Internationale Boltzmann‐Tagung (Wien, 5.–8.9.1981)

Meÿenn, Karl von

doi:10.1002/bewi.19820050311

Cited by 5 publications

(10 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This expression shows that the diffusion tensor of the test particle depends on the spectral auto-correlation tensor of the external perturbation Ĉαα ′ (ω) and on the inverse dielectric matrix (response function) ǫ −1 (ω) both evaluated at the resonance frequencies ω = k • Ω(J). 32 As a result, the diffusion tensor D ij [f, J] depends not only on the action J but is also a functional of the DF f (J, t) itself through the dielectric matrix ǫ αα ′ (k • Ω(J)) defined by Eq. (43).…”

Section: Diffusion Tensor a General Expression Of The Diffusion Tensormentioning

confidence: 99%

“…He emphasized the importance of collisions between particles at large distances which are scattered through small angles. Starting from the Boltzmann equation [32], expanding this equation in terms of a weak deflexion parameter, and making a linear trajectory approximation, he obtained a kinetic equation governing the evolution of the velocity distribution f (v, t) of the electrons. The original form of the equation given by Landau [31] reads…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Kinetic theory of two-dimensional point vortices and fluctuation–dissipation theorem

Chavanis

2023

Eur. Phys. J. Plus

View full text Add to dashboard Cite

We complete the kinetic theory of inhomogeneous systems with long-range interactions initiated in previous works. We use a simpler and more physical formalism. We consider a system of particles submitted to a small external stochastic perturbation and determine the response of the system to the perturbation. We derive the diffusion tensor and the friction by polarization of a test particle. We introduce a general Fokker-Planck equation involving a diffusion term and a friction term. When the friction by polarization can be neglected, we obtain a secular dressed diffusion (SDD) equation sourced by the external noise. When the external perturbation is created by a discrete collection of N field particles, we obtain the inhomogeneous Lenard-Balescu kinetic equation reducing to the inhomogeneous Landau kinetic equation when collective effects are neglected. We consider a multispecies system of particles. When the field particles are at statistical equilibrium (thermal bath), we establish the proper expression of the fluctuation-dissipation theorem for systems with long-range interactions relating the power spectrum of the fluctuations to the response function of the system. In that case, the friction and diffusion coefficients satisfy the Einstein relation and the Fokker-Planck equation reduces to the inhomogeneous Kramers equation. We also consider a gas of Brownian particles with long-range interactions described by N coupled stochastic Langevin equations and determine its mean and mesoscopic evolution. We discuss the notion of stochastic kinetic equations and the role of fluctuations possibly triggering random transitions from one equilibrium state to the other. Our presentation parallels the one given for two-dimensional point vortices in a previous paper [P.H. Chavanis, Eur. Phys. J. Plus 138, 136 (2023)].

show abstract

Section: Diffusion Tensor a General Expression Of The Diffusion Tensormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Kinetic theory of two-dimensional point vortices and fluctuation–dissipation theorem

Chavanis

2023

Eur. Phys. J. Plus

View full text Add to dashboard Cite

show abstract

“…In the present work, two standard lattices are considered: the one-dimensional D1Q3 lattice and the two-dimensional D2Q9 one. Their discrete velocities and Gaussian weights read [11]: D1Q3 : ξ x = [0, 1, −1] c/c s , w i = [2/3, 1/6, 1/6], (6) D2Q9 : ξ x = [0, 1, 1, 0, −1, −1, −1, 0, 1] c/c s , ξ y = [0, 0, 1, 1, 1, 0, −1, −1, −1] c/c s , w i = [2/3, 1/9, 1/36, 1/9, 1/36, 1/9, 1/36, 1/9, 1/36], (7) where c s = 1/ √…”

Section: Isothermal Discrete Velocity Boltzmann Equation (Dvbe)mentioning

confidence: 99%

“…Over the last three decades, the lattice Boltzmann method (LBM) has become a promising alternative to conventional methods in computational fluid dynamics (CFD) [1][2][3][4]. Inherited from lattice gas automata [5], it relies on a simplified statistical description of a gas inspired by the Boltzmann equation, encompassing a macroscopic flow behaviour usually modelled by the Navier-Stokes (NS) equations [6,7]. The great success of the LBM lies in the simplicity of its numerical scheme.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic limits and numerical errors of isothermal lattice Boltzmann schemes

Wissocq

Sagaut

2022

Journal of Computational Physics

View full text Add to dashboard Cite

“…It is well known that the lattice formulation of kinetic theory provides a computationally efficient method to solve conservation equations and is well established for the hydrodynamics [18]. A discrete form of the Maxwell-Boltzmann velocity distribution [19,20] is used in this formulation, which preserves the isotropy of space to fourth order.…”

mentioning

confidence: 99%

Lattice differential operators for computational physics

Ramadugu¹,

Thampi²,

Adhikari³

et al. 2013

EPL

View full text Add to dashboard Cite

We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and lend themselves to recursive techniques to enhance the convergence order. The result is a simple and elegant procedure to derive isotropic and accurate discretizations of differential operators of general applicability across a broad range of problems in computational physics. We show the usefulness of this approach by providing examples from hydrodynamics and electrodynamics.

show abstract

Internationale Boltzmann‐Tagung (Wien, 5.–8.9.1981)

Cited by 5 publications

References 0 publications

Kinetic theory of two-dimensional point vortices and fluctuation–dissipation theorem

Kinetic theory of two-dimensional point vortices and fluctuation–dissipation theorem

Hydrodynamic limits and numerical errors of isothermal lattice Boltzmann schemes

Lattice differential operators for computational physics

Contact Info

Product

Resources

About