Pub Date : 2020-10-22DOI: 10.1080/23324309.2020.1834407
Z. I. Böröczki, M. Szieberth, A. Rineiski, F. Gabrielli
Abstract In this article, different angular flux discretization options, namely discrete ordinates representation and spherical harmonics expansion are compared from the viewpoint of the accuracy of perturbation calculations. The PARTISN discrete ordinates neutron transport solver was coupled with the SEnTRi code, developed at BME, in order to perform perturbation theory calculations in different types of geometry descriptions and angular representations. With the help of the implemented code, the effect of the angular and spatial discretization on the results of perturbation theory calculations was investigated. Exact matches were observed in Cartesian geometries with the direct perturbation method when the discrete ordinates angular representation was used, and small discrepancies were found when the spherical harmonics expansion was applied. In cylindrical geometries, slight differences were observed with both angular expansions, which originate from the nature of the adjoint transport operator in curvilinear coordinate systems. The differences can be reduced to a negligible level with increased expansion order in both cases. Small discrepancies can have a significant effect in sensitivity, uncertainty and transient calculations, which that for high accuracy calculation the discrete ordinates representation of the angular dependent flux should be used or sufficiently high expansion order with the spherical harmonics must be applied.
{"title":"On the Effect of Angular and Spatial Discretization on Perturbation Calculations","authors":"Z. I. Böröczki, M. Szieberth, A. Rineiski, F. Gabrielli","doi":"10.1080/23324309.2020.1834407","DOIUrl":"https://doi.org/10.1080/23324309.2020.1834407","url":null,"abstract":"Abstract In this article, different angular flux discretization options, namely discrete ordinates representation and spherical harmonics expansion are compared from the viewpoint of the accuracy of perturbation calculations. The PARTISN discrete ordinates neutron transport solver was coupled with the SEnTRi code, developed at BME, in order to perform perturbation theory calculations in different types of geometry descriptions and angular representations. With the help of the implemented code, the effect of the angular and spatial discretization on the results of perturbation theory calculations was investigated. Exact matches were observed in Cartesian geometries with the direct perturbation method when the discrete ordinates angular representation was used, and small discrepancies were found when the spherical harmonics expansion was applied. In cylindrical geometries, slight differences were observed with both angular expansions, which originate from the nature of the adjoint transport operator in curvilinear coordinate systems. The differences can be reduced to a negligible level with increased expansion order in both cases. Small discrepancies can have a significant effect in sensitivity, uncertainty and transient calculations, which that for high accuracy calculation the discrete ordinates representation of the angular dependent flux should be used or sufficiently high expansion order with the spherical harmonics must be applied.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"50 1","pages":"347 - 363"},"PeriodicalIF":0.7,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1834407","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44229567","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 : 2020-09-18DOI: 10.1080/23324309.2020.1816551
R. El-Nabulsi
Abstract In this study, a nonlocal approach to neutron diffusion equation with a memory is constructed in terms of moments of the displacement kernel with a modified geometric buckling. This approach leads to a family of partial differential equations which belong to the class of Fisher-Kolmogorov and Swift-Hohenberg equations. The stability of the problem depends on the signs of the second and fourth moments. The energy is a conserved quantity along orbits and a constant of integration is obtained. It was observed that the buckling is affected by the types of the kernel moment and for an explicit symmetric kernel, the ratio between the maximum and the average flux for a slab reactor is less than the ratio obtained using the conventional local diffusion equation, a result which is motivating technically in nuclear reactor engineering.
{"title":"Nonlocal Effects to Neutron Diffusion Equation in a Nuclear Reactor","authors":"R. El-Nabulsi","doi":"10.1080/23324309.2020.1816551","DOIUrl":"https://doi.org/10.1080/23324309.2020.1816551","url":null,"abstract":"Abstract In this study, a nonlocal approach to neutron diffusion equation with a memory is constructed in terms of moments of the displacement kernel with a modified geometric buckling. This approach leads to a family of partial differential equations which belong to the class of Fisher-Kolmogorov and Swift-Hohenberg equations. The stability of the problem depends on the signs of the second and fourth moments. The energy is a conserved quantity along orbits and a constant of integration is obtained. It was observed that the buckling is affected by the types of the kernel moment and for an explicit symmetric kernel, the ratio between the maximum and the average flux for a slab reactor is less than the ratio obtained using the conventional local diffusion equation, a result which is motivating technically in nuclear reactor engineering.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"267 - 281"},"PeriodicalIF":0.7,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1816551","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44420576","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 : 2020-09-18DOI: 10.1080/23324309.2020.1817087
Kai Yan
Abstract Symbolic Implicit Monte Carlo (SIMC) is fully implicit in the value of matter temperature used to calculate the thermal emission. However, it means that the temporal precision of this method is limited, despite this method being more robust than Fleck and Cummings’ IMC method. In this article, we develop a new Monte Carlo method which is accurate for the thermal emission in one time step. Instead of solving a system of nonlinear equations as in SIMC, we rewrite the material energy balance equation as a system of ordinary differential equations by a waveform relaxation method. We find that the initial value problem associated with these ordinary differential equations has an analytical solution, meaning that we can convert the problem into solving a function of the material temperature at the end of a time step. We prove that the function is monotonic during a time step, so that a bisection method can be used to solve the equation. This calculation process avoids having to solve the matrix equations directly and instead they are converged by performing an outer iteration. Numerical experiments are performed to validate the accuracy and efficiency of the current approach.
{"title":"A Modified Symbolic Implicit Monte Carlo Method for Time-Dependent Thermal Radiation Transport","authors":"Kai Yan","doi":"10.1080/23324309.2020.1817087","DOIUrl":"https://doi.org/10.1080/23324309.2020.1817087","url":null,"abstract":"Abstract Symbolic Implicit Monte Carlo (SIMC) is fully implicit in the value of matter temperature used to calculate the thermal emission. However, it means that the temporal precision of this method is limited, despite this method being more robust than Fleck and Cummings’ IMC method. In this article, we develop a new Monte Carlo method which is accurate for the thermal emission in one time step. Instead of solving a system of nonlinear equations as in SIMC, we rewrite the material energy balance equation as a system of ordinary differential equations by a waveform relaxation method. We find that the initial value problem associated with these ordinary differential equations has an analytical solution, meaning that we can convert the problem into solving a function of the material temperature at the end of a time step. We prove that the function is monotonic during a time step, so that a bisection method can be used to solve the equation. This calculation process avoids having to solve the matrix equations directly and instead they are converged by performing an outer iteration. Numerical experiments are performed to validate the accuracy and efficiency of the current approach.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"282 - 302"},"PeriodicalIF":0.7,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1817087","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45995171","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 : 2020-09-18DOI: 10.1080/23324309.2020.1819330
M. Jarrett, B. Kochunas, E. Larsen, T. Downar
Abstract Two-dimensional/one-dimensional (2D/1D) methods have become popular for solving the 3D Boltzmann neutron transport equation on medium-to-large computing platforms. These methods can have a wide range of accuracy that depends largely on the fidelity of the coupling between the 2D and 1D solutions in the spatial and angular variables. In general, methods with higher-order coupling are both more accurate and more computationally expensive. In order to simplify and reduce computation, an isotropic angular coupling term is frequently used. The deficiency of this approximation compared to higher-order angular coupling has been studied experimentally, but there is insufficient theoretical analysis in the literature to supplement the experimental results. In this paper, an asymptotic analysis is applied to the 2D/1D equations with varying orders of angular coupling to facilitate comparison to the simplified PN (SPN) equations. We find that the 2D/1D method with 3 angular coupling moments preserves the 3D SP3 limit, while the 2D/1D method with isotropic coupling does not. As a result, the isotropic coupling method is theoretically less accurate in problems with strong spatial gradients in both the radial and axial dimensions. This analysis provides a theoretical basis for design and optimization of the angular coupling scheme in a 2D/1D method. The results of the theoretical analysis are confirmed by using the Takeda-Ikeda benchmark to compare the accuracy of 2D/1D methods with isotropic and anisotropic coupling implemented in MPACT to SP1 and SP3 finite difference solutions.
{"title":"SP3 Limit of the 2D/1D Transport Equations with Varying Degrees of Angular Coupling","authors":"M. Jarrett, B. Kochunas, E. Larsen, T. Downar","doi":"10.1080/23324309.2020.1819330","DOIUrl":"https://doi.org/10.1080/23324309.2020.1819330","url":null,"abstract":"Abstract Two-dimensional/one-dimensional (2D/1D) methods have become popular for solving the 3D Boltzmann neutron transport equation on medium-to-large computing platforms. These methods can have a wide range of accuracy that depends largely on the fidelity of the coupling between the 2D and 1D solutions in the spatial and angular variables. In general, methods with higher-order coupling are both more accurate and more computationally expensive. In order to simplify and reduce computation, an isotropic angular coupling term is frequently used. The deficiency of this approximation compared to higher-order angular coupling has been studied experimentally, but there is insufficient theoretical analysis in the literature to supplement the experimental results. In this paper, an asymptotic analysis is applied to the 2D/1D equations with varying orders of angular coupling to facilitate comparison to the simplified PN (SPN) equations. We find that the 2D/1D method with 3 angular coupling moments preserves the 3D SP3 limit, while the 2D/1D method with isotropic coupling does not. As a result, the isotropic coupling method is theoretically less accurate in problems with strong spatial gradients in both the radial and axial dimensions. This analysis provides a theoretical basis for design and optimization of the angular coupling scheme in a 2D/1D method. The results of the theoretical analysis are confirmed by using the Takeda-Ikeda benchmark to compare the accuracy of 2D/1D methods with isotropic and anisotropic coupling implemented in MPACT to SP1 and SP3 finite difference solutions.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"303 - 330"},"PeriodicalIF":0.7,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1819330","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41618468","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 : 2020-09-14DOI: 10.1080/23324309.2020.1819331
Yining Shi, Xiaole Han, Wenjun Sun, Peng Song
Abstract The implicit Monte Carlo (IMC) method can exhibit teleportation error in problems with strong coupling between radiation and material. Source tilting method is a technique to reduce the teleportation error by representing the emission source as a linear or higher order function in each zone. In this paper, we propose a new spatial reconstruction scheme for the emission source term in the implicit Monte Carlo method. The new reconstruction scheme takes into account of the propagation direction of each photon. A spatially continuous representation for the emission source can be obtained by the reconstruction. We demonstrate that the new scheme can capture the asymptotic diffusion limit in optically thick regions under certain conditions. Numerical simulations show that the continuous reconstruction scheme can significantly reduce the teleportation error and performs better than the one-sided or central difference reconstruction schemes.
{"title":"A Continuous Source Tilting Scheme for Radiative Transfer Equations in Implicit Monte Carlo","authors":"Yining Shi, Xiaole Han, Wenjun Sun, Peng Song","doi":"10.1080/23324309.2020.1819331","DOIUrl":"https://doi.org/10.1080/23324309.2020.1819331","url":null,"abstract":"Abstract The implicit Monte Carlo (IMC) method can exhibit teleportation error in problems with strong coupling between radiation and material. Source tilting method is a technique to reduce the teleportation error by representing the emission source as a linear or higher order function in each zone. In this paper, we propose a new spatial reconstruction scheme for the emission source term in the implicit Monte Carlo method. The new reconstruction scheme takes into account of the propagation direction of each photon. A spatially continuous representation for the emission source can be obtained by the reconstruction. We demonstrate that the new scheme can capture the asymptotic diffusion limit in optically thick regions under certain conditions. Numerical simulations show that the continuous reconstruction scheme can significantly reduce the teleportation error and performs better than the one-sided or central difference reconstruction schemes.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"50 1","pages":"1 - 26"},"PeriodicalIF":0.7,"publicationDate":"2020-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1819331","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49194222","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 : 2020-07-28DOI: 10.1080/23324309.2020.1800745
G. Olson
Abstract One of the common methods for solving the radiation transport equation is to use a polynomial expansion for the angle variable(s). Recent research that reduces the oscillations and improves the positivity of the gray transport equation solutions is here applied to the multigroup transport equations. Constant scale factors that stretch the time axis and constant scattering opacities that filter the solution greatly increase the accuracy of the solution with no added nonlinearities. No new solution techniques are required. Test problems are presented in one and two dimensions.
{"title":"Stretched and Filtered Multigroup Pn Transport for Improved Positivity and Accuracy","authors":"G. Olson","doi":"10.1080/23324309.2020.1800745","DOIUrl":"https://doi.org/10.1080/23324309.2020.1800745","url":null,"abstract":"Abstract One of the common methods for solving the radiation transport equation is to use a polynomial expansion for the angle variable(s). Recent research that reduces the oscillations and improves the positivity of the gray transport equation solutions is here applied to the multigroup transport equations. Constant scale factors that stretch the time axis and constant scattering opacities that filter the solution greatly increase the accuracy of the solution with no added nonlinearities. No new solution techniques are required. Test problems are presented in one and two dimensions.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"215 - 232"},"PeriodicalIF":0.7,"publicationDate":"2020-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1800745","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45696904","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 : 2020-07-28DOI: 10.1080/23324309.2020.1801749
Steven Audrey Ndjanda Heugang, Hervé Thierry Kamdem Tagne, F. B. Pelap
Abstract The present work deals with the performance assessment of the finite volume method (FVM) and discrete transfer method (DTM) in term of their abilities to accurately satisfy conservation of both scattered energy and asymmetry factor of the scattering phase function, after angular discretization and their computational time to calculate the scattering phase function, in radiative transfer problems. Studies are carried out for many representative benchmark problems dealing with one-dimensional steady state radiative heat transfer through participating gray media under diffuse incident irradiation. For problems considered, tests were performed for a wide range of optical thickness, angular resolution, and anisotropic scattering phase function approximation. The results from both DTM and FVM formulations are presented and compared with available analytical and numerical literature solutions. While the two methods were found to give practically the same results, the DTM was found to be much computationally economical than the FVM, to evaluate the scattering phase function.
{"title":"Discrete Transfer and Finite Volume Methods for Highly Anisotropically Scattering in Radiative Heat Analysis","authors":"Steven Audrey Ndjanda Heugang, Hervé Thierry Kamdem Tagne, F. B. Pelap","doi":"10.1080/23324309.2020.1801749","DOIUrl":"https://doi.org/10.1080/23324309.2020.1801749","url":null,"abstract":"Abstract The present work deals with the performance assessment of the finite volume method (FVM) and discrete transfer method (DTM) in term of their abilities to accurately satisfy conservation of both scattered energy and asymmetry factor of the scattering phase function, after angular discretization and their computational time to calculate the scattering phase function, in radiative transfer problems. Studies are carried out for many representative benchmark problems dealing with one-dimensional steady state radiative heat transfer through participating gray media under diffuse incident irradiation. For problems considered, tests were performed for a wide range of optical thickness, angular resolution, and anisotropic scattering phase function approximation. The results from both DTM and FVM formulations are presented and compared with available analytical and numerical literature solutions. While the two methods were found to give practically the same results, the DTM was found to be much computationally economical than the FVM, to evaluate the scattering phase function.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"195 - 214"},"PeriodicalIF":0.7,"publicationDate":"2020-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1801749","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44109818","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 : 2020-07-28DOI: 10.1080/23324309.2020.1806076
K. Rui, L. Barichello, R. D. da Cunha
Abstract In this work, an explicit formulation to solve two-dimensional radiative transfer problems in anisotropic scattering media is developed. A nodal technique along with the Analytical Discrete Ordinates (ADO) method are used to solve the discrete ordinates approximation of the radiative transfer equation, in Cartesian geometry. To make it possible, the discrete ordinates equations are transversally integrated over regions of the domain reducing the complexity of the model, yielding two one-dimensional equations for average angular intensities in x and y directions. The one-dimensional equations, with approximations for the unknown intensities on the contours of the regions, are then explicitly solved by the ADO method, with respect to the spatial variables, whose solutions are written in terms of eigenvalues and eigenfunctions. The phase function is expanded in terms of Legendre polynomials up to arbitrary order L, to model higher order anisotropy. The eigenvalue problem is derived for this general case and it preserves a relevant feature of the ADO method, which is the reduced order equal to half of the number of discrete directions. Numerical results for the average radiation density and radiative heat flux are presented, for test cases in which the degree of anisotropy can be up to twelve and the albedo assumes different values. A comparative analysis with results available in the literature allows the verification of the formulation and indicates a good performance of the proposed method in coarser meshes.
{"title":"Recent Studies on Two-Dimensional Radiative Transfer Problems in Anisotropic Scattering Media","authors":"K. Rui, L. Barichello, R. D. da Cunha","doi":"10.1080/23324309.2020.1806076","DOIUrl":"https://doi.org/10.1080/23324309.2020.1806076","url":null,"abstract":"Abstract In this work, an explicit formulation to solve two-dimensional radiative transfer problems in anisotropic scattering media is developed. A nodal technique along with the Analytical Discrete Ordinates (ADO) method are used to solve the discrete ordinates approximation of the radiative transfer equation, in Cartesian geometry. To make it possible, the discrete ordinates equations are transversally integrated over regions of the domain reducing the complexity of the model, yielding two one-dimensional equations for average angular intensities in x and y directions. The one-dimensional equations, with approximations for the unknown intensities on the contours of the regions, are then explicitly solved by the ADO method, with respect to the spatial variables, whose solutions are written in terms of eigenvalues and eigenfunctions. The phase function is expanded in terms of Legendre polynomials up to arbitrary order L, to model higher order anisotropy. The eigenvalue problem is derived for this general case and it preserves a relevant feature of the ADO method, which is the reduced order equal to half of the number of discrete directions. Numerical results for the average radiation density and radiative heat flux are presented, for test cases in which the degree of anisotropy can be up to twelve and the albedo assumes different values. A comparative analysis with results available in the literature allows the verification of the formulation and indicates a good performance of the proposed method in coarser meshes.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"233 - 266"},"PeriodicalIF":0.7,"publicationDate":"2020-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1806076","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41737915","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 : 2020-07-05DOI: 10.1080/23324309.2020.1816553
B. Ganapol, J. Patel
Abstract In recent years, the first author has developed three successful numerical methods to solve the 1D radiative transport equation yielding highly precise benchmarks. The second author has shown a keen interest in novel solution methodologies and an ability for their implementation. Here, we combine talents to generate yet another high precision solution, the Matrix Riccati Equation Method (MREM). MREM features the solution to two of the four matrix Riccati ODEs that arise from the interaction principle of particle transport. Through interaction coefficients, the interaction principle describes how particles reflect from- and transmit through- a single slab. On combination with Taylor series and doubling, a high-quality numerical benchmark, to nearly seven places, is established.
{"title":"Matrix Riccati Equation Solution of the 1D Radiative Transfer Equation","authors":"B. Ganapol, J. Patel","doi":"10.1080/23324309.2020.1816553","DOIUrl":"https://doi.org/10.1080/23324309.2020.1816553","url":null,"abstract":"Abstract In recent years, the first author has developed three successful numerical methods to solve the 1D radiative transport equation yielding highly precise benchmarks. The second author has shown a keen interest in novel solution methodologies and an ability for their implementation. Here, we combine talents to generate yet another high precision solution, the Matrix Riccati Equation Method (MREM). MREM features the solution to two of the four matrix Riccati ODEs that arise from the interaction principle of particle transport. Through interaction coefficients, the interaction principle describes how particles reflect from- and transmit through- a single slab. On combination with Taylor series and doubling, a high-quality numerical benchmark, to nearly seven places, is established.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"50 1","pages":"297 - 327"},"PeriodicalIF":0.7,"publicationDate":"2020-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1816553","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49650777","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 : 2020-06-22DOI: 10.1080/23324309.2020.1828470
L. Barletti
Abstract We mathematically describe the apparently paradoxical phenomenon that the electric current in a semiconductor can flow because of collisions, and not despite them. A model of charge transport in a one-dimensional semiconductor crystal is considered, where each electron follows the periodic Hamiltonian trajectories, determined by the semiconductor band structure, and undergoes non-elastic collisions with a phonon bath. Starting from the detailed phase-space model, a closed system of ODEs is obtained for averaged quantities. Such a simplified model is nevertheless capable of describing transient Bloch oscillations, their damping and the consequent onset of a steady current flow, which is in good agreement with the available experimental data.
{"title":"A Mathematical Walk into the Paradox of Bloch Oscillations","authors":"L. Barletti","doi":"10.1080/23324309.2020.1828470","DOIUrl":"https://doi.org/10.1080/23324309.2020.1828470","url":null,"abstract":"Abstract We mathematically describe the apparently paradoxical phenomenon that the electric current in a semiconductor can flow because of collisions, and not despite them. A model of charge transport in a one-dimensional semiconductor crystal is considered, where each electron follows the periodic Hamiltonian trajectories, determined by the semiconductor band structure, and undergoes non-elastic collisions with a phonon bath. Starting from the detailed phase-space model, a closed system of ODEs is obtained for averaged quantities. Such a simplified model is nevertheless capable of describing transient Bloch oscillations, their damping and the consequent onset of a steady current flow, which is in good agreement with the available experimental data.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"50 1","pages":"328 - 346"},"PeriodicalIF":0.7,"publicationDate":"2020-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1828470","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45762224","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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