as shown in FIG. Good. In this case, the cell search is not a burden, but the search region area S of the distance calculation target particle is S = 3L × 3L = 24d × 24d in the two-dimensional case. In the case of L = d, since S = 17L × 17L = 17d × 17d and the search area becomes large, a lot of useless distance calculation occurs. In particular, when the particle density is high, unnecessary distance calculation increases, which increases the calculation time. Even if the overall particle density is low, it is conceivable that the particles are localized, and the optimal setting of the mesh interval L strongly depends on the existence state of the particle to be calculated, but at least the particle size d, electrostatic If the effective distance of the dynamic interaction is set to 8 times the particle size, and the small region is a cell by equally divided mesh, the mesh interval L has an optimum value in the range of d ≦ L ≦ 8d Become. Therefore, the method of setting the size of the small region (mesh spacing L in the above case) when there are a plurality of interactions depending on the distance between the particles as described above is the minimum value and the maximum value of the effective distance of the interaction (described above Then, it is determined according to d and 8d). Further, in the case where the small regions are formed by meshes of equal intervals, the mesh interval L is determined to be d ≦ L ≦ 8d as an intermediate value between the minimum value rmin and the maximum value rmax of the effective distance of interaction.

  Here, FIG. 5 shows a processing flow of the particle behavior calculation processing considering only the interaction by the contact by the conventional neighborhood cell method. In the figure, first, calculation conditions such as various physical parameters necessary for calculation and initial arrangement of particles are read (Step S101), then a mesh is generated (Step S102), and particles existing in the cell are checked (Step S101). S103). As a candidate for contact determination with the target particle, a particle in a cell in the vicinity of the cell where the target particle exists is selected (step S104), and the contact force acting on each particle is calculated and integrated (step S105). In step 106, the completion of calculation of all particles is checked. If not completed (step S106; NO), the process returns to step S104. If completed (step S106; YES), the equation of motion of each particle is solved. Then, acceleration, velocity and displacement are calculated (step S107), and the respective particle positions are updated (step S108). In step S109, it is checked whether or not it is the final time step. If the final time step has been reached (step S109; YES), the calculation is terminated. Otherwise (step S109; NO), the time step is updated ( In step S110), the process returns to step S103 for checking the particles in the cell.

  FIG. 6 is a flowchart showing a particle behavior calculation process according to the first embodiment of the present invention. In the figure, the small regions are squared in the case of two dimensions and are legitimate in the case of three dimensions by equally divided mesh division. In the figure, first, calculation conditions such as various physical parameters necessary for calculation and initial arrangement of particles are read (step S201), then an effective distance of interaction is set (step S202), and a mesh size L is set (step S202). Step S203). Next, a mesh is generated (step S204), and particles present in the cell are checked (step S205). As a candidate for contact determination with the target particle, a particle in a cell near the cell where the target particle exists is selected (step S206), and the contact force acting on each particle is calculated and integrated (step S207). In step 208, the completion of calculation of all particles is checked. If not completed (step S208; NO), the process returns to step S206, and if completed (step S208; YES), the equation of motion of each particle is solved. Then, acceleration, velocity and displacement are calculated (step S209), and the respective particle positions are updated (step S210). In step S211, it is checked whether or not it is the final time step. If the final time step has been reached (step S211; YES), the calculation is terminated. Otherwise (step S211; NO), the time step is updated ( In step S212, the process returns to step S205 for checking the particles in the cell.

  As described above, the steps different from the conventional processing shown in FIG. 5 are to set the effective distance of interaction in step S202 and to set the mesh size L in step S203. Thus, after setting the effective distance of interaction, the mesh size L can be set in consideration of the effective interaction distance by setting the mesh size L. 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. The simplest method can be considered as a method for setting the value to be an effective distance. The effective distance setting method should be appropriately determined according to the calculation object or the purpose of the analysis. In the present invention, the effective distance setting method is not limited. Further, the calculation of the contact force in step S105 in FIG. 5 is the interaction force calculation (step S207) in FIG. 6, and not only the contact force but also calculation of a plurality of interactions is performed. In addition, by dividing the calculation target area into a square in the case of two dimensions and a cubic small area in the case of three dimensions, it is possible to easily find a small area where particles are present and to have an effective interaction. As a value for determining the distance and the size of the small region, the length of one side of the square or the legislature can be clearly associated as the mesh size L.

  FIG. 7 is a flowchart showing a particle behavior calculation process according to the second embodiment of the present invention. Although it is substantially the same as the processing flow of FIG. 6, the particle density calculation process like step S302 is added. That is, before setting the mesh size L in step S305, the particle density calculation process in step S302 and the effective distance setting process for interaction in step S303 are performed. Since the calculation flow is such that the mesh size L can be determined in consideration of the minimum value and the maximum value of the distance, a more optimal mesh size L can be obtained. In this embodiment, the particle density is calculated. However, any value other than the calculation of the particle density may be used as long as the particle density is expressed.

  When a magnetic particle placed in a magnetic field, for example, a two-component developer in electrophotography, is considered as an object of calculation, the particle is located in the vicinity where the magnet 81 is arranged as shown in FIG. A localized situation is assumed. In such a case, the method in which the mesh size is changed may be more effective between the vicinity of the magnet 8 and the others. In such a case, the process of dividing the area is effective.

  In addition, by dividing the calculation target area into a square in the case of two dimensions and a cubic small area in the case of three dimensions, it is possible to easily find a small area where particles are present and to have an effective interaction. As a value for determining the distance and the size of the small region, the length of one side of the square or the legislature can be clearly associated as the mesh size L.

  FIG. 9 is a flowchart showing a particle behavior calculation process according to the third embodiment of the present invention. In this embodiment, the calculation area is divided into a plurality of processes so that effective processing is possible when the particle distribution is localized in the calculation areas in the first and second embodiments. It provides a way to In the figure, first, calculation conditions such as various physical parameters necessary for calculation and initial arrangement of particles are read (step S401), and then an effective distance of interaction is set (step S402). Next, a boundary line (in the case of two dimensions) or a boundary surface (in the case of three dimensions) for dividing the calculation area into two areas is determined, and the calculation area is divided into the calculation area A and the calculation area B (step S403). Subsequently, particle behavior calculation described later is performed for each divided calculation region (steps S404 and S405). Then, the time step is checked (step S406), and if it is the final time step (step S406; YES), the calculation is terminated, otherwise (step S406; NO), the time step is updated (step S407). The process returns to step S404 of the first particle behavior calculation.

  Here, the particle behavior calculation processing in the divided area in FIG. 9 will be described according to the flowchart in FIG. 10. First, the mesh size L in the partial calculation area is set (step S 501), and a mesh corresponding thereto is generated. (Step S502). Thereby, since the area is divided, it is possible to set an appropriate mesh size according to each. Subsequently, the particles in the cell are checked (step S503), distance calculation candidates for the target particle are selected (step S504), and the interactions are calculated and integrated (step S505). Next, confirmation of completion of calculation of all particles in the partial calculation region is performed (step S506). If calculation of all particles is not completed (step S506; NO), the process returns to step S504. If the calculation of the acting force of all particles has been completed (step S506; YES), the equation of motion of each particle is solved from the acting force to obtain acceleration / velocity and displacement (step S507), and each particle in the partial calculation region is obtained. Is updated (step S508).

  Therefore, according to the third embodiment, it is possible to avoid the influence of local state changes such as the localization of particles, and to determine the optimum mesh size L for each divided partial region. Note that the present invention is not limited to the case where the particles are localized, but may be a case where the particle distribution is uniform. In addition, by dividing the calculation target area into a square in the case of two dimensions and a cubic small area in the case of three dimensions, it is possible to easily find a small area where particles are present and to have an effective interaction. As a value for determining the distance and the size of the small region, the length of one side of the square or the legislature can be clearly associated as the mesh size L.

  FIG. 11 is a flowchart showing a particle behavior calculation process according to the fourth embodiment of the present invention. FIG. 11 shows a process flow substantially the same as that in FIG. 9 except that particle density calculation (step S602) is added. The particle behavior calculation processing in the divided areas in steps S605 and S606 is the same as the processing in FIG. 10 as in the third embodiment in FIG. In this embodiment, since the particle density is calculated prior to setting the mesh size L in the partial calculation region in step S602, the mesh size L can be set appropriately according to the density of particles. The operation of the other steps is the same as that of FIG. 9 shown as the third embodiment, and the description is omitted here.

  In addition, by dividing the calculation target area into a square in the case of two dimensions and a cubic small area in the case of three dimensions, it is possible to easily find a small area where particles are present and to have an effective interaction. As a value for determining the distance and the size of the small region, the length of one side of the square or the legislature can be clearly associated as the mesh size L.

  Next, FIG. 12 is a flowchart showing another particle behavior calculation process in the divided area. In the particle behavior calculation process in the divided area shown in the figure, the particle density in the partial calculation area is calculated in step S701, and the effective distance of the interaction in which the mesh size L is set and the particles in the partial calculation area are calculated. It can be set according to the density. As a result, a more optimal mesh size L can be determined. Since the subsequent processing (steps S702 to S709) is the same as the processing (steps S501 to S508) in FIG. 10, the description thereof is omitted.

  In addition, by dividing the calculation target area into a square in the case of two dimensions and a cubic small area in the case of three dimensions, it is possible to easily find a small area where particles are present and to have an effective interaction. As a value for determining the distance and the size of the small region, the length of one side of the square or the legislature can be clearly associated as the mesh size L.

  FIG. 13 is a flowchart showing still another particle behavior calculation process in the divided area. In the particle behavior calculation process in the divided area shown in the figure, the effective distance of interaction in the partial calculation area is set in step S801. This makes it possible to set the effective interaction distance according to the state of each divided region (particle arrangement, magnetic field strength, presence / absence of electric charge, etc.). Can be set. Next, the mesh size L in the partial calculation area is determined (step S802), and a mesh is generated (step S803). The effective distance of interaction suitable for the partial region is determined before the mesh generation, and the mesh size L corresponding to the effective distance is determined. Therefore, an optimal mesh for calculating the particle behavior of the partial region is generated. Subsequently, the particle in the cell is checked (step S804), and the target particle and the distance calculation target particle selection are set (step S805). The interaction force corresponding to the distance between the particles (if contacted, the contact force is also And the acting force for each particle is integrated (step S806). Next, it is confirmed that all the particle calculations in the partial calculation area are completed (step S807). That is, if calculation of all particles in the partial calculation region is completed (step S807; YES), the equation of motion of each particle is solved to obtain acceleration, velocity, and displacement (step S808). Step S807; YES), the process returns to the selection of target particle and distance calculation target particle in Step S805. After the displacement is obtained in step S808, the position of each particle in the partial region is updated in step S809.

  In addition, by dividing the calculation target area into a square in the case of two dimensions and a cubic small area in the case of three dimensions, it is possible to easily find a small area where particles are present and to have an effective interaction. As a value for determining the distance and the size of the small region, the length of one side of the square or the legislature can be clearly associated as the mesh size L.

  Further, FIG. 14 is a flowchart showing a particle behavior calculation process in yet another divided region. In the figure, first, the particle density in the partial calculation region is calculated (step S901), and then the effective distance of interaction is set (step S902). Thereafter, the mesh size L in the partial calculation area is determined (step S903), and a mesh is generated (step S904). In this way, the effective distance of the interaction suitable for the partial area is determined from the effective distance of the interaction appropriately determined according to the particle density in the partial calculation area and the situation of the partial calculation area before mesh generation. As a result, an optimum mesh is generated for calculating the particle behavior of the partial region. Subsequently, the particles in the cell are checked (step S905), the target particle and the distance calculation target particle selection are set (step S906), and the interaction force according to the distance between each particle (if contacted, the contact force is also And the acting force for each particle is integrated (step S907). Next, it is confirmed that calculation of all particles in the partial calculation area is completed (step S908). That is, if calculation of all particles in the partial calculation region is completed (step S908; YES), the equation of motion of each particle is solved to obtain acceleration, velocity, and displacement (step S909). Step S908; NO), the process returns to the particle of interest and distance calculation target particle selection in step S905. Then, after the displacement is obtained in step S909, the position of each particle in the partial region is updated in step S910.

  In addition, by dividing the calculation target area into a square in the case of two dimensions and a cubic small area in the case of three dimensions, it is possible to easily find a small area where particles are present and to have an effective interaction. As a value for determining the distance and the size of the small region, the length of one side of the square or the legislature can be clearly associated as the mesh size L.

  FIG. 15 is a flowchart showing a particle behavior calculation process according to the fifth embodiment of the present invention. In the figure, first, calculation conditions such as various physical parameters necessary for calculation and initial arrangement of particles are read (step S1001), then particle density is calculated (step S1002), and effective distance of interaction is set (step S1003). After the execution, the calculation area is divided (step S1004). Here, the area A and the area B are divided into two partial calculation areas. After the division, the number of particles included in each divided area is counted (steps S1005 and S1006), and the difference NA−NB between the respective count numbers NA and NB is compared with a predetermined value. (Step S1007; YES), particle behavior calculation is performed for each partial region (Steps S1008 and S1009). If the count difference is not less than a predetermined value (Step S1007; NO), the calculation region division processing in Step S1004 is performed. Return to the division calculation area again so that the count difference is small. Note that the particle behavior calculation in the partial region is performed by, for example, the processing flow shown in FIG. Then, after the particle calculation is completed, the time step is confirmed (step S1010). If the time step has reached the final time step (step S1010; YES), the process is terminated. Otherwise, the time step is updated. (Step S1011), the process returns to step S1008 of the first particle calculation process in the partial region. By such processing, the number of particles contained in the region A and the region B can be kept almost equal, and the difference between the regions can be reduced.

  FIG. 16 is a flowchart showing a particle behavior calculation process according to the sixth embodiment of the present invention. In the figure, first, calculation conditions such as various physical parameters necessary for calculation and initial arrangement of particles are read (step S1101), then particle density is calculated (step S1102), and effective distance of interaction is set (step S1103). After the execution, the calculation area is divided (step S1104). Here, the area A and the area B are divided into two partial calculation areas. After the division, the number of particles included in each divided area is counted (steps S1105 and S1106), and the difference NA−NB between the respective count numbers NA and NB is compared with a predetermined value, and if the difference is equal to or smaller than the predetermined value. (Step S1107; YES), particle behavior calculation is performed for each partial region (Steps S1108 and S1109). If the count difference is not less than a predetermined value (Step S1107; NO), the calculation region division processing in Step S1104 is performed. Return. Note that the particle behavior calculation in the partial region is performed by, for example, the processing flow shown in FIG. Then, after the particle calculation is completed, the time step is confirmed (step S1110). If the time step has reached the final time step (step S1110; YES), the process is terminated. Otherwise, the time step is updated. (Step S1111), the process returns to the calculation area dividing process in Step S1104. By such processing, the number of particles contained in the region A and the region B can be kept almost uniform at each time step, and the difference between the partial regions can be reduced without being affected by the movement of particles in the calculation process. can do.

  FIG. 17 is a flowchart showing particle behavior calculation processing according to the seventh embodiment of the present invention. In the figure, first, calculation conditions such as various physical parameters necessary for calculation and initial arrangement of particles are read (step S1201), then particle density is calculated (step S1202), and effective distance of interaction is set (step S1203). After the execution, the calculation area is divided (step S1204). After the division, the particle behavior calculation means is assigned to each partial region for each divided region (step S1205). If the particle behavior calculation means is provided in the number corresponding to the number of partial calculation regions, the particle behavior calculation in each partial region is performed in parallel by each particle behavior calculation means (step S1206). If there is only one particle behavior calculation means, step S1109 of particle behavior calculation in region B is performed after step S1108 of particle behavior calculation in region A as shown in the processing flow of FIG. In the case where a plurality of particle behavior calculation means are available, the particle behavior calculation in the region A and the region B can be performed simultaneously. Since parallel processing can be performed in this way, it is possible to shorten the overall particle behavior calculation time. As described above, in order to perform the particle calculation processing in parallel, an apparatus including a plurality of particle calculation processing means is required. However, personal computers including a plurality of CPUs are also widely used, and are easily used. It is feasible. Then, after each particle behavior calculation in the partial calculation region is completed, the time step is confirmed (step S1207). If the time step has reached the final time step (step S1207; YES), the process is terminated. Otherwise (step S1207; NO), the time step is updated (step S1208), and the process returns to the particle behavior calculation in step S1206. The intra-region particle behavior calculation is performed, for example, by the processing flow shown in FIG.

  FIG. 18 is a flowchart showing particle behavior calculation processing according to the eighth embodiment of the present invention. In the figure, first, calculation conditions such as various physical parameters necessary for calculation and initial arrangement of particles are read (step S1301), then particle density is calculated (step S1302), and effective distance of interaction is set (step S1303). After the execution, the calculation area is divided (step S1303). After the division, particle behavior calculation is performed in parallel for each divided region (step S1306), but steps (start and end of measurement) for measuring the calculation time are provided before and after the particle behavior calculation step. (Steps S1305 and S1306). After all the particle behavior calculations in the partial region are completed and each calculation time measurement is completed (step S1307), the time step is confirmed (step 1308), and the final time step is reached (step S1308; YES). The process ends, otherwise (step S1308; NO), the time step is updated (step S1309), and the calculation times in the partial areas are compared (step S1310). If the difference in calculation time for each partial region is less than or equal to a predetermined value (step S1310; YES), the particle behavior calculation for each region in steps S1305 to S1307 is performed as it is, but the difference in calculation time for each partial region is a predetermined value. In the case of the above (step S1310; NO), the process returns to the area division in step S1304, and correction is performed so as to reduce the difference in calculation time. As described above, when the behavior calculation in each partial region is performed in parallel, the entire calculation time can be shortened by performing the process of equalizing each calculation time.

  Next, FIG. 19 is a block diagram showing a specific apparatus configuration for starting a program for executing each embodiment of the particle behavior calculation method of the present invention. That is, this figure shows hardware constructed from a microprocessor or the like that executes software according to the particle behavior calculation method in the above embodiment. In the figure, the particle behavior calculation system includes an interface (hereinafter abbreviated as I / F) 51, a CPU 52, a ROM 53, a RAM 54, a display device 55, a hard disk 56, a keyboard 57, and a CD-ROM drive 58. A general-purpose processing device is prepared, and a readable recording medium 59 such as a CD-ROM stores a program for executing the particle behavior calculation method of the present invention. Further, a control signal is input from an external device via the I / F 51, and an instruction by the operator or a program of the present invention is automatically activated by the keyboard 57. Then, the CPU 52 performs calculation processing according to the above-described particle behavior calculation method according to the program, stores the processing result in a storage device such as the RAM 54 or the hard disk 56, and outputs it to the display device 55 or the like as necessary. As described above, by using the recording medium recorded with the program for executing the particle behavior calculation method of the present invention, a particle behavior calculation system can be constructed universally without changing the existing system.

  In addition, this invention is not limited to the said Example, It cannot be overemphasized that various deformation | transformation and substitution are possible if it is description in a claim.

It is the schematic which shows a contact model. It is the schematic which shows a mode that the particle | grains which perform contact determination in the calculation object area | region divided | segmented into the small area | region are restrict | limited to the small area | region with the focused particle | grains, and the small area | region which exists in the vicinity. It is the schematic which shows the electrostatic action force and magnetic action force in case two particles with different charge amount exist in the position of the distance r. When the mesh interval L is an effective distance, the state in which the contact determination is performed in the calculation target region divided into the small regions is limited to the particles existing in the small region with the target particle and the small region in the vicinity thereof. FIG. It is a flowchart which shows the particle behavior calculation process which considered only the interaction by the contact by the conventional neighborhood cell method. It is a flowchart which shows the particle behavior calculation process which concerns on 1st Example of this invention. It is a flowchart which shows the particle behavior calculation process which concerns on 2nd Example of this invention. It is the schematic which shows the condition where particle | grains localize in the vicinity which has arrange | positioned the magnet 81. FIG. It is a flowchart which shows the particle behavior calculation process which concerns on the 3rd Example of this invention. It is a flowchart which shows the particle behavior calculation process in the area | region divided | segmented. It is a flowchart which shows the particle behavior calculation process which concerns on the 4th Example of this invention. It is a flowchart which shows another particle behavior calculation process in the area | region divided | segmented. It is a flowchart which shows another particle behavior calculation process in the divided | segmented area | region. It is a flowchart which shows another particle behavior calculation process in the divided | segmented area | region. It is a flowchart which shows the particle behavior calculation process which concerns on the 5th Example of this invention. It is a flowchart which shows the particle behavior calculation process which concerns on the 6th Example of this invention. It is a flowchart which shows the particle behavior calculation process which concerns on the 7th Example of this invention. It is a flowchart which shows the particle behavior calculation process which concerns on the 8th Example of this invention. It is a block diagram which shows the structure of the specific apparatus for starting the program which performs each Example of the particle behavior calculation method of this invention.

Explanation of symbols

11; Spring, 12; Dashpot, 13; Slider, 21, 41;
22, 23, 31, 32, 44; particle, 24; small region, 25, 43; region,
42; cell.

Claims (14)

Considering at least two types of interaction forces depending on the distance between particles between each particle substance, the calculation area for calculating the behavior of the particles is divided into a number of small areas and included in the divided small areas In the particle behavior calculation method for calculating the behavior of particles
An effective distance setting step for determining an effective distance for each interaction acting between particles;
A particle behavior calculation method comprising: a small region size setting step for determining a size of the small region according to a maximum value rmax and a minimum value rmin of an effective distance of interaction. Considering at least two types of interaction forces depending on the distance between particles between each particle substance, the calculation area for calculating the behavior of the particles is divided into a number of small areas and included in the divided small areas In the particle behavior calculation method for calculating the behavior of particles
A particle density calculating step for calculating a density of particles in the calculation region;
An effective distance setting step for determining an effective distance for each interaction acting between particles;
A particle behavior calculation method comprising: a small region size setting step for determining a size of the small region according to a maximum value rmax and a minimum value rmin of an effective distance of interaction and a density of the particle. Considering at least two types of interaction forces depending on the distance between particles between each particle substance, the calculation area for calculating the behavior of the particles is divided into a number of small areas and included in the divided small areas In the particle behavior calculation method for calculating the behavior of particles
An effective distance setting step for determining an effective distance for each interaction acting between particles;
A calculation area dividing step for defining a boundary line or a boundary surface for dividing the whole calculation area into a plurality of partial calculation areas;
A particle behavior calculation method comprising: for each partial calculation region, a small region size setting step for determining a size of the small region according to a maximum value rmax and a minimum value rmin of an effective distance of interaction. Considering at least two types of interaction forces depending on the distance between particles between each particle substance, the calculation area for calculating the behavior of the particles is divided into a number of small areas and included in the divided small areas In the particle behavior calculation method for calculating the behavior of particles
A particle density calculating step for calculating a density of particles in the calculation region;
An effective distance setting step for determining an effective distance for each interaction acting between particles;
A calculation area dividing step for defining a boundary line or a boundary surface for dividing the whole calculation area into a plurality of partial calculation areas;
A small region size setting step for determining the size of the small region in accordance with the maximum value rmax and the minimum value rmin of the effective distance of interaction and the density of the particles for each partial calculation region, Particle behavior calculation method. Considering at least two types of interaction forces depending on the distance between particles between each particle substance, the calculation area for calculating the behavior of the particles is divided into a number of small areas and included in the divided small areas In the particle behavior calculation method for calculating the behavior of particles
An effective distance setting step for determining an effective distance for each interaction acting between particles;
A calculation area dividing step for defining a boundary line or a boundary surface for dividing the whole calculation area into a plurality of partial calculation areas;
A particle density calculating step of calculating a density of particles for each partial calculation region;
A small region size setting step for determining the size of the small region according to the maximum value rmax and the minimum value rmin of the effective distance of interaction and the density of the particles for each partial calculation region, Particle behavior calculation method. Considering at least two types of interaction forces depending on the distance between particles between each particle substance, the calculation area for calculating the behavior of the particles is divided into a number of small areas and included in the divided small areas In the particle behavior calculation method for calculating the behavior of particles
A calculation area dividing step for defining a boundary line or a boundary surface for dividing the whole calculation area into a plurality of partial calculation areas;
An effective distance setting step for determining an effective distance for each interaction acting between particles for each partial calculation region;
A particle behavior calculation method comprising: for each partial calculation region, a small region size setting step for determining a size of the small region according to a maximum value rmax and a minimum value rmin of an effective distance of interaction. Considering at least two types of interaction forces depending on the distance between particles between each particle substance, the calculation area for calculating the behavior of the particles is divided into a number of small areas and included in the divided small areas In the particle behavior calculation method for calculating the behavior of particles
A calculation area dividing step for defining a boundary line or a boundary surface for dividing the whole calculation area into a plurality of partial calculation areas;
An effective distance setting step for determining an effective distance for each interaction acting between particles for each partial calculation region;
A particle density calculating step of calculating a density of particles for each partial calculation region;
A small region size setting step for determining the size of the small region according to the maximum value rmax and the minimum value rmin of the effective distance of interaction and the density of the particles for each partial calculation region, Particle behavior calculation method. Considering at least two types of interaction forces depending on the distance between particles between each particle substance, the calculation area for calculating the behavior of the particles is divided into a number of small areas and included in the divided small areas In the particle behavior calculation method for calculating the behavior of particles
A calculation area dividing step for defining a boundary line or a boundary surface for dividing the whole calculation area into a plurality of partial calculation areas;
A particle counting step for counting the number of particles contained in each of the partial calculation areas;
Grain behavior calculation comprising: a calculation region subdivision step for correcting a boundary line or a boundary surface according to the number of particles included in each partial calculation region and dividing it again into a plurality of partial calculation regions. Method.   The small region is a square in the case of two dimensions or a cube in the case of three dimensions, and the relationship between the maximum value rmax and the minimum value rmin of the effective distance of interaction is defined as rmin ≦ L ≦. The particle behavior calculation method according to claim 1, wherein the particle behavior is set so as to be rmax.   The particle behavior calculation method according to any one of claims 3 to 8, further comprising a step of assigning, for each partial calculation area, a calculation unit that sets a size of the small area for each partial calculation area in the small area size setting step. .   The particle behavior calculation method according to claim 10, further comprising a step of executing the arithmetic processing by the assigned arithmetic means in parallel.   The calculation area subdivision step corrects a boundary line or a boundary surface according to the number of particles included in each partial calculation area or the calculation time required for each behavior calculation for each partial calculation area, and again a plurality of the parts The particle behavior calculation method according to claim 8, wherein the particle behavior is divided into calculation areas.   The calculation area subdivision step corrects the boundary line or the boundary surface according to the number of particles included in each partial calculation area and the calculation time required for each behavior calculation for each partial calculation area, and again the plurality of the parts The particle behavior calculation method according to claim 8, wherein the particle behavior is divided into calculation areas. A computer-readable recording medium storing a program for executing the particle behavior calculation method according to claim 1.

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