Roman Cherniha, Vasyl' Davydovych, Joanna Stachowska-Pietka, Jacek Waniewski
A mathematical model for the poroelastic materials (PEM) with the variable volume is developed in multidimensional case. Governing equations of the model are constructed using the continuity equations, which reflect the well-known physical laws. The deformation vector is specified using the Terzaghi effective stress tensor. In the two-dimensional space case, the model is studied by analytical methods. Using the classical Lie method, it is proved that the relevant nonlinear system of the (1+2)-dimensional governing equations admits highly nontrivial Lie symmetries leading to an infinite-dimensional Lie algebra. The radially-symmetric case is studied in details. It is shown how correct boundary conditions in the case of PEM in the form of a ring and an annulus are constructed. As a result, boundary-value problems with a moving boundary describing the ring (annulus) deformation are constructed. The relevant nonlinear boundary-value problems are analytically solved in the stationary case. In particular, the analytical formulae for unknown deformations and an unknown radius of the annulus are presented.
{"title":"Analysis of a Mathematical Model for Fluid Transport in Poroelastic Materials in 2D Space","authors":"Roman Cherniha, Vasyl' Davydovych, Joanna Stachowska-Pietka, Jacek Waniewski","doi":"arxiv-2409.11949","DOIUrl":"https://doi.org/arxiv-2409.11949","url":null,"abstract":"A mathematical model for the poroelastic materials (PEM) with the variable\u0000volume is developed in multidimensional case. Governing equations of the model\u0000are constructed using the continuity equations, which reflect the well-known\u0000physical laws. The deformation vector is specified using the Terzaghi effective\u0000stress tensor. In the two-dimensional space case, the model is studied by\u0000analytical methods. Using the classical Lie method, it is proved that the\u0000relevant nonlinear system of the (1+2)-dimensional governing equations admits\u0000highly nontrivial Lie symmetries leading to an infinite-dimensional Lie\u0000algebra. The radially-symmetric case is studied in details. It is shown how\u0000correct boundary conditions in the case of PEM in the form of a ring and an\u0000annulus are constructed. As a result, boundary-value problems with a moving\u0000boundary describing the ring (annulus) deformation are constructed. The relevant nonlinear boundary-value problems are analytically solved in the\u0000stationary case. In particular, the analytical formulae for unknown\u0000deformations and an unknown radius of the annulus are presented.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Conjugate line parametrizations of surfaces were first discretized almost a century ago as quad meshes with planar faces. With the recent development of discrete differential geometry, two discretizations of principal curvature line parametrizations were discovered: circular nets and conical nets, both of which are special cases of discrete conjugate nets. Subsequently, circular and conical nets were given a unified description as isotropic line congruences in the Lie quadric. We propose a generalization by considering polar pairs of line congruences in the ambient space of the Lie quadric. These correspond to pairs of discrete conjugate nets with orthogonal edges, which we call principal binets, a new and more general discretization of principal curvature line parametrizations. We also introduce two new discretizations of orthogonal and Gauss-orthogonal parametrizations. All our discretizations are subject to the transformation group principle, which means that they satisfy the corresponding Lie, M"obius, or Laguerre invariance respectively, in analogy to the smooth theory. Finally, we show that they satisfy the consistency principle, which means that our definitions generalize to higher dimensional square lattices. Our work expands on recent work by Dellinger on checkerboard patterns.
{"title":"Principal binets","authors":"Niklas Christoph Affolter, Jan Techter","doi":"arxiv-2409.11322","DOIUrl":"https://doi.org/arxiv-2409.11322","url":null,"abstract":"Conjugate line parametrizations of surfaces were first discretized almost a\u0000century ago as quad meshes with planar faces. With the recent development of\u0000discrete differential geometry, two discretizations of principal curvature line\u0000parametrizations were discovered: circular nets and conical nets, both of which\u0000are special cases of discrete conjugate nets. Subsequently, circular and\u0000conical nets were given a unified description as isotropic line congruences in\u0000the Lie quadric. We propose a generalization by considering polar pairs of line\u0000congruences in the ambient space of the Lie quadric. These correspond to pairs\u0000of discrete conjugate nets with orthogonal edges, which we call principal\u0000binets, a new and more general discretization of principal curvature line\u0000parametrizations. We also introduce two new discretizations of orthogonal and\u0000Gauss-orthogonal parametrizations. All our discretizations are subject to the\u0000transformation group principle, which means that they satisfy the corresponding\u0000Lie, M\"obius, or Laguerre invariance respectively, in analogy to the smooth\u0000theory. Finally, we show that they satisfy the consistency principle, which\u0000means that our definitions generalize to higher dimensional square lattices.\u0000Our work expands on recent work by Dellinger on checkerboard patterns.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a gradient flow model is proposed for conducting ground state calculations in Wigner formalism of many-body system in the framework of density functional theory. More specifically, an energy functional for the ground state in Wigner formalism is proposed to provide a new perspective for ground state calculations of the Wigner function. Employing density functional theory, a gradient flow model is designed based on the energy functional to obtain the ground state Wigner function representing the whole many-body system. Subsequently, an efficient algorithm is developed using the operator splitting method and the Fourier spectral collocation method, whose numerical complexity of single iteration is $O(n_{rm DoF}log n_{rm DoF})$. Numerical experiments demonstrate the anticipated accuracy, encompassing the one-dimensional system with up to $2^{21}$ particles and the three-dimensional system with defect, showcasing the potential of our approach to large-scale simulations and computations of systems with defect.
{"title":"A gradient flow model for ground state calculations in Wigner formalism based on density functional theory","authors":"Guanghui Hu, Ruo Li, Hongfei Zhan","doi":"arxiv-2409.10851","DOIUrl":"https://doi.org/arxiv-2409.10851","url":null,"abstract":"In this paper, a gradient flow model is proposed for conducting ground state\u0000calculations in Wigner formalism of many-body system in the framework of\u0000density functional theory. More specifically, an energy functional for the\u0000ground state in Wigner formalism is proposed to provide a new perspective for\u0000ground state calculations of the Wigner function. Employing density functional\u0000theory, a gradient flow model is designed based on the energy functional to\u0000obtain the ground state Wigner function representing the whole many-body\u0000system. Subsequently, an efficient algorithm is developed using the operator\u0000splitting method and the Fourier spectral collocation method, whose numerical\u0000complexity of single iteration is $O(n_{rm DoF}log n_{rm DoF})$. Numerical\u0000experiments demonstrate the anticipated accuracy, encompassing the\u0000one-dimensional system with up to $2^{21}$ particles and the three-dimensional\u0000system with defect, showcasing the potential of our approach to large-scale\u0000simulations and computations of systems with defect.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
k-Contact geometry appeared as a generalisation of contact geometry to analyse field theories. This work provides a new insightful approach to k-contact geometry by devising a theory of k-contact forms and proving that the kernel of a k-contact form is locally equivalent to a distribution of corank k that is distributionally maximally non-integrable and admits k commuting Lie symmetries: a so-called k-contact distribution. Compact manifolds admitting a global k-contact form are analysed, we give necessary topological conditions for their existence, k-contact Lie groups are defined and studied, we extend the Weinstein conjecture for the existence of closed orbits of Reeb vector fields in compact manifolds to the k-contact setting after studying compact low-dimensional manifolds endowed with a global k-contact form, and we provide some physical applications of some of our results. Polarisations for k-contact distributions are introduced and it is shown that a polarised k-contact distribution is locally diffeomorphic to the Cartan distribution of the first-order jet bundle over a fibre bundle of order k, which is a globally defined polarised k-contact distribution. Then, we relate k-contact manifolds to presymplectic and k-symplectic manifolds on fibre bundles of larger dimension and define for the first time types of submanifolds in k-contact geometry. We also review the theory of Hamiltonian k-vector fields, studying Hamilton-De Donder-Weyl equations in general and in Lie groups, which are here studied in an unprecedented manner. A theory of k-contact Hamiltonian vector fields is developed, which describes the theory of characteristics for Lie symmetries for first-order partial differential equations in a k-contact Hamiltonian manner. Our new Hamiltonian k-contact techniques are illustrated by analysing Hamilton-Jacobi and Dirac equations.
k-contact geometry（接触几何）是接触几何的一种概括，用于分析场论。本研究通过设计 k 接触形式理论，证明 k 接触形式的内核局部等价于 corank k 分布，而 corank k 分布具有最大不可整性，并允许 k 共线对称：即所谓的 k 接触分布，为接触几何学提供了一种新的有洞察力的方法。我们分析了容许全局 k 接触形式的紧凑流形，给出了它们存在的必要拓扑条件，定义并研究了 k 接触李群，在研究了禀赋全局 k 接触形式的紧凑低维流形之后，我们将紧凑流形中里布向量场闭轨道存在性的温斯坦猜想扩展到了 k 接触环境，并提供了我们一些结果的物理应用。我们引入了 k-contact 分布的极化，并证明极化的 k-contact 分布与 k 阶纤维束上的一阶喷流束的 Cartan 分布局部差分同构，后者是全局定义的极化 k-contact 分布。然后，我们将 k 接触流形与更大维度纤维束上的预交错流形和 k 交错流形联系起来，并首次定义了 k 接触几何学中的子流形类型。我们还回顾了哈密顿 k 向量场理论，研究了一般和李群中的哈密顿-德-多德-韦尔方程，并以前所未有的方式对其进行了研究。我们提出了哈密顿 k 接触向量场理论，它以哈密顿 k 接触方式描述了一阶偏微分方程的李斯对称特征理论。通过分析汉密尔顿-雅各比方程和狄拉克方程，我们的新汉密尔顿 k-contact 技术得到了说明。
{"title":"Foundations on k-contact geometry","authors":"Javier de Lucas, Xavier Rivas, Tomasz Sobczak","doi":"arxiv-2409.11001","DOIUrl":"https://doi.org/arxiv-2409.11001","url":null,"abstract":"k-Contact geometry appeared as a generalisation of contact geometry to\u0000analyse field theories. This work provides a new insightful approach to\u0000k-contact geometry by devising a theory of k-contact forms and proving that the\u0000kernel of a k-contact form is locally equivalent to a distribution of corank k\u0000that is distributionally maximally non-integrable and admits k commuting Lie\u0000symmetries: a so-called k-contact distribution. Compact manifolds admitting a\u0000global k-contact form are analysed, we give necessary topological conditions\u0000for their existence, k-contact Lie groups are defined and studied, we extend\u0000the Weinstein conjecture for the existence of closed orbits of Reeb vector\u0000fields in compact manifolds to the k-contact setting after studying compact\u0000low-dimensional manifolds endowed with a global k-contact form, and we provide\u0000some physical applications of some of our results. Polarisations for k-contact\u0000distributions are introduced and it is shown that a polarised k-contact\u0000distribution is locally diffeomorphic to the Cartan distribution of the\u0000first-order jet bundle over a fibre bundle of order k, which is a globally\u0000defined polarised k-contact distribution. Then, we relate k-contact manifolds\u0000to presymplectic and k-symplectic manifolds on fibre bundles of larger\u0000dimension and define for the first time types of submanifolds in k-contact\u0000geometry. We also review the theory of Hamiltonian k-vector fields, studying\u0000Hamilton-De Donder-Weyl equations in general and in Lie groups, which are here\u0000studied in an unprecedented manner. A theory of k-contact Hamiltonian vector\u0000fields is developed, which describes the theory of characteristics for Lie\u0000symmetries for first-order partial differential equations in a k-contact\u0000Hamiltonian manner. Our new Hamiltonian k-contact techniques are illustrated by\u0000analysing Hamilton-Jacobi and Dirac equations.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We examine the color-kinematics duality within the BV formalism, highlighting its emergence as a feature of specific gauge-fixed actions. Our goal is to establish a general framework for studying the duality while investigating straightforward examples of off-shell color-kinematics duality. In this context, we revisit Chern-Simons theory as well as introduce new examples, including BF theory and 2D Yang-Mills theory, which are shown to exhibit the duality off-shell. We emphasize that the geometric structures responsible for flat-space color-kinematics duality appear for general curved spaces as well.
{"title":"Off-shell color-kinematics duality from codifferentials","authors":"Maor Ben-Shahar, Francesco Bonechi, Maxim Zabzine","doi":"arxiv-2409.11484","DOIUrl":"https://doi.org/arxiv-2409.11484","url":null,"abstract":"We examine the color-kinematics duality within the BV formalism, highlighting\u0000its emergence as a feature of specific gauge-fixed actions. Our goal is to\u0000establish a general framework for studying the duality while investigating\u0000straightforward examples of off-shell color-kinematics duality. In this\u0000context, we revisit Chern-Simons theory as well as introduce new examples,\u0000including BF theory and 2D Yang-Mills theory, which are shown to exhibit the\u0000duality off-shell. We emphasize that the geometric structures responsible for\u0000flat-space color-kinematics duality appear for general curved spaces as well.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove eigenvalue bounds for two-dimensional linearized disturbances of parallel flows of micropolar fluids, deriving the Orr-Sommerfeld equations and providing a sufficient condition for linear stability of such flows. We also derive wave speed bounds.
{"title":"Stability and eigenvalue bounds for micropolar shear flows","authors":"Pablo Braz e Silva, Jackellyny Carvalho","doi":"arxiv-2409.11584","DOIUrl":"https://doi.org/arxiv-2409.11584","url":null,"abstract":"We prove eigenvalue bounds for two-dimensional linearized disturbances of\u0000parallel flows of micropolar fluids, deriving the Orr-Sommerfeld equations and\u0000providing a sufficient condition for linear stability of such flows. We also\u0000derive wave speed bounds.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Oscillations of black hole spacetimes exhibit divergent behavior toward the bifurcation sphere and spatial infinity. This divergence can be understood as a consequence of the geometry in these spacetime regions. In contrast, black-hole oscillations are regular when evaluated toward the event horizon and null infinity. Hyperboloidal surfaces naturally connect these regions, providing a geometric regularization of time-harmonic oscillations called quasinormal modes (QNMs). This review traces the historical development of the hyperboloidal approach to QNMs. We discuss the physical motivation for the hyperboloidal approach and highlight current developments in the field.
{"title":"Hyperboloidal Approach to Quasinormal Modes","authors":"Rodrigo Panosso Macedo, Anil Zenginoglu","doi":"arxiv-2409.11478","DOIUrl":"https://doi.org/arxiv-2409.11478","url":null,"abstract":"Oscillations of black hole spacetimes exhibit divergent behavior toward the\u0000bifurcation sphere and spatial infinity. This divergence can be understood as a\u0000consequence of the geometry in these spacetime regions. In contrast, black-hole\u0000oscillations are regular when evaluated toward the event horizon and null\u0000infinity. Hyperboloidal surfaces naturally connect these regions, providing a\u0000geometric regularization of time-harmonic oscillations called quasinormal modes\u0000(QNMs). This review traces the historical development of the hyperboloidal\u0000approach to QNMs. We discuss the physical motivation for the hyperboloidal\u0000approach and highlight current developments in the field.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Two $q$-analogs of the hypercube graph are introduced and shown to be related through a graph quotient. The roles of the subspace lattice graph, of a twisted primitive elements of $U_q(mathfrak{su}(2))$ and of the dual $q$-Krawtchouk polynomials are elaborated upon. This paper is dedicated to Tom Koornwinder.
{"title":"A tale of two $q$-deformations : connecting dual polar spaces and weighted hypercubes","authors":"Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet","doi":"arxiv-2409.11243","DOIUrl":"https://doi.org/arxiv-2409.11243","url":null,"abstract":"Two $q$-analogs of the hypercube graph are introduced and shown to be related\u0000through a graph quotient. The roles of the subspace lattice graph, of a twisted\u0000primitive elements of $U_q(mathfrak{su}(2))$ and of the dual $q$-Krawtchouk\u0000polynomials are elaborated upon. This paper is dedicated to Tom Koornwinder.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a third order operator under the three-point Dirichlet condition. Its spectrum is the so-called auxiliary spectrum for the good Boussinesq equation, as well as the Dirichlet spectrum for the Schr"odinger operator on the unit interval is the auxiliary spectrum for the periodic KdV equation. The auxiliary spectrum is formed by projections of the points of the divisor onto the spectral plane. We estimate the spectrum and the corresponding norming constants in terms of small operator coefficients. This work is the first in a series of papers devoted to solving the inverse problem for the Boussinesq equation.
{"title":"Asymptotics of the divisor for the good Boussinesq equation","authors":"Andrey Badanin, Andrey Badanin","doi":"arxiv-2409.10988","DOIUrl":"https://doi.org/arxiv-2409.10988","url":null,"abstract":"We consider a third order operator under the three-point Dirichlet condition.\u0000Its spectrum is the so-called auxiliary spectrum for the good Boussinesq\u0000equation, as well as the Dirichlet spectrum for the Schr\"odinger operator on\u0000the unit interval is the auxiliary spectrum for the periodic KdV equation. The\u0000auxiliary spectrum is formed by projections of the points of the divisor onto\u0000the spectral plane. We estimate the spectrum and the corresponding norming\u0000constants in terms of small operator coefficients. This work is the first in a\u0000series of papers devoted to solving the inverse problem for the Boussinesq\u0000equation.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"207 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fourier analysis on the discrete hypercubes ${-1,1}^n$ has found numerous applications in learning theory. A recent breakthrough involves the use of a classical result from Fourier analysis, the Bohnenblust--Hille inequality, in the context of learning low-degree Boolean functions. In these lecture notes, we explore this line of research and discuss recent progress in discrete quantum systems and classical Fourier analysis.
{"title":"Three lectures on Fourier analysis and learning theory","authors":"Haonan Zhang","doi":"arxiv-2409.10886","DOIUrl":"https://doi.org/arxiv-2409.10886","url":null,"abstract":"Fourier analysis on the discrete hypercubes ${-1,1}^n$ has found numerous\u0000applications in learning theory. A recent breakthrough involves the use of a\u0000classical result from Fourier analysis, the Bohnenblust--Hille inequality, in\u0000the context of learning low-degree Boolean functions. In these lecture notes,\u0000we explore this line of research and discuss recent progress in discrete\u0000quantum systems and classical Fourier analysis.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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