{"title":"Numerical analysis and integration of dynamical systems and the fractal dimension of boundaries","authors":"L.G.S. Duarte, L.A.C.P. da Mota, J.F.E. Skea","doi":"10.1016/j.cpc.2024.109493","DOIUrl":"10.1016/j.cpc.2024.109493","url":null,"abstract":"<div><div>The set of Maple routines that comprises the package <strong>Ndynamics</strong> has been improved. Apart one of the main motivations for its creation, namely, the routines to calculate the fractal dimension of boundaries (via box counting), the package deals with the numerical evolution of dynamical systems and provide flexible plotting of the results. The package also brings an initial conditions generator, a numerical solver manager, and a focusing set of routines that allow for better analysis of the graphical display of the results. Many new Maple-in-built numerical solvers are now programmed and available for the user of the package. The novelty that the package presented at the time of its release, an optional numerical interface, is maintained and updated.</div></div><div><h3>New version program summary</h3><div><em>Program Title:</em> Ndynamics - Numerical integration of dynamical systems and the fractal dimension of boundaries</div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/swkr5w3kx4.1</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> CC by NC 3.0</div><div><em>Programming language:</em> Maple</div><div><em>Journal reference of previous version:</em> Comput. Phys. Commun. 183 (9) (2012) 2019–2020, <span><span>https://doi.org/10.1016/j.cpc.2012.03.024</span><svg><path></path></svg></span></div><div><em>Does the new version supersede the previous version?:</em> Yes</div><div><em>Nature of problem:</em> Computation and plotting of numerical solutions of dynamical systems and the determination of the fractal dimension of the boundaries.</div><div><em>Solution method:</em> The default method of integration is a fifth-order Runge–Kutta procedure, but the following numerical methods of integration are programmed and now available for the user of the <strong>Ndynamics</strong> package: rkf45, ck45, rosenbrock, rkf45_dae, ck45_dae, rosenbrock_dae, dverk78, lsode, gear, taylorseries, mebdfi, and classical. A box counting method is used to calculate the fractal dimension of the boundaries.</div><div><em>Reasons for new version:</em> The <strong>Ndynamics</strong> package is still being used (as can be seen from the very new citation [1]), so it is worth to update its programming, for instance, by including the new numeric integrators available with the commercial release of Maple (just cited above on the solution method). We have also taken out of usage some such commands that are not available anymore, thus making the package current, more powerful and fixing some aspects. The (at the time of release) great novelty of the package, namely, the possibility of opening an interface for outside maple numerical integration was updated, we have changed the numerical C-integrator suggested and have improved some aspects of the RK45 numerical integration routine available with the present Maple package, the last such upgrade was done more than 12 years ago.</div><div><em>Sum","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"309 ","pages":"Article 109493"},"PeriodicalIF":7.2,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143093086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Development of novel collision detection algorithms for the estimation of fast ion losses in tokamak fusion device","authors":"Taeuk Moon , Tongnyeol Rhee , Jae-Min Kwon , Eisung Yoon","doi":"10.1016/j.cpc.2024.109490","DOIUrl":"10.1016/j.cpc.2024.109490","url":null,"abstract":"<div><div>In the quest for a virtual nuclear fusion reactor that can rapidly respond to user demands, we present a study focusing on the development of a fast ion particle collision module and realistic wall modeling using three-dimensional CAD models. The integration of a neutral beam injection code, NuBDeC Rhee et al. (2019) <span><span>[6]</span></span> within the Virtual KSTAR platform Kwon et al. (2022) <span><span>[5]</span></span> requires efficient detection of the fast ion particle collision events and accurate evaluation of the collision positions on the reactor wall. To achieve this, we investigate six different collision detection algorithms based on the well-known broad and narrow phase framework of collision detection, each utilizing distinct combinations of algorithms based on winding number contour, tri-oval contour, octree, and uniform grid. Furthermore, we explore the utilization of CAD models to create realistic wall surfaces in close resemblance to actual reactor conditions, employing the capabilities of the Unity game engine for mesh-based modeling. Performance tests are conducted, and the total simulation times of the constituent routines are analyzed in comparison. Through this research, in particular, we aim to enhance the reliability and real-time performance of heat load estimation on the plasma-facing components by the neutral beam injection-oriented fast ion losses. The developed fast ion particle collision module and the utilization of realistic wall modeling contribute to improving the authenticity and accuracy of the simulation results.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"309 ","pages":"Article 109490"},"PeriodicalIF":7.2,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An efficient Galerkin method for problems with physically realistic boundary conditions","authors":"Olga Podvigina","doi":"10.1016/j.cpc.2024.109482","DOIUrl":"10.1016/j.cpc.2024.109482","url":null,"abstract":"<div><div>The Galerkin method is often employed for numerical integration of evolutionary equations, such as the Navier–Stokes equation or the magnetic induction equation. Application of the method requires solving at each time step a linear equation of the form <span><math><mi>P</mi><mo>(</mo><mi>A</mi><mi>v</mi><mo>−</mo><mi>f</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>, where <em>v</em> is an element of a finite-dimensional space <span><math><mi>V</mi></math></span> with a basis satisfying the boundary conditions. We propose an algorithm giving an opportunity to reduce the computational cost for such a problem. Suppose there exists a space <span><math><mi>W</mi></math></span> that contains <span><math><mi>V</mi></math></span>, the difference between the dimensions of <span><math><mi>W</mi></math></span> and <span><math><mi>V</mi></math></span> is small compared to the dimension of <span><math><mi>V</mi></math></span>, and solving the problem <span><math><mi>P</mi><mo>(</mo><mi>A</mi><mi>w</mi><mo>−</mo><mi>f</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>, where <em>w</em> is an element of <span><math><mi>W</mi></math></span>, requires less operations than solving the original problem. The solution to <span><math><mi>P</mi><mo>(</mo><mi>A</mi><mi>v</mi><mo>−</mo><mi>f</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span> is found in two steps: we solve the problem <span><math><mi>P</mi><mo>(</mo><mi>A</mi><mi>w</mi><mo>−</mo><mi>f</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span> in <span><math><mi>W</mi></math></span> and compute a correction <span><math><mi>q</mi><mo>=</mo><mi>v</mi><mo>−</mo><mi>w</mi></math></span> that belongs to the kernel of <em>PA</em>, which is a complement to <span><math><mi>V</mi></math></span> in <span><math><mi>W</mi></math></span>; <em>q</em> is computed using a basis in the orthogonal complement to <span><math><mi>V</mi></math></span> in <span><math><mi>W</mi></math></span>. We discuss the algorithm both in the general form and its instance when <span><math><mi>W</mi></math></span> is spanned by Chebyshev polynomials.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"309 ","pages":"Article 109482"},"PeriodicalIF":7.2,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alberto Bocchinfuso, David M. Rogers, Caio Alves, Jorge Ramirez, Dilipkumar N. Asthagiri, Thomas L. Beck, Juan M. Restrepo
{"title":"Multi-level Monte Carlo methods in chemical applications with Lennard-Jones potentials and other landscapes with isolated singularities","authors":"Alberto Bocchinfuso, David M. Rogers, Caio Alves, Jorge Ramirez, Dilipkumar N. Asthagiri, Thomas L. Beck, Juan M. Restrepo","doi":"10.1016/j.cpc.2024.109477","DOIUrl":"10.1016/j.cpc.2024.109477","url":null,"abstract":"<div><div>We describe and compare outcomes of various Multi-Level Monte Carlo (MLMC) method variants, motivated by the potential of improved computational efficiency over rejection based Monte Carlo, which scales poorly with problem dimension. With an eye toward its application to computational chemical physics, we test MLMC's ability to sample trajectories on two problems — a familiar double-well potential, with known stationary distributions, and a Lennard-Jones solid potential (a Galton Board). By sampling Brownian motion trajectories, we are able to compute expectations of observable averages. These multi-basin potential energy problems capture the essence of the challenges with using MLMC, namely, maintaining correspondence of sample paths as time-resolution is varied. Addressing this challenge properly can lead to MLMC significantly outperforming standard Monte Carlo path sampling. We describe the essence of this problem and suggest strategies that circumvent diverging multilevel sample paths for an important class of problems. In the tests we also compare the computational cost of several, “adaptive,” variants of MLMC. Our results demonstrate that MLMC overcomes the collision, time scale limitation of the more familiar Brownian path MC samplers, and our implementation provides tunable error thresholds, making MLMC a promising candidate for application to larger and more complex molecular systems.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"309 ","pages":"Article 109477"},"PeriodicalIF":7.2,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143127917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Max Aehle , Mihály Novák , Vassil Vassilev , Nicolas R. Gauger , Lukas Heinrich , Michael Kagan , David Lange
{"title":"Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations","authors":"Max Aehle , Mihály Novák , Vassil Vassilev , Nicolas R. Gauger , Lukas Heinrich , Michael Kagan , David Lange","doi":"10.1016/j.cpc.2024.109491","DOIUrl":"10.1016/j.cpc.2024.109491","url":null,"abstract":"<div><div>Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications.</div><div>This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"309 ","pages":"Article 109491"},"PeriodicalIF":7.2,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143093126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"STLCutters.jl: A scalable geometrical framework library for unfitted finite element discretisations","authors":"Pere A. Martorell , Santiago Badia","doi":"10.1016/j.cpc.2024.109479","DOIUrl":"10.1016/j.cpc.2024.109479","url":null,"abstract":"<div><div>Approximating partial differential equations for extensive industrial and scientific applications requires leveraging the power of modern high-performance computing. In large-scale parallel computations, the geometrical discretisation rapidly becomes a bottleneck in the simulation pipeline. Unstructured mesh generation is hardly automatic, and meshing algorithms cannot efficiently exploit distributed-memory computers. Besides, partitioning of unstructured meshes relies on graph partitioning strategies, which scale poorly. As a result, the use of dynamic load balancing for locally refined meshes becomes prohibitive. Adaptive Cartesian meshes are far more advantageous, providing cheap and scalable mesh generation, partitioning, and balancing compared to unstructured meshes. However, Cartesian meshes are not suitable for complex geometries when using standard discretisation techniques. Unfitted finite element methods are a promising solution to the abovementioned problems. These numerical schemes rely on Cartesian meshes and can handle complex geometries. Nevertheless, their application is usually constrained to implicit (level set) geometrical representations. The extension to general geometries, e.g., provided by an STL surface mesh, requires advanced intersection algorithms. This work presents an efficient parallel implementation of all the geometric tools required, e.g., for unfitted finite element methods (in a broad sense), for explicit boundary representations. Such geometries can readily be generated using standard computer-aided design tools. The proposed geometrical workflow utilises a multilevel approach to overlapping computations, effectively eliminating bottlenecks in large-scale computations. The numerical results demonstrate perfect weak scalability over 13,000 processors and one billion cells. All these algorithms are implemented in the open-source <span>STLCutters.jl</span> library, written in the Julia programming language. The library is designed to be used in conjunction with the <span>Gridap.jl</span> library provides a high-level interface to the finite element method.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"309 ","pages":"Article 109479"},"PeriodicalIF":7.2,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143127926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kevin Schäfers , Jacob Finkenrath , Michael Günther , Francesco Knechtli
{"title":"Hessian-free force-gradient integrators","authors":"Kevin Schäfers , Jacob Finkenrath , Michael Günther , Francesco Knechtli","doi":"10.1016/j.cpc.2024.109478","DOIUrl":"10.1016/j.cpc.2024.109478","url":null,"abstract":"<div><div>We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for separable Hamiltonian systems with quadratic kinetic energy may be particularly useful when applied to Hamiltonian systems where an evaluation of the Hessian is significantly more expensive than an evaluation of its gradient, e.g. in molecular dynamics simulations of classical systems. Numerical experiments of an N-body problem, as well as applications to the molecular dynamics step in the Hybrid Monte Carlo (HMC) algorithm for lattice simulations of the Schwinger model and Quantum Chromodynamics (QCD) verify these expectations.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"309 ","pages":"Article 109478"},"PeriodicalIF":7.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143127915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"TrussMe-Fem: A toolbox for symbolic-numerical analysis and solution of structures","authors":"Davide Stocco , Matteo Larcher , Matteo Tomasi, Enrico Bertolazzi","doi":"10.1016/j.cpc.2024.109476","DOIUrl":"10.1016/j.cpc.2024.109476","url":null,"abstract":"<div><div>Structural mechanics is pivotal in comprehending how structures respond to external forces and imposed displacements. Typically, the analysis of structures is performed numerically using the direct stiffness method, which is an implementation of the finite element method. This method is commonly associated with the numerical solution of large systems of equations. However, the underlying theory can also be conveniently used to perform the analysis of structures either symbolically or in a hybrid symbolic-numerical fashion. This approach is useful to mitigate the computational burden as the obtained partial or full symbolic solution can be simplified and used to generate lean code for efficient simulations. Nonetheless, the symbolic direct stiffness method is also useful for model reduction purposes, as it allows the derivation of small-scale models that can be used for diminishing simulation time. Despite the mentioned advantages, symbolic computation carries intrinsically complex operations. In particular, the symbolic solution of large linear systems of equations is hard to compute, and it may not always be available due to software capabilities. This paper introduces a toolbox named <span>TrussMe-Fem</span>, whose implementation is based on the direct stiffness method. <span>TrussMe-Fem</span> leverages <span>Maple</span>®'s symbolic computation and <span>Matlab</span>®'s numerical capabilities for symbolic and hybrid symbolic-numerical analyses and solutions of structures. Efficient code generation is also possible by exploiting the simplification of the problem's expressions. The challenges posed by symbolic computation on the solution of large linear systems are addressed by introducing novel routines for the symbolic matrix factorization with the hierarchical representation of large expressions. For this purpose, the <span>TrussMe-Fem</span> toolbox optionally uses the <span>Lem</span> and <span>Last Maple</span>® packages, which are also available as open-source software.</div></div><div><h3>Program summary</h3><div><em>Program Title:</em> <span>TrussMe-Fem</span></div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/m59fyw5hs4.1</span><svg><path></path></svg></span></div><div><em>Developer's repository link:</em> <span><span>https://github.com/StoccoDavide/TrussMe-FEM</span><svg><path></path></svg></span> – Optional dependencies: <span>Lem</span> <span><span>https://github.com/StoccoDavide/LEM</span><svg><path></path></svg></span>, <span>Last</span> <span><span>https://github.com/StoccoDavide/LAST</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> BSD 3-clause.</div><div><em>Programming language:</em> <span>Maple</span>®, <span>Matlab</span>®.</div><div><em>Supplementary material:</em> Usage examples for the <span>TrussMe-Fem</span> toolbox, <span>Lem</span> and <span>Last Maple</span>® packages.</div><div><em>Nature of problem:</em> Structural mechanics is a bran","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"309 ","pages":"Article 109476"},"PeriodicalIF":7.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143127850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"EllipsoidalFiberFoam, a novel Eulerian-Lagrangian solver for resolving translational and rotational motion dynamics of ellipsoidal fibers","authors":"Kazem Reza-Asl, Ebrahim Goshtasbi Rad, Omid Abouali","doi":"10.1016/j.cpc.2024.109481","DOIUrl":"10.1016/j.cpc.2024.109481","url":null,"abstract":"<div><div>A novel Eulerian-Lagrangian MPI parallelized solver is developed to resolve the dynamics of ellipsoidal fibers in the OpenFOAM platform. Due to the nonspherical shape of the ellipsoidal fibers and the dependence of the drag force on the orientation of the fiber, the solver solves the full conservation of linear and angular momentum equations, in addition to the time evolution equation for Euler's parameters, quaternions. To this end, a new parcel type is introduced to represent ellipsoidal fibers with several new properties, including Euler's parameters, angular velocity, and torque class. Finally, new member functions are defined to solve angular momentum and Euler's parameters time evolution equations. The solver is the first publicly available, robust and reliable computational framework for the numerical analysis of ellipsoidal fibers motion. It promotes the capability of the standard Lagrangian OpenFOAM solvers and libraries to capture the orientation and rotational dynamics of nonspherical particles. As validation cases, the solver was applied to four benchmarks: three-dimensional rotation of an ellipsoid in linear shear flow, two-dimensional rotation of a magnetic ellipsoid in linear shear flow subjected to a uniform magnetic field, motion of an ellipsoid in pipe flow, and ellipsoids deposition in three-dimensional bifurcation flow. Comparison of the results with analytical solutions, experimental data and in-silico results indicates close agreements and high accuracy of the developed numerical model for single- and multi-physics test cases.</div></div><div><h3>Program summary</h3><div><em>Program title:</em> EllipsoidalFiberFoam</div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/nf35zjvmr2.1</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> GNU General Public License Version 3</div><div><em>Programming language:</em> C++</div><div><em>Nature of problem:</em> The developed Eulerian-Lagrangian solver introduces the Euler's parameters, angular velocity and hydrodynamic and magnetic torques of ellipsoidal fibers and it solves the equations of conservation of angular momentum and Euler's parameters time evolution to describe the fiber orientation fully. The orientation-dependent drag force and the fiber trajectory are calculated afterward by solving the equations of conservation of linear momentum.</div><div><em>Solution method:</em> Fluid phase velocity and pressure are obtained through the PIMPLE algorithm. For the particulate phase, a new parcel type owning Euler's parameters and angular velocity accompanied by new classes for hydrodynamic and magnetic torques and orientation-based drag force represents an ellipsoidal fiber, and the Lagrangian cloud of the parcel is evolved through the integration of the equations of translational and rotational motion.</div><div><em>Additional comments, including restrictions and unusual features:</em> The current version of the","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"309 ","pages":"Article 109481"},"PeriodicalIF":7.2,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143127920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}