Wepresent first-principles simulations of single grain boundary reflectivity of electrons in noble metals, Cu and Ag. We examine twin and non-twin grain boundaries using nonequilibrium Green’s function and first principles methods. We also investigate the determinants of reflectivity in grain boundaries by modeling atomic vacancies, disorder, and orientation and find that both the change in gra...

In this article, we introduce and study local constant and our preferred local linear nonparametric regression estimators when it is appropriate to assess performance in terms of mean squared relative error of prediction. We give asymptotic results for both boundary and non-boundary cases. These are special cases of more general asymptotic results that we provide concerning the estimation of th...

We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on a finite interval (0, 2π). The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the origin is not asymptotically stable for the linearized system around the origin. We prove th...

In this paper we study boundary element methods for initialNeumann problems for the heat equation. Error estimates for some fully discrete methods are established. Numerical examples are presented.

The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt +∆u+∆θ = 0 and θt −∆θ −∆ut = 0 in Ω× (0,∞), subject to Dirichlet boundary condition: u|Γ = Dνu|Γ = θ|Γ = 0 and initial condition: (u, ut, θ)|t=0 = (u0, v0, θ0) ∈W 2 p,D(Ω)×Lp×Lp. Here, Ω is a bounded or exterior domain in R (n ≥ 2). We assume that the boundary Γ of Ω is a C hypersurface and we define W 2 p,D by ...

In this paper we study boundary element methods for initialNeumann problems for the heat equation. Error estimates for some fully discrete methods are established. Numerical examples are presented.

A finite drop of fluid with large viscosity μ and density ρ is initially at rest hanging under gravity g from the underside of a solid boundary. The initial configuration may be of a general boundary shape, with (vertical) maximum length L(0) = L0 and (horizontal) maximum width w0. The subsequent motion, drop length L(t) as a function of time t , and boundary shape is determined both by a slend...

A Lattice Boltzmann method is applied to demonstrate the comparison results of simulating natural convection in an open end cavity using different hydrodynamic and thermal boundary conditions. The Prandtl number in the present simulation is 0.71, Rayleigh numbers are 104,105 and 106 and viscosities are selected 0.02 and 0.05. On-Grid bounce-back method with first-order accuracy and non-slip met...