We study the formation of azimuthons, i.e., rotating spatial solitons, in media with nonlocal focusing nonlinearity. We show that whole families of these solutions can be found by considering internal modes of classical non-rotating stationary solutions, namely vortex solitons. This offers an exhaustive method to identify azimuthons in a given nonlocal medium. We demonstrate formation of azimut...

This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach space X. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness and the fixed point theorem for condensing maps. As an application, the existence of the mild solution to a nonlocal Cauchy problem for a conc...

We show that under minor technical assumptions any weakly nonlocal Hamiltonian structures compatible with a given nondegenerate weakly nonlocal symplectic operator J can be written as the Lie derivatives of J along a suitably chosen nonlocal vector field. Moreover, we present a new description for local Hamiltonian structures of arbitrary order compatible with a given nondegenerate local Hamilt...

Nonlocal games are used to display differences between classical and quantum world. In this paper, we study nonlocal games with a large number of players. We give simple methods for calculating the classical and the quantum values for symmetric XOR games with onebit input per player, a subclass of nonlocal games. We illustrate those methods on the example of the N-player game (due to Ardehali [...

We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic propert...

We used classification images (A. J. Ahumada, Jr., & J. Lovell, 1971) to estimate the perceptual filter in a task designed to assess both local and nonlocal effects upon contrast detection/discrimination. Three observers performed a yes/no detection or discrimination task of a uniform circular decrement (radius = 0.68 deg) near threshold presented for 100 to 400 ms. Stimuli were presented in ri...

We prove new existence results of mild solutions to fractional differential equations with nonlocal conditions in Banach spaces. The nonlocal item is only assumed to be continuous. This generalizes some recent results in this area.

Local-nonlocal coupling is an organizational principle in protein folding. It envisions a cooperative energetic interplay between local conformational preferences and favorable nonlocal contacts. Previous theoretical studies by our group showed that two classes of native-centric coarse-grained models can capture the experimentally observed high degrees of protein folding cooperativity and diver...

In this article free vibration of a Timoshenko nanobeam with variable cross-section is investigated using nonlocal elasticity theory within the scope of continuum mechanics. Small scale effects are modelled after Eringen’s nonlocal elasticity theory while the non-uniformity is presented by exponentially varying width through the beam length with constant thickness. Analytical solution is achiev...

In this article, electro-thermo nonlocal nonlinear vibration and instability of viscous-fluid-conveying double–walled boron nitride nanotubes (DWBNNTs) embedded on Pasternak foundation are investigated. The DWBNNT is simulated as a Timoshenko beam (TB) which includes rotary inertia and transverse shear deformation in the formulation. Considering electro-mechanical coupling, the nonlinear govern...