Pub Date : 2022-06-07DOI: 10.1080/23324309.2022.2103150
John Ferguson, Mathew Eaton, J. Kópházi
Abstract The Continuous Galerkin Virtual Element Method (CG-VEM) is a recent innovation in spatial discretization methods that can solve partial differential equations (PDEs) using polygonal (2D) and polyhedral (3D) meshes. Recently, a new formulation of CG-VEM was introduced which can construct VEM spaces on polygons with curvilinear edges. This paper presents the application of the curved VEM to the multigroup neutron diffusion equation and demonstrates its benefits over the conventional straight-sided VEM for a number of benchmark verification test cases with curvilinear domains. These domains were constructed using a topological data-structure developed as part of this paper, based on the doubly-connected edge list, with curves and surfaces both represented using non-uniform rational B-splines (NURBS). This data-structure is used both to specify the geometry of the reactor and to represent the curvilinear polygonal mesh. We also present two separate methods of performing integrations on curvilinear polygons, one for homogeneous functions and one for non-homogeneous functions.
{"title":"NURBS Enhanced Virtual Element Methods for the Spatial Discretization of the Multigroup Neutron Diffusion Equation on Curvilinear Polygonal Meshes","authors":"John Ferguson, Mathew Eaton, J. Kópházi","doi":"10.1080/23324309.2022.2103150","DOIUrl":"https://doi.org/10.1080/23324309.2022.2103150","url":null,"abstract":"Abstract The Continuous Galerkin Virtual Element Method (CG-VEM) is a recent innovation in spatial discretization methods that can solve partial differential equations (PDEs) using polygonal (2D) and polyhedral (3D) meshes. Recently, a new formulation of CG-VEM was introduced which can construct VEM spaces on polygons with curvilinear edges. This paper presents the application of the curved VEM to the multigroup neutron diffusion equation and demonstrates its benefits over the conventional straight-sided VEM for a number of benchmark verification test cases with curvilinear domains. These domains were constructed using a topological data-structure developed as part of this paper, based on the doubly-connected edge list, with curves and surfaces both represented using non-uniform rational B-splines (NURBS). This data-structure is used both to specify the geometry of the reactor and to represent the curvilinear polygonal mesh. We also present two separate methods of performing integrations on curvilinear polygons, one for homogeneous functions and one for non-homogeneous functions.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"51 1","pages":"145 - 204"},"PeriodicalIF":0.7,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49300312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-28DOI: 10.1080/23324309.2022.2103151
W. Bennett, R. McClarren
Abstract The widely used AZURV1 transport benchmarks package provides a suite of solutions to isotropic scattering transport problems with a variety of initial conditions. Most of these solutions have an initial condition that is a Dirac delta function in space; as a result these benchmarks are challenging problems to use for verification tests in computer codes. Nevertheless, approximating a delta function in simulation often leads to low orders of convergence and the inability to test the convergence of high-order numerical methods. While there are examples in the literature of integration of these solutions as Green’s functions for the transport operator to produce results for more easily simulated sources, they are limited in scope and briefly explained. For a sampling of initial conditions and sources, we present solutions for the uncollided and collided scalar flux to facilitate accurate testing of source treatment in numerical solvers. The solution for the uncollided scalar flux is found in analytic form for some sources. Since integrating the Green’s functions is often nontrivial, discussion of integration difficulty and workarounds to find convergent integrals is included. Additionally, our uncollided solutions can be used as source terms in verification studies, in a similar way to the method of manufactured solutions.
{"title":"Benchmarks for Infinite Medium, Time Dependent Transport Problems with Isotropic Scattering","authors":"W. Bennett, R. McClarren","doi":"10.1080/23324309.2022.2103151","DOIUrl":"https://doi.org/10.1080/23324309.2022.2103151","url":null,"abstract":"Abstract The widely used AZURV1 transport benchmarks package provides a suite of solutions to isotropic scattering transport problems with a variety of initial conditions. Most of these solutions have an initial condition that is a Dirac delta function in space; as a result these benchmarks are challenging problems to use for verification tests in computer codes. Nevertheless, approximating a delta function in simulation often leads to low orders of convergence and the inability to test the convergence of high-order numerical methods. While there are examples in the literature of integration of these solutions as Green’s functions for the transport operator to produce results for more easily simulated sources, they are limited in scope and briefly explained. For a sampling of initial conditions and sources, we present solutions for the uncollided and collided scalar flux to facilitate accurate testing of source treatment in numerical solvers. The solution for the uncollided scalar flux is found in analytic form for some sources. Since integrating the Green’s functions is often nontrivial, discussion of integration difficulty and workarounds to find convergent integrals is included. Additionally, our uncollided solutions can be used as source terms in verification studies, in a similar way to the method of manufactured solutions.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"51 1","pages":"205 - 221"},"PeriodicalIF":0.7,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48540065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-16DOI: 10.1080/23324309.2022.2063901
G. Coppa
Abstract Starting from the similarity between the spherical harmonics approximation of order one to the linear transport equation (usually referred as P 1 approximation) and the Klein-Gordon equation of the quantum physics, an extended set of equations is introduced, which is proved to be equivalent to the Dirac equation with imaginary mass. Conversely, when a real mass is restored into the extended P 1 system, a new equation is obtained, whose solutions are superposition of the spinors for a spin particle and the corresponding antiparticle.
{"title":"A Transport Theory Route to the Dirac Equation","authors":"G. Coppa","doi":"10.1080/23324309.2022.2063901","DOIUrl":"https://doi.org/10.1080/23324309.2022.2063901","url":null,"abstract":"Abstract Starting from the similarity between the spherical harmonics approximation of order one to the linear transport equation (usually referred as P 1 approximation) and the Klein-Gordon equation of the quantum physics, an extended set of equations is introduced, which is proved to be equivalent to the Dirac equation with imaginary mass. Conversely, when a real mass is restored into the extended P 1 system, a new equation is obtained, whose solutions are superposition of the spinors for a spin particle and the corresponding antiparticle.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"51 1","pages":"54 - 65"},"PeriodicalIF":0.7,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47203688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-16DOI: 10.1080/23324309.2022.2086264
D. C. Sahni
Abstract An important correction in an earlier paper by the author is presented.
摘要本文提出了作者在先前的一篇论文中的一项重要更正。
{"title":"Corrigendum - Density Transform Method for Particle Transport Problems in Spherical Geometry with Linearly Anisotropic Scattering","authors":"D. C. Sahni","doi":"10.1080/23324309.2022.2086264","DOIUrl":"https://doi.org/10.1080/23324309.2022.2086264","url":null,"abstract":"Abstract An important correction in an earlier paper by the author is presented.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"51 1","pages":"139 - 144"},"PeriodicalIF":0.7,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44003710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-16DOI: 10.1080/23324309.2022.2078369
H. Öztürk, Ahmet Tuğralı
Abstract The first application of the U N (Chebyshev polynomials of the second kind) method with higher order approximations is performed to solve the neutron diffusion problem in a slab reactor. The moments of equations are carried out by solving neutron transport equation using first the conventional spherical harmonics (P N) and then the U N method. These differential equations with constant coefficients are then solved together to obtain the diffusion equation corresponding to related approximation. The roots of the diffusion equation are estimated to calculate the diffusion lengths of the neutrons for various values of c, the number of secondary neutrons per collision. Numerical results obtained by the present method with its easily executable equations are tabulated with the ones already existing in literature. A good accordance is observed between them. Better results are also obtained than the conventional P N method for certain values of c.
{"title":"Higher Order U N Method for the Solution of the Neutron Diffusion Problem","authors":"H. Öztürk, Ahmet Tuğralı","doi":"10.1080/23324309.2022.2078369","DOIUrl":"https://doi.org/10.1080/23324309.2022.2078369","url":null,"abstract":"Abstract The first application of the U N (Chebyshev polynomials of the second kind) method with higher order approximations is performed to solve the neutron diffusion problem in a slab reactor. The moments of equations are carried out by solving neutron transport equation using first the conventional spherical harmonics (P N) and then the U N method. These differential equations with constant coefficients are then solved together to obtain the diffusion equation corresponding to related approximation. The roots of the diffusion equation are estimated to calculate the diffusion lengths of the neutrons for various values of c, the number of secondary neutrons per collision. Numerical results obtained by the present method with its easily executable equations are tabulated with the ones already existing in literature. A good accordance is observed between them. Better results are also obtained than the conventional P N method for certain values of c.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"51 1","pages":"66 - 79"},"PeriodicalIF":0.7,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48030517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-16DOI: 10.1080/23324309.2022.2086572
Chih-Yang Wu, D. Hong
Abstract Light transport with fluorescence in a phosphor layer based on radiative transfer theory is an efficient tool for understanding the performance of a phosphor-converted light-emitting diode. In this work, the models based on radiative transfer theory including light conversion of phosphor particles are developed for calculating the light transport in planar remote phosphor layers. The models developed include an ordinary differential approximation and an improved model based on the differential approximation and an integral formulation of the transmission light flux for a phosphor layer with Fresnel boundaries. We calculate the light extraction efficiency (LEE) of a phosphor layer as a function of various parameters, such as the thickness of the layer and the concentration of phosphor. The present models are validated by comparing the results obtained by the present methods, the double spherical harmonics method of order one and a Monte Carlo method. Comparing the results obtained by those methods, one can see that the improvement based on the differential approximation and integral formulation of transmission light flux for calculating the LEE can yield better results for optically thin cases.
{"title":"An Improved Model for Light Transport in the Color Conversion Element of Light-Emitting Diodes","authors":"Chih-Yang Wu, D. Hong","doi":"10.1080/23324309.2022.2086572","DOIUrl":"https://doi.org/10.1080/23324309.2022.2086572","url":null,"abstract":"Abstract Light transport with fluorescence in a phosphor layer based on radiative transfer theory is an efficient tool for understanding the performance of a phosphor-converted light-emitting diode. In this work, the models based on radiative transfer theory including light conversion of phosphor particles are developed for calculating the light transport in planar remote phosphor layers. The models developed include an ordinary differential approximation and an improved model based on the differential approximation and an integral formulation of the transmission light flux for a phosphor layer with Fresnel boundaries. We calculate the light extraction efficiency (LEE) of a phosphor layer as a function of various parameters, such as the thickness of the layer and the concentration of phosphor. The present models are validated by comparing the results obtained by the present methods, the double spherical harmonics method of order one and a Monte Carlo method. Comparing the results obtained by those methods, one can see that the improvement based on the differential approximation and integral formulation of transmission light flux for calculating the LEE can yield better results for optically thin cases.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"51 1","pages":"101 - 111"},"PeriodicalIF":0.7,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44660403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-16DOI: 10.1080/23324309.2022.2063900
Gaël Poëtte
Abstract Monte Carlo-generalized Polynomial Chaos (MC-gPC) has already been thoroughly studied in the literature. MC-gPC both builds a gPC based reduced model of a partial differential equation (PDE) of interest and solves it with an intrusive MC scheme in order to propagate uncertainties. This reduced model captures the behavior of the solution of a set of PDEs subject to some uncertain parameters modeled by random variables. MC-gPC is an intrusive method, it needs modifications of a code in order to be applied. This may be considered a drawback. But, on another hand, important computational gains obtained with MC-gPC have been observed on many applications. The MC-gPC resolution of Boltzmann equation has been investigated in many different ways: the wellposedness of the gPC based reduced model has been proved, the convergence with respect to the truncation order P has been theoretically and numerically studied and the coupling to nonlinear physics has been performed. But the study of the MC noise remains, to our knowledge, to be done. This is the purpose of this paper. We are interested in understanding what can be expected in terms of error estimations with respect to NMC , the number of MC particles. For this, we estimate the variances of non-intrusive gPC and MC-gPC, theoretically and numerically, and compare them in several configurations for several MC schemes (the semi-analog and the non-analog ones). The results show that the MC schemes of the literature used to solve MC-gPC present an excess of variance with respect to the non-intrusive strategies for comparable particle numbers NMC (even if this excess of variance remains acceptable and competitive in many situations).
{"title":"Numerical Analysis of the Monte-Carlo Noise for the Resolution of the Deterministic and Uncertain Linear Boltzmann Equation (Comparison of Non-Intrusive gPC and MC-gPC)","authors":"Gaël Poëtte","doi":"10.1080/23324309.2022.2063900","DOIUrl":"https://doi.org/10.1080/23324309.2022.2063900","url":null,"abstract":"Abstract Monte Carlo-generalized Polynomial Chaos (MC-gPC) has already been thoroughly studied in the literature. MC-gPC both builds a gPC based reduced model of a partial differential equation (PDE) of interest and solves it with an intrusive MC scheme in order to propagate uncertainties. This reduced model captures the behavior of the solution of a set of PDEs subject to some uncertain parameters modeled by random variables. MC-gPC is an intrusive method, it needs modifications of a code in order to be applied. This may be considered a drawback. But, on another hand, important computational gains obtained with MC-gPC have been observed on many applications. The MC-gPC resolution of Boltzmann equation has been investigated in many different ways: the wellposedness of the gPC based reduced model has been proved, the convergence with respect to the truncation order P has been theoretically and numerically studied and the coupling to nonlinear physics has been performed. But the study of the MC noise remains, to our knowledge, to be done. This is the purpose of this paper. We are interested in understanding what can be expected in terms of error estimations with respect to NMC , the number of MC particles. For this, we estimate the variances of non-intrusive gPC and MC-gPC, theoretically and numerically, and compare them in several configurations for several MC schemes (the semi-analog and the non-analog ones). The results show that the MC schemes of the literature used to solve MC-gPC present an excess of variance with respect to the non-intrusive strategies for comparable particle numbers NMC (even if this excess of variance remains acceptable and competitive in many situations).","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"51 1","pages":"1 - 53"},"PeriodicalIF":0.7,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49009556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-16DOI: 10.1080/23324309.2022.2091601
H. Koklu, O. Ozer
Abstract The scattering function analysis is done by Chebyshev and Legendre polynomials in the neutron transport equation. The effect of the scattering coefficients on the critical thicknesses are presented in tables. The analyses are done for PN , TN , and UN methods up to fourth order of the scattering function. By making calculations, the critical thicknesses are obtained with Mark and Marshak boundary conditions. The critical thickness results are found for the corresponding secondary neutron number (c) in tetra anisotropic scattering. So, the neutron transport equation solutions have been done for three different solution methods with two boundary conditions in plane geometrical bare systems. Finally, the numerical results for different scattering types and a brief comment are given in results and discussion. It is shown that our results are in agreement with the existing literature.
{"title":"Analyzing of the Scattering Coefficients in the Neutron Transport Equation for Critical Systems","authors":"H. Koklu, O. Ozer","doi":"10.1080/23324309.2022.2091601","DOIUrl":"https://doi.org/10.1080/23324309.2022.2091601","url":null,"abstract":"Abstract The scattering function analysis is done by Chebyshev and Legendre polynomials in the neutron transport equation. The effect of the scattering coefficients on the critical thicknesses are presented in tables. The analyses are done for PN , TN , and UN methods up to fourth order of the scattering function. By making calculations, the critical thicknesses are obtained with Mark and Marshak boundary conditions. The critical thickness results are found for the corresponding secondary neutron number (c) in tetra anisotropic scattering. So, the neutron transport equation solutions have been done for three different solution methods with two boundary conditions in plane geometrical bare systems. Finally, the numerical results for different scattering types and a brief comment are given in results and discussion. It is shown that our results are in agreement with the existing literature.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"51 1","pages":"112 - 138"},"PeriodicalIF":0.7,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41663051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-04DOI: 10.1080/23324309.2022.2032757
R. McClarren
Abstract Semi-analytic solutions for high-energy density radiation diffusion problems in slab geometry using a two-group model for the frequency (photon energy) variable are presented. To obtain these solutions we specify forms for the heat capacity and emissivity in the high energy group that are a function of the fraction of radiation emission in the low energy group in order to linearize the problem. This results in a linear system of equations that are solved via Laplace and Fourier transforms: the Laplace transform is inverted analytically and the inverse Fourier transform is computed using numerical integration. It is demonstrated that these solutions can be useful in verifying codes for solving the radiation diffusion equations in the high-energy density regime. Additionally, we include solutions for an optically thick problem that can be used to test the asymptotic diffusion limit of codes solving a transport model for radiative transfer.
{"title":"Two-Group Radiative Transfer Benchmarks for the Non-Equilibrium Diffusion Model","authors":"R. McClarren","doi":"10.1080/23324309.2022.2032757","DOIUrl":"https://doi.org/10.1080/23324309.2022.2032757","url":null,"abstract":"Abstract Semi-analytic solutions for high-energy density radiation diffusion problems in slab geometry using a two-group model for the frequency (photon energy) variable are presented. To obtain these solutions we specify forms for the heat capacity and emissivity in the high energy group that are a function of the fraction of radiation emission in the low energy group in order to linearize the problem. This results in a linear system of equations that are solved via Laplace and Fourier transforms: the Laplace transform is inverted analytically and the inverse Fourier transform is computed using numerical integration. It is demonstrated that these solutions can be useful in verifying codes for solving the radiation diffusion equations in the high-energy density regime. Additionally, we include solutions for an optically thick problem that can be used to test the asymptotic diffusion limit of codes solving a transport model for radiative transfer.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"50 1","pages":"583 - 597"},"PeriodicalIF":0.7,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42551503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-29DOI: 10.1080/23324309.2021.1942062
R. Y. Nesterenko
Abstract The work is an extended version of the report presented at the conference ICTT-26. In the Part I we derive the forward and backward time-dependent linear stochastic equations for probability density of the integer number of neutrons and delayed neutron precursors in distributed model of a nuclear reactor. In the Part II we derive the distributed criticality stochastic equations and obtain the analytical solutions for asymptotic neutron number probability density function for a reactor in a close-to-critical state.
{"title":"Stochastic Theory of Neutron Transport in Nuclear Reactor","authors":"R. Y. Nesterenko","doi":"10.1080/23324309.2021.1942062","DOIUrl":"https://doi.org/10.1080/23324309.2021.1942062","url":null,"abstract":"Abstract The work is an extended version of the report presented at the conference ICTT-26. In the Part I we derive the forward and backward time-dependent linear stochastic equations for probability density of the integer number of neutrons and delayed neutron precursors in distributed model of a nuclear reactor. In the Part II we derive the distributed criticality stochastic equations and obtain the analytical solutions for asymptotic neutron number probability density function for a reactor in a close-to-critical state.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"50 1","pages":"528 - 582"},"PeriodicalIF":0.7,"publicationDate":"2021-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46285183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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