相关论文: Mountain pass type solutions for a generalized Fre…
We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised Ornstein-Uhlenbeck systems…
The periodic Anderson model is a classic theoretical model for understanding novel physics in heavy fermion systems. Here, we modify it with the Sachdev-Ye-Kitaev interaction, (random all-to-all interaction) thus the resultant model admits…
This article is proposed to investigate the impacts of heat and mass transfer in magnetohydrodynamic casson fluid embedded in porous medium. The generalized solutions have been traced out for the temperature distribution, mass concentration…
Recently a local mean field theory for both eqilibrium and transport properties of the Coulomb glass was proposed [A. Amir et al., Phys. Rev. B 77, 165207 (2008); 80, 245214 (2009)]. We compare the predictions of this theory to the results…
We study the existence of normalized solutions to the following Choquard equation with $F$ being a Berestycki-Lions type function \begin{equation*} \begin{cases} -\Delta u+\lambda u=(I_{\alpha}\ast F(u))f(u),\quad \text{in}\ \mathbb{R}^N,…
We study the supercooled Stefan problem in arbitrary dimensions. First, we study general solutions and their irregularities, showing generic fractal freezing and nucleation, based on a novel Markovian gluing principle. In contrast, we then…
In this article, we propose a MUSCL-Hancock-type second-order scheme for the discretization of a general class of non-local conservation laws and present its convergence analysis. The main difficulty in designing a MUSCL-Hancock-type scheme…
We establish the existence of an entire solution for a class of stationary Schr\"{o}dinger equations with subcritical discontinuous nonlinearity and lower bounded potential that blows-up at infinity. The abstract framework is related to…
In this work, Holder continuity is obtained for solutions to the nonlocal kinetic Fokker-Planck Equation, and to a family of related equations with general integro-differential operators. These equations can be seen as a generalization of…
The state of a single-species monatomic gas from near-equilibrium to highly nonequilibrium conditions is investigated using analytical and numerical methods. Normal solutions of the Boltzmann equation for Fourier flow (uniform heat flux)…
The Kondo-Spin Glass competition is studied in a theoretical model of a Kondo lattice with an intra-site Kondo type exchange interaction treated within the mean field approximation, an inter-site quantum Ising exchange interaction with…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
We informally review a few PDEs for which the Monge-Kantorovich distance between pairs of solutions, possibly with some judicious cost function, decays: heat equation, Fokker-Planck equation, heat equation with varying coefficients,…
In this work we prove the existence of time-periodic solutions to a model describing a ferrofluid flow heated from below. Navier-Stokes equations satisfied by the fluid velocity are coupled to the temperature equation and the magnetostatic…
The first-passage problem of the Ornstein-Uhlenbeck process to a boundary is a long-standing problem with no known closed-form solution except in specific cases. Taking this as a starting-point, and extending to a general mean-reverting…
With an auxiliary weak external magnetic field, we reexamine the fundamental thermodynamic function, Gibbs free energy F(T, h), to study the phase transitions in the classical spin lattice models. A cross derivative, i.e. the second-order…
In this work, we develop a phase-field-based lattice Boltzmann (LB) method for a two-scalar model of the two-phase flows with interfacial mass/heat transfer. Through the Chapman-Enskog analysis, we show that the present LB method can…
Motivated by recent Hall-effect experiment in YbRh$_2$Si$_2$, we study ground state properties of a Kondo lattice model in a two-dimensional square lattice using variational Monte Carlo method. We show that there are two types of phase…
We shall prove new contraction properties of general transportation costs along nonnegative measure-valued solutions to Fokker-Planck equations in $R^d$, when the drift is a monotone (or $\lambda$-monotone) operator. A new duality approach…
A computer simulation of thermofluctuation nucleation of kinks on dislocations and their dynamics is carried out in the framework of two-dimensional (2D) Frenkel-Kontorova model. It is shown that at relatively low temperatures and applied…