Pub Date : 2011-12-02DOI: 10.1080/00411450.2011.651043
A. Ghizzo, M. E. Mouden, D. Sarto, X. Garbet, Y. Sarazin
Global gyrokinetic Vlasov simulations for trapped ion modes indicate that the ion temperature gradient (ITG) instability saturates via nonlinear toroidal coupling. Trapped Ion modes were studied by solving a Vlasov equation averaged over the cyclotron and bounce motion of trapped ions. The distribution function, for trapped ions, is then calculated in a two-dimensional phase space, parametrized by two adiabatic invariants, the longitudinal action and the magnetic moment, in presence of a magnetic shear. Our model can be viewed as a kinetic version of the standard one-field Hasegawa-Mima-type and a broad frequency spectrum can originate from model for trapped-ion driven turbulence. Some interesting new features, which appear in the nonlinear regime of the instability, are then discussed.
{"title":"Global Gyrokinetic Stability of Temperature-Gradient-Driven Trapped Ion Modes with Magnetic Shear","authors":"A. Ghizzo, M. E. Mouden, D. Sarto, X. Garbet, Y. Sarazin","doi":"10.1080/00411450.2011.651043","DOIUrl":"https://doi.org/10.1080/00411450.2011.651043","url":null,"abstract":"Global gyrokinetic Vlasov simulations for trapped ion modes indicate that the ion temperature gradient (ITG) instability saturates via nonlinear toroidal coupling. Trapped Ion modes were studied by solving a Vlasov equation averaged over the cyclotron and bounce motion of trapped ions. The distribution function, for trapped ions, is then calculated in a two-dimensional phase space, parametrized by two adiabatic invariants, the longitudinal action and the magnetic moment, in presence of a magnetic shear. Our model can be viewed as a kinetic version of the standard one-field Hasegawa-Mima-type and a broad frequency spectrum can originate from model for trapped-ion driven turbulence. Some interesting new features, which appear in the nonlinear regime of the instability, are then discussed.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"10 1","pages":"382 - 418"},"PeriodicalIF":0.0,"publicationDate":"2011-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.651043","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909541","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 : 2011-12-02DOI: 10.1080/00411450.2011.651029
J. Holloway
{"title":"Note from the Editor","authors":"J. Holloway","doi":"10.1080/00411450.2011.651029","DOIUrl":"https://doi.org/10.1080/00411450.2011.651029","url":null,"abstract":"","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"311 - 311"},"PeriodicalIF":0.0,"publicationDate":"2011-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.651029","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909420","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 : 2011-12-01DOI: 10.1080/00411450.2011.629272
B. Guo, Yongqian Han
This article is devoted to establish the well-posedness of solutions and diffusion limit of the small mean free path of the nonlinear transfer equations, which describes the spatial transport of radiation in a material medium. By using the comparison principle, we obtain the lower bound and upper bound of the solution, and then we prove the existence and uniqueness of the global solution. We show that the nonlinear transfer equation has a diffusion limit as the mean free path tends to zero. Our proof is based on asymptotic expansions. We show that the validity of these asymptotic expansions relies only on the smoothness of initial data, while two hypotheses, Fredholm alternative and centering condition, are removed.
{"title":"Diffusion Limit of Small Mean Free Path of Transfer Equation in","authors":"B. Guo, Yongqian Han","doi":"10.1080/00411450.2011.629272","DOIUrl":"https://doi.org/10.1080/00411450.2011.629272","url":null,"abstract":"This article is devoted to establish the well-posedness of solutions and diffusion limit of the small mean free path of the nonlinear transfer equations, which describes the spatial transport of radiation in a material medium. By using the comparison principle, we obtain the lower bound and upper bound of the solution, and then we prove the existence and uniqueness of the global solution. We show that the nonlinear transfer equation has a diffusion limit as the mean free path tends to zero. Our proof is based on asymptotic expansions. We show that the validity of these asymptotic expansions relies only on the smoothness of initial data, while two hypotheses, Fredholm alternative and centering condition, are removed.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"243 - 281"},"PeriodicalIF":0.0,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.629272","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909350","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 : 2011-12-01DOI: 10.1080/00411450.2011.629710
Aditi Simha, R. Evans
Transition rates in continuously driven steady states (relevant to sheared complex fluids) were derived in Evans (2004, 2005) by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the system be used to describe it. This implies that the (nonequilibrium) reservoir, to which the system is weakly coupled, is fully characterized by its mean energy and mean flux. While we expect the resulting prescription for the rates in continuous- and discretized-time models to be equivalent, it is not trivial to see this from the expression for the rates derived in Evans (2005). We demonstrate this equivalence for a model of activated processes solved previously for continuous time (Evans 2005), thus demonstrating consistency of the theory.
{"title":"An Addendum to “Detailed Balance has a Counterpart in Nonequilibrium Steady States”","authors":"Aditi Simha, R. Evans","doi":"10.1080/00411450.2011.629710","DOIUrl":"https://doi.org/10.1080/00411450.2011.629710","url":null,"abstract":"Transition rates in continuously driven steady states (relevant to sheared complex fluids) were derived in Evans (2004, 2005) by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the system be used to describe it. This implies that the (nonequilibrium) reservoir, to which the system is weakly coupled, is fully characterized by its mean energy and mean flux. While we expect the resulting prescription for the rates in continuous- and discretized-time models to be equivalent, it is not trivial to see this from the expression for the rates derived in Evans (2005). We demonstrate this equivalence for a model of activated processes solved previously for continuous time (Evans 2005), thus demonstrating consistency of the theory.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"304 - 309"},"PeriodicalIF":0.0,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.629710","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909369","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 : 2011-12-01DOI: 10.1080/00411450.2011.639432
Chao Liang, W. Ji
When the chord length sampling method is applied to solve radiation transport problems in random media where inclusions are randomly distributed in a background region, inaccuracy occurs due to two major factors: memory effect and boundary effect. In this article, by applying chord length sampling to solve fixed source and eigenvalue problems in 1-D binary stochastic media, an investigation on how and why these two effects give rise to the inaccuracy in the final solutions is performed. The investigation is based on a series of radiation transport simulations for the calculation of reflection rate, flux distribution, and effective multiplication factor.
{"title":"On the Chord Length Sampling in 1-D Binary Stochastic Media","authors":"Chao Liang, W. Ji","doi":"10.1080/00411450.2011.639432","DOIUrl":"https://doi.org/10.1080/00411450.2011.639432","url":null,"abstract":"When the chord length sampling method is applied to solve radiation transport problems in random media where inclusions are randomly distributed in a background region, inaccuracy occurs due to two major factors: memory effect and boundary effect. In this article, by applying chord length sampling to solve fixed source and eigenvalue problems in 1-D binary stochastic media, an investigation on how and why these two effects give rise to the inaccuracy in the final solutions is performed. The investigation is based on a series of radiation transport simulations for the calculation of reflection rate, flux distribution, and effective multiplication factor.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"282 - 303"},"PeriodicalIF":0.0,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.639432","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909410","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 : 2011-10-01DOI: 10.1080/00411450.2011.606555
Dingkang Zhang, F. Rahnema
A hybrid Monte Carlo/deterministic coarse mesh transport method (COMET-PE) has been developed for pure photon or coupled photon and electron transport in heterogeneous problems. The accuracy of the method was evaluated in two highly stylized 2D benchmark problems: (1) a homogeneous rectangular water phantom and (2) a heterogeneous problem that is typical of a 2D vertical slice of lung. It was found that the method produces results that are very close to those of direct Monte Carlo with significantly higher computational efficiency (2–3 orders of magnitude). In both test problems, the maximum and the average energy deposition differences between COMET-PE and the reference Monte Carlo solutions for the pure photon transport case ranged from 2.0%–2.4% and 1.0%–1.2%, respectively. The corresponding differences for the coupled photon and electron transport case ranged from 1.1%–2.2% and 0.5%–0.9%, respectively. The COMET-PE computation time was more than 200 and 700 times shorter than EGSnrc in the homogeneous and the heterogeneous problems, respectively. Therefore, it is concluded that the new incident flux response expansion method is highly accurate and efficient for energy deposition calculation in heterogeneous tissues.
{"title":"A Heterogeneous Coarse Mesh Method for Coupled Photon Electron Transport Problems","authors":"Dingkang Zhang, F. Rahnema","doi":"10.1080/00411450.2011.606555","DOIUrl":"https://doi.org/10.1080/00411450.2011.606555","url":null,"abstract":"A hybrid Monte Carlo/deterministic coarse mesh transport method (COMET-PE) has been developed for pure photon or coupled photon and electron transport in heterogeneous problems. The accuracy of the method was evaluated in two highly stylized 2D benchmark problems: (1) a homogeneous rectangular water phantom and (2) a heterogeneous problem that is typical of a 2D vertical slice of lung. It was found that the method produces results that are very close to those of direct Monte Carlo with significantly higher computational efficiency (2–3 orders of magnitude). In both test problems, the maximum and the average energy deposition differences between COMET-PE and the reference Monte Carlo solutions for the pure photon transport case ranged from 2.0%–2.4% and 1.0%–1.2%, respectively. The corresponding differences for the coupled photon and electron transport case ranged from 1.1%–2.2% and 0.5%–0.9%, respectively. The COMET-PE computation time was more than 200 and 700 times shorter than EGSnrc in the homogeneous and the heterogeneous problems, respectively. Therefore, it is concluded that the new incident flux response expansion method is highly accurate and efficient for energy deposition calculation in heterogeneous tissues.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"127 - 152"},"PeriodicalIF":0.0,"publicationDate":"2011-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.606555","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909283","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 : 2011-10-01DOI: 10.1080/00411450.2011.603403
S. Mansoor, B. Yilbas
Phonon transport in two-layer films, consisting of silicon and aluminum, is considered. Phonon radiative energy transfer is incorporated to predict equilibrium temperature distribution in the silicon film, while the modified two-equation model is used to predict electron and phonon temperatures in the aluminum film. The thermal boundary resistance is introduced at the interface of both films. Equilibrium temperature decay is found to be sharp in the early heating period in the silicon film. Phonon temperature remains higher than electron temperature in the vicinity of the interface of aluminum film. Electron and phonon temperature become the same at mid-thickness of the aluminum film.
{"title":"Temperature Distribution in Silicon-Aluminum Thin Films with Presence of Thermal Boundary Resistance","authors":"S. Mansoor, B. Yilbas","doi":"10.1080/00411450.2011.603403","DOIUrl":"https://doi.org/10.1080/00411450.2011.603403","url":null,"abstract":"Phonon transport in two-layer films, consisting of silicon and aluminum, is considered. Phonon radiative energy transfer is incorporated to predict equilibrium temperature distribution in the silicon film, while the modified two-equation model is used to predict electron and phonon temperatures in the aluminum film. The thermal boundary resistance is introduced at the interface of both films. Equilibrium temperature decay is found to be sharp in the early heating period in the silicon film. Phonon temperature remains higher than electron temperature in the vicinity of the interface of aluminum film. Electron and phonon temperature become the same at mid-thickness of the aluminum film.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"153 - 181"},"PeriodicalIF":0.0,"publicationDate":"2011-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.603403","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909238","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 : 2011-10-01DOI: 10.1080/00411450.2011.604575
J. Holloway
{"title":"Note from the Editor","authors":"J. Holloway","doi":"10.1080/00411450.2011.604575","DOIUrl":"https://doi.org/10.1080/00411450.2011.604575","url":null,"abstract":"","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"183 - 183"},"PeriodicalIF":0.0,"publicationDate":"2011-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.604575","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909273","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 : 2011-10-01DOI: 10.1080/00411450.2011.610205
Edward W. Larsen
The latest in a series of biannual conferences sponsored by the Mathematics and Computation Division of the American Nuclear Society was held May 8–12, 2011 at the Rio Othon Palace Hotel in Rio de Janeiro, Brazil. Since these conferences have not been reviewed previously in this journal, this report will begin with a few words about their purpose and history. Members of the American Nuclear Society (ANS) can belong to two or more technical divisions, which are organized to reflect the members’ specific technical interests. One of these is the Mathematics and Computations (M&C) Division, whose members “promote the advancement of mathematical and computational methods for solving problems arising in all disciplines encompassed by the Society” (http://www.mcd.ans.org). Much of the work done by M&C division members is devoted to the Boltzmann transport equation, which predicts neutron and photon fluxes in nuclear systems. In addition to organizing sessions at annual ANS conferences, the M&C Division sponsors biannual international “topical” conferences, held during odd-numbered years, that focus on topics of interest to members of the division. Because a large
{"title":"International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (MC 2011)","authors":"Edward W. Larsen","doi":"10.1080/00411450.2011.610205","DOIUrl":"https://doi.org/10.1080/00411450.2011.610205","url":null,"abstract":"The latest in a series of biannual conferences sponsored by the Mathematics and Computation Division of the American Nuclear Society was held May 8–12, 2011 at the Rio Othon Palace Hotel in Rio de Janeiro, Brazil. Since these conferences have not been reviewed previously in this journal, this report will begin with a few words about their purpose and history. Members of the American Nuclear Society (ANS) can belong to two or more technical divisions, which are organized to reflect the members’ specific technical interests. One of these is the Mathematics and Computations (M&C) Division, whose members “promote the advancement of mathematical and computational methods for solving problems arising in all disciplines encompassed by the Society” (http://www.mcd.ans.org). Much of the work done by M&C division members is devoted to the Boltzmann transport equation, which predicts neutron and photon fluxes in nuclear systems. In addition to organizing sessions at annual ANS conferences, the M&C Division sponsors biannual international “topical” conferences, held during odd-numbered years, that focus on topics of interest to members of the division. Because a large","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"225 - 242"},"PeriodicalIF":0.0,"publicationDate":"2011-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.610205","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909339","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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