## Search

Now showing items 1-9 of 9

#### A convergent method for linear half-space kinetic equations

(2017-04-23)

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 ...

#### Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model

(2017-04-23)

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 ...

#### Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime

(2017-04-23)

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 ...

#### Learning interacting particle systems: diffusion parameter estimation for aggregation equations

(2018-02-14)

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 ...

#### Bloch dynamics with second order Berry phase correction

(2017-04-23)

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 ...

#### A Variation on the Donsker-Varadhan Inequality for the Principial Eigenvalue

(2017-04-23)

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 ...

#### An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus

(2017-04-23)

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 ...

#### Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation

(2017-04-23)

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 ...

#### Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature

(2017-04-23)

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. ...