A multi-trajectory atom simulation data real-time comparative analysis system and method

Abstract

The application provides a multi-track atomic simulation data real-time comparative analysis system and method, and relates to the technical field of computer simulation data processing. The system comprises: a track synchronous loading module, which is used for acquiring atomic track files of multiple tracks in parallel, and analyzing the atomic track files to obtain atomic coordinate data under a unified time axis; a dynamic registration alignment module, which is used for performing spatial registration on atomic configurations of each track according to the atomic coordinate data; a difference quantification calculation module, which is used for calculating structural difference indexes between tracks according to the atomic coordinate data after spatial registration; and a multi-view linkage rendering module, which is used for generating a visual graph array combined with multiple tracks according to the structural difference indexes and the atomic coordinate data. The application solves the problems of difficult multi-track data synchronous loading, lack of real-time linkage analysis, insufficient quantitative representation of structural differences and imperfect visualization mapping mechanism in the prior art.

Description

Technical Field

[0001] The present invention relates to the technical field of computer simulation data processing, in particular to a real-time comparative analysis system and method for multi-trajectory atomic simulation data. Background Art

[0002] As an important tool for computational materials science and condensed matter physics research, atomic simulation technology has been widely used in materials design, phase transition mechanism research, defect behavior analysis and other fields. Among them, molecular dynamics simulation can generate trajectory data containing atomic coordinates and physical properties, which provides key information for understanding microstructural evolution. Multi-trajectory atomic simulation data analysis aims to reveal the commonalities and differences in material behavior by comparing simulation results of atoms in materials under different parameters or conditions. Such analysis usually involves parallel observation and quantitative comparison of structural evolution, dynamic processes or statistical characteristics of multiple trajectory files.

[0003] The prior art mainly relies on general visualization software or scripts to independently process single atomic motion trajectories, which makes it difficult to achieve synchronous loading and real-time linkage analysis of multi-trajectory data. Users need to manually switch between different windows or tools, resulting in low data comparison efficiency and easy introduction of human error. In addition, existing methods lack a quantitative characterization and visualization mapping mechanism for structural differences between multiple trajectories, and cannot intuitively present differences in evolution paths and statistical distributions of atomic configurations under different simulation conditions. In large-scale simulation studies involving parameter scanning or condition optimization, the hysteresis and non-integration characteristics of traditional analysis processes have become a technical bottleneck restricting the improvement of scientific research efficiency. Summary of the Invention

[0004] In view of this, it is necessary to provide a real-time comparative analysis system and method for multi-trajectory atomic simulation data, so as to solve the problems in the prior art such as difficulty in synchronous loading of multi-trajectory data, lack of real-time linkage analysis, insufficient quantitative characterization of structural differences, and imperfect visualization mapping mechanism.

[0005] In order to solve the above problems, the present invention provides a real-time comparative analysis system for multi-trajectory atomic simulation data, comprising: a trajectory synchronous loading module, configured to obtain atomic trajectory files of a plurality of trajectories in parallel, and parse the atomic trajectory files to obtain atomic coordinate data under a unified time axis, wherein the trajectories are derived from atomic simulation data; a dynamic registration alignment module, configured to perform spatial registration on atomic configurations of each trajectory according to the atomic coordinate data; a difference quantification calculation module, configured to calculate structural difference indexes between trajectories according to the spatially registered atomic coordinate data; The multi-view linkage rendering module is used to generate a visualization array of multiple trajectories based on the structural difference index and the atomic coordinate data. The views in the visualization array correspond one-to-one with the trajectories or the structural difference index, and the perspective of the visualization array is synchronized with the unified time axis in real time.

[0006] In one possible implementation, the trajectory synchronization loading module includes a file parsing submodule and a time axis synchronization submodule; The file parsing submodule is used to identify the atomic trajectory files of the multiple trajectories and obtain the coordinate sequence corresponding to the trajectory; The time axis synchronization submodule is used to establish a time mapping table for a unified time axis according to a preset time step, and to time-align the atomic simulation data in the coordinate sequence according to the time mapping table to obtain atomic coordinate data under a unified time axis.

[0007] In one possible implementation, the dynamic registration and alignment module is further configured to invoke an iterative nearest-point algorithm to spatially register the atomic configurations of each trajectory. The processing steps of the iterative nearest-point algorithm include: Select the first set of atomic positions in the reference configuration and the second set of atomic positions in the configuration to be registered, wherein the configuration to be registered is the original atomic configuration of each trajectory; Under the condition of minimizing the objective function, the rotation matrix and translation vector of the first atomic position set and the second atomic position set are calculated by singular value decomposition, wherein the objective function is the sum of squared position residuals of the nearest neighbor atomic pairs between the reference configuration and the configuration to be registered; The atomic coordinate data of each trajectory are registered according to the rotation matrix and the translation vector.

[0008] In one possible implementation, the difference quantification calculation module includes a global difference measurement submodule and a local difference analysis submodule; The global difference measurement submodule is used to calculate the root mean square deviation of the atomic positions between each trajectory based on the spatially registered atomic coordinate data, and to construct a curve of the root mean square deviation changing over time. The global difference measurement submodule is also used to calculate the atom pair distance based on the spatially registered atom coordinate data, calculate the radial distribution function of the atom radial distribution based on the atom pair distance, and determine the difference spectrum of the radial distribution function; The local difference analysis submodule is used to call the sliding window to scan the atomic configuration of each trajectory. During the scanning process, the strain tensor eigenvalues ​​in the neighborhood of each atom in the window are calculated, and the magnitude statistical histogram and direction statistical histogram of the atomic displacement vector are constructed.

[0009] In one possible implementation, the multi-view linkage rendering module is further used to generate visualization areas for each trajectory and divide the visualization areas into view grids. Each view grid corresponds to a view used to render the atomic configuration or structural difference index of a trajectory. The rendering methods of the view grids include ball-and-stick models, polyhedron models, and point cloud models.

[0010] In one possible implementation, the multi-view linkage rendering module is further configured to map structural difference indicators to atomic color attributes, wherein the mapping process of the color attributes includes: Map the root mean square deviation to atomic color gradient; Map the strain tensor eigenvalues ​​to the polyhedron fill color.

[0011] In one possible implementation, the dynamic registration and alignment module is further configured to preprocess the atomic coordinate data before spatial registration of the atomic configurations of each trajectory. The preprocessing of the atomic coordinate data includes: For each frame of atomic simulation data in each trajectory, calculate the centroid coordinates of the atoms; Subtracting the centroid coordinates from the atomic coordinate data yields zero-centroid atomic coordinate data. Calculate the inertia tensor of the atomic configuration corresponding to the zero-centroid atomic coordinate data, and diagonalize the inertia tensor to obtain the principal axes of inertia; Calculate the rotation matrix used to align the principal axis of inertia with the preset Cartesian coordinate system, and transform the atomic simulation data based on the rotation matrix to obtain the preprocessed atomic coordinate data of each trajectory.

[0012] In one possible implementation, the system further includes an interactive control center, which is used to perform the following operations: Real-time monitoring of the atomic trajectory file loading progress of the trajectory synchronization loading module; The parameters of the iterative nearest point algorithm and the range of values ​​for the objective function are input into the dynamic registration and alignment module; Trigger the execution of the global difference measurement submodule and / or local difference analysis submodule in the difference quantification calculation module; The division parameters of the view grid in the visualization area, the rendering parameters of the view grid, and the mapping parameters of the structural difference index are input into the multi-view linkage rendering module.

[0013] In one possible implementation, the system further includes a result export and report generation module, which is also used to generate a real-time comparison analysis report based on a preset analysis report template when receiving an export instruction from the interactive control center. The real-time comparative analysis results include: the visualization array, the root mean square deviation in the structural difference index, the curve of the root mean square deviation changing over time, the difference spectrum of the radial distribution function, the strain tensor eigenvalues ​​in the structural difference index, the histogram of the magnitude of the atomic displacement vector, and the histogram of the direction.

[0014] This invention also provides a method for real-time comparative analysis of multi-trajectory atomic simulation data, comprising: Atomic trajectory files of multiple trajectories are acquired in parallel and parsed to obtain atomic coordinate data under a unified time axis. The trajectories are derived from atomic simulation data. Spatial registration of the atomic configurations of each trajectory is performed based on the atomic coordinate data; Calculate the structural difference index between trajectories based on the spatially registered atomic coordinate data; Based on the structural difference index and the atomic coordinate data, a visualization array of multiple trajectories is generated, wherein the views in the visualization array correspond one-to-one with the trajectory or the structural difference index, and the perspective of the visualization array is synchronized in real time with the unified time axis.

[0015] The present invention also provides an electronic device, including a memory and a processor, wherein the memory is used to store a program; the processor is coupled to the memory and is used to execute the program stored in the memory to implement the steps of the above-described real-time comparison and analysis method for multi-trajectory atomic simulation data.

[0016] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described method for real-time comparison and analysis of multi-trajectory atomic simulation data.

[0017] The beneficial effects of the above implementation are as follows: The real-time comparison and analysis system for multi-track atomic simulation data provided by this invention achieves parallel reading and unified time axis mapping of multi-track data through a trajectory synchronous loading module, solving the problems of difficult synchronous loading of multi-track data, low efficiency of manual switching and data alignment in traditional methods. The dynamic registration and alignment module eliminates system offset through a spatial transformation algorithm, ensuring the consistency of the benchmark for multi-track comparison and significantly improving the accuracy of structural comparison. The difference quantification calculation module provides a difference metric after the comparison analysis of each trajectory, using structural difference indicators to quantify the comparison analysis results. The multi-view linkage rendering module, through a synchronously updated visualization view array, intuitively presents the structural differences and dynamic evolution patterns between multiple trajectories, enhancing the intuitiveness and depth of atomic simulation data interpretation. Thus, it achieves integrated processing of multi-track atomic simulation data from loading, alignment, quantification to visualization, improving the accuracy of structural comparison and the efficiency of data analysis, and solving the problems of insufficient quantitative representation of structural differences and imperfect visualization mapping mechanisms. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A schematic diagram of the architecture of the real-time comparison and analysis system for multi-trajectory atomic simulation data provided by the present invention; Figure 2 This is a schematic diagram illustrating the principle of the dynamic registration and alignment module provided by the present invention. Figure 3 A schematic diagram illustrating the principle of the difference quantization calculation module provided by this invention; Figure 4 This is a schematic diagram illustrating the data interaction between the multi-view linkage rendering module and the interactive control center provided by the present invention. Figure 5 A flowchart illustrating the real-time comparative analysis method for multi-trajectory atomic simulation data provided by this invention; Figure 6 A schematic diagram of an embodiment of the electronic device provided by the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0021] In the description of the embodiments of this application, unless otherwise stated, "a plurality of" means two or more.

[0022] In this embodiment of the invention, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, apparatus, product or device that includes a series of steps or modules is not necessarily limited to those steps or modules that are explicitly listed, but may include other steps or modules that are not explicitly listed or that are inherent to such process, method, product or device.

[0023] The naming or numbering of steps in the embodiments of the present invention does not mean that the steps in the method flow must be executed in the time / logical order indicated by the naming or numbering. The execution order of the named or numbered process steps can be changed according to the technical purpose to be achieved, as long as the same or similar technical effect can be achieved.

[0024] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0025] The multi-track atomic simulation data real-time comparison and analysis system of this invention can be applied to the analysis of atomic simulation data. It simulates the motion processes of various atoms and simultaneously collects atomic simulation data for each type of atom, generating corresponding atomic trajectory files. One atomic trajectory is generated for each atom type, resulting in multiple trajectory files. These multiple trajectory files are then simultaneously imported into the multi-track atomic simulation data real-time comparison and analysis system provided by this invention for comparative analysis, ultimately generating a combined visualization array of multiple trajectories.

[0026] The following describes in detail the real-time comparison and analysis system for multi-track atomic simulation data provided by this invention.

[0027] Figure 1 This is a schematic diagram of the architecture of a real-time comparative analysis system for multi-trajectory atomic simulation data, such as... Figure 1 As shown, the real-time comparison and analysis system for multi-trajectory atomic simulation data (hereinafter referred to as the system) specifically includes a trajectory synchronous loading module, a dynamic registration and alignment module, a difference quantification calculation module, and a multi-view linkage rendering module, which will be described one by one below.

[0028] The trajectory synchronization loading module is used to acquire atomic trajectory files of multiple trajectories in parallel, and parse the atomic trajectory files to obtain atomic coordinate data under a unified time axis.

[0029] Here, the trajectories originate from atomic simulation data, which consists of the position coordinates of atoms moving within a simulation system. This position coordinate data is stored in time frames, with one position coordinate recorded for each frame. These multiple time frames then form the corresponding trajectories. Since this embodiment involves multiple types of atoms in the material, each atom type corresponds one-to-one with the chemical composition of the material. Because the chemical compositions differ, each atom type exhibits a different trajectory in the simulation system. The trajectory synchronous loading module acquires multiple atomic trajectory files in parallel, without any sequential order. Furthermore, the module incorporates data interfaces for various file parsing tools, enabling parallel parsing of the atomic trajectory files to obtain the corresponding atomic coordinate data for each trajectory.

[0030] Since different types of atoms exhibit different trajectories in the simulation system, this study utilizes the temporal attribute of the position coordinate data in the trajectory to perform temporal alignment on the atomic simulation data. This maps the atomic coordinate data of various trajectories onto a unified coordinate axis, facilitating subsequent analysis of differences in the atomic configuration of the trajectories.

[0031] The dynamic registration and alignment module is used to spatially register the atomic configurations of each trajectory based on atomic coordinate data.

[0032] The purpose of spatial registration here is to align the atomic configurations of different trajectories to a common reference frame, eliminating systematic offsets caused by differences in initial conditions. This can be achieved using rigid transformation and optimal matching algorithms, with the preferred matching algorithm being the iterative nearest-point algorithm.

[0033] The difference quantification calculation module is used to calculate the structural difference index between trajectories based on the spatially registered atomic coordinate data.

[0034] After spatial registration is achieved through the dynamic registration and alignment module, the structural difference indices between trajectories are further analyzed using the difference quantification calculation module. These structural difference indices are divided into global and local indices, specifically the root mean square deviation of atomic positions between trajectories and the strain tensor eigenvalue within each atom's neighborhood, respectively. Additionally, the local difference indices include atomic position vectors generated based on the strain tensor eigenvalues. These structural difference indices measure both global and local differences between trajectories and serve as a quantitative basis for multi-trajectory comparative analysis.

[0035] The multi-view linkage rendering module is used to generate a visualization array of multiple trajectories based on structural difference indicators and atomic trajectory files.

[0036] The multi-view linkage rendering module receives the difference quantization calculation results and raw trajectory data in real time, namely the structural difference index from the difference quantization calculation module and the atomic coordinate data parsed by the trajectory synchronization loading module. Then, based on the structural difference index and atomic coordinate data, it generates a synchronously updated visualization array for joint visualization of the comparative analysis results of each trajectory.

[0037] In this visualization array, each view corresponds one-to-one with a trajectory or structural difference index; that is, each type of atom corresponds to a single view, or each structural difference index corresponds to a single view. Furthermore, the visualization array's perspective is synchronized in real-time with a unified timeline, ensuring that the views and trajectories are aligned on the same timeline.

[0038] This invention, through a trajectory synchronization loading module, achieves parallel reading and unified time-axis mapping of multi-trajectory data, solving the problems of difficult synchronous loading of multi-trajectory data, low efficiency of manual switching and data alignment in traditional methods. The dynamic registration and alignment module eliminates system offset through a spatial transformation algorithm, ensuring the consistency of the benchmark for multi-trajectory comparison and significantly improving the accuracy of structural comparison. The difference quantification calculation module provides a difference metric after comparative analysis of each trajectory, quantifying the comparative analysis results using structural difference indicators. The multi-view linkage rendering module, through a synchronously updated visualization view array, intuitively presents the structural differences and dynamic evolution patterns between multiple trajectories, enhancing the intuitiveness and depth of atomic simulation data interpretation. Thus, it achieves integrated processing of multi-trajectory atomic simulation data from loading, alignment, quantification to visualization, improving the accuracy of structural comparison and the efficiency of data analysis, and solving the problems of insufficient quantitative representation of structural differences and imperfect visualization mapping mechanisms.

[0039] In one possible implementation, the trajectory synchronization loading module includes a file parsing submodule and a timeline synchronization submodule. The timeline synchronization submodule receives the output from the file parsing submodule.

[0040] The file parsing submodule is used to identify atomic trajectory files of multiple trajectories and obtain the coordinate sequence corresponding to the trajectory.

[0041] The file parsing submodule has built-in decoders for multiple formats, enabling it to automatically recognize and parse common atomic trajectory files, including LAMMP Sdump, XYZ, and POSCAR formats. When reading a file, the submodule extracts the coordinate data of the atomic sequences frame by frame. It also extracts atom type identifiers, analog box vector information, and optional physical attribute fields, such as atomic charge, velocity, or force. All parsed data is temporarily stored in a dedicated buffer in system memory and indexed according to the trajectory's source.

[0042] After the file parsing submodule completes its parsing steps, the time axis synchronization submodule then intervenes to receive the corresponding parsing results. Specifically, the time axis synchronization submodule is used to establish a time mapping table for a unified time axis based on a preset time step, and to time-align the atomic simulation data in the coordinate sequence according to the time mapping table to obtain atomic coordinate data under a unified time axis.

[0043] The purpose of the timeline synchronization submodule is to establish a unified time reference across all loaded tracks. By analyzing the frame sequence of each track and based on the simulation time step or frame number recorded in the header of each frame, a global time mapping table is constructed. This global time mapping table defines the correspondence between frames equivalent in physical time or simulation step size across different tracks. For example, if frame 50 of track A corresponds to a simulation time of 100 picoseconds, and frame 30 of track B also corresponds to 100 picoseconds, then an association mapping will be established between frame 50 of track A and frame 30 of track B in the global time mapping table. Correspondingly, with a time step of 20 picoseconds, at 120 picoseconds, an association mapping will be established between frame 60 of track A and frame 40 of track B.

[0044] In this embodiment of the invention, the trajectory synchronization loading module parses the trajectory files acquired in parallel through the file parsing submodule, and then associates the atomic simulation data of each trajectory according to a unified time axis through a time mapping table, ensuring that all subsequent analysis operations are performed based on strictly synchronized time points.

[0045] In one possible implementation, the dynamic registration and alignment module is also used to call the iterative nearest-point algorithm to spatially register the atomic configurations of each trajectory.

[0046] After the trajectory synchronization loading module completes data processing, its output of multiple synchronized atomic coordinate sequences and associated data is transmitted to the dynamic registration and alignment module. The dynamic registration and alignment module is responsible for eliminating systematic spatial deviations between different trajectory atomic configurations caused by initial placement, overall rotation, or translation, so that subsequent comparisons of differences are established under a common geometric reference frame.

[0047] The dynamic registration and alignment module uses the iterative nearest-point algorithm by default to achieve rigid spatial registration of trajectories. For example... Figure 2 As shown, the iterative closest point algorithm consists of four processes: reference selection, transformation parameter calculation, atomic configuration registration, and elastic registration. The specific processing steps of the iterative closest point algorithm are detailed below.

[0048] The first step is the reference selection process, which involves selecting the first set of atomic positions in the reference configuration and the second set of atomic positions in the configuration to be registered. The configuration to be registered is the original atomic configuration of each trajectory, while the reference configuration is preset. The second set of atomic positions includes the position coordinate data of the reference frames in each trajectory under the original atomic configuration. A keyframe with a stable structure and representative atomic distribution is automatically selected from each trajectory as the reference frame for registration. These selected reference frames from each trajectory form the second set of atomic positions. Based on the corresponding reference frame, the first set of atomic positions for the corresponding reference frame can be determined from the reference configuration.

[0049] Next is the transformation parameter calculation process. Here, under the condition of minimizing the objective function, the rotation matrix and translation vector of the first and second atomic position sets are calculated by singular value decomposition.

[0050] For a reference frame selected in the second set of atomic positions, the optimal spatial transformation parameters between it and the corresponding reference frame in the reference configuration need to be calculated. This calculation is achieved by minimizing the sum of squared positional residuals of the nearest neighbor atomic pairs between the reference configuration and the configuration to be registered, denoted as the objective function E. Let P be the first set of atomic positions in the reference configuration and Q be the second set of atomic positions in the configuration to be registered. The iterative nearest-neighbor algorithm finds a rotation matrix R and a translation vector t that minimize the objective function E(R, t), as expressed in the following formula: (1) in, For keyframes in the first atomic position set P, and express The corresponding frame found in the second atomic position set Q through nearest neighbor search, where N represents the number of atoms participating in the registration, and i represents the i-th atom.

[0051] The next step is the atomic configuration registration process, which registers the atomic coordinate data of each trajectory based on the rotation matrix and translation vector.

[0052] After solving the optimal rotation matrix R and translation vector t in the above formula (1) by singular value decomposition, the dynamic registration and alignment module applies these transformation parameters uniformly to all frames of the corresponding trajectory, thereby completing the spatial alignment of the entire trajectory and making each trajectory in a common reference system, thus realizing the spatial position registration of each trajectory.

[0053] Finally, there is the elastic registration process. The dynamic registration and alignment module uses an elastic registration mode as an alternative to handle spatial registration under phase transition processes or large strain plastic deformation. In this elastic registration mode, the dynamic registration and alignment module no longer seeks a global rigid transformation. Instead, it establishes probabilistic correspondences between atoms based on local environmental feature descriptors, such as atomic radial distribution functions or bond angle distributions. This allows it to solve for a non-uniform spatial deformation field, achieving higher-precision local alignment. The coordinate system of the aligned atomic coordinate data is now unified, laying the foundation for the next step of precise difference quantification.

[0054] In this embodiment of the invention, the atomic coordinate data of each trajectory are spatially registered by calling the iterative nearest point algorithm through the dynamic registration and alignment module. This eliminates the systematic spatial deviation between different trajectory atomic configurations caused by initial placement, overall rotation or translation, ensures the benchmark consistency of multi-trajectory comparison, and significantly improves the accuracy of structural comparison.

[0055] In one possible implementation, the dynamic registration alignment module is also used to preprocess the atomic coordinate data before spatial registration of the atomic configurations of each trajectory.

[0056] Here, a preprocessing strategy based on intramolecular inertia principal axis alignment is also set for the dynamic registration and alignment module. After the trajectory synchronous loading module completes the synchronous loading of multiple trajectory data, the dynamic registration and alignment module first performs an additional preprocessing step, which is explained in detail below.

[0057] First, for each frame of atomic simulation data in each trajectory, the centroid coordinates of the atoms are calculated. Then, the centroid coordinates are subtracted from the atomic coordinate data to obtain the zero-centroid atomic coordinate data.

[0058] This step involves zeroing the centroid of the atomic simulation data. For each frame of atomic simulation data for each trajectory, the centroid coordinates of all atoms are calculated. Then, the coordinate system is translated to the centroid, which means subtracting the corresponding centroid coordinates from the atomic coordinate data, thereby achieving zeroing the centroid of the atoms.

[0059] Next, the inertia tensor of the atomic configuration corresponding to the zero-centroid atomic coordinate data is calculated, and the inertia tensor is diagonalized to obtain the principal axes of inertia. Finally, a rotation matrix for aligning the principal axes of inertia with a preset Cartesian coordinate system is calculated, and the atomic simulation data is transformed based on the rotation matrix to obtain preprocessed atomic coordinate data of each trajectory.

[0060] Here, after zero-centroid processing is performed on the atomic coordinate data of each trajectory, the inertia tensor of the zero-centroid configuration is further calculated, and three principal axes of inertia and their directions are obtained by diagonalizing the inertia tensor. A rotation matrix is further calculated, which functions to align the calculated principal axes of inertia with a fixed preset Cartesian coordinate system axis. The rotation matrix is further applied to the atomic coordinate data of all atoms in this frame to implement transformation, thereby obtaining preprocessed atomic coordinate data of each trajectory. The iterative closest point algorithm is further called to perform spatial registration on the atomic configurations of each trajectory.

[0061] In the embodiment of the present invention, alignment is achieved by determining the principal axes of inertia based on zero-centroid processing. For molecules or clusters with significantly anisotropic shapes, the alignment interference caused by their overall rotational degrees of freedom can be effectively eliminated, providing a better initial condition for the subsequent more refined iterative closest point algorithm registration, which may reduce the number of iterations and improve registration stability.

[0062] In a possible implementation, the difference quantization calculation module comprises a global difference measurement submodule and a local difference analysis submodule.

[0063] The multi-trajectory atomic coordinate data under a common reference system processed by the dynamic registration alignment module is sent to the difference quantization calculation module for in-depth quantitative analysis. As Figure 3 shown, the difference quantization calculation module comprises two core submodules, namely the global difference measurement submodule and the local difference analysis submodule, wherein the global difference measurement submodule focuses on characterizing the degree of structural deviation between trajectories on the whole, while the local difference analysis submodule is dedicated to revealing the spatial non-uniformity of structural differences between trajectories. During data processing, the two modules separately calculate corresponding structural difference indicators as quantization results, then encapsulate the difference quantization results, and encapsulate all quantization results calculated by the two modules into a data structure with timestamps and spatial indexes, which is ready to be called by the multi-view linked rendering module.

[0064] The difference quantization calculation process of the global difference measurement submodule and the local difference analysis submodule will be described one by one below.

[0065] The global difference measurement submodule is configured to calculate the root mean square deviation of atomic positions between various trajectories according to the atomic coordinate data after spatial registration, and construct a curve of the root mean square deviation varying with time.

[0066] A key metric calculated by the global difference measurement submodule is the root mean square deviation (RMSD) curve evolving over time. For each synchronization point in time, atoms on each trajectory are matched to form atom pairs. Then, all matched atom pairs are iterated over, and the sum of the squares of the differences in atom coordinate data is calculated. This sum is then divided by the total number of atoms and the square root is taken to obtain the RMSD, a scalar value representing the overall structural difference at that moment. By continuously calculating the RMSD at all time points, a complete RMSD-time curve is generated, showing how the RMSD changes over time.

[0067] The global difference measurement submodule is also used to calculate the atom pair distance based on the spatially registered atom coordinate data, calculate the radial distribution function of the atom radial distribution based on the atom pair distance, and determine the difference spectrum of the radial distribution function.

[0068] During the global quantization difference calculation, the global difference measurement submodule also calculates the radial distribution function difference spectrum based on the atomic pair distance distribution. Specifically, it first calculates the radial distribution function of each trajectory at different time points based on the spatially registered atomic coordinate data, and then obtains the radial distribution function difference spectrum through direct subtraction, squared difference, or other difference measures, thereby revealing the statistical differences of each trajectory in terms of atomic short-range ordering.

[0069] The local difference analysis submodule is used to call a sliding window to scan the atomic configuration of each trajectory. During the scanning process, it calculates the strain tensor eigenvalues ​​in the neighborhood of each atom in the window and constructs the histogram of the magnitude and the histogram of the direction of the atomic displacement vector.

[0070] The local difference analysis submodule employs a sliding window centered on each atom, with the window radius typically set to a multiple of the nearest neighbor atom distance. The sliding window scans the atomic configurations of each trajectory. During the scan, for each sliding window, the strain tensor eigenvalues ​​of the atomic positions in that local region relative to the reference configuration are calculated. Through eigenvalue decomposition, the principal strains and their directions of the strain tensor are extracted, forming a local strain field. The distribution of these local strain eigenvalues ​​can clearly identify defect regions such as lattice distortion, dislocation nuclei, or interfaces. Simultaneously, the local difference analysis submodule also calculates the displacement vector of each atom itself, i.e., the difference between the spatially registered atomic coordinates and the atomic coordinates in the reference configuration, forming a displacement vector field. Furthermore, the magnitudes and directions of these displacement vectors are statistically analyzed, and histograms of magnitude and direction distributions are constructed to quantitatively assess the amplitude preference and directionality of atomic motion.

[0071] Finally, all the quantization results calculated by the two modules are encapsulated, including structural difference index, root mean square deviation curve over time, local strain field, displacement vector field, histogram of atomic displacement vector magnitude, and histogram of orientation. This is then encapsulated into a data structure with timestamps and spatial indexes, ready for use by the subsequent multi-view linkage rendering module.

[0072] In this embodiment of the invention, global difference quantification and difference quantification are performed in the difference quantification calculation module, which not only provides difference measurement after comparative analysis of each trajectory, but also provides multi-level difference measurement from global to local, so as to achieve a fine characterization of the difference between the evolution path and statistical distribution of atomic configuration.

[0073] In one possible implementation, the multi-view linkage rendering module is also used to generate visualization areas for each trajectory and divide the visualization areas into view grids. Each view grid corresponds to a view used to render the atomic configuration or structural difference index of a trajectory. The rendering methods of the view grids include ball-and-stick models, polyhedron models, and point cloud models.

[0074] like Figure 4 As shown, the multi-view linked rendering module receives the quantization results from the differential quantization calculation module and the raw trajectory data provided by the trajectory synchronization loading module, and then generates a synchronously updated multi-view visualization interface. The multi-view linked rendering module adopts a flexible split-screen display architecture, which by default can divide the visualization into 2×2 or 3×3 view grids, with each view grid independently responsible for rendering specific data content. This content can be the atomic configuration of a certain raw trajectory, or structural difference indicators output by the differential quantization calculation module, such as the root mean square deviation map after atomic coloring, a local strain field rendered in polyhedral form with color difference representing strain magnitude, or a displacement vector field represented by arrows. Each view grid has multiple rendering methods, supporting visualization modes for various atomic configurations, which can be flexibly set and selected. Specifically, these include a ball-and-stick model clearly displaying chemical bonds, a polyhedral model highlighting coordination polyhedra, and a point cloud model for quickly previewing the overall morphology.

[0075] Furthermore, the perspective of the visualization array is synchronized with the unified timeline in real time. When the current observation point on the unified timeline is changed, all view grids in the visualization array will automatically update to the data frame corresponding to that point in time. When a 3D rotation, translation, or scaling operation is performed on any view, the same perspective transformation matrix is ​​applied to all other views in real time to ensure the consistency of the observation angle. When a specific atom or region is highlighted, it will be reflected synchronously in all views. Thus, through the time-synchronized visualization mechanism, it is convenient to perform correlation analysis between different data perspectives.

[0076] In one possible implementation, the multi-view linkage rendering module is also used to map structural difference indicators to the color attributes of atoms.

[0077] Based on the quantization results from the difference quantization calculation module, the multi-view linkage rendering module implements color rendering by calling color rendering. The mapping process of color attributes is described in detail below.

[0078] The mapping process consists of two aspects: one is the rendering of the global difference quantization result, which maps the root mean square deviation into atomic color gradients.

[0079] Here, the multi-view linkage rendering module can call a color mapping tool to map continuous root mean square deviations onto a predefined color gradient. For example, the root mean square deviation value of each atom can be mapped to a color gradient from blue to red, where blue represents small differences and red represents large differences, thus visualizing the global difference quantification results in the form of a heatmap.

[0080] For rendering the results of local difference quantization, the strain tensor eigenvalues ​​are mapped to the fill colors of polyhedra. Specifically, the maximum principal strain value in the strain tensor eigenvalues ​​is mapped to the fill colors of polyhedra, thus visually displaying the regions of lattice stretching or compression.

[0081] In this embodiment of the invention, the structural difference indicators of each trajectory are visualized and rendered by color mapping, which can intuitively present the structural differences and dynamic evolution patterns between multiple trajectories, greatly enhancing the intuitiveness and depth of data interpretation.

[0082] In one possible implementation, the real-time comparison and analysis system for multi-trajectory atomic simulation data also includes an interactive control center. For example... Figure 1 As shown, the interactive control center, as the overall control unit of the system, runs through and coordinates the operation of the above-mentioned trajectory synchronization loading module, dynamic registration and alignment module, difference quantization calculation module, and multi-view linkage rendering module.

[0083] Specifically, the interactive control center performs the following operations: First, it monitors the loading progress of the atomic trajectory files in the trajectory synchronization loading module in real time. When an atomic trajectory file is input, it is first received by the interactive control center and then transmitted to the trajectory synchronization loading module for loading and parsing. By monitoring the loading progress of the atomic trajectory files, the center displays the loading progress and basic information in real time.

[0084] Secondly, the parameters of the iterative nearest point algorithm and the range of values ​​for the objective function are input into the dynamic registration and alignment module. The interactive control center is used to control the input parameters of the iterative nearest point algorithm and the range of values ​​for the objective function, such as controlling the threshold for the number of iterations of the iterative nearest point algorithm and the residual tolerance of the sum of squared position residuals corresponding to the objective function, ensuring that the parameters meet the requirements before being passed to the dynamic registration and alignment module.

[0085] Thirdly, it runs the global difference measurement submodule and / or local difference analysis submodule within the difference quantification calculation module. The interactive control center monitors the difference quantification calculation instructions in real time. When an instruction is received, it triggers the difference quantification calculation module to run the global difference measurement submodule and / or local difference analysis submodule to perform difference quantification calculation, thereby allowing for convenient selection of global and local difference indicators for calculation and display.

[0086] Fourthly, the view grid division parameters, view grid rendering parameters, and structural difference index mapping parameters in the visualization area are input into the multi-view linkage rendering module. The interactive control center is also used to assist in the configuration of the multi-view linkage rendering module. It can receive the input view grid division parameters, view grid rendering parameters, and structural difference index mapping parameters in real time, and then pass them to the multi-view linkage rendering module to realize the data visualization rendering operation.

[0087] This invention, through the design of an interactive control center to control the workflow of the entire system for multi-trajectory comparative analysis, improves the practicality and efficiency of the system in large-scale simulation studies such as parameter scanning and condition optimization. It realizes the integrated processing of multi-trajectory atomic simulation data from loading, alignment, quantization to visualization, effectively overcoming the technical bottlenecks of lagging and non-integrated analysis processes in existing technologies.

[0088] In one possible implementation, the real-time comparative analysis system for multi-trajectory atomic simulation data also includes a result export and report generation module. This module monitors the output of the multi-view linked rendering module and the difference quantification calculation module in real time, and then generates a corresponding real-time comparative analysis report according to a preset custom report template.

[0089] Specifically, the results export and report generation module is also used to generate a real-time comparative analysis report based on a preset analysis report template when receiving an export command from the interactive control center. The real-time comparative analysis results include: a visualization array, root mean square deviation (RMSD) in the structural difference index, the RMSD curve over time, the difference spectrum of the radial distribution function, the eigenvalues ​​of the strain tensor in the structural difference index, the histogram of the magnitude of the atomic displacement vector, and the histogram of the direction.

[0090] The export and report generation module integrates the scattered results elements output by the system modules into a structured, comprehensive analysis report. The report typically includes multi-trajectory comparison screenshots at key time points, graphs showing the changes of global indicators such as root mean square deviation over time, histograms of the statistical distribution of local strain or displacement, and data tables summarizing key statistics. It also supports outputting the final document in various formats, such as Portable Document format, Hypertext Markup Language, or PowerPoint format, and allows setting data filtering conditions according to specific needs, such as exporting only analysis results within a specific time range.

[0091] The following section details the real-time comparative analysis method for multi-track atomic simulation data provided by this invention.

[0092] The method for real-time comparative analysis of multi-track atomic simulation data is applied to the aforementioned real-time comparative analysis system for multi-track atomic simulation data. Figure 5 This is a flowchart illustrating the real-time comparative analysis method for multi-trajectory atomic simulation data provided by the present invention, as shown below. Figure 5 As shown, the real-time comparative analysis method for multi-trajectory atomic simulation data is implemented through steps 501 to 504, which are explained in detail below.

[0093] Step 501: Obtain atomic trajectory files of multiple trajectories in parallel, and parse the atomic trajectory files to obtain atomic coordinate data under a unified time axis. The trajectories are derived from atomic simulation data.

[0094] Step 502: Spatial registration of the atomic configurations of each trajectory based on the atomic coordinate data.

[0095] Step 503: Calculate the structural difference index between trajectories based on the spatially registered atomic coordinate data.

[0096] Step 504: Based on the structural difference index and atomic coordinate data, generate a visualization array of multiple trajectories. The views in the visualization array correspond one-to-one with the trajectories or structural difference indexes, and the perspective of the visualization array is synchronized with the unified time axis in real time.

[0097] The real-time comparison and analysis method for multi-track atomic simulation data provided in the above embodiments can realize the technical solutions described in the embodiments of each module of the real-time comparison and analysis system for multi-track atomic simulation data. The principles of each step can be found in the corresponding content in the embodiments of each module or unit of the real-time comparison and analysis system for multi-track atomic simulation data. Their technical effects can also be referred to each other, and will not be repeated here.

[0098] like Figure 6 As shown, the present invention also provides an electronic device 600. The electronic device 600 includes a processor 601, a memory 602, and a display 603. Figure 6Only some components of the electronic device 600 are shown, but it should be understood that it is not required to implement all the components shown, and more or fewer components may be implemented instead.

[0099] In some embodiments, memory 602 may be an internal storage unit of electronic device 600, such as a hard disk or memory of electronic device 600. In other embodiments, memory 602 may also be an external storage device of electronic device 600, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on electronic device 600.

[0100] Furthermore, the memory 602 may include both internal storage units of the electronic device 600 and external storage devices. The memory 602 is used to store application software and various types of data installed on the electronic device 600.

[0101] In some embodiments, processor 601 may be a central processing unit (CPU), microprocessor, or other data processing chip, used to run program code stored in memory 602 or process data, such as the real-time comparison and analysis method for multi-track atomic simulation data in this invention.

[0102] In some embodiments, display 603 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. Display 603 is used to display information from electronic device 600 and to display a visual user interface. Components 601-603 of electronic device 600 communicate with each other via a system bus.

[0103] In some embodiments of the present invention, when the processor 601 executes the real-time comparison analysis program in the memory 602, the following steps can be implemented: acquiring atomic trajectory files of multiple trajectories in parallel, and parsing the atomic trajectory files to obtain atomic coordinate data under a unified time axis, wherein the trajectories originate from atomic simulation data; spatially registering the atomic configurations of each trajectory according to the atomic coordinate data; calculating the structural difference index between trajectories based on the spatially registered atomic coordinate data; and generating a combined visualization array of multiple trajectories based on the structural difference index and the atomic coordinate data, wherein the views in the visualization array correspond one-to-one with the trajectories or the structural difference index, and the viewpoint of the visualization array is synchronized in real time with the unified time axis.

[0104] It should be understood that when the processor 601 executes the real-time comparison and analysis program in the memory 602, in addition to the functions mentioned above, it can also perform other functions, as detailed in the description of the corresponding method embodiments above.

[0105] Furthermore, the embodiments of the present invention do not specifically limit the type of electronic device 600 mentioned. Electronic device 600 can be a mobile phone, tablet computer, personal digital assistant (PDA), wearable device, laptop computer, or other portable electronic device. Exemplary embodiments of portable electronic devices include, but are not limited to, portable electronic devices running iOS, Android, Microsoft, or other operating systems. The aforementioned portable electronic device can also be other portable electronic devices, such as a laptop computer with a touch-sensitive surface (e.g., a touch panel). It should also be understood that in some other embodiments of the present invention, electronic device 600 may not be a portable electronic device, but rather a desktop computer with a touch-sensitive surface (e.g., a touch panel).

[0106] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements a real-time comparative analysis method for multi-trajectory atomic simulation data provided by the methods described above. This method includes: acquiring atomic trajectory files of multiple trajectories in parallel and parsing the atomic trajectory files to obtain atomic coordinate data under a unified time axis, wherein the trajectories originate from atomic simulation data; spatially registering the atomic configurations of each trajectory according to the atomic coordinate data; calculating structural difference indices between trajectories based on the spatially registered atomic coordinate data; and generating a visualization array of multiple trajectories based on the structural difference indices and the atomic coordinate data, wherein the views in the visualization array correspond one-to-one with the trajectories or the structural difference indices, and the viewpoint of the visualization array is synchronized with the unified time axis in real time.

[0107] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0108] The above provides a detailed description of the real-time comparison and analysis system and method for multi-trajectory atomic simulation data provided by the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A real-time comparative analysis system for multi-trajectory atomic simulation data, characterized in that, include: The trajectory synchronous loading module is used to acquire atomic trajectory files of multiple trajectories in parallel, and parse the atomic trajectory files to obtain atomic coordinate data under a unified time axis. The trajectories are derived from atomic simulation data. The dynamic registration and alignment module is used to spatially register the atomic configurations of each trajectory based on the atomic coordinate data. The difference quantification calculation module is used to calculate the structural difference index between trajectories based on the spatially registered atomic coordinate data. The multi-view linkage rendering module is used to generate a visualization array of multiple trajectories based on the structural difference index and the atomic coordinate data. The views in the visualization array correspond one-to-one with the trajectories or the structural difference index, and the perspective of the visualization array is synchronized with the unified time axis in real time. The dynamic registration and alignment module is further used to call the iterative nearest point algorithm to spatially register the atomic configurations of each trajectory. The processing of the iterative nearest point algorithm includes: Select the first set of atomic positions in the reference configuration and the second set of atomic positions in the configuration to be registered, wherein the configuration to be registered is the original atomic configuration of each trajectory; Under the condition of minimizing the objective function, the rotation matrix and translation vector of the first atomic position set and the second atomic position set are calculated by singular value decomposition, wherein the objective function is the sum of squared position residuals of the nearest neighbor atomic pairs between the reference configuration and the configuration to be registered; The atomic coordinate data of each trajectory are registered according to the rotation matrix and the translation vector; The difference quantification calculation module includes a global difference measurement submodule and a local difference analysis submodule; The global difference measurement submodule is used to calculate the root mean square deviation of the atomic positions between each trajectory based on the spatially registered atomic coordinate data, and to construct a curve of the root mean square deviation changing over time. The global difference measurement submodule is also used to calculate the atom pair distance based on the spatially registered atom coordinate data, calculate the radial distribution function of the atom radial distribution based on the atom pair distance, and determine the difference spectrum of the radial distribution function; The local difference analysis submodule is used to call the sliding window to scan the atomic configuration of each trajectory. During the scanning process, the strain tensor eigenvalues ​​in the neighborhood of each atom in the window are calculated, and the magnitude statistical histogram and direction statistical histogram of the atomic displacement vector are constructed.

2. The real-time comparison and analysis system for multi-trajectory atomic simulation data according to claim 1, characterized in that, The trajectory synchronization loading module includes a file parsing submodule and a time axis synchronization submodule; The file parsing submodule is used to identify the atomic trajectory files of the multiple trajectories and obtain the coordinate sequence corresponding to the trajectory; The time axis synchronization submodule is used to establish a time mapping table for a unified time axis according to a preset time step, and to time-align the atomic simulation data in the coordinate sequence according to the time mapping table to obtain atomic coordinate data under a unified time axis.

3. The real-time comparison and analysis system for multi-trajectory atomic simulation data according to claim 1, characterized in that, The multi-view linkage rendering module is also used to generate visualization areas for each trajectory and divide the visualization areas into view grids. Each view grid corresponds to a view used to render the atomic configuration or structural difference index of a trajectory. The rendering methods of the view grids include ball-and-stick models, polyhedron models, and point cloud models.

4. The real-time comparison and analysis system for multi-trajectory atomic simulation data according to claim 3, characterized in that, The multi-view linkage rendering module is also used to map structural difference indicators to atomic color attributes, and the mapping process of the color attributes includes: Map the root mean square deviation to atomic color gradient; Map the strain tensor eigenvalues ​​to the polyhedron fill color.

5. The real-time comparison and analysis system for multi-trajectory atomic simulation data according to claim 1, characterized in that, The dynamic registration and alignment module is further used to preprocess the atomic coordinate data before spatially registering the atomic configurations of each trajectory. The preprocessing of the atomic coordinate data includes: For each frame of atomic simulation data in each trajectory, calculate the centroid coordinates of the atoms; Subtracting the centroid coordinates from the atomic coordinate data yields zero-centroid atomic coordinate data. Calculate the inertia tensor of the atomic configuration corresponding to the zero-centroid atomic coordinate data, and diagonalize the inertia tensor to obtain the principal axes of inertia; Calculate the rotation matrix used to align the principal axis of inertia with the preset Cartesian coordinate system, and transform the atomic simulation data based on the rotation matrix to obtain the preprocessed atomic coordinate data of each trajectory.

6. The real-time comparison and analysis system for multi-trajectory atomic simulation data according to claim 1, characterized in that, The system also includes an interactive control center, which is used to perform the following operations: Real-time monitoring of the atomic trajectory file loading progress of the trajectory synchronization loading module; The parameters of the iterative nearest point algorithm and the range of values ​​for the objective function are input into the dynamic registration and alignment module; Trigger the execution of the global difference measurement submodule and / or local difference analysis submodule in the difference quantification calculation module; The division parameters of the view grid in the visualization area, the rendering parameters of the view grid, and the mapping parameters of the structural difference index are input into the multi-view linkage rendering module.

7. The real-time comparison and analysis system for multi-trajectory atomic simulation data according to claim 6, characterized in that, The system also includes a result export and report generation module, which is further used to generate a real-time comparison analysis report based on a preset analysis report template when receiving the export instruction from the interactive control center. The real-time comparative analysis results include: the visualization array, the root mean square deviation in the structural difference index, the curve of the root mean square deviation changing over time, the difference spectrum of the radial distribution function, the strain tensor eigenvalues ​​in the structural difference index, the histogram of the magnitude of the atomic displacement vector, and the histogram of the direction.

8. A method for real-time comparative analysis of multi-trajectory atomic simulation data, characterized in that, include: Atomic trajectory files of multiple trajectories are acquired in parallel and parsed to obtain atomic coordinate data under a unified time axis. The trajectories are derived from atomic simulation data. Spatial registration of the atomic configurations of each trajectory is performed based on the atomic coordinate data; Calculate the structural difference index between trajectories based on the spatially registered atomic coordinate data; Based on the structural difference index and the atomic coordinate data, a visualization array of multiple trajectories is generated, wherein the views in the visualization array correspond one-to-one with the trajectory or the structural difference index, and the perspective of the visualization array is synchronized in real time with the unified time axis. The step of spatially registering the atomic configurations of each trajectory based on the atomic coordinate data includes: calling the iterative nearest point algorithm to spatially register the atomic configurations of each trajectory, wherein the processing of the iterative nearest point algorithm includes: Select the first set of atomic positions in the reference configuration and the second set of atomic positions in the configuration to be registered, wherein the configuration to be registered is the original atomic configuration of each trajectory; Under the condition of minimizing the objective function, the rotation matrix and translation vector of the first atomic position set and the second atomic position set are calculated by singular value decomposition, wherein the objective function is the sum of squared position residuals of the nearest neighbor atomic pairs between the reference configuration and the configuration to be registered; The atomic coordinate data of each trajectory are registered according to the rotation matrix and the translation vector; The structural difference index calculated based on the spatially registered atomic coordinate data includes: Based on the spatially registered atomic coordinate data, the root mean square deviation of the atomic positions between each trajectory is calculated, and a curve showing the change of the root mean square deviation over time is constructed. Based on the spatially registered atomic coordinate data, the atomic pair distance is calculated, the radial distribution function of the atomic radial distribution is calculated based on the atomic pair distance, and the difference spectrum of the radial distribution function is determined. The sliding window is invoked to scan the atomic configuration of each trajectory. During the scanning process, the strain tensor eigenvalues ​​in the neighborhood of each atom in the window are calculated, and the magnitude statistical histogram and direction statistical histogram of the atomic displacement vector are constructed.

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