相关论文: Discrete-to-Continuum Limits of Long-Range Electri…

The discrete and charge-separated nature of matter - electrons and nuclei - results in local electrostatic fields that are ubiquitous in nanoscale structures and are determined by their shape, material, and environment. Such fields are…

We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…

We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice and we give…

Epitaxially grown heterogeneous nanowires present dislocations at the interface between the phases if their radius is big. We consider a corresponding variational discrete model with quadratic pairwise atomic interaction energy. By…

Studies on nanoscale materials merit careful development of an electrostatics model concerning discrete point charges within dielectrics. The discrete charge dielectric model treats three unique interaction types derived from an external…

Two-dimensional (2D) electronic materials are of significant technological interest due to their exceptional properties and broad applicability in engineering. The transition from nanoscale physics, that dictates their stable…

The theory of elastic interaction of micron size axially symmetric colloidal particles immersed into confined nematic liquid crystal has been proposed. General formulas are obtained for the self energy of one colloidal particle and…

In this paper we present two atomistic models for the energy of a one-dimensional elastic crystal. We assume that the macroscopic displacement equals the microscopic one. The energy of the first model is given by a two-body interaction…

A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…

We study the effects of long-range electrostatic interactions on the thermal fluctuations of free-standing crystalline membranes exhibiting spontaneous electric polarization directed at each point along the local normal to the surface. We…

Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the…

Point polarizable molecules at fixed spatial positions have solvable electrostatic properties in classical approximation, the most familiar being the Clausius-Mossotti (CM) formula. This paper generalizes the model and imagines various…

We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases…

The equilibrium binding energy is an important factor in the design of materials and devices. However, it presents great computational challenges for materials built up from nanostructures. Here we investigate the binding-energy scaling law…

Nano- and microscale particles, such as colloids, commonly interact over ranges much shorter than their diameters, so it is natural to treat them as "sticky," interacting only when they touch exactly. The lowest-energy states, free…

We report measurements of the spatial dependence of the electron energy distribution in carbon nanotubes, from which electron interactions are determined. Using nonequilibrium tunneling spectroscopy with multiple superconducting probes, we…

In the first part of this paper, we apply a well known discrete-to-continuum approach to a Frenkel-Kontorova-type model of an infinitely long one-dimensional chain of atoms weakly interacting with a line of fixed atoms. The rescaled model…

The boundary problem of linear classical optics about the interaction of electromagnetic radiation with a thin dielectric film has been solved under explicit consideration of its discrete structure. The main attention has been paid to the…

We analyze a generalization of the hard sphere dipole system in two dimensions in which the interaction range of the interaction can be varied. We focus on the system in the limit the interaction becomes increasingly short-ranged, while the…

The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on…