Related papers: Simplified P$_N$ Equations for Nonclassical Transp…
We study a quantum and classical correspondence related to the Strichartz estimates. First we consider the orthonormal Strichartz estimates on manifolds with ends. Under the nontrapping condition we prove the global-in-time estimates on…
This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…
The transport of energetic particles in a spatially varying magnetic field is described by the focused transport equation. In the past two versions of this equation were investigated. The more commonly used standard form described a…
The stochastic differential and integral equations describing the system of particles weakly interacting among themselves which are absorbed and scattered by particles of a medium are considered. The time-dependent transport equation with…
We study the nonlocal Stefan problem, where the phase transition is described by a nonlocal diffusion as well as the change of enthalpy functions. By using a stochastic optimization approach introduced for the local case, we construct…
We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as $t\to -\infty$ to asymptotic dynamics as $t\to +\infty$. The main novelty is the construction of modified…
We summarize semiclassical modeling methods, including drift-diffusion, kinetic transport equation and Monte Carlo simulation approaches, utilized in studies of spin dynamics and transport in semiconductor structures. As a review of the…
We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…
A recent proposal (see quant-ph/9803068) to simulate semiclassical corrections to classical dynamics by suitable classical stochastic fluctuations is applied to the specific instance of charged beam dynamics in particle accelerators. The…
Physically motivated expressions for the transport cross sections describing classical scattering in the Lennard-Jones potential are proposed. These expressions, which agree with the numerical results better than to within $\pm 1%$, can be…
We derive radiative transport equations for solutions of a Schr\"odinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the…
Astrophysical observations originate from matter that interacts with radiation or transported particles. We develop a pragmatic approximation in order to enable multi-dimensional simulations with basic spectral radiative transfer when the…
We present a scattering-state description for the non-equilibrium multichannel charge transport in the presence of electron-vibration couplings. It is based on an expansion of scattering orders of eigenchannel states. Examining charge…
This paper develops a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the spectral decomposition of an unperturbed interface Hamiltonian, we present a…
Here we show how an anisotropic fluid in the diffusion limit can be equivalent to an isotropic fluid in the streaming out limit, in spherical symmetry. For a particular equation of state this equivalence is total, from one fluid we can…
Abstract interpretation techniques can be made more precise by distinguishing paths inside loops, at the expense of possibly exponential complexity. SMT-solving techniques and sparse representations of paths and sets of paths avoid this…
We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This,…
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on…