Related papers: A splitting scheme for the quantum Liouville-BGK e…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
This study investigates a class of initial-boundary value problems pertaining to the time-fractional mixed sub-diffusion and diffusion-wave equation (SDDWE). To facilitate the development of a numerical method and analysis, the original…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
While it is known that alloy components can segregate to grain boundaries (GBs), and that the atomic mobility in GBs greatly exceeds the atomic mobility in the lattice, little is known about the effect of GB segregation on GB diffusion.…
We present a method for constructing numerical schemes with up to 3rd strong convergence order for solution of a class of stochastic differential equations, including equations of the Langevin type. The construction proceeds in two stages.…
We propose a short-memory operator splitting scheme for solving the constant-Q wave equation, where the fractional stress-strain relation contains multiple Caputo fractional derivatives with order much smaller than 1. The key is to exploit…
A Wigner-Poisson kinetic equation describing charge transport in doped semiconductor superlattices is proposed. Electrons are supposed to occupy the lowest miniband, exchange of lateral momentum is ignored and the electron-electron…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
An explicit finite-difference scheme is presented for solving the two-dimensional Biot equations of poroelasticity across the full range of frequencies. The key difficulty is to discretize the Johnson-Koplik-Dashen (JKD) model which…
In this work, we propose a class of high order semi-Lagrangian scheme for a general consistent BGK model for inert gas mixtures. The proposed scheme not only fulfills indifferentiability principle, but also asymptotic preserving property,…
We present and analyze two mathematical models for the self consistent quantum transport of electrons in a graphene layer. We treat two situations. First, when the particles can move in all the plane $\RR^2$, the model takes the form of a…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
Power grid partitioning is an important requirement for resilient distribution grids. Since electricity production is progressively shifted to the distribution side, dynamic identification of self-reliant grid subsets becomes crucial for…
We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…
In this paper, a unified gas-kinetic wave-particle scheme (UGKWP) for the disperse dilute gas-particle multiphase flow is proposed. The gas phase is always in the hydrodynamic regime. However, the particle phase covers different flow…
In collisionless and weakly collisional plasmas, the particle distribution function is a rich tapestry of the underlying physics. However, actually leveraging the particle distribution function to understand the dynamics of a weakly…
Digital quantum computers have the potential to study the dynamics of complex quantum systems. Nonequilibrium open quantum systems are, however, less straightforward to be implemented. Here we consider a collisional model representation of…
We present an efficient numerical approach for treating ballistic quantum transport across devices described by tight binding (TB) Hamiltonians designated to systems with localized potential defects. The method is based on the wave function…
We consider a generic and explicit tamed Euler--Maruyama scheme for multidimensional time-inhomogeneous stochastic differential equations with multiplicative Brownian noise. The diffusive coefficient is uniformly elliptic, H\"older…
In classical kinetic theory, the BBGKY hierarchy is an infinite chain of integro-differential equations that describes the full time-reversal-invariant (Liouville) system of interacting (quasi)-particles in terms of $N$-particle…