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The Lifshitz formula and methods of its preparation in the literature are considered. It is shown that in Lifshitz's work itself, this formula is given without a consistent conclusion. Moreover, the approach to the conclusion proposed in…
A mean-field approach (filtering out subgrid scales) is applied to the Boltzmann equation in order to derive a subgrid turbulence model based on kinetic theory. It is demonstrated that the only Smagorinsky type model which survives in the…
On the basis of the Vlasov chain of equations, a new infinite dispersion chain of equations is obtained for the distribution functions of mixed higher order kinematical values. In contrast to the Vlasov chain, the dispersion chain contains…
We show that minimizers of the Heitmann-Radin energy (R. C. Heitmann, C. Radin, J. Stat. Phys. 22, 281-287, 1980) are unique if and only if the particle number N belongs to an infinite sequence whose first thirty-five elements are 1, 2, 3,…
The paper is mainly concerned with an approximate three-ball inequality for solutions in elliptic periodic homogenization. We consider a family of second order operators $\mathcal{L}_\epsilon$ in divergence form with rapidly oscillating and…
We consider the variational problem with a mass constraint arising from the two-dimensional dispersion managed nonlinear Schr\"odinger equation with power-law type nonlinearity. We prove a threshold phenomenon with respect to mass for the…
The paradigmatic model for heterogeneous media used in diffusion studies is built from reflecting obstacles and surfaces. It is well known that the crowding effect produced by these reflecting surfaces slows the dispersion of Brownian…
Bose-Einstein condensates in a double-well potential contain the essential ingredients to study many-body systems within a rich classical phase-space that includes an unstable point and a separatrix. Employing a selfconsistent finite…
In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…
Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their…
We consider the minor process of (Hermitian) matrix diffusions with constant diagonal drifts. At any given time, this process is determinantal and we provide an explicit expression for its correlation kernel. This is a measure on the…
The Fokker-Planck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…
For a finitely irreducible countable Markov shift and a potential with summable variations, we provide a condition on the associated pressure function which ensures that Bowen's Gibbs state, the equilibrium state, and the minimizer of the…
In \cite{CHMY04}, we studied $p$-mean curvature and the associated $p$-minimal surfaces in the Heisenberg group from the viewpoint of PDE and differential geometry. In this paper, we look into the problem through the variational…
The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the…
We consider the magnetic Lorentz gas proposed by Bobylev et al. [4], which describes a point particle moving in a random distribution of hard-disk obstacles in $\mathbb{R}^2$ under the influence of a constant magnetic field perpendicular to…
Phase coarsening is a fundamental process of microstructure evolution in multiphase materials. A thorough understanding of its kinetics is of great significance for material processing and performance. Generally, coarsening can be divided…
We consider the Lorentz gas in a distribution of scatterers which microscopically converges to a periodic distribution, and prove that the Lorentz gas in the low density limit satisfies a linear Boltzmann equation. This is in contrast with…