In this paper, we show that the anisotropic nonlocal total variation involved in the image regularization model of Gilboa and Osher [15] as well as in the perceptual color correction model of Bertalmı́o et al. [4] possesses a dual formulation. We then obtain novel formulations of their solutions, which provide new insights on these models. In particular, we show that the model of Bertalmı́o et al...

We study the effect of nonlocal optical response on the optical properties of metallic nanowires, by numerically implementing the hydrodynamical Drude model for arbitrary nanowire geometries. We first demonstrate the accuracy of our frequency-domain finite-element implementation by benchmarking it in a wide frequency range against analytical results for the extinction cross section of a cylindr...

This paper is concerned with the surface and small scale effects on transverse vibration of a viscoelastic single-layered graphene sheet (SLGS) subjected to an in-plane magnetic field. The SLGS is surrounded by an elastic medium which is simulated as Visco-Pasternak foundation. In order to investigate the small scale effects, the nonlocal elasticity theory is employed due to its simplicity and ...

Abstract. In this paper we present the first results on substructuring methods for nonlocal operators, specifically, an instance of the nonlocal p-Laplace operator. We present a nonlocal variational formulation of this operator, proving a nonlocal Poincaré inequality and upper bound to establish a spectral equivalence. We then introduce a nonlocal two-domain variational formulation utilizing no...

We study the bound states of two-dimensional bright solitons in nonlocal nonlin-ear media. The general properties and stability of these multisolitary structures are investigated analytically and numerically. We have found that a steady bound state of coherent nonrotating and rotating solitary structures (azimuthons) can exist above some threshold power. A dipolar nonrotating multisoliton occur...