Related papers: Slow manifold reduction for plasma science

We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

These notes are devoted to the problem of finite-dimensional reduction for parabolic PDEs. We give a detailed exposition of the classical theory of inertial manifolds as well as various attempts to generalize it based on the so-called…

Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…

Actions of Lie groups on presymplectic manifolds are analyzed, introducing the suitable comomentum and momentum maps. The subsequent theory of reduction of presymplectic dynamical systems with symmetry is studied. In this way, we give a…

The aim of this work is to introduce a numerical method to cope with the multiscale nature of confined plasma physics. These investigations are focused on fluid plasma description under large magnetic field. The difficulties in this context…

The similarity theory is derived for ultra-relativistic laser-plasma interactions. First, it is shown that the most fundamental S-similarity is valid for both under- and overdense plasmas. Then, the particular case of tenious plasma is…

The aim of this paper is to generalize the classical Marsden-Weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which in- herit the polysymplectic structure. This…

This is the first of a series of papers devoted to the development of the invariant imbedding theory of mode conversion in inhomogeneous plasmas. A new version of the invariant imbedding theory of wave propagation in inhomogeneous media…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

We construct smooth, non-symmetric plasma equilibria which possess closed, nested flux surfaces and solve the magnetohydrostatic (steady three-dimensional incompressible Euler) equations with a small force. The solutions are also `nearly'…

Ultracold quasineutral plasmas generated in the laboratory are generically inhomogeneous and ex- hibit small charge imbalances. As will be demonstrated, via a hydrodynamic theory as well as microscopic simulations, the latter lead to…

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…

The classical method for deriving the macroscopic dynamics of a lattice Boltzmann system is to use a combination of different approximations and expansions. Usually a Chapman-Enskog analysis is performed, either on the continuous Boltzmann…

The numerical simulation of realistic reactive flows is a major challenge due to the stiffness and high dimension of the corresponding kinetic differential equations. Manifold-based model reduction techniques address this problem by…

An important physical model describing the dynamics of dilute weakly ionized plasmas in the collisional kinetic theory is the Vlasov-Poisson-Boltzmann system for which the plasma responds strongly to the self-consistent electrostatic force.…

The relaxation of temperatures and velocities of the components of a quasi-equilibrium two-component homogeneous completely ionized plasma is investigated on the basis of a generalization of the Chapman-Enskog method applied to the Landau…

A general approach to provide approximate parameterizations of the "small" scales by the "large" ones, is developed for stochastic partial differential equations driven by linear multiplicative noise. This is accomplished via the concept of…

Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated…

This work is concerned with the dynamics of a slow-fast stochastic evolutionary system quantified with a scale parameter. An invariant foliation decomposes the state space into geometric regions of different dynamical regimes, and thus…