Related papers: Saturation and linear transport equation
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…
We discuss recent findings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties. It is shown that the time dependent density matrix renormalization method can be used successfully to find…
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…
In this study, we consider the simulation of subsurface flow and solute transport processes in the stationary limit. In the convection-dominant case, the numerical solution of the transport problem may exhibit non-physical diffusion and…
In recent years, the study of biological transportation networks has attracted significant interest, focusing on their self-regulating, demand-driven nature. This paper examines a mathematical model for these networks, featuring nonlinear…
Newell-Whitham type car-following model with hyperbolic tangent optimal velocity function in a one-lane circuit has a finite set of the exact solutions for steady traveling wave, which expressed by elliptic theta function. Each solution of…
Recent work has revealed a general procedure for incorporating disorder into the semiclassical model of carrier transport, whereby the predictions of quantum linear response theory can be recovered within a quantum kinetic approach based on…
We prove an existence and uniqueness theorem for exact WKB solutions of general singularly perturbed linear second-order ODEs in the complex domain. These include the one-dimensional time-independent complex Schr\"odinger equation. Notably,…
A quasi-distribution function in phase space (based on Wigner functions) is used to write down the quantum version of Boltzmann equation (Wigner-Boltzmann transport equation). The relaxation time approximation is show to be a good approach…
We introduce a gradient flow formulation of linear Boltzmann equations. Under a diffusive scaling we derive a diffusion equation by using the machinery of gradient flows.
This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific computing. The PD-WG method is based on a variational…
The paper is devoted to a new approach of the homogenization of linear transport equations induced by a uniformly bounded sequence of vector fields $b_\epsilon(x)$, the solutions of which $u_\epsilon(t,x)$ agree at $t=0$ with a bounded…
In this work, a multirate in time approach resolving the different time scales of a convection-dominated transport and coupled fluid flow is developed and studied in view of goal-oriented error control by means of the Dual Weighted Residual…
The asymptotic analysis of a linear high-field Wigner-BGK equation is developped by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number $\epsilon$, evolution equations are…
A recently proposed nonlinear transport equation is used to model bulk viscous cosmologies that may be far from equilibrium, as happens during viscous fluid inflation or during reheating. The asymptotic stability of the de Sitter and…
Electrons are the carriers of heat and electricity in materials, and exhibit abundant transport phenomena such as ballistic, diffusive, and hydrodynamic behaviors in systems with different sizes. The electron Boltzmann transport equation…
Recently a Dynamic-Monge-Kantorovich formulation of the PDE-based $L^1$-optimal transport problem was presented. The model considers a diffusion equation enforcing the balance of the transported masses with a time-varying conductivity that…
In this manuscript, we study a nonlinear model of tumor growth, described by a coupled hyperbolic-elliptic system of partial differential equations. In this model, the compressible flow of tumor cells is modeled by a transport equation for…
The distributed computing analysis of the accuracy of automodel solutions for the Green's function of a wide class of superdiffusive transport of perturbation on a uniform background is carried out. The approximate automodel solutions have…
We consider the neural sparse representation to solve Boltzmann equation with BGK and quadratic collision model, where a network-based ansatz that can approximate the distribution function with extremely high efficiency is proposed.…