We prove that energy conservation holds for weak solutions to classical VlasovPoisson systems with proper regularity.In particular,there exists a solution that conserves energy with|v|^(m)f0∈L^(1)_(x,v)for m>9/4.
We consider asymptotic behaviors of the Vlasov-Poisson system with radiation damping in three space dimensions.For any smooth solution with compact support,we prove a sub-linear growth estimate of its velocity support...We consider asymptotic behaviors of the Vlasov-Poisson system with radiation damping in three space dimensions.For any smooth solution with compact support,we prove a sub-linear growth estimate of its velocity support.As a consequence,we derive some new estimates of the charge densities and the electrostatic field in this situation.展开更多
In this work, we apply a semi-Lagrangian spectral method for the Vlasov-Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the appro...In this work, we apply a semi-Lagrangian spectral method for the Vlasov-Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space-velocity domain with a BDF timestepping scheme. The resulting method possesses good conservation properties, which have been assessed by a series of numerical tests conducted on some standard benchmark problems including the two-stream instability and the Landau damping test cases. In the Hermite case, we also investigate the numerical behavior in dependence of a scaling parameter in the Gaussian weight. Confirming previous results from the literature, our experiments for different representative values of this parameter, indicate that a proper choice may significantly impact on accuracy, thus suggesting that suitable strategies should be developed to automatically update the parameter during the time-advancing procedure.展开更多
We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Pois-son system written as a hyperbolic system using Hermite polynomials in the velocity vari-able.These schemes are designed to be syst...We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Pois-son system written as a hyperbolic system using Hermite polynomials in the velocity vari-able.These schemes are designed to be systematically as accurate as one wants with prov-able conservation of mass and possibly total energy.Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov-Poisson system.The proposed scheme employs the discontinuous Galerkin discretization for both the Vlasov and the Poisson equations,resulting in a consistent description of the distribu-tion function and the electric field.Numerical simulations are performed to verify the order of the accuracy and conservation properties.展开更多
In this article, we are concerned with the construction of global smooth small-amplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions....In this article, we are concerned with the construction of global smooth small-amplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions. Compared with the former result obtained by Duan and Liu in [12] for the two species model, we do not ask the initial perturbation to satisfy the neutral condition and our result covers all physical collision kernels for the full range of intermolecular repulsive potentials.展开更多
In this note it is shown that the Vlasov-Poisson-Fokker-Planck system in the three-dimensional whole space driven by a time-periodic background profile near a positive constant state admits a time-periodic small-ampli...In this note it is shown that the Vlasov-Poisson-Fokker-Planck system in the three-dimensional whole space driven by a time-periodic background profile near a positive constant state admits a time-periodic small-amplitude solution with the same period. The proof follows by the Serrin＇s method on the basis of the exponential time-decay property of the linearized system in the case of the constant background profile.展开更多
In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the targe...In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings.展开更多
In this paper,we propose a new conservative high-order semi-Lagrangian finite difference(SLFD)method to solve linear advection equation and the nonlinear Vlasov and BGK models.The finite difference scheme has better c...In this paper,we propose a new conservative high-order semi-Lagrangian finite difference(SLFD)method to solve linear advection equation and the nonlinear Vlasov and BGK models.The finite difference scheme has better computational flexibility by working with point values,especially when working with high-dimensional problems in an operator splitting setting.The reconstruction procedure in the proposed SLFD scheme is motivated from the SL finite volume scheme.In particular,we define a new sliding average function,whose cell averages agree with point values of the underlying function.By developing the SL finite volume scheme for the sliding average function,we derive the proposed SLFD scheme,which is high-order accurate,mass conservative and unconditionally stable for linear problems.The performance of the scheme is showcased by linear transport applications,as well as the nonlinear Vlasov-Poisson and BGK models.Furthermore,we apply the Fourier stability analysis to a fully discrete SLFD scheme coupled with diagonally implicit Runge-Kutta(DIRK)method when applied to a stiff two-velocity hyperbolic relaxation system.Numerical stability and asymptotic accuracy properties of DIRK methods are discussed in theoretical and computational aspects.展开更多
We construct(modified)scattering operators for the Vlasov-Poisson system in three dimensions,mapping small asymptotic dynamics as t→−∞to asymptotic dynamics as t→+∞.The main novelty is the construction of modified...We construct(modified)scattering operators for the Vlasov-Poisson system in three dimensions,mapping small asymptotic dynamics as t→−∞to asymptotic dynamics as t→+∞.The main novelty is the construction of modified wave operators,but we also obtain a new simple proof of modified scattering.Our analysis is guided by the Hamiltonian structure of the Vlasov-Poisson system.Via a pseudo-conformal inversion,we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.展开更多
By one-dimensional Vlasov-Poisson simulation, the critical initial state marking the transition between the Landau scenario, in which the electric fields definitively damped to zero and the O＇NEIL scenario, in which ...By one-dimensional Vlasov-Poisson simulation, the critical initial state marking the transition between the Landau scenario, in which the electric fields definitively damped to zero and the O＇NEIL scenario, in which the Landau damping is stopped after a certain damping stage, is studied. It is found that the critical initial amplitude e＊ can only exist when the product of the wave number （k~） and the electron thermal velocity （vth） is moderate, that is, 0.2 〈 k^vth 〈 0.7. Otherwise, no critical initial amplitude is found. The value c＊ increases with the increase in km for a fixed Vth, and also increases with the increase in Vth for a fixed kin. When kmVth is fixed, the value s＊ also changes with the wave number and the electron thermal velocity, even though the damping rate and the oscillation frequency are the same in this case.展开更多
基金supported by the National Natural Science Foundation of China(11871024)。
文摘We prove that energy conservation holds for weak solutions to classical VlasovPoisson systems with proper regularity.In particular,there exists a solution that conserves energy with|v|^(m)f0∈L^(1)_(x,v)for m>9/4.
基金supported by the National Natural Science Foundation of China(11871024)。
文摘We consider asymptotic behaviors of the Vlasov-Poisson system with radiation damping in three space dimensions.For any smooth solution with compact support,we prove a sub-linear growth estimate of its velocity support.As a consequence,we derive some new estimates of the charge densities and the electrostatic field in this situation.
文摘In this work, we apply a semi-Lagrangian spectral method for the Vlasov-Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space-velocity domain with a BDF timestepping scheme. The resulting method possesses good conservation properties, which have been assessed by a series of numerical tests conducted on some standard benchmark problems including the two-stream instability and the Landau damping test cases. In the Hermite case, we also investigate the numerical behavior in dependence of a scaling parameter in the Gaussian weight. Confirming previous results from the literature, our experiments for different representative values of this parameter, indicate that a proper choice may significantly impact on accuracy, thus suggesting that suitable strategies should be developed to automatically update the parameter during the time-advancing procedure.
基金the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under Grant Agreement No.633053.the Science Challenge Project(No.TZ2016002)+2 种基金the National Natural Science Foundation of China(No.11971025)the Natural Science Foundation of Fujian Province(No.2019J06002)the NSAF(No.U1630247)。
文摘We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Pois-son system written as a hyperbolic system using Hermite polynomials in the velocity vari-able.These schemes are designed to be systematically as accurate as one wants with prov-able conservation of mass and possibly total energy.Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov-Poisson system.The proposed scheme employs the discontinuous Galerkin discretization for both the Vlasov and the Poisson equations,resulting in a consistent description of the distribu-tion function and the electric field.Numerical simulations are performed to verify the order of the accuracy and conservation properties.
基金supported by the Fundamental Research Funds for the Central Universitiessupported by a grant from the National Science Foundation of China under contract 11501556+1 种基金supported by a grant from the National Natural Science Foundation under contract 11501187supported by three grants from the National Natural Science Foundation of China under contracts 10925103,11271160,and 11261160485
文摘In this article, we are concerned with the construction of global smooth small-amplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions. Compared with the former result obtained by Duan and Liu in [12] for the two species model, we do not ask the initial perturbation to satisfy the neutral condition and our result covers all physical collision kernels for the full range of intermolecular repulsive potentials.
基金supported by the General Research Fund(Project No.409913)from RGC of Hong Kongsupported by grants from the National Natural Science Foundation of China(11101188 and 11271160)
文摘In this note it is shown that the Vlasov-Poisson-Fokker-Planck system in the three-dimensional whole space driven by a time-periodic background profile near a positive constant state admits a time-periodic small-amplitude solution with the same period. The proof follows by the Serrin＇s method on the basis of the exponential time-decay property of the linearized system in the case of the constant background profile.
基金AFOSR and NSF for their support of this work under grants FA9550-19-1-0281 and FA9550-17-1-0394 and NSF grant DMS 191218。
文摘In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings.
基金Research of Linjin Li and Jingmei Qiu is supported by the NSF grant NSF-DMS-1818924the Air Force Office of Scientific Computing FA9550-18-1-0257 and the University of Delawarethe Italian Ministry of Instruction,University and Research(MIUR)to support this research with funds coming from the PRIN Project 2017,No.2017KKJP4X and ITN-ETN Horizon 2020 Project,Project Reference 642768.
文摘In this paper,we propose a new conservative high-order semi-Lagrangian finite difference(SLFD)method to solve linear advection equation and the nonlinear Vlasov and BGK models.The finite difference scheme has better computational flexibility by working with point values,especially when working with high-dimensional problems in an operator splitting setting.The reconstruction procedure in the proposed SLFD scheme is motivated from the SL finite volume scheme.In particular,we define a new sliding average function,whose cell averages agree with point values of the underlying function.By developing the SL finite volume scheme for the sliding average function,we derive the proposed SLFD scheme,which is high-order accurate,mass conservative and unconditionally stable for linear problems.The performance of the scheme is showcased by linear transport applications,as well as the nonlinear Vlasov-Poisson and BGK models.Furthermore,we apply the Fourier stability analysis to a fully discrete SLFD scheme coupled with diagonally implicit Runge-Kutta(DIRK)method when applied to a stiff two-velocity hyperbolic relaxation system.Numerical stability and asymptotic accuracy properties of DIRK methods are discussed in theoretical and computational aspects.
基金Open Access funding provided by EPFL LausanneThe authors were supported in part by NSF grant DMS-17000282.
文摘We construct(modified)scattering operators for the Vlasov-Poisson system in three dimensions,mapping small asymptotic dynamics as t→−∞to asymptotic dynamics as t→+∞.The main novelty is the construction of modified wave operators,but we also obtain a new simple proof of modified scattering.Our analysis is guided by the Hamiltonian structure of the Vlasov-Poisson system.Via a pseudo-conformal inversion,we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.
基金supported by National Natural Science Foundation of China (Nos.11147025, 10947108, 11075105)the National Basic Research Program of China (No.2009GB105002)+1 种基金the Natural Science Foundation of Shandong Province of China (No.Q2008A05)the Foundation of Qufu Normal University of China (No.BSQD09011)
文摘By one-dimensional Vlasov-Poisson simulation, the critical initial state marking the transition between the Landau scenario, in which the electric fields definitively damped to zero and the O＇NEIL scenario, in which the Landau damping is stopped after a certain damping stage, is studied. It is found that the critical initial amplitude e＊ can only exist when the product of the wave number （k~） and the electron thermal velocity （vth） is moderate, that is, 0.2 〈 k^vth 〈 0.7. Otherwise, no critical initial amplitude is found. The value c＊ increases with the increase in km for a fixed Vth, and also increases with the increase in Vth for a fixed kin. When kmVth is fixed, the value s＊ also changes with the wave number and the electron thermal velocity, even though the damping rate and the oscillation frequency are the same in this case.
