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...

It is known that all causal correlations between two parties which output each 1 bit, a and b, when receiving each 1 bit, x and y, can be expressed as convex combinations of local correlations (i.e., correlations that can be simulated with local random variables) and nonlocal correlations of the form a+b=xy mod 2. We show that a single instance of the latter elementary nonlocal correlation suff...

The Casimir force is calculated between plates with thin metallic coating. Thin films are described with spatially dispersive nonlocal dielectric functions. For thin films the nonlocal effects are more relevant than for half-spaces. However, it is shown that even for film thickness smaller than the mean free path for electrons, the difference between local and nonlocal calculations of the Casim...

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...

The solutions of surface modes in cylindrical metallic wires and cavities are obtained within a nonlocal dielectric formalism. We compare the results with those obtained from standard local approaches. The specular reflection model is applied to describe the nonlocal potentials in the vicinity of the wires and cavities. The external probe exciting the surface plasmons are fast electron beams tr...

Boundary-spanning search has been argued to be important for the success of innovation. There are various kinds of dimensions about organizational search activities. Past studies on boundary-spanning search have focused mainly on technological dimension. We characterize the boundary-spanning search on geographic dimension. We propose a conceptual model and 6 hypotheses. Data from 156 firms were...

We develop and analyze an optimization–based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the ...

Recently, graphene sheets have shown significant potential for environmental engineering applications such as wastewater treatment. In the present work, the posbuckling response of orthotropic single-layered graphene sheet (SLGS) is investigated in a closedform analytical manner using the nonlocal theory of Eringen. Two opposite edges of the plate are subjected to normal stresses. The nonlocali...

In this paper, we study solutions to a nonlocal 1-Laplacian equation given by − ∫ ΩJ J(x− y) uψ(y)− u(x) |uψ(y)− u(x)| dy = 0 for x ∈ Ω, with u(x) = ψ(x) for x ∈ ΩJ \ Ω. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J . We also show that solutions in the...

The nonlocal vacuum condensates or vacuum correlators describe the distribution of quarks and gluons in the non-perturbative QCD vacuum [1]. Physically, it means that vacuum quarks and gluons can flow through the vacuum with nonzero momentum. Nonlocal condensates play an important role in hadron physics. In particular, they are of principle importance in the study of the distribution functions ...