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Entropic multipliers method for Langevin diffusion and weighted log Sobolev inequalities

Journal of Functional Analysis, ISSN 0022-1236, 12/2019, Volume 277, Issue 11, p. 108288

In his work about hypocoercivity, Villani considers in particular convergence to equilibrium for the kinetic Langevin process. While his convergence results in...

Hypocoercivity | Langevin diffusion | Weighted logarithmic Sobolev inequality | Entropic convergence

Hypocoercivity | Langevin diffusion | Weighted logarithmic Sobolev inequality | Entropic convergence

Journal Article

Nonlinearity, ISSN 0951-7715, 07/2018, Volume 31, Issue 8, pp. 3748 - 3769

The equations of the temperature-accelerated molecular dynamics (TAMD) method for the calculations of free energies and partition functions are analyzed....

Poisson equation | longtime convergence | molecular dynamics | stochastic differential equation | MATHEMATICS, APPLIED | KINETIC-EQUATIONS | HYPOCOERCIVITY | PHYSICS, MATHEMATICAL | FREE-ENERGY | Probability | Condensed Matter | Mathematics | Statistical Mechanics | Analysis of PDEs | Physics

Poisson equation | longtime convergence | molecular dynamics | stochastic differential equation | MATHEMATICS, APPLIED | KINETIC-EQUATIONS | HYPOCOERCIVITY | PHYSICS, MATHEMATICAL | FREE-ENERGY | Probability | Condensed Matter | Mathematics | Statistical Mechanics | Analysis of PDEs | Physics

Journal Article

Science China Mathematics, ISSN 1674-7283, 6/2019, Volume 62, Issue 6, pp. 1219 - 1232

In this paper, we solve Beck and Wayne’s conjecture on the optimal enhanced dissipation rate for the 2-D linearized Navier-Stokes equations around the bar...

Kolmogorov flow | 35Q35 | hypocoercivity method | Mathematics | Applications of Mathematics | 35Q30 | Navier-Stokes equations | enhanced dissipation | MATHEMATICS | MATHEMATICS, APPLIED

Kolmogorov flow | 35Q35 | hypocoercivity method | Mathematics | Applications of Mathematics | 35Q30 | Navier-Stokes equations | enhanced dissipation | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 05/2018, Volume 52, Issue 3, pp. 1051 - 1083

We prove the consistency of Galerkin methods to solve Poisson equations where the differential operator under consideration is hypocoercive. We show in...

Poisson equation | Error estimates | Langevin dynamics | Spectral methods | FOKKER-PLANCK EQUATION | POINCARE INEQUALITY | MATHEMATICS, APPLIED | spectral methods | KINETIC-EQUATIONS | BEHAVIOR | HYPOCOERCIVITY | error estimates | Operators (mathematics) | Tensors | Computer simulation | Mathematical analysis | Differential equations | Galerkin method | Convergence | Mathematical Physics | Numerical Analysis | Physics | Computer Science

Poisson equation | Error estimates | Langevin dynamics | Spectral methods | FOKKER-PLANCK EQUATION | POINCARE INEQUALITY | MATHEMATICS, APPLIED | spectral methods | KINETIC-EQUATIONS | BEHAVIOR | HYPOCOERCIVITY | error estimates | Operators (mathematics) | Tensors | Computer simulation | Mathematical analysis | Differential equations | Galerkin method | Convergence | Mathematical Physics | Numerical Analysis | Physics | Computer Science

Journal Article

ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 09/2018, Volume 52, Issue 5, pp. 1651 - 1678

We consider a kinetic-fluid model with random initial inputs which describes disperse two-phase flows. In the light particle regime, using energy estimates, we...

Hypocoercivity | Stochastic Galerkin method | Uncertainty quantification | Kinetic theory | Two-phase flow | HYDRODYNAMIC LIMIT | MATHEMATICS, APPLIED | uncertainty quantification | stochastic Galerkin method | NAVIER-STOKES EQUATIONS | FOKKER-PLANCK SYSTEM | COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | kinetic theory | hypocoercivity | SCHEMES | Randomness | Galerkin method | Polynomials | Two phase flow | Sobolev space | Regularity

Hypocoercivity | Stochastic Galerkin method | Uncertainty quantification | Kinetic theory | Two-phase flow | HYDRODYNAMIC LIMIT | MATHEMATICS, APPLIED | uncertainty quantification | stochastic Galerkin method | NAVIER-STOKES EQUATIONS | FOKKER-PLANCK SYSTEM | COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | kinetic theory | hypocoercivity | SCHEMES | Randomness | Galerkin method | Polynomials | Two phase flow | Sobolev space | Regularity

Journal Article

Kinetic and Related Models, ISSN 1937-5093, 2018, Volume 11, Issue 5, pp. 1139 - 1156

In this paper, we study the generalized polynomial chaos (gPC) based stochastic Galerkin method for the linear semiconductor Boltzmann equation under diffusive...

Stochastic Galerkin method | Uncertainty quantification | Multiscale problem | Semiconductor Boltzmann equation | Uniform spectral convergence | Uniform regularity | multiscale problem | MATHEMATICS, APPLIED | stochastic Galerkin method | TRANSPORT-EQUATIONS | KINETIC-EQUATIONS | APPROXIMATION | HYPOCOERCIVITY | LIMIT | MATHEMATICS | ASYMPTOTIC-PRESERVING SCHEME | uniform spectral convergence | REGULARITY | RELAXATION SCHEMES | UNCERTAINTY | COEFFICIENTS | uniform regularity | semiconductor Boltzmann equation

Stochastic Galerkin method | Uncertainty quantification | Multiscale problem | Semiconductor Boltzmann equation | Uniform spectral convergence | Uniform regularity | multiscale problem | MATHEMATICS, APPLIED | stochastic Galerkin method | TRANSPORT-EQUATIONS | KINETIC-EQUATIONS | APPROXIMATION | HYPOCOERCIVITY | LIMIT | MATHEMATICS | ASYMPTOTIC-PRESERVING SCHEME | uniform spectral convergence | REGULARITY | RELAXATION SCHEMES | UNCERTAINTY | COEFFICIENTS | uniform regularity | semiconductor Boltzmann equation

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 11/2015, Volume 83, Issue 3, pp. 331 - 379

In this article we develop a new abstract strategy for proving ergodicity with explicit computable rate of convergence for diffusions associated with a...

Fiber lay-down | Fokker–Planck equation | N-particle Langevin dynamics | Hypocoercivity | Spherical velocity Langevin dynamics | Ergodicity | Mathematics | Generalized Dirichlet forms | Hypoellipticity | Primary 37A25 | Secondary 58J65 | Poincaré inequality | Operator semigroups | Non-symmetric diffusions | Kolmogorov backward equation | Singularly distorted diffusions | Degenerate diffusions | Analysis | Stratonovich SDEs on manifolds | Rate of convergence | Nonsymmetric diffusions | N-particle langevin dynamics | Fokker-Planck equation | MARKOV-PROCESSES | MATHEMATICS | LANGEVIN DYNAMICS | CONVERGENCE | Poincare inequality

Fiber lay-down | Fokker–Planck equation | N-particle Langevin dynamics | Hypocoercivity | Spherical velocity Langevin dynamics | Ergodicity | Mathematics | Generalized Dirichlet forms | Hypoellipticity | Primary 37A25 | Secondary 58J65 | Poincaré inequality | Operator semigroups | Non-symmetric diffusions | Kolmogorov backward equation | Singularly distorted diffusions | Degenerate diffusions | Analysis | Stratonovich SDEs on manifolds | Rate of convergence | Nonsymmetric diffusions | N-particle langevin dynamics | Fokker-Planck equation | MARKOV-PROCESSES | MATHEMATICS | LANGEVIN DYNAMICS | CONVERGENCE | Poincare inequality

Journal Article

KINETIC AND RELATED MODELS, ISSN 1937-5093, 10/2019, Volume 12, Issue 5, pp. 969 - 993

In this paper we study the general discrete-velocity models of Boltzmann equation with uncertainties from collision kernel and random inputs. We follow the...

UNIFORM REGULARITY | MATHEMATICS, APPLIED | discrete-velocity Boltzmann models | KINETIC-EQUATIONS | APPROXIMATION | sensitivity analysis | HYPOCOERCIVITY | MODEL | PRESERVING AP SCHEMES | MATHEMATICS | hypocoecivity | stochastic Galerkin | EQUILIBRIUM | UNCERTAINTY | Kinetic equations with uncertainties | DIFFUSIVE LIMIT

UNIFORM REGULARITY | MATHEMATICS, APPLIED | discrete-velocity Boltzmann models | KINETIC-EQUATIONS | APPROXIMATION | sensitivity analysis | HYPOCOERCIVITY | MODEL | PRESERVING AP SCHEMES | MATHEMATICS | hypocoecivity | stochastic Galerkin | EQUILIBRIUM | UNCERTAINTY | Kinetic equations with uncertainties | DIFFUSIVE LIMIT

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2019, Volume 376, pp. 634 - 659

In this paper, we study the bipolar Boltzmann-Poisson model, both for the deterministic system and the system with uncertainties, with asymptotic behavior...

Bipolar Boltzmann-Poisson model | Uncertainty quantification | Stochastic AP scheme | Diffusive scaling | Sensitivity analysis | gPC-SG method | SPECTRAL CONVERGENCE | UNIFORM REGULARITY | AP SCHEMES | GALERKIN METHOD | HYPOCOERCIVITY | LINEAR KINETIC-EQUATIONS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RELAXATION SCHEMES | NUMERICAL SCHEMES | UNCERTAINTY | CONSERVATION-LAWS | Electric fields | Analysis | Models | Mathematical analysis | Asymptotic properties | Polynomials | Mathematical models | Galerkin method | Semiconductor doping | Asymptotic methods | Convergence | Mathematics - Numerical Analysis

Bipolar Boltzmann-Poisson model | Uncertainty quantification | Stochastic AP scheme | Diffusive scaling | Sensitivity analysis | gPC-SG method | SPECTRAL CONVERGENCE | UNIFORM REGULARITY | AP SCHEMES | GALERKIN METHOD | HYPOCOERCIVITY | LINEAR KINETIC-EQUATIONS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RELAXATION SCHEMES | NUMERICAL SCHEMES | UNCERTAINTY | CONSERVATION-LAWS | Electric fields | Analysis | Models | Mathematical analysis | Asymptotic properties | Polynomials | Mathematical models | Galerkin method | Semiconductor doping | Asymptotic methods | Convergence | Mathematics - Numerical Analysis

Journal Article

Chinese Annals of Mathematics, Series B, ISSN 0252-9599, 9/2019, Volume 40, Issue 5, pp. 765 - 780

The authors study the fluid dynamic behavior of the stochastic Galerkin (SG for short) approximation to the kinetic Fokker-Planck equation with random...

65L60 | Hyperbolic equations | Uncertainty quantification | Mathematics, general | Mathematics | Applications of Mathematics | Stochastic Galerkin methods | 35L65 | SPACE | MATHEMATICS | UNIFORM REGULARITY | FOKKER-PLANCK SYSTEM | COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | HYPOCOERCIVITY | MODEL | Case studies | Fluid dynamics

65L60 | Hyperbolic equations | Uncertainty quantification | Mathematics, general | Mathematics | Applications of Mathematics | Stochastic Galerkin methods | 35L65 | SPACE | MATHEMATICS | UNIFORM REGULARITY | FOKKER-PLANCK SYSTEM | COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | HYPOCOERCIVITY | MODEL | Case studies | Fluid dynamics

Journal Article

Reports on Mathematical Physics, ISSN 0034-4877, 06/2016, Volume 77, Issue 3, pp. 267 - 292

Markov Chain Monte Carlo (MCMC) methods are statistical methods designed to sample from a given measure π by constructing a Markov chain that has π as...

nonreversible diffusions | Hamiltonian Monte Carlo | Markov chain Monte Carlo | hypocoercivity | PHYSICS, MATHEMATICAL | Markov processes | Monte Carlo method | Algorithms | Analysis | Monte Carlo methods | Asymptotic properties | Dynamics | Preserves | Markov chains | Statistical methods | Diffusion

nonreversible diffusions | Hamiltonian Monte Carlo | Markov chain Monte Carlo | hypocoercivity | PHYSICS, MATHEMATICAL | Markov processes | Monte Carlo method | Algorithms | Analysis | Monte Carlo methods | Asymptotic properties | Dynamics | Preserves | Markov chains | Statistical methods | Diffusion

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 11/2011, Volume 64, Issue 11, pp. 1497 - 1546

In this paper we study the large‐time behavior of classical solutions to the two‐species Vlasov‐Maxwell‐Boltzmann system in the whole space \input amssym...

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY-LOSS TYPE | ENERGY METHOD | STABILITY | EXPONENTIAL DECAY | EQUILIBRIUM | CAUCHY-PROBLEM | HYPOCOERCIVITY | GLOBAL CLASSICAL-SOLUTIONS | EQUATION

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY-LOSS TYPE | ENERGY METHOD | STABILITY | EXPONENTIAL DECAY | EQUILIBRIUM | CAUCHY-PROBLEM | HYPOCOERCIVITY | GLOBAL CLASSICAL-SOLUTIONS | EQUATION

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2019, Volume 397, p. 108838

The Boltzmann equation may contain uncertainties in initial/boundary data or collision kernel. To study the impact of these uncertainties, a stochastic...

Boltzmann equation with uncertainty | Stochastic Galerkin | Asymptotic-preserving schemes | Fluid dynamic limit | UNIFORM REGULARITY | KINETIC-EQUATIONS | GENERALIZED POLYNOMIAL CHAOS | HYPOCOERCIVITY | MODEL | PHYSICS, MATHEMATICAL | NUMERICAL SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION-LAWS | EFFICIENT | PROPAGATION | Boltzmann transport equation | Uncertainty | Galerkin method | Mathematical analysis | Isotopes

Boltzmann equation with uncertainty | Stochastic Galerkin | Asymptotic-preserving schemes | Fluid dynamic limit | UNIFORM REGULARITY | KINETIC-EQUATIONS | GENERALIZED POLYNOMIAL CHAOS | HYPOCOERCIVITY | MODEL | PHYSICS, MATHEMATICAL | NUMERICAL SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION-LAWS | EFFICIENT | PROPAGATION | Boltzmann transport equation | Uncertainty | Galerkin method | Mathematical analysis | Isotopes

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2018, Volume 50, Issue 2, pp. 1790 - 1816

We study the Vlasov Poisson Fokker Planck system with uncertainty and multiple scales. Here the uncertainty, modeled by random variables, enters the solution...

Hypocoercivity | Uncertainty quantification | Vlasov-Poisson-Fokker-Planck system | Random input | random input | MATHEMATICS, APPLIED | uncertainty quantification | HIGH-FIELD LIMIT | CONVERGENCE ANALYSIS | STOCHASTIC GALERKIN METHOD | APPROXIMATION | POLYNOMIAL CHAOS | LINEAR KINETIC-EQUATIONS | PRESERVING AP SCHEMES | hypocoercivity | PARTIAL-DIFFERENTIAL-EQUATIONS | RANDOM WAVE SPEED | HYPERBOLIC-EQUATIONS

Hypocoercivity | Uncertainty quantification | Vlasov-Poisson-Fokker-Planck system | Random input | random input | MATHEMATICS, APPLIED | uncertainty quantification | HIGH-FIELD LIMIT | CONVERGENCE ANALYSIS | STOCHASTIC GALERKIN METHOD | APPROXIMATION | POLYNOMIAL CHAOS | LINEAR KINETIC-EQUATIONS | PRESERVING AP SCHEMES | hypocoercivity | PARTIAL-DIFFERENTIAL-EQUATIONS | RANDOM WAVE SPEED | HYPERBOLIC-EQUATIONS

Journal Article

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Uniform regularity for linear kinetic equations with random input based on hypocoercivity

SIAM-ASA Journal on Uncertainty Quantification, ISSN 2166-2525, 2017, Volume 5, Issue 1, pp. 1193 - 1219

In this paper we study the effect of randomness in kinetic equations that preserve mass. Our focus is in proving the analyticity of the solution with respect...

Hypocoercivity | Uncertainty | Kinetic theory | Quantification | Uniform regularity | FOKKER-PLANCK EQUATION | quantification | HIGH-FIELD REGIME | POLYNOMIAL CHAOS | GALERKIN METHOD | uncertainty | PHYSICS, MATHEMATICAL | ELLIPTIC PDES | hypocoercivity | GLOBAL EQUILIBRIUM | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | STOCHASTIC COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | ERROR ANALYSIS | BOLTZMANN-EQUATION | uniform regularity | kinetic theory

Hypocoercivity | Uncertainty | Kinetic theory | Quantification | Uniform regularity | FOKKER-PLANCK EQUATION | quantification | HIGH-FIELD REGIME | POLYNOMIAL CHAOS | GALERKIN METHOD | uncertainty | PHYSICS, MATHEMATICAL | ELLIPTIC PDES | hypocoercivity | GLOBAL EQUILIBRIUM | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | STOCHASTIC COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | ERROR ANALYSIS | BOLTZMANN-EQUATION | uniform regularity | kinetic theory

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2016, Volume 48, Issue 1, pp. 538 - 568

A new coercivity estimate on the spectral gap of the linearized Boltzmann collision operator for multiple species is proved. The assumptions on the collision...

Hypocoercivity | Energy method | Boltzmann equation | Multispecies mixture | Spectral gap | Rate of convergence to equilibrium | energy method | MATHEMATICS, APPLIED | rate of convergence to equilibrium | EQUILIBRIUM | spectral gap | KINETIC-MODEL | CONVERGENCE | COLLISION OPERATOR | EQUATION | multispecies mixture | hypocoercivity

Hypocoercivity | Energy method | Boltzmann equation | Multispecies mixture | Spectral gap | Rate of convergence to equilibrium | energy method | MATHEMATICS, APPLIED | rate of convergence to equilibrium | EQUILIBRIUM | spectral gap | KINETIC-MODEL | CONVERGENCE | COLLISION OPERATOR | EQUATION | multispecies mixture | hypocoercivity

Journal Article

KINETIC AND RELATED MODELS, ISSN 1937-5093, 08/2019, Volume 12, Issue 4, pp. 909 - 922

In [L. Liu and S. Jin, Multiscale Model. Simult., 16, 1085-1114, 2018], spectral convergence and long-time decay of the numerical solution towards the global...

multiple scales | UNIFORM REGULARITY | MATHEMATICS, APPLIED | KINETIC-EQUATIONS | sensitivity analysis | The Boltzmann equation with uncertainties | INPUTS | hypocoercivity | MATHEMATICS | EQUILIBRIUM | TREND | gPC stochastic Galerkin method | large random perturbation

multiple scales | UNIFORM REGULARITY | MATHEMATICS, APPLIED | KINETIC-EQUATIONS | sensitivity analysis | The Boltzmann equation with uncertainties | INPUTS | hypocoercivity | MATHEMATICS | EQUILIBRIUM | TREND | gPC stochastic Galerkin method | large random perturbation

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2018, Volume 61, Issue 1, pp. 137 - 150

In this paper, we study the large time behaviour of the solution of the Fokker-Planck equation with general potential. For the long range potential, we prove...

hypocoercivity method | large time behavior | Mathematics | Applications of Mathematics | Fokker-Planck equation | 35B40 | MATHEMATICS | MATHEMATICS, APPLIED | EQUILIBRIUM | TREND

hypocoercivity method | large time behavior | Mathematics | Applications of Mathematics | Fokker-Planck equation | 35B40 | MATHEMATICS | MATHEMATICS, APPLIED | EQUILIBRIUM | TREND

Journal Article

Kinetic and Related Models, ISSN 1937-5093, 2018, Volume 11, Issue 4, pp. 953 - 1009

We study hypocoercivity for a class of linearized BGK models for continuous phase spaces. We develop methods for constructing entropy functionals that enable...

BGK models | Hypocoercivity | Lyapunov functionals | Perturbation methods for matrix equations | Kinetic equations | MATHEMATICS | MATHEMATICS, APPLIED | perturbation methods for matrix equations | DECAY | LARGE-TIME BEHAVIOR | hypocoercivity

BGK models | Hypocoercivity | Lyapunov functionals | Perturbation methods for matrix equations | Kinetic equations | MATHEMATICS | MATHEMATICS, APPLIED | perturbation methods for matrix equations | DECAY | LARGE-TIME BEHAVIOR | hypocoercivity

Journal Article

Rivista di Matematica della Universita di Parma, ISSN 0035-6298, 2015, Volume 6, Issue 1, pp. 1 - 68

Journal Article

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