相关论文: Continuum limits of atomistic energies allowing sm…

We have written expressions for the free energy of a cholesteric liquid crystal in an approximation using the elasticity constants K_1, K_2, K_3 and the energy variation and the corresponding energy and energy gradient along the direction…

We derive expressions for determination of the stress and the elastic constants in systems composed of particles interacting via non-central two-body potentials as thermal averages of products of first and second partial derivatives of the…

One-dimensional ideal diatomic gas is simulated through possible types of motion of a molecule. Energy of each type of its motion is calculated from theory and numerical method. Calculation of kinetic energy of an atom in…

We calculate mean square deviations for crystals in one and two dimensions. For the two dimensional lattices, we consider several distinct geometries (i.e. square, triangular, and honeycomb), and we find the same essential phenomena for…

We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also…

The aim of this paper is twofold. First, we set up the theory of elastic matter sources within the framework of general relativity in a self-contained manner. The discussion is primarily based on the presentation of Carter and Quintana but…

This paper is devoted to the characterization of the energy release rate of a crack which is merely closed, connected, and with density $1/2$ at the tip. First, the blow-up limit of the displacement is analyzed, and the convergence to the…

We derive the non-retarded energy shift of a neutral atom for two different geometries. For an atom close to a cylindrical wire we find an integral representation for the energy shift, give asymptotic expressions, and interpolate…

Methods for estimating the correlation energy of molecules and other electronic systems are discussed based on the assumption that the correlation energy can be partitioned between atomic regions. In one method, the electron density is…

This review introduces the elasticity theory of two-dimensional crystals and nematic liquid crystals on curved surfaces, the energetics of topological defects (disclinations, dislocations and pleats) in these ordered phases, and the…

We study the energy spectrum of atoms trapped in a vertical 1D optical lattice in close proximity to a reflective surface. We propose an effective model to describe the interaction between the atoms and the surface at any distance. Our…

We derive geometrically linearized theories for incompressible materials from nonlinear elasticity theory in the small displacement regime. Our nonlinear stored energy densities may vary on the same (small) length scale as the typical…

We initiate the development of a theory of the elasticity of nanoscale objects based upon new physical concepts which remain properly defined on the nanoscale. This theory provides a powerful way of understanding nanoscale elasticity in…

We consider a one dimensional infinite acoustic chain of harmonic oscillators whose dynamics is perturbed by a random exchange of velocities, such that the energy and momentum of the chain are conserved. Consequently, the evolution of the…

We prove long-time existence of solutions for the equations of atomistic elastodynamics on a bounded domain with time-dependent boundary values as well as their convergence to a solution of continuum nonlinear elastodynamics as the…

In this paper we analyze a two-dimensional discrete model of nearest-neighbour Lennard-Jones interactions under the microscopical constraint that points on a lattice triangle maintain their order. This can be understood as a microscopical…

We study free-discontinuity functionals in nonlinear elasticity, where discontinuities correspond to the phenomenon of cavitation. The energy comprises two terms: a volume term accounting for the elastic energy; and a surface term…

We discuss a class of models for particulate gels in which the particle contacts are described by an effective interaction combining a two-body attraction and a three-body angular repulsion. Using molecular dynamics, we show how varying the…

Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…

A novel formulation of the electron energy relaxation terms is presented here, which is applicable to plasma flows and discharges wherein the electron temperature could be higher or lower than the gas temperature. It is demonstrated that…