Related papers: Slow manifold reduction for plasma science
We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a…
Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective…
Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…
The slow drift along a manifold of periodic orbits is a key mathematical structure underlying bursting dynamics in many scientific applications. While classical averaging theory, as formalised by the Pontryagin-Rodygin theorem, provides a…
We give an exponentially-accurate normal form for a Lagrangian particle moving in a rotating shallow-water system in the semi-geostrophic limit, which describes the motion in the region of an exponentially-accurate slow manifold (a region…
A model of an electron-beam-plasma system is introduced to model the electrical breakdown physics of low-pressure nitrogen irradiated by an intense pulsed electron beam. The rapidly rising beam current induces an electric field which drives…
The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects. Euler-Poincar\'e…
Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which…
This contribution, built on the companion paper [1], is focused on the different mathematical approaches available for the analysis of the quasilinear approximation in plasma physics.
Reduced order models are becoming increasingly important for rendering complex and multiscale spatio-temporal dynamics computationally tractable. The computational efficiency of such surrogate models is especially important for design,…
Surrogate modeling for complex physical systems typically faces a trade-off between data-fitting accuracy and physical consistency. Physics-consistent approaches typically treat physical laws as soft constraints within the loss function, a…
We present the standard electromagnetic Particle-in-Cell method, starting from the discrete approximation of derivatives on a uniform grid. The application to second-order, centered, finite-difference discretization of the equations of…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
A theory is proposed that describes mutual conversion of two electromagnetic modes in cold low-density plasma, specifically, in the high-frequency limit where the ion response is negligible. In contrast to the classic (Landau--Zener-type)…
We analyze possible motion control of microparticles by means of external electromagnetic fields which induce potential wells having fixed spatial distribution but deepening over time up to some limit. It is assumed that given particles are…
A comprehensive theory is proposed to describe the propagation and absorption of ultra-intense, short laser pulse through the under-dense plasma. The kinetic aspects of plasma are fully incorporated using extensive particle-in-cell (PIC)…
This article concerns two methods for reducing large systems of chemical kinetics equations, namely, the method of intrinsic low-dimensional manifolds (ILDMs) due to Maas and Pope and an iterative method due to Fraser and further developed…
We derive conditions under which a general nonlinear mechanical system can be exactly reduced to a lower-dimensional model that involves only the most flexible degrees of freedom. This Slow-Fast Decomposition (SFD) enslaves exponentially…
The scattered field formalism is combined to the particle-in-cell method to model relativistic laser-plasma dynamics in complex field configurations. Despite the strong nonlinearity of the interactions, we demonstrate the validity of this…
In this thesis we study the classical and quantum momentum maps and the theory of reduction. We focus on the notion of momentum map in Poisson geometry and we discuss the classification of the momentum map in this framework. Furthermore, we…