Related papers: Boundary value for a nonlinear transport equation …
In the paper, we study the plane Couette flow of a rarefied gas between two parallel infinite plates at $y=\pm L$ moving relative to each other with opposite velocities $(\pm \alpha L,0,0)$ along the $x$-direction. Assuming that the…
The object of this paper is twofold. Firstly, we study a class of generalized Newtonian fluid related to "power law ". For the corresponding non-Newtonian Navier-Stokes problems, the existence of a weak and periodic solutions is proved in…
Driven Langevin processes have appeared in a variety of fields due to the relevance of natural phenomena having both deterministic and stochastic effects. The stochastic currents and fluxes in these systems provide a convenient set of…
We derive an exact solution of an explicitly time-dependent multichannel model of quantum mechanical nonadiabatic transitions. Our model corresponds to the case of a single linear diabatic energy level interacting with a band of an…
This paper studies the nonlinear stochastic partial differential equation of fractional orders both in space and time variables: \[ \left(\partial^\beta+\frac{\nu}{2}(-\Delta)^{\alpha/2}\right)u(t,x) =…
The critical behaviour of $d$-dimensional semi-infinite systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of…
Topological defects resulted from boundary constraints in confined liquid crystals have attracted extensive research interests. In this paper, we use numerical simulation to study the phase transition dynamics in the context of stochastic…
A nonlinear Landau-Zener model was proposed recently to describe, among a number of applications, the nonadiabatic transition of a Bose-Einstein condensate between Bloch bands. Numerical analysis revealed a striking phenomenon that…
The transport property of cold and dense nucleon matter is important for nuclear physics but is relatively less studied than that at finite temperatures. In this paper, we present a primary study of bulk and shear viscosities in the limit…
We comment on the recent work by Yamaguchi and Barr\'e [Phys. Rev. E 107, 054203 (2023)], which uses linear stability analysis of the Vlasov equation to characterize phase transitions in a generalized Hamiltonian Mean Field (gHMF) model. By…
We formalize the derivation of a generalized coarse-graining $n$-resolved master equation by introducing a virtual detector counting the number of transferred charges in single-electron transport. Our approach enables the convenient…
The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited…
Consider the steady neutron transport equation in 2D convex domains with in-flow boundary condition. In this paper, we establish the diffusive limit while the boundary layers are present. Our contribution relies on a delicate decomposition…
In this paper, we prove the existence and uniqueness of solutions of the fractional p-Laplace equation with a polynomial drift of arbitrary order driven by superlinear transport noise. By the monotone argument, we first prove the existence…
We study the compressible Navier-Stokes system driven by physically relevant transport noise, where the noise influences both the continuity and momentum equations. Our approach is based on transforming the system into a partial…
In this review we deal with open (dissipative and stochastic) quantum systems within the Bohmian mechanics framework which has the advantage to provide a clear picture of quantum phenomena in terms of trajectories, originally in…
We consider a branched transport type problem which describes the magnetic flux through type-I superconductors in a regime of very weak applied fields. At the boundary of the sample, deviation of the magnetization from being uniform is…
The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…
We study a stochastic version of the classical Becker-D\"oring model, a well-known kinetic model for cluster formation that predicts the existence of a long-lived metastable state before a thermodynamically unfavorable nucleation occurs,…
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the…