Related papers: The Singular Behaviour of Ambipolar Diffusion Reve…
This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…
The stability of nonaxisymmetric perturbations in differentially rotating astrophysical accretion disks is analyzed by fully incorporating the properties of shear flows. We verify the presence of discrete unstable eigenmodes with complex…
The formation of stars is governed by the intricate interplay of nonideal magnetohydrodynamic (MHD) effects, gravity, and turbulence. Computational challenges have hindered a comprehensive 3D exploration of this interplay, posing a…
We study a three-dimensional, incompressible, viscous, micropolar fluid with anisotropic microstructure on a periodic domain. Subject to a uniform microtorque, this system admits a unique nontrivial equilibrium. We prove that when the…
We study the large time behavior of solutions to a non-local diffusion equation, $u_t=J*u-u$ with $J$ smooth, radially symmetric and compactly supported, posed in $\mathbb{R}_+$ with zero Dirichlet boundary conditions. In sets of the form…
We study the boundary localization phenomenon, known as whispering gallery modes, for weak solutions to semilinear Dirichlet eigenvalue problems in the unit ball $B_1 \subseteq \mathbb{R}^d$ ($d \geq 2$) of the form \[ \begin{cases} -\Delta…
We present a complete analysis of the problem of convection-diffusion in low Re, 2-dimensional flows with distributions of singularities, such as those found in open-space microfluidics and in groundwater flows. Using Boussinesq…
We consider the nonlinear eigenvalue problem $[D(u(t))u(t)']' + \lambda g(u(t)) = 0$, $u(t) > 0$, $t \in I := (0,1)$, $u(0) = u(1) = 0$, which comes from the porous media type equation. Here, $D(u) = pu^{2n} + \sin u$ ($n \in \mathbb{N}$,…
The second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane, limiting half-space, makes harmonious oscillations in the plane. The kinetic equation with modelling integral of collisions in the form…
This paper investigates boundary hemivariational inequality problems associated with both stationary and non-stationary two and three-dimensional convective Brinkman-Forchheimer equations (or Navier-stokes equations with damping), which…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
This paper presents a global stability result on perturbations near a background magnetic field to the 2D incompressible magnetohydrodynamic (MHD) equations with only magnetic diffusion on the periodic domain. The stability result provides…
We investigate the general stability of 1D spherically symmetric ionized Bondi accretion onto a massive object in the specific context of accretion onto a young stellar object. We first derive a new analytic expression for a steady state…
This paper is concerned with a time periodic competition-diffusion system \begin{equation*} \begin{cases} {u_t}={u_{xx}}+u(r_1(t)-a_1(t)u-b_1(t)v),\quad t>0,~x\in \mathbb R, {v_t}=d{v_{xx}}+v(r_2(t)-a_2(t)u-b_2(t)v),\quad t>0,~x\in \mathbb…
Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for…
We study dynamics of a probe particle, which performs biased diffusive motion in a one-dimensional adsorbed monolayer of mobile hard-core particles undergoing continuous exchanges with a vapor phase. In terms of a mean-field-type approach,…
The present work investigates the asymptotic behaviors, at the zero-noise limit, of the first collision-time and first collision-location related to a pair of self-stabilizing diffusions and of their related particle approximations. These…
Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due…
We introduce quantum circuits in two and three spatial dimensions which are classically simulable, despite producing a high degree of operator entanglement. We provide a partial characterization of these "automaton" quantum circuits, and…
Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs).…