We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cos-mological acceleration problems. This construction is based on the special non-local form of the Einstein-Hilbert action explicitly revealing the fact that this action within the covariant curvature expansion begins with curvature-squared...

We study localized light bullets and X waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multidimensional nonlinear waves. For X waves we show that a local cascading limit in terms of a nonlinear Schrödinger equation does not exist-one needs to use the nonlocal description, because the nonlocal response function d...

We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cos-mological acceleration problems. This construction is based on the special non-local form of the Einstein-Hilbert action explicitly revealing the fact that this action within the covariant curvature expansion begins with curvature-squared...

In this paper, a size-dependent first-order shear deformation plate model is formulated in the framework of the higher-order generalized nonlocal strain-gradient (GNSG) theory. This modelemploys ...

A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a “small deformation” setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived. In the finite deformation setting, it is shown th...

This paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. The graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. Nonlocal governing equations of motion for this double-layer graphene s...

We exploit a recently developed nonlocal vector calculus to provide a variational analysis for a general class of nonlocal diffusion problems given by a linear integral equation on bounded domains in R. The ubiquity of the nonlocal operator is illustrated by a number of applications ranging from continuum mechanics to graph theory. These applications elucidate different interpretations of the o...

Density functionals for nuclei usually include an effective 3-body interaction that depends on a fractional power of the density. Using insights from the many-body theory of the low-density two-component Fermi gas, we consider a new, nonlocal, form for the energy functional that is consistent with the Fock-space representation of interaction operators. In particular, there is a unique spatially...

In the quantized two-dimensional non-linear supersymmetric σ-model, the supercurrent supermultiplet, which contains the energy-momentum tensor, is transformed by the nonlocal symmetry of the model into the isospin current supermultiplet. This effect incorporates supersymmetry into the known infinite-dimensional Yangian deformation symmetry of plain σ-models, leads to precisely the same nontrivi...

The aim of the paper is to provide conditions ensuring the existence of non-trivial non-negative periodic solutions to a system of doubly degenerate parabolic equations containing delayed nonlocal terms and satisfying Dirichlet boundary conditions. The employed approach is based on the theory of the Leray-Schauder topological degree theory, thus a crucial purpose of the paper is to obtain a pri...