Related papers: A Vlasov Algorithm Derived from Phase Space Conser…
We propose a new Eulerian numerical approach for constructing the forward flow maps in continuous dynamical systems. The new algorithm improves the original formulation developed in [23, 24] so that the associated partial differential…
The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. Here, a novel, implicit, particle-in-cell based…
The numerical resolution of the Vlasov equation provides complementary information with respect to analytical studies and forms an important research tool in domains such as plasma physics. The study of mean-field models for systems with…
We present a mechanistic model for a Newtonian fluid called fluid particle dynamics. By analyzing the concept of ``fluid particle'' from the point of view of a Voronoi tessellation of a molecular fluid, we propose an heuristic derivation of…
The modification of the Vlasov equation, in its standard form describing a charged particle distribution in the six-dimensional phase space, is derived explicitly within a formal Hamiltonian approach for arbitrarily curved spacetime. The…
The linearized Vlasov equation for a plasma system in a uniform magnetic field and the corresponding linear Vlasov operator are studied. The spectrum and the corresponding eigenfunctions of the Vlasov operator are found. The spectrum of…
The Vlasov--Maxwell equations are used for the kinetic description of magnetized plasmas. As they are posed in an up to 3+3 dimensional phase space, solving this problem is extremely expensive from a computational point of view. In this…
State estimation in non-linear models is performed by tracking the posterior distribution recursively. A plethora of algorithms have been proposed for this task. Among them, the Gaussian particle filter uses a weighted set of particles to…
The Vlasov-Poisson equations, fundamental in plasma physics and astrophysical applications, are rendered linear, finite-dimensional, and discrete by second quantization. Conditions for correspondence between the pre-quantized and quantized…
In this work, we develop and rigorously analyze a new class of particle methods for the magnetized Vlasov--Poisson--Fokker--Planck system. The proposed approach addresses two fundamental challenges: (1) the curse of dimensionality, which we…
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of…
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…
We revisit in one dimension the waterbag method to solve numerically Vlasov-Poisson equations. In this approach, the phase-space distribution function $f(x,v)$ is initially sampled by an ensemble of patches, the waterbags, where $f$ is…
The Sutherland approximation to the van der Waals forces is applied to the derivation of a self-consistent Vlasov-type field in a liquid filling a half space, bordering vacuum. The ensuing Vlasov equation is then derived, and solved to…
In this work, the recently introduced fluid-like treatment of the phase-space has been further extended and some interesting outcomes have been presented. A modified form of the Vlasov equation has been presented which describes the…
We obtain a natural extension of the Vlasov-Poisson system for stellar dynamics to spaces of constant Gaussian curvature $\kappa\ne 0$: the unit sphere $\mathbb S^2$, for $\kappa>0$, and the unit hyperbolic sphere $\mathbb H^2$, for…
We analyze the system of equations describing the flow of a dilute particle system coupled with an incompressible non-Newtonian fluid in a bounded domain. In this setting, both PDEs are connected via a drag force, or the friction force. We…
We propose a class of Particle-In-Cell (PIC) methods for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on the motion of particles in the plane orthogonal to the…
Certain features of the method of characteristics are of considerable interest in relation with Vlasov simulation [H. Abbasi {\it et al}, Phys. Rev. E \textbf{84}, 036702 (2011)]. A Vlasov simulation scheme of this kind can be recurrence…
We consider Vlasov-type scaling for the Glauber dynamics in continuum with a positive integrable potential, and construct rescaled and limiting evolutions of correlation functions. Convergence to the limiting evolution for the positive…