相关论文: Orbit-averaged Guiding-center Fokker-Planck Operat…
We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov-Vicsek models that can be considered a non-local non-linear Fokker-Planck type equation describing the dynamics of individuals with orientational…
We study the transport of active Brownian particles (ABPs) in three-dimensional (3D) oscillatory geometries, which are spatially periodic. We establish a generalized Fick-Jacobs approach, which reduces a 3D system to an effective 1D system…
A quadratic optimal transport metric on the set of probability measure over $\R^2$ is introduced. The quadratic cost is given by the euclidean norm on $\R^2$ associated to some well chosen symmetric positive matrix, which makes the metric…
Turbulent transport near the X-point of a large tokamak is examined using local, gradient-driven simulations that determine the saturated plasma profiles. The distribution of a representative set of particle tracers evolving within these…
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting…
In this paper, we develop an operator splitting scheme for the fractional kinetic Fokker-Planck equation (FKFPE). The scheme consists of two phases: a fractional diffusion phase and a kinetic transport phase. The first phase is solved…
We consider the Vlasov-Fokker-Planck operator with a strong external magnetic field. We show a maximal type estimate on this operator using a nilpotent approach on vector field polynomial operators and including the notion of representation…
In this Letter, we present a new formulation of loss cone theory as a reaction-diffusion system, which accounts for loss cone events through a sink term and can be orbit-averaged. It can recover the standard approach based on boundary…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a novel approach using periodic orbit theory to analyze plasma turbulence, identifying fundamental structures…
Low density plasmas are characterized by a large scale separation between the gyromotion of particles around local magnetic fields and the macroscopic scales of the system, often making global kinetic simulations computationally…
An explicit formula is obtained for the generalized Macdonald functions on the $N$-fold Fock tensor spaces, calculating a certain matrix element of a composition of several screened vertex operators. As an application, we prove the…
The study of fluctuation-induced transport is concerned with the directed motion of particles on a substrate when subjected to a fluctuating external field. Work over the last two decades provides now precise clues on how the average…
Single-site dynamical mean field theory is used to determine the magnetic and orbital-ordering phase diagram for a model of electrons moving on a lattice with three orbital states per site and with the fully rotationally invariant…
Optimal power flow (OPF) over power transmission networks poses challenging large-scale nonlinear optimization problems, which involve a large number of quadratic equality and indefinite quadratic inequality constraints. These…
The evolution operator method is used to solve the generalized Fokker-Planck equations and the generalized diffusion-wave equations in the (1+1) dimensional space in which $x\in\mathbb{R}$ and $t\in\mathbb{R}_+$. These equations contain…
The microscopic structure of spin-orbit fields for the technologically important Fe/GaAs interface is uncovered from first principles. A symmetry based method allows to obtain the spin-orbit fields---both their magnitude and…
We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The…
Using the method of nonequilibrium statistical operator by Zubarev, an approach is proposed for the description of kinetics which takes into account the nonlinear hydrodynamic fluctuations for a quantum Bose system. Non-equilibrium…
The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…