JP4726189B2 - Particle behavior calculation result display method - Google Patents

Description

  The present invention relates to a technique for displaying a particle behavior analysis result obtained using a periodic boundary condition on a display device.

  In general, in a copying machine or a printer using electrophotographic technology, a visible image made of toner is formed on the surface of a photosensitive member by a developing device.

  In this developing device, in order to control the behavior of the toner and perform appropriate development, a stirring member or a transport member is generally used, and the toner or toner is transported by the movement or rotation of the stirring member or the transport member. Therefore, the behavior of the carrier particles is appropriately controlled.

  In recent years, particle behavior calculation has been performed to analyze the behavior of particles in such a stirred state and transported state, and is being utilized for elucidating the phenomenon of electrophotography and optimizing the structure of a developing device. At that time, in a system in which the symmetry of the system can be assumed, such as a phenomenon on a cylinder that is uniform in the longitudinal direction, the periodic boundary condition described in Non-Patent Document 1 is used for the purpose of shortening the calculation time and reducing the computer memory. The calculation method used is used. In this method, it is assumed that a part of a region where particles are present is cut out and the cut out region is continuous in the direction of the axis of symmetry. Then, a periodic boundary condition is set on the cut-out surface, and a process is performed in which particles flowing out from one periodic boundary surface at a certain time flow in from the same relative position on the other periodic boundary surface. By using this method, it is possible to handle only particles in a periodic boundary region surrounded by two periodic boundary surfaces in the calculation, so that the calculation time can be shortened and the computer memory can be reduced.

  Here, the display of the result obtained by the calculation using the periodic boundary condition will be described with reference to FIG.

  FIG. 15 shows the positions of particles at three times, t0 seconds, t1 seconds, and t2 seconds, with respect to the results obtained by two types of particle behavior analysis obtained using the periodic boundary conditions. In the figure, (a) shows a display example of the behavior of one particle, and (b) shows a display example of the behavior of many particles. Here, the behavior of the particles in the two-dimensional cross section is assumed, and the case where the periodic boundary condition is added in the horizontal direction in the figure is assumed. Moreover, in (b), the moving member exists in the periodic boundary region.

  In FIG. 15A, 401 and 402 represent periodic boundary surfaces, and 1301 represents particles. In FIG. 15B, 403a represents particles, and 404a and 405a represent members.

By performing the display as shown in FIG. 15, it is possible to visually grasp the position and velocity of the particles at each time within the periodic boundary region surrounded by the two periodic boundary surfaces. In addition, by continuously displaying, the movement of particles can be displayed as an animation, and dynamic behavior can be grasped.
Edited by the Society of Powder Engineering, Introduction to Powder Simulation P48, P68 (1998)

  However, in the display method as shown in FIG. 15, although the movement of particles in the periodic boundary region can be grasped, the movement of particles passing through the periodic boundary surface and flowing into the adjacent region, It is difficult to visually grasp the positional relationship between particles and the behavior of particles in the entire region before cutting into the periodic boundary region.

  For example, in FIG. 15A, it is determined whether the particle 1301 has moved to the left in the figure between t0 seconds and t1 seconds, or has passed through the periodic boundary surface 402 and flowed in from the periodic boundary surface 401. Can not. This is particularly problematic in FIG. 15 (b) where a large number of particles are displayed. In addition, in the animation display by continuous display at each time, although the overall behavior of the particles can be grasped, it is difficult to grasp the inflow and outflow at the periodic boundary surface.

  In particular, in the case of a system in which particles are transported in a direction perpendicular to the periodic boundary surface, it is important to evaluate how far each particle has been transported. In this method, however, there is always a particle in the periodic boundary region. Since it is displayed as, it is difficult to grasp only by the display result.

  Therefore, the present invention has been made in view of the above-described problems, and its purpose is to use particles and period in an actual system before cutting into a periodic boundary region using a result of particle behavior calculation using a periodic boundary condition. It is to enable easy and interactive display and grasping of the movement of particles passing through the boundary surface.

In order to solve the above-described problems and achieve the object, the particle behavior calculation result display method according to the present invention is a particle behavior calculation result display method for analyzing the behavior of particles by calculation and displaying on the display device, This selects a portion of the area for displaying the particles as periodic boundary region, and setting the control unit periodic boundary conditions, the steps of the control unit a plurality of areas is set for coupling with the periodic boundary region, said plurality of in the region, and applying a number control unit based on the periodic boundary region, the control unit, from the coordinates of the particles moving at the periodic boundary region stored in the calculation result data storage unit, the boundary of the region Obtain the number of times the particles have passed , store the periodic boundary passage number calculated based on the number of times in the periodic boundary passage number table , based on the region number n counted based on the periodic boundary passage number , Duplicate Among the regions, characterized in that it comprises the step of controlling the display device a particle in the region corresponding to the region number n To display so, the.

  According to the present invention, using the result of the particle behavior calculation using the periodic boundary condition, the movement of the particle in the actual system before passing into the periodic boundary region and the particle passing through the periodic boundary surface can be displayed easily and interactively. It becomes possible to grasp.

  Preferred embodiments of the present invention will be described below with reference to the drawings.

(First embodiment)
The first embodiment of the present invention will be described below. In the present embodiment, description will be made by taking, as an example, a result display of particle behavior analysis when a periodic boundary condition is added to one axis of a rectangular coordinate system based on particles and members in a two-dimensional cross section.

  FIG. 1 is a configuration diagram of a processing program of the particle behavior analysis result display device.

  In FIG. 1, reference numeral 100 denotes a control unit, which controls the entire processing of the program.

  Reference numeral 101 denotes a periodic boundary condition setting unit, which sets periodic boundary conditions and conditions related to the display, such as periodic boundary mapping information representing the periodic boundary conditions and the number of the periodic boundary region to be displayed.

  Reference numeral 102 denotes a particle behavior display unit, which displays each particle and a structure based on the conditions set by the periodic boundary condition setting unit 101.

  Hereinafter, the periodic boundary condition setting unit 101 and the particle behavior display unit 102 which are features of the present embodiment will be described in detail with reference to FIGS.

  FIG. 2 is a block diagram showing the configuration of the particle behavior analysis result display device according to the first embodiment of the present invention. Before describing the processing in the periodic boundary condition setting unit 101 and the particle behavior display unit 102 with reference to FIG. 3, the configuration of the particle behavior analysis result display device will be described first.

  As illustrated in FIG. 2, the particle behavior analysis result display device includes a CPU 200, a RAM 201, a display device 202, an input unit 203, an external storage device 204, and a bus 205. Further, the RAM 201 includes a program storage unit 201a, a calculation result data storage unit 201b, a current display time data storage unit 201c, a display area number data storage unit 201d, a periodic boundary mapping data storage unit 201e, a display A particle data storage unit 201f and a display structure data storage unit 201g are provided.

  The configuration of each unit will be described in detail. The CPU 200 is a central processing unit and controls each unit connected via the bus 205. The storage units 201a to 201g of the RAM 201 store the program, calculation result data, current display time data, display cycle number data, cycle boundary mapping data, display particle data, and display structure data shown in FIG. Is done. The display device 202 includes a display, a printer, and the like, and displays data to be displayed under the control of the CPU 200. The input unit 203 includes a keyboard, a mouse, and the like, and inputs input data from the outside into the apparatus. The external storage device 204 is composed of a hard disk or the like and stores various data.

  Here, the contents of each data will be described.

  The calculation result data is a value related to calculation conditions such as time-series data of particle positions and velocities obtained by particle behavior analysis, information on the number of particles and periodic boundary conditions. The current display time data is the time of data to be displayed on the display device. The region number data to be displayed is region number data indicating from what number to what region to display when the periodic boundary region stored in the calculation result data is defined as 0th. The periodic boundary mapping data is data representing the periodic boundary conditions used in the calculation. In the case of a rectangular coordinate system, the periodic boundary mapping data has the same direction as the normal of the periodic boundary surface and a size equal to the distance between the two periodic boundary surfaces. Defined as having a periodic boundary vector. The display particle data is a particle number for identifying a particle to be displayed, coordinate data representing a position in a display region, or the like. The display structure data is data such as a structure number for identifying the structure to be displayed, and coordinates, vectors, and angles of points, which are geometric information of the structure.

  Here, the region number data to be displayed will be described using a specific example. For example, the first area represents the first area in the direction of the periodic boundary vector, counting from the 0th area (periodic boundary area stored in the calculation result data). Further, the −1st region represents the first region in the direction opposite to the periodic boundary vector.

FIG. 3 is a flowchart showing a processing procedure in the periodic boundary condition setting unit 101 and the particle behavior display unit 102 shown in FIG. With reference to the particle behavior analysis result display device shown in FIG. 2, the procedure for setting the periodic boundary condition and the particle behavior display will be described.
(1) First, the periodic boundary condition setting unit 101 sets a periodic boundary vector and stores it in the periodic boundary mapping data storage unit 201e (step S301). This is defined as a periodic boundary vector obtained based on the periodic boundary condition data stored in the calculation result data 201b.
(2) Next, the minimum value Nmin and the maximum value Nmax of the area number to be displayed are set and stored in the area number data storage unit 201d to be displayed (step S302).
(3) Next, in the particle behavior display unit 102, a display time is set and stored in the current display time data storage unit 201c (step S303).
(4) Next, the area number n to be displayed is counted and stored in the area number data storage unit 201d to be displayed (step S304). In the first count, the minimum value NNmin of the area number to be displayed is set.
(5) Next, the particle number m is counted (step S305) and stored in the display particle data storage unit 201f. Further, the coordinates of the particle m in the region n are obtained by the equation (1) and stored in the display particle data storage unit 201f (step S306).

Coordinate of region n = coordinate of region 0 + n × periodic boundary vector (1)
Here, the coordinates of the region 0 are coordinates obtained by the particle behavior calculation, and are stored in the calculation result data storage unit 201b.
(6) Next, a particle display is created using the particle coordinates obtained in (5) (step S307).
(7) By performing the processes (5) to (6) for all the particles (step S308), the display creation of all the particles is completed.
(8) Next, the structure number k is counted and stored in the display structure data storage unit 201g (step S309). Further, the coordinates of the structure k in the region n are obtained by the equation (1) and stored in the display structure data storage unit 201g together with data such as vector values representing the structure (step S310). Here, the coordinates of the display structure represent coordinates such as points constituting the structure.
(9) Next, a structure display is created using the structure data obtained in (8) (step S311).
(10) By performing the processes (8) to (9) for all the structures (step S312), the display creation of all the structures is completed.
(11) By performing the processes (4) to (10) for all the set region numbers n (Nmin ≦ n ≦ Nmax) (step S313), the display for the set all-cycle boundary region is completed. To do.

  The feature of this embodiment is that not only particles in the periodic boundary region used in the calculation but also particles in the preceding and following regions can be displayed by connecting and displaying an arbitrary number of periodic boundary regions. It is possible to visually represent the overall behavior of the system and the movement of particles near the periodic boundary surface. This will be described with reference to FIG. 4 which is an example in which the method of this embodiment is applied to the analysis result of FIG. 15B shown in the conventional example.

  FIG. 4 is a display example in which the present embodiment is applied to the display of the behavior of a large number of particles shown in FIG. 15B, and shows the display result when the first to first areas are set. . Here, (a) shows the result after t0 seconds, (b) shows the result after t1 seconds, and (c) shows the result after t2 seconds. Note that 401, 402, 406, and 407 represent periodic boundary surfaces, and 408 represents a periodic boundary vector B. Further, 403a, 403b, and 403c represent particles, 404a, 404b, and 404c and 405a, 405b, and 405c represent members. Each of the second areas is shown.

  As can be seen from FIG. 4A, by displaying the particles and the structure by connecting the periodic boundary regions for three periods, not only the behavior of the particles in the periodic boundary regions cut out by calculation, but also before cutting out. It is possible to display the behavior of the entire system and the behavior of particles near the periodic boundary surface. Furthermore, as can be seen from FIGS. 4A to 4C, it is possible to display a process in which the behavior of the particles of the entire system changes with time.

  In addition, since the number of region displays can be set arbitrarily, for example, display with a system size corresponding to an actual phenomenon is possible regardless of the size of the periodic boundary surface set at the time of particle behavior calculation. As a result, it is possible to display in a size and shape more suitable for the actual system.

  As described above, by using the method of the present embodiment, it is possible to display the entire system corresponding to the actual phenomenon regardless of the size of the periodic boundary region set by the calculation, and as a result, the phenomenon can be visualized. Easier to grasp. Further, by continuously displaying FIGS. 4A to 4C, the behavior of the particles can be displayed in an animated manner, so that the velocity and direction of the particles can be evaluated.

  In the above description, the display of the two-dimensional analysis has been described, but the present invention can also be applied to the display of the three-dimensional analysis result.

  In the above description, the case where the periodic boundary condition is added to one axis of the rectangular coordinate system has been described. However, the periodic boundary condition for two or three axes, and the periodic boundary for the circumferential direction of the cylindrical coordinate system. The method of the present embodiment can also be applied to conditions.

  Here, an example in which the method of the present embodiment is applied to the periodic boundary conditions of two axes and the cylindrical coordinate system will be described with reference to FIG.

  FIG. 16A shows a case where a periodic boundary condition is added to two axes of a rectangular coordinate system, and shows results of three regions in the horizontal direction and two regions in the vertical direction. Here, 1601 represents a periodic boundary surface in the horizontal direction in the figure, and 1602 represents a periodic boundary surface in the vertical direction.

  At this time, the coordinates of the particles and members can be obtained using Equation (2).

Coordinates of vertical region nt and horizontal region ny = coordinate of region 0 + nt × vertical periodic boundary vector + ny × horizontal periodic boundary vector (2)
FIG. 16B shows a case in which a periodic boundary condition is added in the circumferential direction of the cylindrical coordinate system, and a case in which three periods are displayed with respect to the result of performing the particle behavior calculation by cutting out the region of the angle θ in the circumferential direction. Is shown. Here, 1603 and 1604 represent periodic boundary surfaces, and 1605 represents central coordinates in the periodic boundary conditions. Although not shown in the figure, it is assumed that a rotation vector perpendicular to the drawing is defined. At this time, the coordinates of the particles and members can be obtained by using the transfer image based on the rotation center coordinates, the rotation vector, the region number n, and the rotation angle θ.

  For example, in the figure, an x axis is taken in the horizontal direction, a y axis is taken in the vertical direction, a z axis is taken in the direction perpendicular to the figure, and a rotation vector parallel to the z axis is assumed. Further, assuming that the particle coordinates (x0, y0), the rotation center coordinates (X, Y), and the rotation angle θ of the region 0, the particle coordinates (x, y) in the region number n can be expressed by Expression (3). it can.

... (3)
Hereinafter, as one specific application example of the present embodiment, a case where the method of the present embodiment is applied to developer behavior analysis in an electrophotographic apparatus will be described.

  FIG. 14 is a diagram illustrating a part of an image forming apparatus in an electrophotographic apparatus. In the figure, 1401 is a photosensitive drum, 1402 is a developing device, 1403 is a transfer member, 1404 is a cleaning device, 1405 is a charging member, and 1406 is a developing hopper.

  The developing hopper 1406 is equipped with a developing sleeve 1407 for transporting toner, which is a developer, to the photosensitive drum 1401, and the toner is transported when the developing sleeve 1407 rotates. Since the developing device 1402 can assume a symmetry with respect to the longitudinal direction in the vicinity of the center portion, calculation using a periodic boundary condition is used. By applying the method of this embodiment to this calculation result, it is possible to display the result according to the actual size of the developing device 1402 regardless of the size of the periodic boundary region, and the toner transport state in the developing device 1402 Can be visually displayed and evaluated. The present embodiment can also be applied to the display of calculation results of toner agitation and conveyance states in the development hopper 1406, the cleaning device 1404, and the like.

(Second Embodiment)
In the first embodiment, by connecting and displaying the periodic boundary regions used in the calculation, the behavior of the particles in the entire system corresponding to the actual phenomenon can be obtained regardless of the size of the periodic boundary region set in the calculation. Can be displayed. However, in the first embodiment, since it is difficult to identify each particle, it is difficult to visually confirm whether or not the particle has passed through the periodic boundary surface when focusing on one particle. Also, it is difficult to visually grasp how far each particle has been transported.

  The second embodiment is for solving such a problem, and it is possible to determine whether or not each particle has passed the periodic boundary surface based on the position data of each particle. And Based on the determination result, the coordinates of the particles at each time are obtained, and the particles are displayed so that each particle passes through the periodic boundary surface and how one particle behaves. It is characterized in that it can be displayed.

  FIG. 5 shows the configuration of the processing program of the second embodiment. In the figure, reference numerals 100 to 102 are the same as those in FIG.

  Reference numeral 501 denotes a calculation unit for periodic boundary surface passage information, which creates a periodic boundary passage number table indicating how many times each particle has passed the periodic boundary surface at each time.

  Hereinafter, the periodic boundary surface passage information calculation unit 501 and the particle behavior display unit 102 which are features of the present embodiment will be described in detail with reference to FIGS.

  FIG. 6 is a block diagram showing a configuration of a particle behavior analysis result display device according to the second exemplary embodiment of the present invention. Compared to FIG. 2 showing the configuration according to the first embodiment, the periodic boundary passage number table storage unit 601, the time data storage unit 602 at the time of passage determination, the particle displacement vector data storage unit 603, and the display particle An attribute data storage unit 604 is added.

  Here, the periodic boundary passage frequency table is a table storing how many times each particle has passed through the periodic boundary surface at each time. The time data at the time of passage determination is a value indicating the time of passage determination. The particle displacement vector data storage unit is a displacement vector representing the displacement of the particle from one step before. The display particle attribute data is attribute data such as colors and marks (symbols) defined for each particle to be displayed in order to make the behavior of particles easy to understand. For example, the color corresponding to each periodic boundary region is determined. Then, the color of the periodic boundary region existing at the calculation start time is defined as the particle color. Reference numerals 200 to 205 and 201a to 201g in the RAM 201 are the same as those in FIG.

FIG. 7 is a flowchart showing a processing procedure in the periodic boundary surface passage information calculation unit 501 shown in FIG. A processing procedure for calculating periodic boundary surface passage information will be described with reference to the particle behavior analysis result display device shown in FIG.
(1) First, a periodic boundary vector is set and stored in the periodic boundary mapping data storage unit 201e (step S301). This is defined using the periodic boundary condition data stored in the calculation result data storage unit 201b.
(2) Next, 0 is stored in all the tables of the periodic boundary passage count table storage unit 601 (step S701).
(3) Next, the time is set as the calculation start time (step S702).
(4) Next, the time i is counted and stored in the time data storage unit 602 at the time of passage determination (step S703).
(5) Next, the particle number m is counted (step S305) and stored in the display particle data storage unit 201f.
(6) Next, the displacement vector U of the particle m is obtained based on the coordinate of the particle m at the time i and the coordinate of the time i−1, and stored in the particle displacement vector data storage unit 603 (step S704). . (7) Next, based on the displacement vector U of the particle m obtained in (6) and the periodic boundary vector B, it is determined whether or not the particle m has passed the periodic boundary surface, and an increase / decrease value of the number of passages is obtained. (Step S705). The passage number increase / decrease value is a value indicating which of two periodic boundary surfaces has passed, and is +1 for a periodic boundary surface in the same direction as the periodic boundary vector, and -1 for a periodic boundary surface in the opposite direction. If it has not passed, 0 is set.

Then, the value obtained by adding the passage number increase / decrease value and the periodic boundary passage number at time i-1 is set as the periodic boundary passage number at time i, and stored in the periodic boundary passage number table storage unit 601 (step S706).
(8) By performing the processes of (5) to (7) for all particles (step S308), a periodic boundary passage number table of all particles at time i is created.
(9) By performing the processes of (4) to (8) for all times of particle behavior calculation (step S707), the periodic boundary passage frequency table of all particles at all times is completed.

  Here, a periodic boundary surface passage determination method, which is a feature of the present embodiment, will be described.

  As a basic idea in determination, it is considered that the moving distance of particles within one step time is sufficiently smaller than the size of the periodic boundary region, and the moving distance in the direction of the periodic boundary vector is 1 / of the distance between the two periodic boundary surfaces. If it is greater than 2, it is determined that the particle has flowed from the adjacent periodic boundary region. Specifically, the determination is made using Expression (4). The left side of Equation (4) represents the movement distance in the direction of the periodic boundary vector within one step time, and the right side represents 1/2 of the distance between the two periodic boundary surfaces.

... (4)
Further, in determining which periodic boundary region has flowed in, it is assumed that the flow has flowed from a periodic boundary region in the direction opposite to the movement vector based on the particle movement vector within one step time. Specifically, when the periodic boundary vector B and the displacement vector U are oriented in the same direction (B · U> 0: where B and U represent vectors), the particle is in the opposite direction to the periodic boundary vector. , It is assumed that the particles flow in from the periodic boundary region in the direction of the periodic boundary vector when facing in the opposite direction (B · U <0).

  A specific example of the determination method will be described in detail with reference to FIG.

  FIGS. 8A and 8B are diagrams for explaining pass determination of the periodic boundary surface. FIG. 8A shows a case where the periodic boundary surface 402 is passed. FIG. 8B shows a case where the periodic boundary surface 401 is passed. Indicates a case where neither periodic boundary surface passes. Here, 401 and 402 indicate periodic boundary surfaces, and 408 indicates a periodic boundary vector B. 801a, 802a, and 803a represent particles at time i-1, 801b, 802b, and 803b represent particles at time i, and 801c, 802c, and 803c represent displacement vectors U, respectively.

  In FIG. 8A, since the equation (4) is satisfied (the moving distance of the particles is larger than ½ of the distance of the periodic boundary surface), it is determined that the particles have passed the periodic boundary surface. Since the periodic boundary vector B and the displacement vector U are in opposite directions (B · U <0), it is determined that the particle has passed through the periodic boundary surface 402 in the same direction of the periodic boundary vector.

  In FIG. 8B, since the expression (4) is satisfied (the moving distance of the particles is larger than half of the distance of the periodic boundary surface), it is determined that the particles have passed the periodic boundary surface. Since the periodic boundary vector B and the displacement vector U are directed in the same direction (B · U> 0), it is determined that the particle has passed through the periodic boundary surface 401 in the direction opposite to the periodic boundary vector.

  In FIG.8 (c), since Formula (4) is not satisfy | filled (the moving distance of particle | grains is smaller than 1/2 of the distance of a periodic boundary surface), it determines with a particle | grain moving within the periodic boundary area | region.

  Next, the periodic boundary passage count table will be described with reference to FIG. FIG. 9 shows a table from time 0 seconds to 3 Δt seconds for particles of particle numbers 1 and 2.

  As a way of looking at this table, it shows which number of the periodic boundary region the particles in the zeroth periodic boundary region at the time 0 second were in at each time. Further, a positive integer represents a periodic boundary region in the direction of the periodic boundary vector, and a negative number represents a periodic boundary region in the direction opposite to the periodic boundary vector. This value can be obtained by adding the number of passes through which periodic boundary surface, and when passing through the periodic boundary surface in the same direction as the periodic boundary vector, +1 is added to the periodic boundary surface in the opposite direction. When passing through the plane, it is the result of adding -1 in each time.

  According to FIG. 9, the particle 1 passes through the periodic boundary surface (402 in FIG. 8) in the same direction as the periodic boundary vector at time Δt seconds, and again passes through the periodic boundary surface in the same direction at time 3Δt seconds. Recognize. Further, after passing through the periodic boundary surface (402 in FIG. 8) in the same direction as the periodic boundary vector at time 2Δt seconds, the particle 2 passes through the opposite periodic boundary surface (401 in FIG. 8) at time 3Δt seconds. I understand that.

Next, the processing procedure for displaying the particle behavior using the periodic boundary surface passage information will be described with reference to the flowchart shown in FIG.
(1) The minimum value Nmin and the maximum value Nmax of the area number to be displayed are set and stored in the area number data storage unit 201d to be displayed (step S302).
(2) Next, the attribute data of the particles to be displayed are set and stored in the particle attribute data storage unit 604 (step S1001). The display particle attribute data is attribute data such as a color or a mark (symbol) defined for each particle to be displayed. Here, a color corresponding to a periodic boundary region existing at the calculation start time is defined as a particle color.
(3) Next, the display time is set and stored in the current display time data storage unit 201c (step S303).
(4) Next, the area number n to be displayed is counted and stored in the area number data storage unit 201d to be displayed (step S304). In the first count, the minimum value Nmin of the area numbers to be displayed is used.
(5) Next, the particle number m is counted (step S305) and stored in the display particle data storage unit 201f. Further, the coordinates of the particle m in the region n are obtained by the equation (1) and stored in the display particle data storage unit 201f (step S306).
(6) Next, based on the periodic boundary passage frequency table 601, the periodic boundary region where the particle m in the region number n was at the calculation start time is obtained and stored in the display particle data storage unit 201 f (step) S1002).

The number of the periodic boundary region at which the particle m was at the calculation start time can be obtained as a value n−α obtained by subtracting the periodic boundary passage number α of the particle m at the time i from the region number n to be displayed.
(7) Next, a particle display is created using the particle display attribute data of the particle m, the number of the periodic boundary region at the calculation start time, and the coordinates of the particle m (step S1003).
(8) By performing the processes (5) to (7) on all particles (step S308), the display creation of all particles is completed.
(9) Next, the structure number k is counted and stored in the display structure data storage unit 201g (step S309). Further, the coordinates of the structure k in the region n are obtained by the equation (1) and stored in the display structure data storage unit 201g together with data such as vector values representing the structure (step S310). Here, the coordinates of the display structure represent coordinates such as points constituting the structure.
(10) Next, a display of the structure is created using the structure data obtained in (9) (step S311).
(11) By performing the processes (9) to (10) for all the structures (step S312), the display creation of all the structures is completed.
(12) By performing the processing of (4) to (11) for all the set region numbers n (Nmin ≦ n ≦ Nmax) (step S313), the display for the set full cycle boundary region is completed. To do.

  The feature of this embodiment is to determine which periodic boundary surface each particle has passed using the displacement vector U of each particle, and which periodic boundary region each particle is in at each time based on the result. Can be easily obtained. And by using the information, it is possible to express how each particle is transported through the periodic boundary region. This will be described with reference to FIG. 11 which is an example in which the present embodiment is applied to the analysis result of FIG. 4 shown in the first embodiment.

  FIG. 11 is a display example in which the present embodiment is applied to the particle behavior display shown in FIG. 4, and shows a display result when the first to first regions are set. Here, (a) shows the result after t0 seconds as the calculation start time, (b) shows the result after t1 seconds, and (c) shows the result after t2 seconds. In addition, 1101 is a particle in the 0th region at t0 seconds, 1102 is a particle in the -1st region, 1103 is a particle in the 1st region, 1104 is a particle in the -2nd cycle. Represents. Note that 401, 402, 406, 407, 408, 404a to 404c, and 405a to 405c are the same as those in FIG.

  As can be seen from FIG. 4, it is possible to grasp how particles that were in each region at the calculation start time t0 seconds are transported from the left to the right of the drawing with time. Further, by displaying the particles and the structure by connecting the periodic boundary regions for three periods, it is possible to grasp not only the behavior of the particles in the periodic boundary region cut out by calculation but also the behavior in the entire system.

  As described above, by using the method of this embodiment, it is possible to display how each particle is transported when moving in the periodic boundary region. Further, by continuously displaying FIGS. 11A to 11C, the behavior of the particles can be displayed in an animated manner, so that the velocity and direction of the particles can be evaluated.

  In the above description, the display of the two-dimensional analysis has been described, but the present invention can also be applied to the display of the three-dimensional analysis result.

  In the above description, the result display of the particle behavior analysis when a periodic boundary condition is added to one axis of the rectangular coordinate system has been described. However, the periodic boundary condition for two or three axes, the cylindrical coordinate system This method can also be applied to periodic boundary conditions in the circumferential direction.

  In particular, when this method is applied to a cylindrical coordinate system, the passage of the periodic boundary surface is determined based on the movement angle of the particles within one step time instead of the displacement vectors 801c to 803c in FIG. Specifically, when the absolute value of the movement angle is larger than ½ of the rotation angle θ of the periodic boundary, it is assumed that the particles have flowed from the adjacent periodic boundary region through the periodic boundary surface. Moreover, what is necessary is just to determine using the rotation angle direction in determination of which periodic boundary area | region flowed in. Specifically, it is assumed that the fluid flows from the periodic boundary region in the direction opposite to the rotation angle direction.

  Note that by applying the method of the present embodiment to the display of the structure, it is possible to grasp the movement of the structure in the entire system corresponding to the actual phenomenon. In particular, in the calculation in the case where the position of the structure changes due to the interaction with the particle, the movement of the particle and the movement of the structure can be displayed together.

(Third embodiment)
In the third embodiment, a case will be described in which the behavior of the focused particle is displayed using the periodic boundary passage count table calculated in the second embodiment.

  The block diagram showing the configuration of the processing program of the third embodiment and the configuration of the particle behavior analysis result display device is the same as the configuration shown in the second embodiment, so the description is omitted here.

Below, the processing procedure of the display of the particle behavior using the periodic boundary surface passage information when this embodiment is used will be described using the flowchart shown in FIG.
(1) The minimum value Nmin and the maximum value Nmax of the area number to be displayed are set and stored in the area number data storage unit 201d to be displayed (step S302).
(2) Next, the display time is set and stored in the current display time data storage unit 201c (step S303).
(3) Next, the particle number m is counted (step S305) and stored in the display particle data storage unit 201f.
(4) Next, based on the periodic boundary passage count table 601, which periodic boundary region the particle m is at time i is obtained (step S 1201), and is obtained using equation (1) based on the region number. The coordinates of the particles m to be stored are stored in the display particle data storage unit 201f (step S1202).
(5) Next, a particle display is created using the particle coordinates obtained in (4) (step S307).
(7) By performing the processes (3) to (5) for all the particles (step S308), the display creation of all the particles is completed.
(8) Next, the area number n to be displayed is counted and stored in the area number data storage unit 201d to be displayed (step S304). In the first count, the minimum value Nmin of the area numbers to be displayed is used.
(9) Next, the structure number k is counted and stored in the display structure data storage unit 201g (step S309). Further, the coordinates of the structure k in the region n are obtained by the equation (1) and stored in the display structure data storage unit 201g together with data such as vector values representing the structure (step S310).
(10) Next, a display of the structure is created using the structure data obtained in (9) (step S311).
(11) By performing the processes (9) to (10) for all the structures (step S312), the display creation of all the structures is completed.
(12) By performing the processes (8) to (11) for all the set region numbers n (Nmin ≦ n ≦ Nmax) (step S313), the display for the set all-cycle boundary region is completed. To do.

  The feature of this embodiment is that the position coordinates of the particles at each time can be easily obtained based on the periodic boundary passage count table. This will be described with reference to FIG. 13 which is an example in which the present embodiment is applied to the analysis result of FIG. 15A shown in the conventional example.

  FIG. 13 is a display example of the particle behavior of one particle shown in FIG. 15 (a). (A) shows the result after t0 seconds, (b) shows the result after t1 seconds, and (c) shows t2. The result after 2 seconds is shown. Reference numeral 1301 denotes particles at t0 seconds. Note that 401 and 402 are the same as those in FIG. As can be seen from FIG. 13, it is possible to display a phenomenon in which the particles 1301 pass through the periodic boundary surface 402 and flow into the adjacent periodic boundary region.

  As described above, by using this embodiment, even when a particle moves between periodic boundary regions, it is possible to display and evaluate a trajectory at which one particle of interest moves at each time. Is possible. Further, by continuously displaying the three displays of FIGS. 13 (a) to 13 (c), the behavior of the particles can be displayed in an animated manner, so that the speed and direction of the particles can be evaluated.

  Moreover, it is also possible to obtain | require the movement distance of each particle | grain using Formula (5).

Movement distance = Σ | coordinates of particles at time i−coordinates of particles at time i−1 | (5)
Here, the coordinates of the particles at time i and time i-1 are obtained by equation (1).

  In the above description, the display of the two-dimensional analysis has been described, but the present invention can also be applied to the display of the three-dimensional analysis result.

  In the above description, the result display of the particle behavior analysis when a periodic boundary condition is added to one axis of a rectangular coordinate system has been described. This method can also be applied to periodic boundary conditions in the circumferential direction.

  Note that the locus of the structure can be grasped by applying the method of the present embodiment to the display of the structure. In particular, in the calculation when the position of the structure changes due to the interaction with the particles, the movement of the structure can be visually grasped.

(Other embodiments)
An object of the present invention is to supply a storage medium storing software program codes for realizing the functions of the embodiments to the system or apparatus, and the computer of the system or apparatus (or CPU, MPU, etc.) stores it. It is also achieved by reading and executing the program code stored on the medium.

  In this case, the program code itself read from the storage medium realizes the functions of the above-described embodiments, and the storage medium storing the program code constitutes the present invention.

  Examples of the storage medium for supplying the program code include a floppy (registered trademark) disk, a hard disk, a magneto-optical disk, a CD-ROM, a CD-R, a CD-RW, a DVD-ROM, a DVD-RAM, and a DVD. -RW, DVD-R, magnetic tape, nonvolatile memory card, ROM, etc. can be used.

  Further, by executing the program code read by the computer, not only the functions of the above embodiments are realized, but also an OS (operating system) running on the computer based on the instruction of the program code Includes a case where the function of the above-described embodiment is realized by performing part or all of the actual processing.

  Further, after the program code read from the storage medium is written in a memory provided in a function expansion board inserted into the computer or a function expansion unit connected to the computer, the function expansion is performed based on the instruction of the program code. This includes the case where the CPU or the like provided in the board or function expansion unit performs part or all of the actual processing, and the functions of the above-described embodiments are realized by the processing.

  As described above in detail, according to the above-described embodiment, the movement of particles flowing into the adjacent region through the periodic boundary surface, the positional relationship of the particles near the periodic boundary surface, and the entire region before cutting out The behavior of the particles can be displayed, and as a result, the calculation result can be easily grasped visually.

  Also, when moving in a periodic boundary region, such as in a system where particles are transported in a direction perpendicular to the periodic boundary surface, how much distance each particle travels at each time is transported. Can be displayed and evaluated.

  Moreover, since the behavior of particles can be displayed in an animated manner by continuously displaying the particles, the velocity and direction of the particles can be evaluated.

  In addition, by applying the above embodiment to the developer behavior analysis of an electrophotographic apparatus, the actual developer dimensions can be obtained even when calculated using periodic boundary conditions for a longitudinally uniform system such as a developer. The display corresponding to the shape and shape can be performed, and as a result, the developer behavior can be predicted.

It is a program block diagram which shows roughly the structural example of the processing program in a particle behavior analysis result display apparatus. It is a block diagram which shows the structure of the particle behavior analysis result display apparatus which concerns on the 1st Embodiment of this invention. It is a flowchart which shows the procedure of the process which concerns on the 1st Embodiment of this invention. It is a figure which shows the example of a particle behavior display for demonstrating the particle behavior analysis result display apparatus which concerns on the 1st Embodiment of this invention. It is a program block diagram which shows schematically the structural example of the processing program in the particle behavior analysis result display apparatus which concerns on the 2nd Embodiment of this invention. It is a block diagram which shows the structure of the particle behavior analysis result display apparatus which concerns on the 2nd Embodiment of this invention. It is a flowchart which shows the procedure of a process for demonstrating the calculation part of the periodic interface passing information of the particle behavior analysis result display apparatus which concerns on the 2nd Embodiment of this invention. It is a figure which shows the example of the processing method for demonstrating the calculation part of the periodic interface passing information of the particle behavior analysis result display apparatus which concerns on the 2nd Embodiment of this invention. It is a figure which shows the example of the periodic boundary passage frequency table for demonstrating the calculation part of the periodic boundary surface passage information of the particle behavior analysis result display apparatus which concerns on the 2nd Embodiment of this invention. It is a flowchart which shows the procedure of a process for demonstrating the particle | grain display part of the particle | grain behavior analysis result display apparatus which concerns on the 2nd Embodiment of this invention. It is a figure which shows the example of a particle behavior display for demonstrating the particle behavior analysis result display apparatus which concerns on the 2nd Embodiment of this invention. It is a flowchart which shows the procedure of a process for demonstrating the particle | grain display part of the particle behavior analysis result display apparatus which concerns on the 3rd Embodiment of this invention. It is a figure which shows the example of a particle behavior display for demonstrating the particle behavior analysis result display apparatus which concerns on the 3rd Embodiment of this invention. 1 is a diagram illustrating a part of an image forming apparatus in an electrophotographic apparatus. It is explanatory drawing for demonstrating the display part of the particle | grains of the conventional process. It is a figure which shows the example of a particle behavior display for demonstrating the particle behavior analysis result display apparatus which concerns on the 1st Embodiment of this invention.

Explanation of symbols

100 control unit 200 CPU
201 RAM
202 Display device 203 Input unit 204 External storage device 205 Bus

Claims (3)

A particle behavior calculation result display method for analyzing particle behavior by calculation and displaying it on a display device,
This selects a portion of the area for displaying the particles as periodic boundary region, the steps of the control unit sets the periodic boundary condition,
A step of control unit a plurality of areas is set for coupling with the periodic boundary region,
It said plurality of regions, the steps of the control unit the number based on the periodic boundary regions confer,
The control unit obtains the number of times the particles have passed through the boundary of the region from the coordinates of the particles moving in the periodic boundary region stored in the calculation result data storage unit, and the number of periodic boundary passages calculated based on the number of times was stored in the periodic boundary passing number table on the basis of the counted area number n based on the periodic boundary passing times, the one of the plurality of areas, tables Shimesuru so the particles in the region corresponding to the region number n A step of controlling the display device ;
A particle behavior calculation result display method comprising: The program for making a computer perform each process of Claim 1. Computer readable storage medium storing a program of claim 2.

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