Pub Date : 2011-09-01DOI: 10.1080/00411450.2011.596607
R. Sánchez, L. Bourhrara
We present an existence result for the kinetic neutron transport equation with a general albedo boundary condition. The proof is constructive in the sense that we build a sequence that converges to the solution of the problem by iterating on the albedo term. Both nonhomogeneous and albedo boundary conditions are studied.
{"title":"Existence Result for the Kinetic Neutron Transport Problem with a General Albedo Boundary Condition","authors":"R. Sánchez, L. Bourhrara","doi":"10.1080/00411450.2011.596607","DOIUrl":"https://doi.org/10.1080/00411450.2011.596607","url":null,"abstract":"We present an existence result for the kinetic neutron transport equation with a general albedo boundary condition. The proof is constructive in the sense that we build a sequence that converges to the solution of the problem by iterating on the albedo term. Both nonhomogeneous and albedo boundary conditions are studied.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"69 - 84"},"PeriodicalIF":0.0,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.596607","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909143","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 : 2011-09-01DOI: 10.1080/00411450.2011.603402
M. Boulanouar
This work deals with new results in abstract time-dependent transport equations. We prove a general generation theorem that recovers all known results. We conclude our work by significant remarks and comments on other studies in literature of the transport equation.
{"title":"New Results in Abstract Time-Dependent Transport Equations","authors":"M. Boulanouar","doi":"10.1080/00411450.2011.603402","DOIUrl":"https://doi.org/10.1080/00411450.2011.603402","url":null,"abstract":"This work deals with new results in abstract time-dependent transport equations. We prove a general generation theorem that recovers all known results. We conclude our work by significant remarks and comments on other studies in literature of the transport equation.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"125 - 85"},"PeriodicalIF":0.0,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.603402","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909203","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 : 2011-07-10DOI: 10.1080/00411450.2011.563813
G. Busoni, L. Prati
In this article we study a model constituted by three integro-differential equations describing the densities of nucleons and of two groups of mesons (depending on their energy—high or low) diffusing in the Earth’s atmosphere. We assume that the secondary particles, produced after the collisions in air of the primary ones with particles in the air, have a lower energy with respect to the incident ones; indeed the transformation of mass into energy is considered not to be relevant by astrophysicists. We list assumptions that allow us to prove existence and uniqueness of non-negative solutions for the densities through generalization of the theory of evolution operators and evolution systems in Banach spaces. In the special case in which certain operators are bounded, the densities can be written as series of the form ∑ i xiFi (E) where the factors Fi (E) are given by the actions of suitable linear operators on the initial datum, and it is also proved that these can be obtained by recurrent formulas. The truncation of the series allows the estimate of the corresponding committed error.
{"title":"Theory of Evolution Systems Applied to a Cosmic Ray Diffusion Model","authors":"G. Busoni, L. Prati","doi":"10.1080/00411450.2011.563813","DOIUrl":"https://doi.org/10.1080/00411450.2011.563813","url":null,"abstract":"In this article we study a model constituted by three integro-differential equations describing the densities of nucleons and of two groups of mesons (depending on their energy—high or low) diffusing in the Earth’s atmosphere. We assume that the secondary particles, produced after the collisions in air of the primary ones with particles in the air, have a lower energy with respect to the incident ones; indeed the transformation of mass into energy is considered not to be relevant by astrophysicists. We list assumptions that allow us to prove existence and uniqueness of non-negative solutions for the densities through generalization of the theory of evolution operators and evolution systems in Banach spaces. In the special case in which certain operators are bounded, the densities can be written as series of the form ∑ i xiFi (E) where the factors Fi (E) are given by the actions of suitable linear operators on the initial datum, and it is also proved that these can be obtained by recurrent formulas. The truncation of the series allows the estimate of the corresponding committed error.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"23 - 67"},"PeriodicalIF":0.0,"publicationDate":"2011-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.563813","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58908756","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 : 2011-07-10DOI: 10.1080/00411450.2014.922480
V. Lisý, J. Tóthová
Analytical solutions of the generalized Langevin equation have been found for the time correlation functions describing the motion of a charged Brownian particle in an external magnetic field when the thermal random force in weakly viscoelastic fluids is exponentially correlated in the time. To obtain a correct description at short times, inertial effects are included into the consideration. The found mean square displacement of the particle motion across the field contains a term proportional to the time, a constant term, and exponentially decaying contributions. The solution for a particle trapped in a harmonic well is also found.
{"title":"Brownian Motion of Charged Particles Driven by Correlated Noise in Magnetic Field","authors":"V. Lisý, J. Tóthová","doi":"10.1080/00411450.2014.922480","DOIUrl":"https://doi.org/10.1080/00411450.2014.922480","url":null,"abstract":"Analytical solutions of the generalized Langevin equation have been found for the time correlation functions describing the motion of a charged Brownian particle in an external magnetic field when the thermal random force in weakly viscoelastic fluids is exponentially correlated in the time. To obtain a correct description at short times, inertial effects are included into the consideration. The found mean square displacement of the particle motion across the field contains a term proportional to the time, a constant term, and exponentially decaying contributions. The solution for a particle trapped in a harmonic well is also found.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"42 1","pages":"365 - 380"},"PeriodicalIF":0.0,"publicationDate":"2011-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2014.922480","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910689","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 : 2011-07-10DOI: 10.1080/00411450.2010.529980
A. Amirov, Zekeriya Ustaoglu, Bayram Heydarov
In this article we present the solvability of an overdetermined coefficient inverse problem for planar transport equation with no scattering. To compute the approximate solution of the problem we propose a numerical method by using centered difference formulas where the data is given on a part of the boundary of the domain rather than the whole boundary. To demonstrate the computational feasibility of the proposed approximation method, some computational experiments are performed and the results are presented.
{"title":"Solvability of a Two Dimensional Coefficient Inverse Problem for Transport Equation and a Numerical Method","authors":"A. Amirov, Zekeriya Ustaoglu, Bayram Heydarov","doi":"10.1080/00411450.2010.529980","DOIUrl":"https://doi.org/10.1080/00411450.2010.529980","url":null,"abstract":"In this article we present the solvability of an overdetermined coefficient inverse problem for planar transport equation with no scattering. To compute the approximate solution of the problem we propose a numerical method by using centered difference formulas where the data is given on a part of the boundary of the domain rather than the whole boundary. To demonstrate the computational feasibility of the proposed approximation method, some computational experiments are performed and the results are presented.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"1 - 22"},"PeriodicalIF":0.0,"publicationDate":"2011-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2010.529980","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58908945","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 : 2010-11-10DOI: 10.1080/00411450.2011.651032
Brent Young
Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly supported in momentum space, vanishes on characteristics with vanishing angular momentum, and for β⩾3/2 has -norm strictly below a positive, critical value . Everything else being equal, data leading to finite time blow-up can be found with -norm surpassing for any β>1, with if and only if β⩾3/2. In their paper, the critical value for β=3/2 is calculated explicitly while the value for all other β is merely characterized as the infimum of a functional over an appropriate function space. In this work, the existence of minimizers is established, and the exact expression of is calculated in terms of the famous Lane-Emden functions. Numerical computations of the are presented along with some elementary asymptotics near the critical exponent 3/2.
{"title":"Optimal -Control for the Global Cauchy Problem of The Relativistic Vlasov-Poisson System","authors":"Brent Young","doi":"10.1080/00411450.2011.651032","DOIUrl":"https://doi.org/10.1080/00411450.2011.651032","url":null,"abstract":"Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly supported in momentum space, vanishes on characteristics with vanishing angular momentum, and for β⩾3/2 has -norm strictly below a positive, critical value . Everything else being equal, data leading to finite time blow-up can be found with -norm surpassing for any β>1, with if and only if β⩾3/2. In their paper, the critical value for β=3/2 is calculated explicitly while the value for all other β is merely characterized as the infimum of a functional over an appropriate function space. In this work, the existence of minimizers is established, and the exact expression of is calculated in terms of the famous Lane-Emden functions. Numerical computations of the are presented along with some elementary asymptotics near the critical exponent 3/2.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"331 - 359"},"PeriodicalIF":0.0,"publicationDate":"2010-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.651032","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909479","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 : 2010-06-28DOI: 10.1080/00411450.2011.651035
T. Manos, S. Ruffo
The Hamiltonian Mean Field model is a prototype for systems with long-range interactions. It describes the motion of N particles moving on a ring, coupled with an infinite-range potential. The model has a second-order phase transition at the energy density Uc =3/4 and its dynamics is exactly described by the Vlasov equation in the N→∞ limit. Its chaotic properties have been investigated in the past, but the determination of the scaling with N of the Lyapunov Spectrum (LS) of the model remains a challenging open problem. Here we show that the N −1/3 scaling of the Maximal Lyapunov Exponent (MLE), found in previous numerical and analytical studies, extends to the full LS; scaling is “precocious” for the LS, meaning that it becomes manifest for a much smaller number of particles than the one needed to check the scaling for the MLE. Besides that, the N −1/3 scaling appears to be valid not only for U>Uc , as suggested by theoretical approaches based on a random matrix approximation, but also below a threshold energy Ut ≈0.2. Using a recently proposed method (GALI) devised to rapidly check the chaotic or regular nature of an orbit, we find that Ut is also the energy at which a sharp transition from weak to strong chaos is present in the phase-space of the model. Around this energy the phase of the vector order parameter of the model becomes strongly time dependent, inducing a significant untrapping of particles from a nonlinear resonance.
{"title":"Scaling with System Size of the Lyapunov Exponents for the Hamiltonian Mean Field Model","authors":"T. Manos, S. Ruffo","doi":"10.1080/00411450.2011.651035","DOIUrl":"https://doi.org/10.1080/00411450.2011.651035","url":null,"abstract":"The Hamiltonian Mean Field model is a prototype for systems with long-range interactions. It describes the motion of N particles moving on a ring, coupled with an infinite-range potential. The model has a second-order phase transition at the energy density Uc =3/4 and its dynamics is exactly described by the Vlasov equation in the N→∞ limit. Its chaotic properties have been investigated in the past, but the determination of the scaling with N of the Lyapunov Spectrum (LS) of the model remains a challenging open problem. Here we show that the N −1/3 scaling of the Maximal Lyapunov Exponent (MLE), found in previous numerical and analytical studies, extends to the full LS; scaling is “precocious” for the LS, meaning that it becomes manifest for a much smaller number of particles than the one needed to check the scaling for the MLE. Besides that, the N −1/3 scaling appears to be valid not only for U>Uc , as suggested by theoretical approaches based on a random matrix approximation, but also below a threshold energy Ut ≈0.2. Using a recently proposed method (GALI) devised to rapidly check the chaotic or regular nature of an orbit, we find that Ut is also the energy at which a sharp transition from weak to strong chaos is present in the phase-space of the model. Around this energy the phase of the vector order parameter of the model becomes strongly time dependent, inducing a significant untrapping of particles from a nonlinear resonance.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"40 1","pages":"360 - 381"},"PeriodicalIF":0.0,"publicationDate":"2010-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.651035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909528","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 : 2010-06-15DOI: 10.1080/00411450.2012.671209
B. Ganapol
Proteinaceous aggregation occurs through self-assembly—a process not entirely understood. In a recent article, Knowles and colleagues (2009) presented an analytical theory for amyloid fibril growth via secondary rather than primary nucleation. Remarkably, with only a single kinetic parameter, the authors were able to unify growth characteristics for a variety of experimental data. In essence, they seem to have uncovered the underlying allometric law governing the evolution of filament elongation simply from two coupled nonlinear ordinary differential equations originally obtained from a master equation. While this work adds significantly to our understanding of filament self-assembly, it required an “approximate” analytical solution representation for the moments of the chain length distribution. If this were always true, the discovery of such scaling laws would be infrequent. Here, we show that the same results are found by purely numerical means. In addition, the numerical method used features a highly accurate solution strategy for the coupled Ordinary Differential Equations (ODEs) based only on a fundamental finite difference scheme and convergence acceleration. Once a reliable numerical solution has been established, a dimensional analysis then provides the scaling laws.
{"title":"An Accurate Numerical Solution to the Kinetics of Breakable Filament Assembly","authors":"B. Ganapol","doi":"10.1080/00411450.2012.671209","DOIUrl":"https://doi.org/10.1080/00411450.2012.671209","url":null,"abstract":"Proteinaceous aggregation occurs through self-assembly—a process not entirely understood. In a recent article, Knowles and colleagues (2009) presented an analytical theory for amyloid fibril growth via secondary rather than primary nucleation. Remarkably, with only a single kinetic parameter, the authors were able to unify growth characteristics for a variety of experimental data. In essence, they seem to have uncovered the underlying allometric law governing the evolution of filament elongation simply from two coupled nonlinear ordinary differential equations originally obtained from a master equation. While this work adds significantly to our understanding of filament self-assembly, it required an “approximate” analytical solution representation for the moments of the chain length distribution. If this were always true, the discovery of such scaling laws would be infrequent. Here, we show that the same results are found by purely numerical means. In addition, the numerical method used features a highly accurate solution strategy for the coupled Ordinary Differential Equations (ODEs) based only on a fundamental finite difference scheme and convergence acceleration. Once a reliable numerical solution has been established, a dimensional analysis then provides the scaling laws.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"153 - 174"},"PeriodicalIF":0.0,"publicationDate":"2010-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671209","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909625","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 : 2010-03-31DOI: 10.1080/00411450.2011.563704
F. André
A tentative explanation of oscillations in helix traveling waves tubes (TWT) in the nonlinear regime is proposed here based on a parametric oscillation mechanism. This model explains why the TWT oscillates slightly before saturation and why this type of oscillation occurs at a lower beam current than other types of oscillations in the linear regime.
{"title":"Parametric Oscillations in Traveling Waves Tubes for Telecommunication Systems","authors":"F. André","doi":"10.1080/00411450.2011.563704","DOIUrl":"https://doi.org/10.1080/00411450.2011.563704","url":null,"abstract":"A tentative explanation of oscillations in helix traveling waves tubes (TWT) in the nonlinear regime is proposed here based on a parametric oscillation mechanism. This model explains why the TWT oscillates slightly before saturation and why this type of oscillation occurs at a lower beam current than other types of oscillations in the linear regime.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"8 1","pages":"360 - 369"},"PeriodicalIF":0.0,"publicationDate":"2010-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.563704","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58908691","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 : 2010-03-31DOI: 10.1080/00411450.2011.567857
A. Olivetti, J. Barré, B. Marcos, F. Bouchet, R. Kaiser
By means of a dynamical ansatz, we study the breathing dynamics in systems of trapped interacting particles in a unified context, including a wide range of power law interactions and interaction strengths, at linear and nonlinear levels. We present detailed numerical tests of the general theory, and, motivated by Magneto-Optical Traps modeling, we extend it to the case of space-dependent friction and diffusion.
{"title":"Breathing Dynamics for Systems of Interacting Particles in the Microcanonical and Canonical Descriptions","authors":"A. Olivetti, J. Barré, B. Marcos, F. Bouchet, R. Kaiser","doi":"10.1080/00411450.2011.567857","DOIUrl":"https://doi.org/10.1080/00411450.2011.567857","url":null,"abstract":"By means of a dynamical ansatz, we study the breathing dynamics in systems of trapped interacting particles in a unified context, including a wide range of power law interactions and interaction strengths, at linear and nonlinear levels. We present detailed numerical tests of the general theory, and, motivated by Magneto-Optical Traps modeling, we extend it to the case of space-dependent friction and diffusion.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"39 1","pages":"524 - 551"},"PeriodicalIF":0.0,"publicationDate":"2010-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2011.567857","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58908857","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：