Plasmons in metals can oscillate on a sub-wavelength length scale and this large-k response constitutes an inherent prerequisite for fascinating effects such as perfect imaging and intriguing wave phenomena associated with the epsilon-near-zero (ENZ) regime. While there is no upper cut-off within the local-response approximation (LRA) of the plasma polarization, nonlocal dynamics suppress respo...

Hardy’s non-locality theorem for multiple two-level systems is explored in the context of generalized nonlocal theory. We find nonlocal but non-signaling probabilities, providing Hardy’s nonlocal argument, which are higher than those in Quantum Mechanics. Maximum probability of success of Hardy’s argument is obtained for three two-level systems in quantum as well as in a more generalized theory...

Classical continuum models exhibit strong mesh dependency during strain softening. For such materials, the phenomenon may be regularized via the gradient-enhanced nonlocal formulation. The paper discusses the implicit gradient framework and demonstrates that standard nonlocal enhancement may serve only as a partial localization limiter. The over-nonlocal approach, where the weight for the nonlo...

A new Reynolds stress anisotropy closure that includes nonlocal and nonequilibrium effects in turbulent flows has been obtained from a recently proposed nonlocal anisotropy formulation. This formulation is based on a new nonlocal derivation of the rapid pressurestrain correlation, which rigorously accounts for nonlocal effects on the anisotropy due to spatial variations in the mean velocity gra...

Image nonlocal self-similarity has been widely adopted as natural image prior in various low-level vision tasks such as image restoration, while the low-rank matrix recovery theory has been drawing much attention to describe and utilize the image nonlocal self-similarities. However, whether the low-rank prior models exist to characterize the nonlocal self-similarity for a wide range of natural ...

We prove Dirichlet’s principle for a nonlocal p-Laplacian system which arises in the nonlocal setting of peridynamics when p = 2. This nonlinear model includes boundary conditions imposed on a nonzero volume collar surrounding the domain. Our analysis uses nonlocal versions of integration by parts techniques that resemble the classical Green and Gauss identities. The nonlocal energy functional ...

The standard one-dimensional diffusion equation is extended to include nonlocal temporal and spatial medium responses. How such nonlocal effects arise in a photopolymer is discussed. It is argued that assuming rapid polymer chain growth, any nonlocal temporal response can be dealt with so that the response can be completely understood in terms of a steady-state nonlocal spatial response. The re...

In this paper we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using thes...

In this paper, we consider the nonlocal FredholmVolterra integral equation of the second kind, with continuous kernels. We consider three different numerical methods,the Trapezoidal rule, Simpson rule and Collocation method to reduce the nonlocal F-VIE to a nonlocal algebraic system of equations. The algebraic system is computed numerically, when the historical memory of the problem (nonlocal f...

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...