Related papers: Discrete-to-Continuum Limits of Long-Range Electri…
We derive a rigorous theory of the interaction between photons and spatially extended excitons confined in quantum dots in inhomogeneous photonic materials. We show that, beyond the dipole approximation, the radiative decay rate is…
We develop and solve a continuum theory for the piezoelectric response of one dimensional nanotubes and nanowires, and apply the theory to study electromechanical effects in BN nanotubes. We find that the polarization of a nanotube depends…
Plastic deformation of heterogeneous solid structures is often characterized by random intermittent local plastic events. On the mesoscale this feature can be represented by a spatially fluctuating local yield threshold. Here we study the…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
We derive continuum limits of atomistic models in the realm of nonlinear elasticity theory rigorously as the interatomic distances tend to zero. In particular we obtain an integral functional acting on the deformation gradient in the…
We consider a mathematical model that describes the flow of a Nematic Liquid Crystal (NLC) film placed on a flat substrate, across which a spatially-varying electric potential is applied. Due to their polar nature, NLC molecules interact…
Concentrated electric field and its energy in materials, containing nanofibers, are discussed. It is shown that the electric field in the vicinity of the end of a fiber is proportional to the external applied field and to the fiber length,…
The interaction between quantum two-level systems is typically short-range in free space and most photonic environments. Here we show that diminishing momentum isosurfaces with equal frequencies can create a significantly extended range of…
We present a multiscale atomistic-to-continuum method for ionic crystals with defects. Defects often play a central role in ionic and electronic solids, not only to limit reliability, but more importantly to enable the functionalities that…
We model the stabilization of clusters and lattices of cuboidal particles with long-ranged magnetic dipolar and short-ranged surface interactions. Two realistic systems were considered: one with magnetization orientated in the [001]…
We investigate theoretically the formation of collective excitations in atomic scale quasi-one dimensional metallic nanostructures. The response of the system is calculated within the linear response theory and random phase approximation.…
The dynamic response of an interacting electron system is determined by an extension of the relaxation-time approximation forced to obey local conservation laws for number, momentum and energy. A consequence of these imposed constraints is…
The dielectric response of nano-confined fluids is crucial across technologies and biological systems, yet its calculation and interpretation from molecular simulations are often muddled by unclear boundary conditions. We re-derive the…
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…
The wealth of complex polar topologies recently found in nanoscale ferroelectrics result from a delicate balance between the materials intrinsic tendency to develop a homogeneous polarization and the electric and mechanic boundary…
In this work, we study the effect of dipole-dipole interparticle interactions on the static thermodynamic and magnetic properties of an ensemble of immobilized monodisperse superparamagnetic nanoparticles. We assume that magnetic…
In this paper we derive the continuum limit of a multiple-species, interacting particle system by proving a $\Gamma$-convergence result on the interaction energy as the number of particles tends to infinity. As the leading application, we…
Response of a single-walled carbon nanotube to external electric field, F, is calculated analytically within the classical electrostatics. Field-induced charge density distribution is approximately linear along the axis of metallic nanotube…
The electric double layer (EDL) formed around charged nanostructures at the liquid-solid interface determines their electrochemical activity and influences their electrical and optical polarizability. We experimentally demonstrate that…
In the recent trend of extending discrete-to-continuum limit passages for gradient flows of single-species particle systems with singular and nonlocal interactions to particles of opposite sign, any annihilation effect of particles with…