We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main ...

In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface ...

We study in this work a continuum model derived from 1D attachment-detachment-limited (ADL) type step flow on vicinal surface, $ u_t=-u^2(u^3)_{hhhh}$, where $u$, considered as a function of step height $h$, is the step ...

In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation. Specifically, we construct an estimator $\widehat{\nu}$ with partial observed data to approximate the ...

We derive the semiclassical Bloch dynamics with the second order Berry phase correction, based on a two-scale WKB asymptotic analysis. For uniform external electric field, the bi-characteristics system after a positional ...

The purpose of this short note is to give a variation on the classical Donsker-Varadhan inequality, which bounds the first eigenvalue of a second-order elliptic operator on a bounded domain $\Omega$ by the largest mean first ...

We study an isoperimetric problem the energy of which contains the perimeter of a set, Coulomb repulsion of the set with itself, and attraction of the set to a background nucleus as a point charge with charge $Z$. For the ...

We study a phase-field variational model for the solvaiton of charged molecules with an implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and ...

We consider a model of an electron in a crystal moving under the influence of an external electric field: Schr\"{o}dinger's equation with a potential which is the sum of a periodic function and a general smooth function. ...