Journal of Computational Physics最新文献

{"title":"Efficient stochastic response analysis of high-dimensional nonlinear systems subject to multiplicative noise via the DR-PDEE","authors":"Jianbing Chen ,&nbsp;Tingting Sun ,&nbsp;Pol D. Spanos ,&nbsp;Jie Li","doi":"10.1016/j.jcp.2025.113929","DOIUrl":"10.1016/j.jcp.2025.113929","url":null,"abstract":"<div><div>Significant challenges persist for the reliable probabilistic analyses of high-dimensional nonlinear dynamical systems subject to multiplicative white noise, particularly at the level of probability density. To address this issue, an efficient method is proposed by employing the dimension-reduced probability density evolution equation (DR-PDEE) to determine the probability density of the responses in such systems. The starting point of the method is that, in many cases, only a limited number of quantities in a system are of interest. Thus, the corresponding DR-PDEE is a one- or two-dimensional partial differential equation (PDE) that governs the instantaneous probability density function (PDF) of the quantity/response(s) of interest in high-dimensional stochastic dynamical systems. This is with the stipulation that the response meets the path continuity condition, and there is no restriction on the excitations being multiplicative or additive. The intrinsic drift and diffusion functions in the DR-PDEE are conditional expectation functions of these responses of the original high-dimensional systems that can be reliably estimated, where assessing the latter is specific to multiplicative noise problems. Interestingly, for a wide class of systems subject to multiplicative local noise, the intrinsic diffusion functions are analytically determinable. Subsequently, the instantaneous PDF of the quantity of interest can be efficiently obtained by numerically integrating the one- or two-dimensional DR-PDEE. The accuracy and efficiency of the DR-PDEE are verified by several typical nonlinear high-dimensional dynamical systems. Particularly, the DR-PDEE captures accurately the refined traits that are easily overlooked, and the tail range of response PDFs.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113929"},"PeriodicalIF":3.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686398","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":"Non-oscillatory entropy stable DG schemes for hyperbolic conservation law","authors":"Yuchang Liu ,&nbsp;Wei Guo ,&nbsp;Yan Jiang ,&nbsp;Mengping Zhang","doi":"10.1016/j.jcp.2025.113926","DOIUrl":"10.1016/j.jcp.2025.113926","url":null,"abstract":"<div><div>In this paper, we propose a class of non-oscillatory, entropy-stable discontinuous Galerkin (NOES-DG) schemes for solving hyperbolic conservation laws. By incorporating a specific form of artificial viscosity, our new scheme directly controls entropy production and suppresses spurious oscillations. To address the stiffness introduced by the artificial terms, which can restrict severely time step sizes, we employ the integrating factor strong stability-preserving Runge-Kutta method for time discretization. Furthermore, our method remains compatible with positivity-preserving limiters under suitable CFL conditions in extreme cases. Various numerical examples demonstrate the efficiency of the proposed scheme, showing that it maintains high-order accuracy in smooth regions and avoids spurious oscillations near discontinuities.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113926"},"PeriodicalIF":3.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644167","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":"Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections","authors":"Dong Min Roh ,&nbsp;Dean Lee ,&nbsp;Pieter Maris ,&nbsp;Esmond Ng ,&nbsp;James P. Vary ,&nbsp;Chao Yang","doi":"10.1016/j.jcp.2025.113921","DOIUrl":"10.1016/j.jcp.2025.113921","url":null,"abstract":"<div><div>Subspace projection methods utilizing perturbative corrections have been proposed for computing the lowest few eigenvalues and corresponding eigenvectors of large Hamiltonian matrices. In this paper, we build upon these methods and introduce the term Subspace Projection with Perturbative Corrections (SPPC) method to refer to this approach. We tailor the SPPC for nuclear many-body Hamiltonians represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). We use the hierarchical structure of the NCSM Hamiltonian to partition the Hamiltonian as the sum of two matrices. The first matrix corresponds to the Hamiltonian represented in a small configuration space, whereas the second is viewed as the perturbation to the first matrix. Eigenvalues and eigenvectors of the first matrix can be computed efficiently. Because of the split, perturbative corrections to the eigenvectors of the first matrix can be obtained efficiently from the solutions of a sequence of linear systems of equations defined in the small configuration space. These correction vectors can be combined with the approximate eigenvectors of the first matrix to construct a subspace from which more accurate approximations of the desired eigenpairs can be obtained. We show by numerical examples that the SPPC method can be more efficient than conventional iterative methods for solving large-scale eigenvalue problems such as the Lanczos, block Lanczos and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The method can also be combined with other methods to avoid convergence stagnation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113921"},"PeriodicalIF":3.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644163","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":"A generalized transformed path integral approach for stochastic processes","authors":"Gnana Murugan Subramaniam,&nbsp;Prakash Vedula","doi":"10.1016/j.jcp.2025.113925","DOIUrl":"10.1016/j.jcp.2025.113925","url":null,"abstract":"<div><div>In this paper, we present the generalized transformed path integral (GTPI) approach: a grid-based path integral approach for probabilistic description in a large class of stochastic dynamical systems. We showcase the application of our proposed approach to non-singular systems, as well as to singular systems such as second-order (and higher-order) dynamical systems, dynamical systems with zero process noise, and certain dynamical systems with non-white noise excitation. As a part of the approach, we present a novel framework for the description of stochastic dynamical systems in terms of a complementary system—the standard transformed stochastic dynamical system—obtained through a dynamic transformation of the state variables. The state mean and covariance of the transformed system do not change with evolution and the choice of our transformation parameters ensure that they are zero and identity respectively. Thus, the probability density function (PDF) for the state of the transformed system can be evolved in a transformed space where greater numerical accuracy for the distribution can be ensured. A fixed grid in the transformed space coordinates corresponds to an adaptive grid in the original space coordinates; it allows the proposed approach to more efficiently address the challenge of large drift, diffusion, or concentration of PDF in the stochastic dynamical system. In addition, error bounds for distributions in the transformed space can be easily obtained using Chebyshev's inequality. We use an operator splitting–based solution of the Fokker-Planck equation associated with the transformed system to derive a novel short-time propagator and update relations for the evolution of the transformed state PDF in the transformed space. Necessary update relations for the mean and covariance of the original state variables, used in the evolution of the transformed state PDF, are derived from the underlying stochastic models. Illustrative examples were considered to showcase the benefits of the GTPI approach over conventional fixed grid (FG) approaches in a large class of stochastic dynamical systems. In all the cases, results obtained using the GTPI approach show excellent agreement with results from Monte Carlo simulations and available analytical (and stationary) solutions, while results from the FG approach show large errors. The effect of simulation parameters and system parameters on the numerical error in our approach were also studied.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113925"},"PeriodicalIF":3.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644165","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":"Mathematical theory and numerical method for subwavelength resonances in multi-layer high contrast elastic media","authors":"Yajuan Wang,&nbsp;Youjun Deng,&nbsp;Fanbo Sun,&nbsp;Lingzheng Kong","doi":"10.1016/j.jcp.2025.113924","DOIUrl":"10.1016/j.jcp.2025.113924","url":null,"abstract":"<div><div>In this paper, we develop a rigorous mathematical framework and numerical method for analyzing and computing the subwavelength resonances of multi-layer structures in elastic system, respectively. The system considered is constituted of a finite alternance of high-contrast segments, called the “resonators”, and a background medium. Firstly, based on layer potential theory, we derive an integral equation explicitly involving the geometric and material configurations. By the Gohberg-Sigal theory, it is theoretically demonstrated that the number of resonance frequencies increases as the number of resonators increases. There are <span><math><mn>6</mn><mo>⋅</mo><mo>⌈</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo></math></span> resonance frequencies for <span><math><mo>⌈</mo><mfrac><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo></math></span> resonators (high contrast domain) within the <em>N</em>-layer structure. In addition, we derive the quantitative expressions for the subwavelength resonance frequencies within concentric balls, i.e., coaxial resonators, calculated by solving the corresponding eigenvalue problem of an explicit matrix. Finally, some numerical experiments are also provided to collaborate with the theoretical results.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113924"},"PeriodicalIF":3.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644164","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":"Multiple scales analysis of a nonlinear timestepping instability in simulations of solitons","authors":"Benjamin A. Hyatt ,&nbsp;Daniel Lecoanet ,&nbsp;Evan H. Anders ,&nbsp;Keaton J. Burns","doi":"10.1016/j.jcp.2025.113923","DOIUrl":"10.1016/j.jcp.2025.113923","url":null,"abstract":"<div><div>The susceptibility of timestepping algorithms to numerical instabilities is an important consideration when simulating partial differential equations (PDEs). Here we identify and analyze a pernicious numerical instability arising in pseudospectral simulations of nonlinear wave propagation resulting in finite-time blow-up. The blow-up time scale is independent of the spatial resolution and spectral basis but sensitive to the timestepping scheme and the timestep size. The instability appears in multi-step and multi-stage implicit-explicit (IMEX) timestepping schemes of different orders of accuracy and has been found to manifest in simulations of soliton solutions of the Korteweg-de Vries (KdV) equation and traveling wave solutions of a nonlinear generalized Klein-Gordon equation. Focusing on the case of KdV solitons, we show that modal predictions from linear stability theory are unable to explain the instability because the spurious growth from linear dispersion is small and nonlinear sources of error growth converge too slowly in the limit of small timestep size. We then develop a novel multi-scale asymptotic framework that captures the slow, nonlinear accumulation of timestepping errors. The framework allows the solution to vary with respect to multiple time scales related to the timestep size and thus recovers the instability as a function of a slow time scale dictated by the order of accuracy of the timestepping scheme. We show that this approach correctly describes our simulations of solitons by making accurate predictions of the blow-up time scale and transient features of the instability. Our work demonstrates that studies of long-time simulations of nonlinear waves should exercise caution when validating their timestepping schemes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113923"},"PeriodicalIF":3.8,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642524","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":"Friedrichs' systems discretized with the DGM: domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions","authors":"Francesco Romor ,&nbsp;Davide Torlo ,&nbsp;Gianluigi Rozza","doi":"10.1016/j.jcp.2025.113915","DOIUrl":"10.1016/j.jcp.2025.113915","url":null,"abstract":"<div><div>Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the linearized Euler equations of gas dynamics, the equations of compressible linear elasticity and the Dirac-Klein-Gordon system. FS were studied to approximate PDEs of mixed elliptic and hyperbolic type in the same domain. For this and other reasons, the discontinuous Galerkin method (DGM) represents the most common and versatile choice of approximation space for FS in the literature. We implement a distributed memory solver for stationary FS in <span>deal.II</span>. Our focus is model order reduction. Since FS model hyperbolic PDEs, they often suffer from a slow Kolmogorov <em>n</em>-width decay. We develop and combine two approaches to tackle this problem in the context of large-scale applications. The first is domain decomposable reduced-order models (DD-ROMs). We will show that the DGM offers a natural formulation of DD-ROMs, in particular regarding interface penalties, compared to the continuous finite element method. We also develop new repartitioning strategies to obtain more efficient local approximations of the solution manifold. The second approach involves shallow graph neural networks used to infer the limit of a succession of projection-based linear ROMs corresponding to lower viscosity constants: the heuristic behind concerns the development of a multi-fidelity super-resolution paradigm to mimic the mathematical convergence to vanishing viscosity solutions while exploiting to the most interpretable and certified projection-based DD-ROMs.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113915"},"PeriodicalIF":3.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644168","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":"Random batch sum-of-Gaussians algorithm for molecular dynamics simulations of Yukawa systems in three dimensions","authors":"Chen Chen ,&nbsp;Jiuyang Liang ,&nbsp;Zhenli Xu","doi":"10.1016/j.jcp.2025.113922","DOIUrl":"10.1016/j.jcp.2025.113922","url":null,"abstract":"<div><div>Yukawa systems have drawn widespread interest across various applications, including plasma physics, colloidal science, and astrophysics, due to their critical role in modeling electrostatic interactions. In this paper, we introduce a novel random batch sum-of-Gaussians (RBSOG) algorithm for molecular dynamics simulations of three-dimensional Yukawa systems with periodic boundary conditions. We develop a sum-of-Gaussians (SOG) decomposition of the Yukawa kernel, dividing the interactions into near-field and far-field components. The near-field component, singular but compactly supported in a local domain, is calculated directly. The far-field component, represented as a sum of smooth Gaussians, is treated using the random batch approximation in Fourier space with an adaptive importance sampling strategy to reduce the variance of force calculations. Unlike the traditional Ewald decomposition, which introduces discontinuities and significant truncation error at the cutoff, the SOG decomposition achieves high-order smoothness and accuracy near the cutoff, allowing for efficient and energy-stable simulations. Additionally, by avoiding the use of the fast Fourier transform, our method achieves optimal <span><math><mi>O</mi><mo>(</mo><mi>N</mi><mo>)</mo></math></span> complexity while maintaining high parallel scalability. Finally, unlike previous random batch approaches, the proposed adaptive importance sampling strategy achieves nearly optimal variance reduction across the regime of the coupling parameters, which is essential for handling varying coupling strengths across weak and strong regimes of electrostatic interactions. Rigorous theoretical analyses are presented, including SOG decomposition construction, variance estimation, and simulation convergence. We validate the performance of RBSOG method through numerical simulations of one-component plasma under weak and strong coupling conditions, using up to 10⁶ particles and 1024 CPU cores. As a practical application in fusion ignition, we simulate high-temperature, high-density deuterium-<em>α</em> mixtures to study the energy exchange between deuterium and high-energy <em>α</em> particles. Due to the flexibility of the Gaussian approximation, the RBSOG method can be readily extended to other dielectric response functions, offering a promising approach for large-scale simulations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"531 ","pages":"Article 113922"},"PeriodicalIF":3.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642523","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":"A two-stage two-derivative fourth order positivity-preserving discontinuous Galerkin method for hyperbolic conservation laws","authors":"Tianjiao Li ,&nbsp;Juan Cheng ,&nbsp;Chi-Wang Shu","doi":"10.1016/j.jcp.2025.113912","DOIUrl":"10.1016/j.jcp.2025.113912","url":null,"abstract":"<div><div>In this paper, a fourth order positivity-preserving (PP) scheme for hyperbolic conservation laws based on the two-stage two-derivative fourth order (<span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>) time discretization and discontinuous Galerkin (DG) spatial discretization is developed. We construct a local Lax–Friedrichs type PP flux in the sense that the DG scheme with this flux satisfies the PP property. We use the strong stability preserving (SSP) <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> time discretization and obtain the PP conditions for one-dimensional scalar conservation laws. With a PP limiter introduced in Zhang and Shu (2010) <span><span>[51]</span></span>, the SSP <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> DG schemes are rendered preserving the positivity without losing conservation or high order accuracy. We carry out the extension of the method to two dimensions on rectangular meshes. Based on this idea, we further develop high-order DG schemes which can preserve the positivity of density and pressure for compressible Euler equations. Numerical tests for the fourth order DG schemes are reported to demonstrate the effectiveness of the algorithms.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"530 ","pages":"Article 113912"},"PeriodicalIF":3.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600548","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":"Unified gas-kinetic wave-particle method for multiscale flow simulation of partially ionized plasma","authors":"Zhigang Pu ,&nbsp;Kun Xu","doi":"10.1016/j.jcp.2025.113918","DOIUrl":"10.1016/j.jcp.2025.113918","url":null,"abstract":"<div><div>The unified gas-kinetic wave-particle (UGKWP) method is constructed for partially ionized plasma (PIP). This method possesses both multiscale and unified preserving (UP) properties. The multiscale property allows the method to capture a wide range of plasma physics, from the particle transport in the kinetic regime to the two-fluid and magnetohydrodynamics (MHD) in the near continuum regimes, with the variation of local cell Knudsen number and normalized Larmor radius. The unified preserving property ensures that the numerical time step is not limited by the particle collision time in the continuum regime for the capturing of dissipative macroscopic solutions of the resistivity, Hall-effect, and all the way to the ideal MHD equations. The UGKWP is clearly distinguishable from the classical single scale particle-in-cell/Monte Carlo Collision (PIC/MCC) methods. The UGKWP method combines the evolution of microscopic velocity distribution with the evolution of macroscopic mean field quantities, granting it UP properties. Moreover, the time step in UGKWP is not constrained by the plasma cyclotron period through the Crank-Nicolson scheme for fluid and electromagnetic field interactions. The momentum and energy exchange between different species is approximated by the Andries-Aoki-Perthame (AAP) model. Overall, the UGKWP method enables a smooth transition from the PIC method in the rarefied regime to the MHD solvers in the continuum regime. This method has been extensively tested on a variety of phenomena ranging from kinetic Landau damping to the macroscopic flow problems, such as the Brio-Wu shock tube, Orszag-Tang vortex, and geospace environmental modeling (GEM) magnetic reconnection. These tests demonstrate that the proposed method can capture the fundamental features of PIP across different scales seamlessly.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"530 ","pages":"Article 113918"},"PeriodicalIF":3.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600549","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}