Pub Date : 2013-06-07DOI: 10.1080/00411450.2014.886591
O. Morandi
A mathematical model for the quantum transport of a two-band semiconductor that includes the self-consistent electrostatic potential is analyzed. Corrections beyond the usual effective mass approximation are considered. Transparent boundary conditions are derived for the multiband envelope Schrödinger model. The existence of a solution of the nonlinear system is proved by using an asymptotic procedure. Some numerical examples are included. They illustrate the behavior of the scattering and the resonant states.
{"title":"Mathematical Analysis of a Nonparabolic Two-Band Schrödinger-Poisson Problem","authors":"O. Morandi","doi":"10.1080/00411450.2014.886591","DOIUrl":"https://doi.org/10.1080/00411450.2014.886591","url":null,"abstract":"A mathematical model for the quantum transport of a two-band semiconductor that includes the self-consistent electrostatic potential is analyzed. Corrections beyond the usual effective mass approximation are considered. Transparent boundary conditions are derived for the multiband envelope Schrödinger model. The existence of a solution of the nonlinear system is proved by using an asymptotic procedure. Some numerical examples are included. They illustrate the behavior of the scattering and the resonant states.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"1 1","pages":"133 - 161"},"PeriodicalIF":0.0,"publicationDate":"2013-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2014.886591","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910443","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}
Pub Date : 2013-04-16DOI: 10.1080/00411450.2013.860900
J. Densmore
We present an extension of our recent examination of the method of moments when moments are computed on a spatial grid instead of through integration over the entire domain to include time dependence. For the problem we consider, we show that (i) the flux-weighted average of x remains equal to its initial value but (ii) the flux-weighted average of (x − xa )2 differs from its initial value by an additional error term when moments are determined in this manner, where x is the spatial variable and xa is an arbitrary point. We also present numerical examples that confirm the accuracy of our results.
{"title":"Spatial Moments of Continuous Transport Problems Computed on Grids: Time-Dependent Problems","authors":"J. Densmore","doi":"10.1080/00411450.2013.860900","DOIUrl":"https://doi.org/10.1080/00411450.2013.860900","url":null,"abstract":"We present an extension of our recent examination of the method of moments when moments are computed on a spatial grid instead of through integration over the entire domain to include time dependence. For the problem we consider, we show that (i) the flux-weighted average of x remains equal to its initial value but (ii) the flux-weighted average of (x − xa )2 differs from its initial value by an additional error term when moments are determined in this manner, where x is the spatial variable and xa is an arbitrary point. We also present numerical examples that confirm the accuracy of our results.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"42 1","pages":"85 - 98"},"PeriodicalIF":0.0,"publicationDate":"2013-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2013.860900","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910322","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}
Pub Date : 2013-04-16DOI: 10.1080/00411450.2013.853193
B. Yilbas, S. Bin Mansoor
Energy transfer is mainly governed by the phonon transport in dielectric films. The polarization and dispersion of the phonons alter the thermal resistance of the film as the film size becomes comparable to the mean path of the substrate material. This is because of the quasi-ballistic behavior of the transport characteristics. In this case, the ballistic phonons do not undergo scattering in the film while suppressing the thermal resistance increase across the film. In the present study, the quasi-ballistic phonon transport and the effect of heat source size on the phonon transport characteristics are investigated in the two-dimensional silicon film. The heat source is located at one edge of the film while other edges assumed to be at uniform temperature. Since the Knudsen number is small (∼1), the Boltzmann transport equation is solved numerically, incorporating the polarization and dispersion of phonons, to obtain phonon intensity distribution in the film. Equivalent equilibrium temperature is introduced to assess the phonon intensity distribution in the film. The transient behavior of the phonon transport is incorporated in the analysis to predict the time to reach steady state value of equivalent temperature in the film. It is found that the size of the heat source has a significant effect on the phonon transport in the film. The effective thermal conductivity reduces significantly as the heat source size reduces.
{"title":"Influence of Heat Source Size on Phonon Transport in Thin Silicon Film","authors":"B. Yilbas, S. Bin Mansoor","doi":"10.1080/00411450.2013.853193","DOIUrl":"https://doi.org/10.1080/00411450.2013.853193","url":null,"abstract":"Energy transfer is mainly governed by the phonon transport in dielectric films. The polarization and dispersion of the phonons alter the thermal resistance of the film as the film size becomes comparable to the mean path of the substrate material. This is because of the quasi-ballistic behavior of the transport characteristics. In this case, the ballistic phonons do not undergo scattering in the film while suppressing the thermal resistance increase across the film. In the present study, the quasi-ballistic phonon transport and the effect of heat source size on the phonon transport characteristics are investigated in the two-dimensional silicon film. The heat source is located at one edge of the film while other edges assumed to be at uniform temperature. Since the Knudsen number is small (∼1), the Boltzmann transport equation is solved numerically, incorporating the polarization and dispersion of phonons, to obtain phonon intensity distribution in the film. Equivalent equilibrium temperature is introduced to assess the phonon intensity distribution in the film. The transient behavior of the phonon transport is incorporated in the analysis to predict the time to reach steady state value of equivalent temperature in the film. It is found that the size of the heat source has a significant effect on the phonon transport in the film. The effective thermal conductivity reduces significantly as the heat source size reduces.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"42 1","pages":"65 - 84"},"PeriodicalIF":0.0,"publicationDate":"2013-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2013.853193","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910308","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}
Pub Date : 2013-04-16DOI: 10.1080/00411450.2013.866144
M. Boulanouar
In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.
{"title":"On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population","authors":"M. Boulanouar","doi":"10.1080/00411450.2013.866144","DOIUrl":"https://doi.org/10.1080/00411450.2013.866144","url":null,"abstract":"In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"42 1","pages":"130 - 99"},"PeriodicalIF":0.0,"publicationDate":"2013-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2013.866144","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910358","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}
Pub Date : 2013-01-01DOI: 10.1080/00411450.2013.838792
D. Rostamy, F. Zabihi, A. Niroomand, A. Mollazeynal
A wave equation with a nonlocal boundary condition is considered. Then we purpose a new finite element method for solving this equation. Also, we obtain a priori and a posteriori error estimates. The theory is illustrated by some numerical examples.
{"title":"New Finite Element Method for Solving a Wave Equation with a Nonlocal Conservation Condition","authors":"D. Rostamy, F. Zabihi, A. Niroomand, A. Mollazeynal","doi":"10.1080/00411450.2013.838792","DOIUrl":"https://doi.org/10.1080/00411450.2013.838792","url":null,"abstract":"A wave equation with a nonlocal boundary condition is considered. Then we purpose a new finite element method for solving this equation. Also, we obtain a priori and a posteriori error estimates. The theory is illustrated by some numerical examples.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"42 1","pages":"41 - 62"},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2013.838792","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910243","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}
Pub Date : 2013-01-01DOI: 10.1080/00411450.2013.771366
J. Morel, J. Ragusa, M. Adams, G. Kanschat
The 1-D one-speed slab-geometry P N equations with isotropic scattering can be modified via an alternative moment closure to preserve the two asymptotic eigenmodes associated with the transport equation. Pomraning referred to these equations as the asymptotic P N equations. It is well-known that the 1-D slab-geometry S N+1 equations with Gauss quadrature are equivalent to the standard P N equations. In this article, we first show that if any quadrature set meets a certain criterion, the corresponding S N+1 equations will be equivalent to a set of P N equations with a quadrature-dependent closure. We then derive a particular family of quadrature sets that make the S N+1 equations equivalent to the asymptotic P N equations. Next we theoretically demonstrate several of the properties of these sets, relate them to an existing family of quadratures, numerically generate several example quadrature sets, and give numerical results that confirm several of their theoretically predicted properties.
{"title":"Asymptotic P N -Equivalent S N+1 Equations","authors":"J. Morel, J. Ragusa, M. Adams, G. Kanschat","doi":"10.1080/00411450.2013.771366","DOIUrl":"https://doi.org/10.1080/00411450.2013.771366","url":null,"abstract":"The 1-D one-speed slab-geometry P N equations with isotropic scattering can be modified via an alternative moment closure to preserve the two asymptotic eigenmodes associated with the transport equation. Pomraning referred to these equations as the asymptotic P N equations. It is well-known that the 1-D slab-geometry S N+1 equations with Gauss quadrature are equivalent to the standard P N equations. In this article, we first show that if any quadrature set meets a certain criterion, the corresponding S N+1 equations will be equivalent to a set of P N equations with a quadrature-dependent closure. We then derive a particular family of quadrature sets that make the S N+1 equations equivalent to the asymptotic P N equations. Next we theoretically demonstrate several of the properties of these sets, relate them to an existing family of quadratures, numerically generate several example quadrature sets, and give numerical results that confirm several of their theoretically predicted properties.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"42 1","pages":"20 - 3"},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2013.771366","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909804","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}
Pub Date : 2013-01-01DOI: 10.1080/00411450.2013.821413
B. S. Yilbas, S. Mansoor
Phonon and carrier transport in silicon-aluminum film pairs is examined. The energy transport equation for electrons and lattice subsystems for aluminum film is derived from the Boltzmann equation. Equivalent equilibrium temperature for lattice phonons and electrons are computed across the silicon and aluminum film. Reflection and transmittance of phonons at the silicon interface are considered to account for the thermal boundary resistance. The influence of film thickness on equivalent equilibrium temperature is also examined. Electron and lattice phonon temperature predictions are compared with their counterparts obtained from the modified two-equation model for the aluminum film. It is found that the solution of Boltzmann equation predicts slightly higher temperature at the silicon interface than that of the modified two-equation model. The nonlinear behavior of lattice phonon temperature at the aluminum interface extends toward the aluminum film with increasing film thickness.
{"title":"Lattice Phonon and Electron Temperatures in Silicon-Aluminum Thin Films Pair: Comparison of Boltzmann Equation and Modified Two-Equation Model","authors":"B. S. Yilbas, S. Mansoor","doi":"10.1080/00411450.2013.821413","DOIUrl":"https://doi.org/10.1080/00411450.2013.821413","url":null,"abstract":"Phonon and carrier transport in silicon-aluminum film pairs is examined. The energy transport equation for electrons and lattice subsystems for aluminum film is derived from the Boltzmann equation. Equivalent equilibrium temperature for lattice phonons and electrons are computed across the silicon and aluminum film. Reflection and transmittance of phonons at the silicon interface are considered to account for the thermal boundary resistance. The influence of film thickness on equivalent equilibrium temperature is also examined. Electron and lattice phonon temperature predictions are compared with their counterparts obtained from the modified two-equation model for the aluminum film. It is found that the solution of Boltzmann equation predicts slightly higher temperature at the silicon interface than that of the modified two-equation model. The nonlinear behavior of lattice phonon temperature at the aluminum interface extends toward the aluminum film with increasing film thickness.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"15 1","pages":"21 - 39"},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2013.821413","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909816","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}
Pub Date : 2012-12-01DOI: 10.1080/00411450.2012.747539
S. Charfi
This article is concerned with the spectral properties of a transport operator with diffuse reflection boundary condition arising in L 1-spaces. Furthermore, a practical way to study asymptotic behavior of the solution of the transport operator without restriction on the initial data is given.
{"title":"On the Time Asymptotic Behavior of a Transport Operator with Diffuse Reflection Boundary Condition","authors":"S. Charfi","doi":"10.1080/00411450.2012.747539","DOIUrl":"https://doi.org/10.1080/00411450.2012.747539","url":null,"abstract":"This article is concerned with the spectral properties of a transport operator with diffuse reflection boundary condition arising in L 1-spaces. Furthermore, a practical way to study asymptotic behavior of the solution of the transport operator without restriction on the initial data is given.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"529 - 551"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.747539","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909745","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}
Pub Date : 2012-12-01DOI: 10.1080/00411450.2012.694827
E. Jamelot, A. Baudron, J. Lautard
In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nédélec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3® code.
本文给出了用raviart - thomas - nsamdsamlec有限元离散的混合SPN方程的一种区域分解方法。该领域分解基于迭代Schwarz算法，采用Robin接口条件处理通信。在描述了这种方法之后，我们详细说明了如何优化收敛性。最后给出了在实际三维环境下的数值计算结果。计算是用APOLLO3®代码的MINOS求解器完成的。
{"title":"Domain Decomposition for the SPN Solver MINOS","authors":"E. Jamelot, A. Baudron, J. Lautard","doi":"10.1080/00411450.2012.694827","DOIUrl":"https://doi.org/10.1080/00411450.2012.694827","url":null,"abstract":"In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nédélec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3® code.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"495 - 512"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.694827","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909670","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}
Pub Date : 2012-12-01DOI: 10.1080/00411450.2012.695317
Hong Zhimin, Yan Zaizai, Chen Jian-rui
This article is concerned with a numerical algorithm for solving approximate solutions of Fredholm integral equations of the second kind with random sampling. We use Simpson’s rule for solving integral equations, which yields a linear system. The Monte Carlo method, based on the simulation of a finite discrete Markov chain, is employed to solve this linear system. To show the efficiency of the method, we use numerical examples. Results obtained by the present method indicate that the method is an effective alternate method.
{"title":"Monte Carlo Method for Solving the Fredholm Integral Equations of the Second Kind","authors":"Hong Zhimin, Yan Zaizai, Chen Jian-rui","doi":"10.1080/00411450.2012.695317","DOIUrl":"https://doi.org/10.1080/00411450.2012.695317","url":null,"abstract":"This article is concerned with a numerical algorithm for solving approximate solutions of Fredholm integral equations of the second kind with random sampling. We use Simpson’s rule for solving integral equations, which yields a linear system. The Monte Carlo method, based on the simulation of a finite discrete Markov chain, is employed to solve this linear system. To show the efficiency of the method, we use numerical examples. Results obtained by the present method indicate that the method is an effective alternate method.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"513 - 528"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.695317","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909682","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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