Related papers: Stochastic Galerkin Methods for the Boltzmann-Pois…
We present an algorithm for solving the one-dimensional space collisional Boltzmann transport equation (BTE) for electrons in low-temperature plasmas (LTPs). Modeling LTPs is useful in many applications, including advanced manufacturing,…
To understand quantum optics experiments, we must perform calculations that consider the principal sources of noise, such as losses, spectral impurity and partial distinguishability. In both discrete and continuous variable systems, these…
A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic…
We have developed a multi-scale self-consistent method to study the charge conductivity of a porous system or a metallic matrix alloyed by randomly distributed nonmetallic grains and vacancies by incorporating Schr\"{o}dinger's equation and…
We describe preliminary results from an effort to quantify the uncertainties in parton distribution functions and the resulting uncertainties in predicted physical quantities. The production cross section of the $W$ boson is given as a…
This paper is devoted to the construction of structure preserving stochastic Galerkin schemes for Fokker-Planck type equations with uncertainties and interacting with an external distribution, that we refer to as a background distribution.…
When impurity and phonon scattering coexist, the Boltzmann equation has been solved accurately for nonlinear electron transport in a quantum wire. Based on the calculated non-equilibrium distribution of electrons in momentum space, the…
For a number of applications like low-source reactor start-up or neutron coincidence counting it is necessary to take into account the stochastic nature of neutron transport and go beyond the average neutron density, which is solution of a…
The interplay between electronic interactions and disorder is neglected in the conventional Boltzmann theory of transport, yet can play an essential role in determining the resistivity of unconventional metals. When quasiparticles are…
Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…
A nonlinear Poisson--Boltzmann equation with transmission boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic…
In this article, we study quantum randomness of stochastic cosmological particle production scenario using quantum corrected higher order Fokker Planck equation. Using the one to one correspondence between particle production in presence of…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
Collective orders and photo-induced phase transitions in quantum matter can evolve on timescales which are orders of magnitude slower than the femtosecond processes related to electronic motion in the solid. Quantum Boltzmann equations can…
We study the influence of inelastic electron-electron scattering on the temperature variation of the Seebeck coefficient in the normal phase of quasi-one-dimensional organic superconductors. The theory is based on the numerical solution of…
As is well known, the fluctuations from a stable stationary nonequilibrium state are described by a linearized nonhomogeneous Boltzmann-Langevin equation. The stationary state itself may be described by a nonlinear Boltzmann equation. The…
We present a numerical algorithm to solve the Boltzmann equation for the electron distribution function in magnetic multilayer heterostructures with non-collinear magnetizations. The solution is based on a scattering matrix formalism for…
We study the nonequilibrium dynamics of photoinduced phase transitions in charge ordered (CO) systems with a strong electron-lattice interaction and analyze the interplay between electrons, periodic lattice distortions, and a phonon thermal…
The space- and temperature-dependent electron distribution $n(r,T)$ determines optoelectronic properties of disordered semiconductors. It is a challenging task to get access to $n(r,T)$ in random potentials, avoiding the time-consuming…