Related papers: Stochastic Galerkin Methods for the Boltzmann-Pois…
Under low-collisionality conditions the isotropic part of the electron velocity distribution function in a plasma becomes non-local and the electrons can be described by a single global distribution function . This is also the regime…
In this paper, we study the Boltzmann equation with uncertainties and prove that the spectral convergence of the semi-discretized numerical system holds in a combined velocity and random space, where the Fourier-spectral method is applied…
Reversible electropermeabilization, commonly referred to as electroporation, is a transient increase in cell membrane permeability induced by short, high-voltage electric pulses. We present a stochastically perturbed version of a…
In this paper we present a model based on dynamics of the electrons in the plasma using a simplified Boltzmann equation coupled with a Poisson equation. The motivation arose to simulate active plasma resonance spectroscopy which is used for…
We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the…
The Boltzmann equation, an integro-differential equation for the molecular distribution function in the physical and velocity phase space, governs the fluid flow behavior at a wide range of physical conditions, including compressible,…
In this work, a lattice Boltzmann scheme is developed for numerical solution of the phonon Boltzmann equation under Callaway's dual relaxation model in the hydrodynamic limit. Through a Chapman-Enskog expansion to the lattice Boltzmann…
Uncertainty Quantification through stochastic spectral methods is rising in popularity. We derive a modification of the classical stochastic Galerkin method, that ensures the hyperbolicity of the underlying hyperbolic system of partial…
The objective of electrical impedance tomography is to deduce information about the conductivity inside a physical body from electrode measurements of current and voltage at the object boundary. In this work, the unknown conductivity is…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve…
A semiclassical theory is developed for time-dependent current fluctuations in mesoscopic conductors. The theory is based on the Boltzmann-Langevin equation for a degenerate electron gas. The low-frequency shot-noise power is related to…
We solve a Schrodinger equation for inelastic quantum transport that retains full quantum coherence, in contrast to previous rate or Boltzmann equation approaches. The model Hamiltonian is the zero temperature 1d Holstein model for an…
Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This…
The prediction of thermo-mechanical behaviour of heterogeneous materials such as heat and moisture transport is strongly influenced by the uncertainty in parameters. Such materials occur e.g. in historic buildings, and the durability…
Intrusive Uncertainty Quantification methods such as stochastic Galerkin are gaining popularity, whereas the classical stochastic Galerkin approach is not ensured to preserve hyperbolicity of the underlying hyperbolic system. We apply a…
Electric, thermal and thermoelectric transport in correlated electron systems probe different aspects of the many-body dynamics, and thus provide complementary information. These are well studied in the low- and high-temperature limits,…
Numerical approximation of the Boltzmann equation presents a challenging problem due to its high-dimensional, nonlinear, and nonlocal collision operator. Among the deterministic methods, the Fourier-Galerkin spectral method stands out for…
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…
In this paper the Boltzmann equation describing the carrier transport in a semiconductor is considered. A modified Chapman-Enskog method is used, in order to find approximate solutions in the weakly non-homogeneous case. These solutions…