JP2023026022A - Particle arrangement system, particle arrangement method, and particle arrangement program - Google Patents

Abstract

To suppress the calculation cost of particle arrangement even when the number of particles to be simulated increases.SOLUTION: A particle arrangement system 10, which is a system for arranging particles to be simulated in a space for simulation, includes a block generation part 11 for generating a block having a shape capable of combining a plurality of blocks without a gap in the space, having all boundaries as periodic boundaries and having the particles arranged therein, and an arrangement part 12 for arranging the particles by combining the plurality of generated blocks so that the periodic boundaries corresponding to each other are adjacent to each other in the space.SELECTED DRAWING: Figure 1

Description

The present invention relates to a particle placement system, a particle placement method, and a particle placement program for arranging particles to be simulated in a simulation space.

Behaviors of a plurality of particles are analyzed by particle method simulation such as DEM (Discrete Element Method). In order to perform the simulation, first, it is necessary to arrange the particles to be simulated in the simulation space. Conventionally, a method for automatically arranging particles has been proposed. For example, Patent Literature 1 discloses that after arranging particles so as to allow them to overlap, the particles are moved to obtain a state in which particles do not overlap each other.

JP 2006-259910 A

However, the method disclosed in Patent Document 1 requires information processing such as simulation or judgment for the initial placement of individual particles, and the calculation cost increases as the number of particles to be simulated increases.

In addition, as a method of arranging particles other than the above, for example, an arbitrary initial particle group is generated in a space for simulation, and a simulation is performed in which the particles fall into a preset frame by gravity. There is a drop-type filling that packs particles into the Alternatively, there is a method of sequentially generating particles randomly in a simulation space, and discarding, moving, growing, and adopting the particles based on preset constraints. These methods also increase the calculation cost as the number of particles to be simulated increases, similar to the method disclosed in Patent Document 1. Also, the procedure becomes complicated when the particles are packed into an arbitrary shape.

The present invention has been made in view of the above, and is capable of suppressing the calculation cost of arranging particles and appropriately arranging particles even when the number of particles to be simulated increases. It is an object of the present invention to provide a particle placement system, a particle placement method, and a particle placement program.

In order to achieve the above object, a particle placement system according to the present invention is a particle placement system that places particles to be simulated in a simulation space, and has a shape that allows a plurality of particles to be combined without gaps in the space, and all A block generating means for generating a block whose boundary is a periodic boundary and in which particles are arranged; locating means for locating the

In the particle placement system according to the present invention, all boundaries are periodic boundaries, and particles are placed by combining blocks in which particles are placed. Therefore, even if the number of particles increases, the particles can be arranged by combining blocks in the area where the particles are arranged. The processing of block combinations is a simple process and thus has a low computational cost. Also, the number of particles handled when creating a block can be made smaller than the number of particles to be arranged. Therefore, the computational cost of creating blocks is also small compared to conventional particle placement. Therefore, according to the particle placement system according to the present invention, even when the number of particles to be simulated increases, it is possible to reduce the calculation cost of particle placement and to appropriately place particles. can.

The block generating means arranges the particles inside a region having a periodic boundary defined by a boundary other than one direction set in advance, sets a partial region having a thickness in the one direction in the region, and includes the particles in the partial region. Particles may be moved while their positional relationship is fixed, and blocks may be generated with the boundaries of the partial regions as periodic boundaries. Further, the block generating means may arrange the particles inside the region by applying a unidirectional force to the particles to move them. According to this configuration, blocks can be easily and appropriately generated. As a result, the particles can be arranged easily and reliably.

The block generation means may perform processing for homogenizing the arrangement of particles inside the block. Further, as the homogenization process, the block generation means fixes the positions of the particles near a predetermined position in one direction set in advance in the block, and simulates the movement of the particles whose positions are not fixed at the predetermined position. may be repeated while changing . According to this configuration, it is possible to suppress unevenness in the arrangement of the particles in each block, and it is possible to achieve a homogenized arrangement of the particles.

By the way, the present invention can be described as an invention of a particle placement system as described above, and can also be described as an invention of a particle placement method and a particle placement program as follows. These are substantially the same inventions with only different categories, and have similar actions and effects.

That is, the particle arrangement method according to the present invention is a particle arrangement method that is a method of operating a particle arrangement system that arranges particles to be simulated in a simulation space, and has a shape that allows a plurality of particles to be combined without gaps in the space, and A block generation step of generating a block in which all boundaries are periodic boundaries and particles are arranged therein; and combining a plurality of blocks generated in the block generation step such that the corresponding periodic boundaries are adjacent to each other in space. and a placing step of placing the particles at.

Further, a particle placement program according to the present invention is a particle placement program that causes a computer to operate as a particle placement system that places particles to be simulated in a simulation space, and a plurality of such computers are combined in space without gaps. and a block generating means for generating a block in which all boundaries are periodic boundaries and in which particles are arranged; It functions as an arranging means for arranging particles by combining a plurality of them.

According to the present invention, even when the number of particles to be simulated increases, it is possible to suppress the computational cost of arranging the particles and to appropriately arrange the particles.

It is a figure showing functional composition of a particle arrangement system concerning an embodiment of the present invention. FIG. 4 is a diagram showing an overview of the arrangement of particles; FIG. 4 is a diagram for explaining block generation; 4 is a flow chart showing a particle placement method, which is a process executed by the particle placement system according to the embodiment of the present invention; It is a figure which shows the structure of the particle arrangement|positioning program which concerns on embodiment of this invention with a recording medium.

Hereinafter, embodiments of a particle placement system, a particle placement method, and a particle placement program according to the present invention will be described in detail along with the drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and overlapping descriptions are omitted.

FIG. 1 shows the functional configuration of a particle placement system 10 according to this embodiment. The particle arrangement system 10 is a system (apparatus) that arranges particles to be simulated in a simulation space (computational area). The simulation analyzes the behavior of multiple particles in a three-dimensional simulation space. The particles are, for example, spherical (having a constant distance from the center to the surface). Also, the particles may have shapes other than those described above.

In the simulation, for example, the positions and velocities of a plurality of particles are calculated for each time step, which is the simulation time. In the simulation, the force applied to each particle is calculated, and the position and velocity of the particle are calculated based on the calculated force. The force applied to each particle is, for example, interaction force generated by interaction between particles, such as contact force due to contact (collision). A simulation is performed based on DEM, for example. Alternatively, the simulation may be based on other particle methods such as SPH (Smoothed Particle Hydrodynamics) or MPS (Moving Particle Semi-implicit method). The simulation may involve many particles, ie large-scale particle method calculations may be performed.

The particles to be simulated, that is, the particles to be placed by the particle placement system 10 include arbitrary particles that have been the targets of conventional particle simulations. For example, earth and sand or powder can be targeted. Alternatively, a fluid or solid may be targeted assuming that it consists of a plurality of particles.

The above simulation is used for simulating natural phenomena such as landslides in terrain. In this case, a collection of particles corresponds to a stratum (eg, sedimentary layer, rock or sand layer). Also, the above simulation may be used in any field such as academic, industrial, game, and CG (computer graphics) fields. For example, it may be used to represent movement of powder structures in sandbox games, or erosion and weathering of structures in movies or animations.

In order to perform a simulation, it is necessary to arrange particles in space as the initial state of the simulation. The particle placement system 10, for example, places particles in space as the initial state of the simulation. When arranging particles in space as an initial state, it is necessary that the arrangement appropriately represents the object to be simulated. For example, when simulating a landslide, it is necessary that the particles to be arranged are uniformly packed in a region corresponding to the stratum appropriately so as to correspond to the stratum.

Specifically, the particle placement system 10 is configured by a computer including hardware such as a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), and a memory. Each function of the particle placement system 10, which will be described later, is exhibited by the operation of these components by a program or the like. The particle placement system 10 may be realized by one computer, or may be realized by a computer system configured by connecting a plurality of computers to each other via a network. It should be noted that the particle placement system 10 does not necessarily need to include a GPU as an arithmetic device, and may be configured to include only a CPU.

An overview of particle placement by the particle placement system 10 according to the present embodiment will be described. The particle placement system 10 first generates a block 20 as shown in FIG. 2(a). The block 20 is a cuboid in which particles are arranged. Subsequently, as shown in FIG. 2B, the particle placement system 10 combines and places the blocks 20 in the area where the particles are placed in the space to generate the aggregate 30 of blocks. Subsequently, as shown in FIG. 2C, the particle placement system 10 deletes the particles not used for the simulation from the block assembly 30 to obtain an initial particle placement 40 .

Next, functions of the particle placement system 10 according to this embodiment will be described. As shown in FIG. 1, the particle placement system 10 includes a block generation section 11 and a placement section 12 .

The block generation unit 11 is a block generation means for generating a block 20 having a shape that allows a plurality of blocks to be combined without gaps in space, all boundaries being periodic boundaries, and particles arranged therein. The block generating unit 11 arranges particles inside a region whose periodic boundary is a boundary in a direction other than a preset one direction, sets a partial region having a thickness in the one direction in the region, and includes particles in the partial region. The particles may be moved while fixing the positional relationship, and the block 20 may be generated with the boundary of the partial region as the periodic boundary. The block generation unit 11 may arrange the particles inside the region by applying a unidirectional force to the particles to move them. The block generation unit 11 may perform processing for homogenizing the arrangement of particles inside the block 20 . As the homogenization process, the block generation unit 11 fixes the positions of the particles near a predetermined position in one direction set in advance in the block 20, and simulates the movement of the particles whose positions are not fixed. It may be repeated while changing.

The boundaries of the blocks 20 generated by the block generation unit 11, that is, the faces forming the rectangular parallelepiped blocks 20 are periodic boundaries (boundaries satisfying periodic boundary conditions). That is, block 20 is a full-surface periodic boundary grain block. Of the faces forming the rectangular parallelepiped block 20, the faces facing each other are the corresponding periodic boundaries. In addition, since the blocks 20 are rectangular parallelepipeds as described above, the two blocks 20 can be combined with their corresponding periodic boundary surfaces in close contact with each other without gaps. In addition, since the surfaces where the blocks 20 are in close contact with each other form corresponding periodic boundaries, there is no uneven distribution of the particles due to the presence of the surfaces. Moreover, since all the faces of the block 20 are periodic boundaries, another block 20 can be combined by bringing the periodic boundaries into close contact with each other in the direction of an arbitrary face of the block 20 . As a result, a collection of blocks 30 can be generated to include any initial arrangement 40 as described above.

The block generator 11 generates blocks 20 as follows. The block generation unit 11 arranges the particles inside a region whose periodic boundary is a boundary other than a preset boundary in one direction. For example, as shown in FIG. 3A, the block generator 11 forms a region with four planes 21 perpendicular to the x direction (x axis) and y direction (y axis) of the space as periodic boundaries. The diagram shown in FIG. 3 is a diagram viewed from a direction parallel to the xy plane of the space, and the vertical direction is the z direction. Some of these faces 21 become faces of the blocks 20 . The process of using the surface of the region as the periodic boundary may be performed in the same manner as in the conventional method (the same applies to the following).

Further, as shown in FIG. 3(a), the block generation unit 11 generates a surface 22 which is not a periodic boundary and which is perpendicular to the spatial z-direction (z-axis) surrounded by the four surfaces 21. do. When the above region is viewed from above in the z direction, it is a rectangle formed by four planes 21 perpendicular to the x and y directions. The block generator 11 generates particles of arbitrary size and shape at random positions above the region in the z direction. The block generation unit 11 stores in advance parameters of particles used for arranging particles, such as the radius of particles, and generates particles based on the information. As will be described later, the block generator 11 also simulates the behavior of particles for arranging the particles. This simulation may be performed in the same manner as the conventional DEM-based simulation. The block generation unit 11 also pre-stores parameters for the simulation, such as friction coefficient, elastic coefficient, viscous damping coefficient, and restitution coefficient, and uses them for the simulation.

The block generation unit 11 performs a simulation of applying a downward force in the z direction, such as gravity, to the generated particles. Particles subjected to gravity fall to the bottom surface 22, which is a plane perpendicular to the z-direction. The block generator 11 generates a large number of particles and performs the above simulation. As a result of this simulation, the bottom surface 22 is filled with particles as shown in FIG. 3(a). That is, the block generation unit 11 performs the gravity falling type filling of the particles in the above region (the box whose sides are periodic boundaries). The block generator 11 continues the filling until the length from the bottom surface 22 of the region filled with particles reaches a certain length longer than the length of the block 20 in the z direction.

In this way, the block generation unit 11 applies a force in the z direction to the generated particles inside the region with the planes 21 in the x direction and the y direction other than the preset z direction as periodic boundaries to move the particles. to place the particles inside the region.

Subsequently, the block generation unit 11 sets two partial regions 23 and 24 having a thickness in the z direction in the region. The two sub-regions 23, 24 are set to contain grains located in a portion of the z-direction thickness. The positions of the two partial regions 23 and 24 are positions where the length from the bottom surface 22 is a preset length longer than the length of the block 20 in the z direction. In addition, the thickness of the two partial regions 23 and 24 in the z direction is, for example, sufficiently smaller than the z direction of the finally generated block 20, and the particles contained in the partial regions 23 and 24 form at least one layer. It is as thick as

The two partial areas 23, 24 are continuous in the z-direction. The block generation unit 11 divides the particles included in the partial area 23, for example, the particles whose center of gravity is included in the partial area 23, into the above-described surface as shown in FIG. 22 below. This movement is only in the z direction and does not change the position in the x and y directions. At this time, among the particles not to be moved, particles present at a certain distance in the z direction from the bottom surface 22 of the above region may be deleted. The constant distance for removing particles may be adjusted so that the number of particles or the particle volume fraction of particles included in the block 20 to be finally generated is a predetermined value. Thereby, the block generator 11 can arbitrarily adjust the number of particles or the particle volume fraction of the particles included in the block 20 . Also, particles above the partial region 23 in the z direction are not used in subsequent processing.

When moving the particles in the partial region 23 downward, the block generation unit 11 moves the particles to a position where a gap is formed between the particles that are not to be moved (the position that the particles that are not to be moved and the particles that are to be moved do not overlap). . As shown in FIG. 3(b), among the aggregates of particles configured in this way, the particles of the partial area 24 are located on the upper side in the z direction, and the particles of the partial area 23 are located on the lower side. becomes. Since the two partial regions 23 and 24 are continuous in the z-direction as described above, the boundary surface between the partial regions 23 and 24 can be a periodic boundary. The block generation unit 11 sets the upper and lower surfaces in the z direction of the region where the particles are located shown in FIG. 3B as periodic boundaries.

Subsequently, the block generation unit 11 fixes the positional relationship with respect to the partial area 23 for particles included in the partial area 23 , for example, particles whose center of gravity is included in the partial area 23 . In addition, the block generation unit 11 fixes the positional relationship with respect to the partial area 24 for particles included in the partial area 24 , for example, particles whose center of gravity is included in the partial area 24 . Other particles are allowed to move freely in space. In this state, the block generation unit 11 performs a simulation in which particles included in the partial area 23 are brought closer to the partial area 24 side in the z direction. That is, the block generator 11 performs a simulation of compressing the block at this point in the z-direction. This simulation is a simulation of movement of particles in a region sandwiched between partial regions 23 and 24 . In this simulation, gravity may or may not be applied to the particles.

The block generation unit 11 sets the length between the outer (lower in the z-direction) surface of the partial region 23 after movement and the outer (upper in the z-direction) surface of the partial region 24 to a preset final until it reaches the length of the block 20 to be generated. FIG. 3(c) shows the collection of particles after moving through the partial area 23 (the length between the partial areas 23 and 24 is shorter than that shown in FIG. 3(b)). Note that the length between the outer (lower in the z-direction) surface of the partial region 23 and the outer (upper in the z-direction) surface of the partial region 24 before the movement is longer than the length of the block 20. . Note that the longer the length in the z direction of the region where the particles are located before moving the partial region 23, the higher the density of the particles in the finally generated block 20 becomes. As described above, the block generation unit 11 sets the particles included in the post-movement partial region 23 as the lower lid in the z direction and the particles included in the partial region 24 as the upper lid in the z direction, and creates the block at this time as Generate.

By the above processing, it is possible to generate blocks whose periodic boundaries are the faces of the rectangular parallelepiped. However, the generated blocks have a biased arrangement of particles. The biased arrangement of the particles is caused by the partial regions 23 and 24 in which the positions of the particles are fixed. The block generation unit 11 homogenizes the arrangement of particles to remove the uneven arrangement of particles in the block as follows.

The blocks generated as described above shown in FIG. )) is defined as a periodic boundary, the particles as a whole can be moved (shifted) in the z-direction while the positional relationship between the particles is fixed.

In the block shown in FIG. 3C, the block generator 11 sets two partial regions 25 and 26 having a thickness in the z direction in the block. The two partial areas 25,26 may be of similar size to the two partial areas 23,24 described above. The positions of the two partial areas 25 and 26 are preset positions other than the two partial areas 23 and 24 described above. The two partial regions 25, 26 are continuous in the z-direction.

As shown in FIG. 3D, the block generation unit 11 fixes the positional relationship between the particles such that the particles included in the two partial areas 25 and 26 are located at the lower end and the upper end of the block, respectively. The whole particle is moved (shifted) in the z direction. In the block shown in FIG. 3(c), the partial region 25 positioned above in the z direction is positioned at the lower end of the block after movement as shown in FIG. The partial area 26 positioned on the lower side is positioned at the upper end of the block after the movement.

Subsequently, the block generation unit 11 fixes the positional relationship with respect to the partial area 25 for particles included in the partial area 25 , for example, particles whose center of gravity is included in the partial area 25 . In addition, the block generation unit 11 fixes the positional relationship of particles included in the partial area 26 , for example, particles whose center of gravity is included in the partial area 26 , with respect to the partial area 26 . Other particles are allowed to move freely in space. In this state, the block generator 11 simulates the movement of particles in the area sandwiched between the partial areas 25 and 26 . In this simulation, gravity may or may not be applied to the particles. In this simulation, the particles included in the two partial regions 23 and 24 whose positional relationship was fixed by the processing described above are also moved. That is, this simulation is a relaxation calculation for relaxing the load on the particle. This relaxation reduces the bias in particle placement.

Subsequently, the block generation unit 11 sets two new partial regions 25 and 26 (the process shown in FIG. 3(c)), and performs the relaxation calculation (the process shown in FIG. 3(d)). . The block generator 11 repeats setting and relaxation calculation for the two partial regions 25 and 26 . This repetition is performed, for example, until the uneven distribution of particles in the entire block becomes a problem-free state in terms of simulation. For example, simulation of relaxation calculation is repeated until a globally homogeneous contact internal stress occurs in each particle. Alternatively, the above repetition may be performed a preset number of times.

As described above, the block generation unit 11, as a process of homogenizing the arrangement of particles inside the block, generates particles near predetermined positions in one direction in the block (the The position of the particle) may be fixed, and the movement of the particle whose position is not fixed may be repeatedly simulated while changing the predetermined position.

The block generation unit 11 outputs information indicating the block 20 generated as described above, more specifically, information indicating the arrangement position of particles included in the block (for example, information on coordinates in the block) to the arrangement unit 12. .

The arranging unit 12 is arranging means for arranging particles by combining a plurality of blocks 20 generated by the block generating unit 11 such that corresponding periodic boundaries are adjacent to each other in space. The placement unit 12 receives information indicating the block 20 from the block generation unit 11 . Using the input information, the placement unit 12 combines blocks 20 containing particles and places them in space so as to include the area where the particles used in the simulation are placed. The area in which the particles used in the simulation are arranged is set in advance by the user and stored in the arrangement unit 12 . The placement unit 12 combines the plurality of blocks 20 so that the corresponding periodic boundaries are adjacent to each other without gaps.

The placement unit 12 deletes particles placed in areas other than positions where particles used in the simulation are placed, from the aggregate 30 of blocks combined with the blocks 20 . Note that if there is no particle placed at a position other than the area, the particle is not deleted. The above results in an initial arrangement 40 of the particles in space.

Physical properties of the block 20 itself or a combination of the blocks 20 are calculated before or after the arrangement 40 of the particles in the initial state by the arrangement unit 12, and the arrangement of the particles by the block 20 is suitable for performing the simulation. You can check whether That is, the performance of block 20 may be verified. For example, as physical properties (mechanical properties) of the block 20 itself or a combination of the blocks 20, the packing rate of particles, the number of connections, the compressibility, or the breaking property may be calculated. The number of connections is the number of particles that are connected to other particles. Fracture properties can be determined by numerical triaxial compression experiments. These physical properties can be calculated by conventional methods. The shape of the combination of the blocks 20 when calculating the physical properties may be a preset shape for calculating the physical properties. For example, when conducting a numerical triaxial compression experiment, it may have a columnar shape.

If the calculated physical properties are not appropriate, the blocks 20 may be generated again by the block generator 11 . In this case, the conditions for generating the blocks 20 are changed so that the physical properties of the generated blocks 20 are different. The block 20 may be used to arrange the particles 40 only when macroscopically homogeneous properties are obtained by the block 20 .

The arrangement unit 12 may calculate the physical properties related to the block 20 and determine whether the calculated physical properties are appropriate. In this case, the placement unit 12 stores in advance information (for example, criteria for making the above determination) for performing these operations. When the placement unit 12 determines that the calculated physical properties are appropriate, the placement unit 12 performs the initial state placement 40 of the particles in the space. If the placement unit 12 determines that the calculated physical properties are not appropriate, it instructs the block generation unit 11 to generate blocks 20 under different conditions. In this case, the placement unit 12 stores in advance how the conditions for generating the blocks 20 are changed.

The particles are simulated using the initial arrangement 40 of the particles in space generated by the arrangement unit 12 . The particle placement system 10 has a function of simulating particles, and may perform particle simulation. Alternatively, particles may be simulated in a system other than the particle placement system 10 . In this case, the placement unit 12 outputs (transmits) information indicating the initial state placement 40 of the particles in space to the system. The above is the function of the particle placement system 10 according to the present embodiment.

Subsequently, a particle placement method, which is a process (operation method performed by the particle placement system 10) executed by the particle placement system 10 according to the present embodiment, will be described with reference to the flowchart of FIG.

In this process, first, the block generation unit 11 fills particles in a region having periodic boundaries in the x and y directions and not having periodic boundaries in the z direction (S01, block generation step). As described above, this filling brings the particles into the state shown in FIG. 3(a). Subsequently, the block generation unit 11 generates blocks having periodic boundaries in the z direction (S02, block generation step). In this process, as described above, two partial regions 23 and 24 that are continuous in the z direction are set as shown in FIGS. is moved below the location where the particles are packed.

Subsequently, the block generating unit 11 performs a simulation of bringing the particles included in the partial area 23 closer to the partial area 24 side, that is, a simulation of compressing the block at this point in the z direction (S03, block generating step). This treatment is performed so that the particles change from the state shown in FIG. 3(b) to the state shown in FIG. 3(c). Subsequently, the block generator 11 repeats the relaxation calculation for the block (S04, block generation step). The relaxation calculation is to homogenize the arrangement of particles, and is performed as shown in FIGS. 3(c) and 3(d) as described above. By the above processing (S01 to S04), a block 20 having a shape that can be combined in a space without gaps, all boundaries being periodic boundaries, and particles arranged inside is generated.

Subsequently, the arrangement unit 12 arranges particles by combining a plurality of blocks 20 generated by the block generation unit 11 so that corresponding periodic boundaries are adjacent to each other in space (S05, arrangement step). As described above, at this time, particles arranged at positions other than the area where the particles used in the simulation are arranged may be deleted. The generated initial state arrangement 40 of particles is used for particle simulation. The above is the processing executed by the particle placement system 10 according to the present embodiment.

In this embodiment, all boundaries are periodic boundaries, and particles are arranged by combining blocks 20 in which particles are arranged. Therefore, even if the number of particles increases, the particles can be arranged by combining blocks in the area where the particles are arranged. The processing of combinations in block 20 is a simple process and thus has a low computational cost. Also, the number of particles handled when creating a block can be made smaller than the number of particles to be arranged. Therefore, the computational cost of creating block 20 is also small compared to conventional particle placement. Therefore, according to the present embodiment, even when the number of particles to be simulated increases, the calculation cost for arranging the particles can be suppressed and the particles can be arranged appropriately.

Further, as in the present embodiment, particles are arranged inside a region having a periodic boundary defined by a boundary other than a preset one direction (for example, the planes 21 in the x direction and the y direction), and the particles are arranged in the region. A partial region 23 having a thickness (for example, in the z-direction) is set, particles included in the partial region are moved while their positional relationship is fixed, and blocks are generated with the boundary of the partial region 23 as a periodic boundary. may At that time, the particles may be placed inside the region by applying a unidirectional force (for example, gravity) to the particles to move them. According to this configuration, it is possible to easily and appropriately generate a block in which all boundaries are periodic boundaries. As a result, the particles can be arranged easily and reliably.

However, blocks whose boundaries are all periodic boundaries need not necessarily be generated as described above, and may be generated by other methods. Further, when arranging the particles inside the region, it is not always necessary to use a method of applying a unidirectional force to the particles to move them. For example, a method of randomly generating particles within the region may be used. may

Further, as in the present embodiment, processing for homogenizing the arrangement of particles inside the block may be performed. Specifically, as the homogenization process, the position of particles near a predetermined position in one preset direction (for example, the z direction) in the block is fixed, and the movement of particles whose positions are not fixed is simulated ( relaxation calculation) may be repeatedly performed while changing the predetermined position. According to this configuration, it is possible to suppress the bias in the arrangement of the particles in each block 20, and it is possible to achieve a homogenized arrangement of the particles. However, the homogenization process does not necessarily have to be performed. Also, when the homogenization treatment is performed, it may be performed by a method other than the above.

In the above-described embodiment, the space in which the particles are arranged is a three-dimensional space, but it may be a space other than the three-dimensional space, such as a two-dimensional space. In that case, the block 20 used for arranging the particles may have a dimensional shape corresponding to the space in which the particles are arranged.

Subsequently, a particle placement program for executing a series of processes by the particle placement system 10 described above will be described. As shown in FIG. 5, the particle placement program 100 is stored in a program storage area 111 formed on a computer-readable recording medium 110 that is inserted into and accessed by a computer or that the computer has. The recording medium 110 may be a non-temporary recording medium.

A particle placement program 100 comprises a block generation module 101 and a placement module 102 . Functions realized by executing the block generation module 101 and the placement module 102 are the same as the functions of the block generation unit 11 and the placement unit 12 of the particle placement system 10 described above, respectively.

Part or all of the particle placement program 100 may be transmitted via a transmission medium such as a communication line, received by another device, and recorded (including installation). Also, each module of the particle placement program 100 may be installed in any one of a plurality of computers instead of one computer. In that case, the above-described series of processes are performed by the computer system comprising the plurality of computers.

DESCRIPTION OF SYMBOLS 10... Particle placement system 11... Block generation part 12... Placement part 100... Particle placement program 101... Block generation module 102... Placement module 110... Recording medium 111... Program storage area.

Claims (7)

A particle arrangement system for arranging particles to be simulated in a simulation space,
a block generation means for generating a block having a shape that allows a plurality of blocks to be combined without gaps in the space, all boundaries being periodic boundaries, and having the particles arranged therein;
arranging means for arranging particles by combining a plurality of blocks generated by the block generating means such that corresponding periodic boundaries are adjacent to each other in the space;
A particle placement system comprising: The block generating means arranges particles inside a region having a periodic boundary defined by a boundary other than one direction set in advance, sets a partial region having a thickness in the one direction in the region, and includes the particles in the partial region. 2. The particle placement system according to claim 1, wherein the particles are moved while fixing the positional relationship, and the block is generated with the boundary of the partial region as a periodic boundary. 3. The particle placement system according to claim 2, wherein the block generation means places the particles inside the region by applying the force in the one direction to the particles to move the particles. 4. The particle placement system according to any one of claims 1 to 3, wherein said block generation means performs a process of homogenizing the placement of particles inside said block. As the homogenization process, the block generation means fixes the positions of particles in the vicinity of a predetermined position in one direction set in advance in the block, and simulates the movement of particles whose positions are not fixed in the predetermined position. 5. The particle placement system according to claim 4, wherein the placement is repeated while changing the position. A particle placement method that is a method of operating a particle placement system that places particles to be simulated in a simulation space,
a block generation step of generating a block having a shape that can be combined in a plurality without gaps in the space, all boundaries being periodic boundaries, and having the particles arranged therein;
an arrangement step of arranging particles by combining a plurality of blocks generated in the block generation step such that corresponding periodic boundaries are adjacent to each other in the space;
Particle placement methods, including A particle placement program that causes a computer to operate as a particle placement system that places particles to be simulated in a simulation space,
the computer,
a block generation means for generating a block having a shape that allows a plurality of blocks to be combined without gaps in the space, all boundaries being periodic boundaries, and having the particles arranged therein;
arranging means for arranging particles by combining a plurality of blocks generated by the block generating means so that corresponding periodic boundaries are adjacent to each other in the space;
A particle placement program that functions as a

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