JP2008040673A - Atomic arrangement simulation method, atomic arrangement simulation apparatus, atomic arrangement simulation program and recording medium recoeded with same program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To appropriately arrange atoms in a preset shape. <P>SOLUTION: The atomic arrangement simulation method for performing simulation for arraying atoms in a preset shape comprises: a temporary arrangement step of temporarily arranging the atoms in the shape; an annealing step of annealing the atoms arranged by the temporary arrangement step on the basis of potentials between the atoms; and a coarseness and minuteness adjustment step of adjusting the coarseness and minuteness relation of the atoms annealed by the annealing step. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to an atom arrangement simulation method, an atom arrangement simulation apparatus, an atom arrangement simulation program, and a recording medium on which the program is recorded, and in particular, an atom arrangement simulation method for appropriately arranging atoms in a preset shape, The present invention relates to an atomic arrangement simulation device, an atomic arrangement simulation program, and a recording medium on which the program is recorded.

  Conventionally, molecular simulation is known as a methodology for exploring phenomena in general material science using computers based on classical mechanics, quantum mechanics, and the like. Molecular simulation can elucidate the properties of a substance at the molecular level, such as the potential energy and the most stable structure of the molecule.

Here, the molecular simulation is mainly used for prediction of physical properties of a material, and is not used as a technique for arranging atoms in a complicated shape, for example. Therefore, conventionally, a finite element method or the like is used in which a complicated shape of an object is divided into finite regions, modeled, and calculated. In this method, a mesh generation program or the like is used to uniformly divide an object by a triangular or quadrangular region in the case of two-dimensional calculation (see, for example, Patent Document 1).
JP 2001-67495 A

  However, when the mesh generation method shown in Patent Document 1 described above is applied to, for example, atomic arrangement in molecular dynamics, when only triangular elements are used, the object region is filled with triangles. The length is not constant and often differs. Also, depending on the shape of the arrangement of atoms, the triangle may be very distorted. Therefore, simply arranging atoms at mesh lattice points results in a non-physical state such that the distance between atoms varies depending on the direction (the atoms have anisotropy).

  The present invention has been made in view of the above-described problems, and an atomic arrangement simulation method, an atomic arrangement simulation apparatus, an atomic arrangement simulation program, and the program for appropriately arranging atoms in a preset shape are recorded. An object of the present invention is to provide a recording medium.

  In order to achieve the above-described object, the present invention provides an atomic arrangement simulation method for performing a simulation for arranging atoms in a preset shape, and a temporary arrangement step of temporarily arranging atoms in the shape; An annealing step for annealing the atoms arranged by the step based on an interatomic potential, and a density adjustment step for adjusting a density relationship of the atoms annealed by the annealing step. Thereby, atoms can be appropriately arranged in a preset shape.

  Further, the provisional arrangement step generates a large number of meshes in the shape and arranges atoms at each lattice point of the generated mesh, or arranges atoms in the frame of the shape and then arranges atoms in the shape. It is preferable to arrange atoms by generating and filling. This makes it possible to place atoms temporarily by using a method of generating meshes and placing atoms, or by first placing atoms in a shape frame and then generating and placing atoms inside the shape. Depending on the method, the method can be changed and temporarily arranged.

  Furthermore, the annealing step is preferably performed by adjusting the temperature in the vicinity of the melting point of the material forming the shape by molecular dynamics. Thereby, atoms can be appropriately arranged in a preset shape while adjusting the energy of the atoms to be in a minimum state.

  Further, the present invention provides an atomic arrangement simulation apparatus for performing a simulation for arranging atoms in a preset shape, temporary arrangement means for temporarily arranging atoms in the shape, and atoms arranged by the temporary arrangement means as atoms. An annealing means for annealing based on the inter-potential and a density adjusting means for adjusting the density relation of atoms annealed by the annealing means. Thereby, atoms can be appropriately arranged in a preset shape.

  Further, the temporary arrangement means generates a large number of meshes in the shape and arranges atoms at each lattice point of the generated mesh, or arranges atoms in the frame of the shape and then arranges atoms in the shape. It is preferable to arrange atoms by generating and filling. This makes it possible to place atoms temporarily by using a method of generating meshes and placing atoms, or by first placing atoms in a shape frame and then generating and placing atoms inside the shape. Depending on the method, the method can be changed and temporarily arranged.

  Furthermore, it is preferable that the annealing means performs annealing by adjusting the temperature in the vicinity of the melting point of the material forming the shape by molecular dynamics. Thereby, atoms can be appropriately arranged in a preset shape while adjusting the energy of the atoms to be in a minimum state.

  Further, the present invention provides an atomic arrangement simulation program for performing, on a computer, an atomic arrangement simulation process for performing a simulation for arranging atoms in a preset shape, a temporary arrangement process for temporarily arranging atoms in the shape, An annealing process for annealing atoms arranged by the temporary arrangement process based on an interatomic potential and a density adjustment process for adjusting a density relationship between atoms annealed by the annealing process are executed by a computer. Thereby, atoms can be appropriately arranged in a preset shape. Further, by installing the execution program in the computer, the atomic arrangement simulation process can be easily realized.

  Further, the provisional arrangement process generates a large number of meshes in the shape and arranges atoms at each lattice point of the generated mesh, or arranges atoms in the shape frame and then arranges atoms in the shape. It is preferable to arrange atoms by generating and filling. This makes it possible to place atoms temporarily by using a method of generating meshes and placing atoms, or by first placing atoms in a shape frame and then generating and placing atoms inside the shape. Depending on the method, the method can be changed and temporarily arranged.

  Furthermore, the annealing treatment is preferably performed by adjusting the temperature in the vicinity of the melting point of the material forming the shape by a molecular dynamics method. Thereby, atoms can be appropriately arranged in a preset shape while adjusting the energy of the atoms to be in a minimum state.

  The present invention also provides a computer-readable recording medium in which the atomic configuration simulation program according to any one of claims 7 to 9 is recorded. Thus, the atomic arrangement simulation program can be easily installed on the plurality of other computers by the recording medium.

  According to the present invention, atoms can be appropriately arranged in a preset shape.

<Outline of the present invention>
In the present invention, for example, when atoms are arranged in a preset shape, the atoms are not optimally selected based on the interatomic potential after the atoms are appropriately arranged, instead of selecting and arranging the optimal position from the beginning. To move to a stable point. As a calculation method at this time, for example, a molecular dynamics method can be used. However, the present invention is not limited to this. For example, a method for searching for a stable point of the potential, such as a Monte Carlo method, may be used. Good.

  The molecular dynamics method (MD method) is a static and dynamic stable structure of a system by solving Newton's equations in classical mechanics under two (or more) interatomic potentials. It is also a method for analyzing dynamic processes. Molecular dynamics enables the calculation of various ensembles (statistical groups) such as constant temperature, constant pressure, constant energy, constant product, and constant chemical potential. It is also possible to add various constraint conditions such as coupling length and position fixing.

  Hereinafter, embodiments in which an atom arrangement simulation method, an atom arrangement simulation apparatus, an atom arrangement simulation program, and a recording medium storing the program according to the present invention are suitably implemented will be described with reference to the drawings.

<Apparatus configuration in the present embodiment>
First, an atomic arrangement simulation apparatus according to this embodiment will be described with reference to the drawings. FIG. 1 is a diagram illustrating an example of a hardware configuration of an atomic arrangement simulation apparatus according to the present embodiment.

  1 includes an input device 11, an output device 12, a drive device 13, an auxiliary storage device 14, a memory device 15, a CPU (Central Processing Unit) 16 that performs various controls, and a network. And a connection device 17, which are connected to each other via a system bus B.

  The input device 11 has a pointing device such as a keyboard and a mouse operated by a user, and inputs various operation signals such as execution of a program from the user. The output device 12 has a display for displaying various windows and data necessary for operating the computer main body for performing the processing in the present invention. Can be displayed.

  Here, in the present invention, the execution program installed in the computer main body is provided by the recording medium 18 such as a CD-ROM. The recording medium 18 on which the program is recorded can be set in the drive device 13, and the execution program included in the recording medium 18 is installed from the recording medium 18 to the auxiliary storage device 14 via the drive device 13.

  The auxiliary storage device 14 is a storage means such as a hard disk, and accumulates an execution program according to the present invention, a control program provided in a computer, input data and processing results necessary for an atomic arrangement simulation according to the present invention, and further necessary. I / O can be performed according to

  The memory device 15 stores an execution program read from the auxiliary storage device 14 by the CPU 16. The memory device 15 includes a ROM (Read Only Memory), a RAM (Random Access Memory), and the like.

  Based on a control program such as an OS (Operating System) and an execution program read and stored by the memory device 15, the CPU 16 performs various operations and inputs / outputs data to / from each hardware component. Each process can be realized by controlling the process. Further, the CPU 16 can acquire various types of information necessary during execution of the program from the auxiliary storage device 14, and can store processing results and the like in the auxiliary storage device 14.

  The network connection device 17 acquires an execution program from another terminal connected to the communication network by connecting to a communication network or the like, or an execution result obtained by executing the program or an execution in the present invention The program itself can be provided to other terminals.

<Atom configuration simulation device: functional configuration example>
Next, a functional configuration example of the atomic arrangement simulation device 10 will be described with reference to the drawings. FIG. 2 is a diagram illustrating an example of a functional configuration of the atomic arrangement simulation apparatus. The atomic arrangement simulation apparatus 10 includes an input means 21, an output means 22, a storage means 23, a temporary arrangement means 24, an annealing means 25, a density adjustment means 26, a screen generation means 27, a transmission / reception means 28, And a control means 29.

  The input unit 21 receives input of each instruction information and the like accompanying the execution of the atomic arrangement simulation from the user or the like. Note that the input unit 21 includes, for example, a keyboard, a pointing device such as a mouse, a voice input interface such as a microphone, and the like.

  Further, the output means 22 displays the contents of the instructions input by the input means 21, the contents of edits of the atomic configuration simulation generated based on the contents of the instructions, the contents of the edit results, etc., and outputs them by voice. Note that the output means 22 includes a display, a speaker, and the like.

  Further, the storage means 23 stores the result of the atomic arrangement simulation, the result of the temporary arrangement, the input data and the like. The storage means 23 can also acquire and store input data and the like from an external server (not shown) connected via a communication network or the like via the transmission / reception means 28.

  The temporary arrangement means 24 temporarily arranges atoms at a position applicable as a previous stage when arranging atoms at the most stable position with respect to a preset shape. In addition, when arranging atoms at appropriate positions, for example, a large number of meshes are generated in a preset shape, and atoms are arranged at each lattice point of the generated mesh, or a preset shape is used. There is a technique of arranging atoms by generating and filling atoms inside the shape after arranging atoms in the frame.

  The annealing means 25 anneals the atoms temporarily arranged by the temporary arrangement means 24 based on the interatomic potential. In the above-described annealing, for example, molecular dynamics can be used.

  The density adjusting means 26 determines whether or not the atoms arranged by the annealing means 25 are arranged uniformly between atoms within a preset shape, and adjusts the density of the atoms.

  The screen generation unit 27 displays the state of the atoms temporarily arranged in a shape preset by the temporary arrangement unit 24, the initial setting and execution result display in the annealing unit 25, and the arrangement result of the adjusted atoms in the density adjustment unit 26. Is displayed.

  The transmission / reception means 28 is a communication interface for acquiring necessary data from an external device or the like connected via a communication network such as the Internet, and for transmitting an atomic arrangement simulation result in the present invention.

  The control unit 29 controls the entire functional configuration in the atomic arrangement simulation apparatus 10. Specifically, the control means 29 causes the temporary placement means 24 to temporarily place atoms based on the input information from the user input by the input means 21, anneals by the annealing means 25, or the density adjustment means 26. To control the process of adjusting the density of atoms.

  Thereby, atoms can be appropriately arranged even for complex shapes using molecular dynamics.

<Atom configuration simulation processing example>
Next, an atomic arrangement simulation processing procedure by the execution program in the present invention will be described. FIG. 3 is a flowchart showing an example of an atomic arrangement simulation processing procedure in the present embodiment.

  As shown in FIG. 3, in the atom arrangement simulation according to the present embodiment, for example, when atoms are arranged in a complicated shape, an optimal position is not selected instead of selecting an optimal point from the beginning as described above. An atom is temporarily arranged in (S01). In addition, when placing atoms at an appropriate position, place the atoms using the mesh generation method as described above, or generate atoms inside the shape after filling them into the shape frame. There is a method of arranging atoms by doing so. Detailed description will be given later.

  In addition, after the atoms are temporarily arranged by the process of S01, annealing is performed in a state where the temperature of the system is kept in the vicinity of the melting point, such as a material for forming a shape for arranging the atoms (S02). In the process of S02, for example, annealing is performed by forcing the temperature of the entire system to be near the melting point by the scaling method using, for example, the molecular dynamics method. In addition, the annealing method using the molecular dynamics method in the process of S02 will be described later.

  After the annealing by the process of S02 is completed, it is determined whether or not there is local density in the system (S03). Here, when the density exists (NO in S03), atoms are generated in the coarse part, and the atoms in the dense part are erased, thereby adjusting the density of the system (S04). That is, by generating or erasing a predetermined number of atoms according to the density relationship between atoms, the density of the system can be relaxed and stabilized. The stable state means a state where the potential energy of the entire system is ideally the smallest.

  Thereafter, the process of S02 is performed by reflecting the arrangement contents of the atoms obtained in the process of S04. If there is no density in the system (NO in S03), the process is terminated. Thereby, for example, even for a complicated shape, atoms can be appropriately arranged using molecular dynamics or the like. Also, for example, even if the area in which atoms are arranged is complicated, it is possible to perform annealing calculation without manually correcting it, even if it is an area that would create a “distorted” mesh geometrically. By relaxing, a high quality mesh can be obtained. Further, even in non-stationary calculations that require remeshing, the mesh shape can be quickly changed by the interaction of atoms. Note that the progress and results of the above-described atomic arrangement simulation processing are generated by the screen generation means 27 and output by the output means 22 for the corresponding screen.

<S01: Temporary Arrangement Process of Atom>
Next, the temporary arrangement process of atoms in the above-described process of S01 will be specifically described. FIG. 4 is a flowchart illustrating an example of a procedure for temporarily arranging atoms.

  When placing atoms at appropriate positions, as described above, place the atoms using the mesh generation method, or place atoms in the shape frame and then generate and fill the inside of the shape. There is a method to arrange atoms. Therefore, in the processing procedure shown in FIG. 4, an example in which the two processes described above are combined will be described.

  As shown in FIG. 4, when atoms are arranged in a preset shape as a procedure for temporary arrangement of atoms in this embodiment, it is first determined whether or not to generate a mesh (S11).

  When mesh generation is performed (YES in S11), a mesh is generated within a preset shape (system) using the conventional mesh generation method described above (S12). Further, after the processing of S12 is completed, atoms are arranged at the lattice points of the generated mesh (S13), and the coordinates of the arranged atoms (for example, XY coordinates in the case of two dimensions) are generated (S14).

  In addition, in the process of S11, when mesh generation is not performed (NO in S11), atoms are arranged along a frame having a preset shape as described above (S15), and atoms are generated inside the shape. (S16).

  In addition, about the temporary arrangement | positioning process mentioned above, although the process was divided | segmented based on whether the mesh production | generation in the process of S11 is performed, it is not limited to this, For example, the magnitude | size of the atom to arrange | position, an atom It may be set according to the shape or the like to be arranged, or may be determined by providing a determination criterion other than that shown in S11.

  Here, the mesh generation in the process of S12 described above will be described. Specifically, for example, the mesh generation is based on the technique described in Patent Document 1 described above, a mesh generation method in which points are sequentially added to a two-dimensional or three-dimensional area, and Delaunay division is performed using a triangular or tetrahedral element. Can be used. Note that the above method checks whether a newly added point is included in the circumscribed circle or circumscribed sphere of an existing triangle or tetrahedral element, and an element having a circumscribed circle or circumscribed sphere including the point. And a new connection branch is generated from the new point toward the remaining outer peripheral point to form a new element.

  In addition to the methods described above, conventional typical triangular element division methods include a partial region division method, a stepwise space division method, a recursive bisection method, and a node combination method.

  The partial region division method is a method of dividing a given region into simple and easy-to-handle partial regions such as a convex region and a region without a hole, and then dividing each partial region into triangular elements. The partial area is divided by mapping a regular lattice with a mapping function or adding an internal node according to a simple rule.

  The hierarchical space division method is a method of hierarchically subdividing a two-dimensional region into a quadtree and a three-dimensional region into an octree. The recursive bisection method is a method of recursively dividing an area into two until a shape that can be used as a triangular element is obtained. Further, the node coupling method is a method in which nodes are first arranged at the boundary and inside of a region and then connected to form a mesh.

  In the processing of S12, the above-described triangular mesh generation method can be used. However, in the present invention, the method is not limited to the triangular mesh, and may be a quadrilateral mesh, for example.

  Here, FIG. 5 is a diagram illustrating an example of the atomic arrangement after mesh generation in the processes of S12 and S13. In FIG. 5, in order to clarify the generated mesh shape, the arranged atoms are extracted in a predetermined region and enlarged and displayed.

  As a result of the processing of S12 and S13 described above, a triangular mesh 30 is arranged in a region having a predetermined shape as shown in FIG. Note that atoms 31 are arranged at lattice points of the mesh. However, in the temporary arrangement using the conventional mesh generation method or the like, as shown in FIG. 5, the shape of the mesh varies depending on the location, such as the number of joints.

  Moreover, FIG. 6 is a figure which shows an example of the atomic arrangement | positioning in the process of S15 and S16. Note that FIG. 6 shows the state in which atoms are generated in a step having a complicated shape in a stepwise manner.

  In FIG. 6, as an example of a complicated shape, a central opening 41 and a peripheral opening 42 are provided inside a corrugated outer frame 40. In the example of FIG. 6, there are eight peripheral openings 42 around the central opening 41. In the present embodiment, the shape shown in FIG. 6 is a complex shape, but the present invention is not limited to this, and the present invention can be applied to an uncomplicated shape.

  At this time, in the case where atoms are arranged along a shape frame and atoms are generated inside a complicated shape, if atoms 43 are generated one after another as shown in FIG. As indicated by an arrow 44 in FIG. 6 (a), it flows downward while passing between the outer frame 40, the central opening 41, and the peripheral opening 42.

  Further, the atoms are gradually filled in the shape as shown in FIGS. 6B to 6D, and are finally temporarily arranged as shown in FIG. 6D. However, in this case as well, at the present time, as in the conventional case, the size and shape of the atoms are unevenly arranged depending on the location. Therefore, in this embodiment, annealing calculation using the molecular dynamics described above is performed. 5 and 6 described above are generated by the screen generation unit 27 and output by the output unit 22.

<S02: Annealing technique using molecular dynamics method>
Next, an annealing method using the molecular dynamics method will be specifically described. FIG. 7 is a flowchart for explaining an annealing process procedure using the molecular dynamics method in this embodiment.

  First, initial conditions to be input in the molecular dynamics method are set (S21). The initial conditions include, for example, initial coordinates of atoms, interatomic potential, temperature, pressure, etc., and at least one of them is arbitrarily selected and set. In the present embodiment, calculation (formula) and parameter setting, initial atom arrangement and temperature setting, which will be described later, are performed as initial settings.

  Next, the atomic force is calculated (S22). Specifically, based on the various conditions set in S21, ideally, a state close to the distribution expected in the thermal equilibrium state in the system is solved by solving the equations of motion of a very large number of particle systems over a long period of time. Can be realized.

  Further, by performing statistical processing on the position coordinates of the atoms obtained at this time, thermodynamic properties (internal energy, specific heat, thermal conductivity, etc.) can be acquired. In addition, by statistically processing the position coordinates and velocity of atoms at each time, dynamic properties (diffusion coefficient, viscosity coefficient, elastic constant, etc.) can be acquired. Thereby, annealing can be performed with high accuracy.

  Here, the equation of motion to be actually solved by the molecular dynamics method is Newton's equation of equation (1) shown below.

なお、上述した（１）式において、ｍ_ｉは原子の質量であり、ｘ_ｉは原子の位置座標であり、またＦ_ｉは原子ｉに働く原子間相互作用の合力である。

In the above formula (1), m _i is the mass of the atom, x _i is the position coordinate of the atom, and F _i is the resultant force of the interaction between atoms acting on the atom i.

Moreover, the resultant force F _i described above is expressed by the following equation (2).

なお、上述した（２）式において、φ_ｉｊは、原子ｉと原子ｊの間のポテンシャル関数である。

In the above equation (2), φ _ij is a potential function between atom i and atom j.

Next, in the molecular dynamics method, the position x _i (t) of the molecule i at time t is calculated by numerically integrating the above equation of motion. Here, when x _i is expanded to a quadratic term for a minute time t, it is expressed by the following equations (3) and (4).

ここで、上述した式（３）、（４）におけるｖ_ｉは分子ｉの速度である。

Here, v _i in the above formulas (3) and (4) is the velocity of the molecule i.

  Also, the following formulas (5) and (6) are derived from the sum and difference of the above formulas (3) and (4).

なお、上述した式（５）、（６）がいわゆるＶｅｒｌｅｔのアルゴリズムの標準形である。

The above-described equations (5) and (6) are standard forms of the so-called Verlet algorithm.

However, in this method, the error is large because a small term (order of square of Δt) is added to the difference between two large terms (order of Δt raised to the zeroth power) in the above formula (5). Specifically, in the molecular dynamics method, the time step Δt is generally in the order of femto (10 ⁻¹⁵ ), and the coordinate (position) x is in the order of angstrom (10 ⁻¹⁰ ). Therefore, in the right side of Equation (5) described above, the difference between the first term and the second term is on the order of 10 ⁻¹⁰ (an order smaller than Δt), but (Δt) ² of the third term is 10 ^−15. Therefore, depending on the value of F _i (t) / m _i (specifically, when the force is very small), it is expected that a digit loss will occur on the computer. Therefore, in the numerical integration method shown in the above equation (5), the accumulated error increases as the calculation time is increased. Therefore, there is a method of obtaining the speed from the following equation (7) and obtaining the position from the following equation (8).

この方法は、一般に蛙跳び法（ｌｅａｐ−ｆｒｏｇ ｍｅｔｈｏｄ）と呼ばれており、Ｖｅｒｌｅｔのアルゴリズムの一つである。なお、上述した式（７）を以下に示す式（９）とすれば、上述された式（５）が導出されることから、両者は本質的に同じであることが分かる。

This method is generally called a leap-frog method and is one of Verlet's algorithms. In addition, if Formula (7) mentioned above is made into Formula (9) shown below, since Formula (5) mentioned above will be derived | led-out, it turns out that both are essentially the same.

このように、上述した式を用いて算出された位置及び速度に基づいて、位置、速度の更新を行う（Ｓ２３、Ｓ２４）。

In this way, the position and speed are updated based on the position and speed calculated using the above-described equations (S23, S24).

Next, in this embodiment, temperature and energy are calculated (S25). Specifically, the simplest and direct temperature control method is used. For example, if the kinetic energy of the system is K, the number of particles in the system is N, the mass of the particles is m, the temperature of the system is T, and the Boltzmann constant is k _B , the following equation (10) holds.

ただし、ｖ_ｉは各原子の速度、ｖ^〜は全原子の平均速度である。したがって、系の温度Ｔは、以下に示す式（１１）となる。

However, v _i is the velocity of each atom, v ^~ is the average speed of all atoms. Therefore, the system temperature T is expressed by the following equation (11).

なお、このときの原子の速度は、以下に示す式（１２）となる。

At this time, the velocity of the atoms is expressed by the following formula (12).

ただし、Ｔ_ｃは目標とする温度であり、Ｔは系の温度である。

Where _Tc is the target temperature and T is the system temperature.

Incidentally, in the above relational expression, the use of V _{i 'instead} of V _i, the right side of the equation (11) described above, following expressions (13), and the temperature of the system is consistent with the set temperature T _c I understand that.

  Next, after calculating the temperature and energy in the process of S25 described above, it is determined whether or not to control the temperature based on the calculation result (S26). If the temperature is controlled (YES in S26), the temperature scaling is performed. (S27). Specifically, the temperature information is corrected based on preset calibration data having appropriate values. Note that the calibration data is data for scaling the temperature so that, for example, the melting point of a system such as a complex shape in which atoms are arranged has a temperature in the vicinity thereof.

  In the process of S26, when temperature control is not performed (NO in S26), or after the process of S27 is finished, it is determined whether or not the annealing is finished (S28). Here, when the annealing is not finished (NO in S28), the process returns to S22 and the above-described processing is performed with the setting changed. If the annealing process is to be terminated (YES in S28), the process is terminated.

  As described above, in this embodiment, first, atoms are arranged at appropriate positions, and then annealing calculation is performed by the molecular dynamics method by the molecular dynamics method to move the atoms to the optimum stable point. Specifically, the temperature of the entire system is relaxed by, for example, calculating about 100,000 steps in a state where the temperature of the entire system is forcibly kept near the melting point by the scaling method. In this way, for example, by annealing using molecular dynamics or the like, when the material forming the metal or the like is melted at a high temperature and then slowly cooling to a solid, the process of becoming a state of almost minimum energy By emulating and finding an approximate solution with a small amount of calculation, atoms can be arranged appropriately even for complex shapes.

  Here, FIG. 8 is a diagram illustrating an example of an atomic arrangement relaxed by annealing. In FIG. 8, in order to clarify the generated mesh shape, the arranged atoms are extracted in a predetermined region and enlarged and displayed. According to the present embodiment, as shown in FIG. 8, meshes 50 having similar shapes can be arranged, and by arranging atoms 51 at the lattice points, atoms can be appropriately arranged even for complicated shapes. can do. 8 described above is generated by the screen generation means 27 and output by the output means 22.

<Atom configuration simulation program>
Here, the atomic arrangement simulation apparatus according to the present invention generates an execution program that can cause a computer to execute each process in the above-described configurations, and installs the atomic arrangement simulation program in, for example, a general-purpose personal computer or a server. Thus, the above-described atomic arrangement simulation process in the present invention can be realized.

  Thereby, atoms can be appropriately arranged in a preset shape. Further, by installing the execution program in the computer, the atomic arrangement simulation process can be easily realized.

  Further, if the above-described atomic arrangement simulation program is recorded in a computer-readable recording medium and provided, the atomic arrangement simulation program can be easily installed in a plurality of other computers by the recording medium.

  As described above, according to the present invention, atoms can be appropriately arranged in a preset shape. In addition, according to the present invention, atoms can be appropriately arranged even for complicated shapes using molecular dynamics.

  Further, according to the present invention, it can be used to improve a mesh used in a conventional finite element method or the like. Specifically, for example, even in a region where a geometrically “distorted” mesh is created when the shape of the arrangement of atoms is complicated, it is not necessary to manually correct it as in the past. It is possible to obtain a high-quality mesh by relaxing the annealing calculation. Further, even in non-stationary calculations that require remeshing, the mesh shape can be quickly changed by the interaction of atoms. Furthermore, according to the present invention, it is possible to deal with meshes having different roughness by changing the size of atoms, and depending on how the interatomic potential is selected, the present invention can be applied to quadrilateral meshes.

  The preferred embodiments of the present invention have been described in detail above, but the present invention is not limited to such specific embodiments, and various modifications can be made within the scope of the gist of the present invention described in the claims. Can be changed.

It is a figure which shows an example of the hardware constitutions of the atomic arrangement | positioning simulation apparatus in a present Example. It is a figure which shows an example of a function structure of an atomic arrangement | positioning simulation apparatus. It is a flowchart which shows an example of the atomic arrangement | sequence simulation processing procedure in a present Example. It is a flowchart which shows an example of the temporary arrangement | positioning process procedure of an atom. It is a figure which shows an example of the atomic arrangement | positioning after the mesh production | generation in the process of S12 and S13. It is a figure which shows an example of the atomic arrangement | positioning in the process of S15, S15. It is a flowchart for demonstrating the annealing process procedure using the molecular dynamics method in a present Example. It is a figure which shows an example of the atomic arrangement | positioning eased by annealing.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Atom arrangement simulation apparatus 11 Input apparatus 12 Output apparatus 13 Drive apparatus 14 Auxiliary storage apparatus 15 Memory apparatus 16 CPU
DESCRIPTION OF SYMBOLS 17 Network connection apparatus 18 Recording medium 21 Input means 22 Output means 23 Storage means 24 Temporary arrangement means 25 Annealing means 26 Roughness adjustment means 27 Screen generation means 28 Transmission / reception means 29 Control means 30, 50 Mesh 31, 43, 51 Atom 40 Outer frame 41 Center opening 42 Peripheral opening 44 Arrow

Claims (10)

In an atomic arrangement simulation method for performing a simulation for arranging atoms in a preset shape,
A temporary placement step of temporarily placing atoms in the shape;
An annealing step for annealing the atoms arranged in the temporary arrangement step based on the interatomic potential;
An atomic arrangement simulation method comprising: a density adjustment step for adjusting a density relationship between atoms annealed by the annealing step. The temporary placement step includes
By generating a large number of meshes in the shape and arranging atoms at each lattice point of the generated mesh, or by arranging atoms in the shape frame and generating and filling atoms inside the shape The atom arrangement simulation method according to claim 1, wherein atoms are arranged. The annealing step includes
The atomic arrangement simulation method according to claim 1 or 2, wherein the annealing is performed by adjusting the temperature in the vicinity of the melting point of the material forming the shape by a molecular dynamics method. In an atomic arrangement simulation apparatus that performs a simulation for arranging atoms in a preset shape,
Temporary placement means for temporarily placing atoms in the shape;
Annealing means for annealing the atoms arranged by the temporary arrangement means based on the interatomic potential;
An atomic arrangement simulation apparatus comprising: a density adjusting unit that adjusts a density relationship between atoms annealed by the annealing unit. The temporary placement means includes
By generating a large number of meshes in the shape and arranging atoms at each lattice point of the generated mesh, or by arranging atoms in the shape frame and generating and filling atoms inside the shape The atom arrangement simulation apparatus according to claim 4, wherein atoms are arranged. The annealing means is
6. The atomic arrangement simulation apparatus according to claim 4, wherein annealing is performed by adjusting a temperature in the vicinity of a melting point of the material forming the shape by a molecular dynamics method. In an atomic arrangement simulation program for executing on a computer an atomic arrangement simulation process for performing simulation for arranging atoms in a preset shape,
Temporary placement processing for temporarily placing atoms in the shape;
Annealing treatment for annealing atoms arranged by the temporary arrangement treatment based on an interatomic potential;
An atomic arrangement simulation program for causing a computer to execute a density adjustment process for adjusting a density relationship between atoms annealed by the annealing process. The temporary placement process is:
By generating a large number of meshes in the shape and arranging atoms at each lattice point of the generated mesh, or by arranging atoms in the shape frame and generating and filling atoms inside the shape The atom arrangement simulation program according to claim 7, wherein atoms are arranged. The annealing process is
The atomic arrangement simulation program according to claim 7 or 8, wherein annealing is performed by adjusting a temperature in the vicinity of a melting point of the material forming the shape by a molecular dynamics method.   A computer-readable recording medium on which the atomic configuration simulation program according to any one of claims 7 to 9 is recorded.

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