Related papers: Analysis of Boundary Conditions for Crystal Defect…
We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow for the simulation of a broad class of differential algebraic conditions. Our approach is…
Atomistic simulations have become a powerful tool in materials research due to the extremely fine spatial and temporal resolution provided by such techniques. In order to understand the fundamental principles which govern material behavior…
We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears for instance when…
We present a new variational model for computing the electronic first-order density matrix of a crystalline material in presence of a local defect. A natural way to obtain variational discretizations of this model is to expand the…
We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in…
In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence…
This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in…
Periodic boundary conditions are a common theoretical and computational tool used to emulate effectively infinite domains. However, two-dimensional periodic domains are topologically distinct from the infinite plane, eliciting the question:…
The foundations of irradiation damage theory were laid in the 1950s and 60s within the framework of chemical reaction kinetics. While helpful to analyze qualitative aspects of irradiation damage, the theory contained gaps that delayed its…
This paper presents a consistent approach to prescribe traction boundary conditions in atomistic models. Due to the typical multiple-neighbor interactions, finding an appropriate boundary condition that models a desired traction is a…
Methods for correcting residual energy errors of configuration interaction (CI) calculations of molecules and other electronic systems are discussed based on the assumption that the energy defect can be mapped onto atomic regions. The…
This paper is concerned with the Boundary Element simulation of elastic domains that contain thin inclusions that have elastic material properties, which are different to the domain. With thin inclusions we mean inclusions with extreme…
Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate…
Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface, the network can be rendered…
So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems…
The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…
An efficient method is proposed for numerical solutions of nonlinear Schr\"{o}dinger equations in an unbounded domain. Through approximating the kinetic energy term by a one-way equation and uniting it with the potential energy equation,…
The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability…
The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the…
Constructing a quantum description of crystals from scattering experiments is of paramount importance to explain their macroscopic properties and to evaluate the pertinence of theoretical ab-initio models. While reconstruction methods of…