Nonlocal Case Research Articles

Generation of bright spatial quasi-solitons by arbitrary initial beam profiles in local and nonlocal (1+1)-Dimensional nonlinear media

In this paper we demonstrate numerically that it is possible to generate bright spatial quasi-solitons, in media that are described by the (1+1)-Dimensional local and nonlocal Nonlinear Schrodinger Equation, using initial condition field distributions that are distinct from the analytical solution. In the local case different initial conditions were considered and in the nonlocal case different response functions and degrees of nonlocality were considered, obtaining the same behavior: at the beginning the initial profile is reshaped and after some distance, the beam propagates almost without change or in an small oscillatory way. The propagated intensity profile in the local case evolves to hyperbolic secant and in the nonlocal case to Gaussian, regardless of the degree of nonlocality. Analytical formulas for the propagated intensity profile are given.

Non-local non-linear sigma models

We study non-local non-linear sigma models in arbitrary dimension, focusing on the scale invariant limit in which the scalar fields naturally have scaling dimension zero, so that the free propagator is logarithmic. The classical action is a bi-local integral of the square of the arc length between points on the target manifold. One-loop divergences can be canceled by introducing an additional bi-local term in the action, proportional to the target space laplacian of the square of the arc length. The metric renormalization that one encounters in the two-derivative non-linear sigma model is absent in the non-local case. In our analysis, the target space manifold is assumed to be smooth and Archimedean; however, the base space may be either Archimedean or ultrametric. We comment on the relation to higher derivative non-linear sigma models and speculate on a possible application to the dynamics of M2-branes.

Perey-effect in continuum-discretized coupled-channel description of (d, p) reactions

The Perey effect in two-body channels of (d, p) reactions has been known for a long time. It arises when the nonlocal two-body deuteron-target and/or proton-target problem is approximated by a local one, manifesting itself in a reduction of the scattering channel wave functions in the nuclear interior. However, the (d, p) reaction mechanism requires explicit accounting for three-body dynamics involving the target and the neutron and proton in the deuteron. Treating nonlocality of the nucleon-target interactions within a three-body context requires significant effort and demands going beyond the widely-used adiabatic approximation, which can be done using a continuum-discretized coupled-channel (CDCC) method. However, the inclusion of nonlocal interactions into the CDCC description of (d, p) reactions has not been developed yet. Here, we point out that, similarly to the two-body nonlocal case, nonlocality in a three-body channel can be accounted for by introducing the Perey factors. We explain this procedure and present the first CDCC calculations to our knowledge including the Perey effect.

A Potential-Based Formalism for Modeling Local and Hydrodynamic Nonlocal Responses From Plasmonic Waveguides

In this paper, we propose a general boundary integral equation (BIE) approach for solving both exterior (e.g., scattering) and interior (e.g., guided wave propagation) problems involving general plasmonic waveguiding structures with arbitrary cross-sectional geometries and with a continuous translational symmetry in the direction of wave propagation. Contrary to the field-based approach which deals with the electric and magnetic fields, we employ a potential-based formalism instead, involving vector and scalar potentials, and match them at the media interfaces. The proposed approach can handle not only conventional plasmonic waveguides on the order of a few hundred nanometers but also those whose critical sizes are a few nanometers and in which the nonlocal hydrodynamic effects need to be accounted for. The BIEs describing the interaction of light with the plasmonic waveguide are solved by the method of moments (MoM) algorithm. Two illustrative examples, the first one of which deals with the scattering problem, while the second computes the dispersion diagram of a plasmonic cylinder, are considered for both local and nonlocal cases. An excellent agreement is observed between the numerical and theoretical results, with the latter being derived from the generalized Mie theory.

Globalizing F-invariants

In this paper we define and study the global Hilbert-Kunz multiplicity and the global F-signature of prime characteristic rings which are not necessarily local. Our techniques are made meaningful by extending many known theorems about Hilbert-Kunz multiplicity and F-signature to the non-local case.

Waves in dual-phase-lag thermoelastic materials with voids based on Eringen’s nonlocal elasticity

The main idea of the present work is to extend Eringen’s theory of nonlocal elasticity to generalized thermoelasticity with dual-phase-lag and voids. Then we study the propagation of time harmonic plane waves in an infinite nonlocal dual-phase-lag thermoelastic medium with voids. Three sets of coupled dilatational waves and an independent transverse wave may travel with distinct speeds through the medium. All these waves are found to be dispersive in nature. The coupled dilatational waves are damping, while the transverse wave is undamped in a certain range of the angular frequency. Coupled dilatational waves are found to be influenced by the presence of voids, thermal field and elastic nonlocal parameter, while the transverse wave is found to be influenced by the nonlocal parameter, but independent of void and thermal parameters. For a particular model, the effects of angular frequency, elastic nonlocality parameter, and some voids and thermal parameters on the wave speeds and damping coefficients of all the propagating waves have been studied numerically. Some comparisons are made between the results obtained for local and nonlocal cases. All the computed results have been depicted graphically and explained in details.

Human mobility in bike-sharing systems: Structure of local and non-local dynamics.

The understanding of human mobility patterns in different transportation modes is an interdisciplinary research field with a direct impact in aspects as varied as urban planning, traffic optimization, sustainability, the reduction of operating costs as well as the mitigation of pollution in urban areas. In this paper, we study the global activity of users in bike-sharing systems operating in the cities of Chicago and New York. For this transportation mode, we explore the temporal and spatial characteristics of the mobility of cyclists. In particular, through the analysis of origin-destination matrices, we characterize the spatial structure of the displacements of users. We apply a mobility model for the global activity of the system that classifies the displacements between stations in local and non-local transitions. In local transitions, cyclists move in a region around each station whereas, in the non-local case, bike users travel with long-range displacements in a similar way to Lévy flights. We reproduce the spatial dynamics by using Monte Carlo simulations. The obtained results are similar to the observed in real data and reveal that the model implemented captures important characteristics of the global spatial dynamics in the systems analyzed.

What the PCC tells us about “abstract” agreement, head movement, and locality

Based on the cross- and intra-linguistic distribution of Person Case Constraint (PCC) effects, this paper shows that there can be no agreement in ϕ-features (PERSON, NUMBER, GENDER/NOUN-CLASS) which systematically lacks a morpho-phonological footprint. That is, there is no such thing as “abstract” ϕ-agreement, null across the entire paradigm. Applying the same diagnostic to instances of clitic doubling, we see that these do involve syntactic agreement. This cannot be because clitic doubling is agreement; it behaves like movement (and unlike agreement) in a variety of respects. Nor can this be because clitic doubling, qua movement, is contingent on prior agreement—since the claim that all movement depends on prior agreement is demonstrably false. Clitic doubling requires prior agreement because it is an instance of non-local head movement, and movement of X0 to Y0 always requires a prior syntactic relationship between Y0 and XP. In local head movement (the kind that is already permitted under the Head Movement Constraint), this requirement is trivially satisfied by (c-)selection. But in non-local cases, agreement must fill this role.

Periodic solutions for a fractional asymptotically linear problem

We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the pseudo-index theory developed by Bartolo, Benci and Fortunato [11] after transforming the problem to a degenerate elliptic problem in a half-cylinder with a Neumann boundary condition, via a Caffarelli-Silvestre type extension in periodic setting. The periodic nonlocal case, considered here, presents, respect to the cases studied in the literature, some new additional difficulties and a careful analysis of the fractional spaces involved is necessary.

Mixed Local-Nonlocal Vector Schrödinger Equations and Their Breather Solutions**Supported by the Natural Science Foundation of Liaoning Province of China under Grant No. 201602678

To the best of our knowledge, all nonlinearities in the known nonlinear integrable systems are either local or nonlocal. A natural problem is whether there exist some nonlinear integrable systems with both local and nonlocal nonlinearities, and how to solve this kinds of spectral nonlinear integrable systems with both local and nonlocal nonlinearities. Recently, some novel mixed local-nonlocal vector Schrödinger equations are presented, which are different from the single local and nonlocal coupled Schrödinger equation. We investigate the Darboux transformation of mixed local-nonlocal vector Schrödinger equations with a spectral problem. Starting from a special Lax pairs, the mixed local-nonlocal vector Schrödinger equations are constructed. We obtain the one- and two- and N-soliton solution formulas of the mixed local-nonlocal vector Schrödinger equations with N-fold Darboux transformation. Based on the obtained solutions, the propagation and interaction structures of these multi-solitons are shown, the evolution structures of the one-solitons are exhibited, the overtaking elastic interactions among the two-breather solitons are considered. We find that unlike the local and nonlocal cases, the mixed local-nonlocal vector Schrödinger equations have some novel results. The results in this paper might be helpful for understanding some physical phenomena described in plasmas.

Lamellar phase solutions for diblock copolymers with nonlocal diffusions

For a diblock copolymer with total chain length γ>0 and mass ratio m∈(−1,1), we consider the problem of minimizing the doubly nonlocal free energy Eε(u)=H(u)+1ε2s∫ΩW(u)dx+12∫Ω|(−γ2Δ)−12(u−m)|2dxin a domain Ω, where H(u) is a fractional Hs-norm with s∈(0,12), and W is a double-well potential. This arises in the study of micro-phase separation phenomena for diblock copolymers with nonlocal diffusions.On the unit interval, we identify the Γ-limit as ε→0+, and also find explicit isolated local minimizers associated the lamellar morphology phase in the case m=0, provided that the chain is sufficiently short or the nonlocal interaction is sufficiently strong (i.e. as s→0+). We stress that such extra condition is new for the nonlocal case and is not present in the classical model. The proof, while elementary, requires a careful analysis of the nonlocal integrals.

Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory

Abstract In this study, nonlinear wave modulation in nanorods is examined on the basis of nonlocal elasticity theory. Eringen's nonlocal elasticity theory is employed to derive nonlinear equations for the motion of nanorods. The analysis of the modulation of axial waves in nonlocal elastic media is performed, and the reductive perturbation method is used for the solution of the nonlinear equations. The propagation of weakly nonlinear and strongly dispersive waves is investigated, and the nonlinear Schrödinger (NLS) equation is acquired as an evolution equation. For the purpose of a numerical investigation of the nonlocal impacts on the NLS equation, it has been investigated whether envelope solitary wave solutions exist by utilizing the physical and geometric features of the carbon nanotubes. Amplitude dependent wave frequencies, phase and group velocities have been obtained and they have compared for the linear local, the linear nonlocal, the nonlinear local and the nonlinear nonlocal cases.

Superradiance in a ghost-free scalar theory

We study superradiance effect in the ghost-free theory. We consider a scattering of a ghost-free scalar massless field on a rotating cylinder. We assume that cylinder is thin and empty inside, so that its interaction with the field is described by a delta-like potential. This potential besides the real factor, describing its height, contains also imaginary part, responsible for the absorption of the field. By calculating the scattering amplitude we obtained the amplification coefficient both in the local and non-local (ghost-free) models and demonstrated that in the both cases it is greater than 1 when the standard superradiance condition is satisfied. We also demonstrated that dependence of the amplification coefficient on the frequency of the scalar field wave may be essentially modified in the non-local case.

Optical properties of spatially dispersive Mie-resonant halide perovskite nanoparticles

We have proposed a mechanism explaining the unusual blue shift of photoluminescence peak in relatively large perovskite nanoparticles, where the quantum confinement effect is insignificant. We performed theoretical analysis of the absorption and scattering cross-sections of incident light in such nanoparticles in classical (local) and nonlocal cases. The blue shift for the scattering and absorption features in spectra around the exciton peak was obtained from the model, which can be related to that the previously observed shift of the luminescence peak in perovskite nanoparticles with a diameter less than 100 nm owing to the exciton nonlocality.

Nonlocal Plasmonic Modes and Plasmonic Band Structures in Cylindrically Curved Graphene

In this paper, hydrodynamic model has been analytically solved to investigate the nonlocal plasmons in cylindrically curved graphene layers. Within the quasi-static approximation, the dispersion relations for both local and nonlocal cases have been derived; the nonlocal effect is found to shift the dispersion relations upwards. High-order azimuthal modes possess different cutoff frequencies due to such nonlocality, which may occur even in large-scale highly doped structures. In periodically doped cases, the nonlocal effect can modify the corresponding plasmonic band structures, i.e., moving the locations of the bandgaps. The periodicity has made the material more sensitive to the plasmon nonlocality. Our investigations may lead to more attentions to the nonlocal plasmonic responses in graphene which are important for graphene-plasmon-based photonic devices.

Nonlocal heat flux effects on temperature evolution of the solar atmosphere

Context. Heat flux is one of the main energy transport mechanisms in the weakly collisional plasma of the solar corona. There, rare binary collisions let hot electrons travel over long distances and influence other regions along magnetic field lines. Thus, the fully collisional heat flux models might not describe transport well enough since they consider only the local contribution of electrons. The heat flux in weakly collisional plasmas at high temperatures with large mean free paths has to consider the nonlocality of the energy transport in the frame of nonlocal models in order to treat energy balance in the solar atmosphere properly. Aims. We investigate the impact of nonlocal heat flux on the thermal evolution and dynamics of the solar atmosphere by implementing a nonlocal heat flux model in a 3D magnetohydrodynamic simulation of the solar corona. Methods. We simulate the evolution of solar coronal plasma and magnetic fields considering both a local collision dominated and a nonlocal heat flux model. The initial magnetic field is obtained by a potential extrapolation of the observed line-of-sight magnetic field of AR11226. The system is perturbed by moving the plasma at the photosphere. We compared the simulated evolution of the solar atmosphere in its dependence on the heat flux model. Results. The main differences for the average temperature profiles were found in the upper chromosphere/transition region. In the nonlocal heat transport model case, thermal energy is transported more efficiently to the upper chromosphere and lower transition region and leads to an earlier heating of the lower atmosphere. As a consequence, the structure of the solar atmosphere is affected with the nonlocal simulations producing on average a smoother temperature profile and the transition region placed about 500 km higher. Using a nonlocal heat flux also leads to two times higher temperatures in some of the regions in the lower corona. Conclusions. The results of our 3D MHD simulations considering nonlocal heat transport supports the previous results of simpler 1D two-fluid simulations. They demonstrated that it is important to consider a nonlocal formulation for the heat flux when there is a strong energy deposit, like the one observed during flares, in the solar corona.

Unique global solution to the thermally radiative magnetohydrodynamics equations

In this paper, we consider a non-equilibrium diffusion approximation model in thermally radiative magnetohydrodynamics (MHD) which describe the compressible viscous, heat-conducting fluid coupled with the Maxwell equations governing the behavior of the magnetic field with taking into account the radiation effect under the non-local thermal equilibrium case. The system consists of the radiative transfer equation coupled with the compressible MHD equations, and the magnetic diffusion coefficient, viscosity coefficient, heat-conducting coefficient are all allowed to be positive constants. We prove existence, uniqueness and regularity of global-in-time classical solutions to one-dimensional case of this model. Based on the fundamental local existence results and global-in-time a priori estimates, we can establish the global existence of a unique classical solutions with large initial data to the initial-boundary value problems.

Global dynamics and spreading speeds for a partially degenerate system with non-local dispersal in periodic habitats

This paper is concerned with the global dynamics and spreading speeds of a partially degenerate non-local dispersal system with monostable nonlinearity in periodic habitats. We first obtain the existence of the principal eigenvalue for a periodic eigenvalue problem with partially degenerate non-local dispersal. Then we study the coexistence and extinction dynamics. Finally, the existence and characterization of spreading speeds are considered. In particular, we show that the spreading speed is linearly determinate. Overall, we extend the existing results on global dynamics and spreading speeds for the degenerate reaction–diffusion system to the degenerate non-local dispersal case. The extension is non-trivial and meaningful.

Existence, uniqueness and regularity of multi-dimensional nonlocal balance laws with damping

In this article, we generalize some existence and uniqueness results in [22] for scalar nonlocal balance laws to multi-dimensional nonlocal balance laws. Also in the multi-dimensional case it is possible to get rid of the Entropy condition which is usually postulated to guarantee a unique weak solution of (local) balance laws but which we prove to be redundant in the nonlocal case. We start with a well known existence theorem for linear balance laws and the explicit formula for a solution to obtain a fixed-point problem in the nonlocal term. Using Banach's fixed-point theorem we prove existence and uniqueness of a fixed-point. This existence and uniqueness result is used for constructing and proving a unique solution of the multi-dimensional nonlocal balance law on a sufficiently small time horizon. While in many publications the nonlocal term will be considered over the entire space domain, we present an existence and uniqueness result which allows rather general integration areae for the nonlocal term. Eventually, we obtain a unique weak solution on every finite time horizon. Existence and uniqueness are complemented by stability results and an exhaustive study on more regular weak solutions in case the data is more regular.

Nonlocal logarithmic nonlinear optical soliton

The propagation of optical beam in (1 + 2)-dimensional nonlocal logarithmic nonlinear media is studied. The numerical simulation shows that the intensity profiles of solitons undergo a gradual and continuous transition from a Gaussian-shaped function in the general nonlocal media to an approximately hyperbolic secant function in the local case. Due to the nonlocal effect, the stability of solitons increases with the increase of nonlocality degree. Concretely speaking, the quasi-stable solitons can be formed in local and weakly nonlocal (nonlocality degree α < 0.5) logarithmic nonlinear media. In general nonlocal case (0.5 ≤ α≤1), the completely stable solitons can be formed. In special case (α = 1), even the initial power increase largely, the solitons can still exist even the initial power has large change for the saturable nonlinear contract effect. However, when α = 1.1, the solitons cannot be formed at any initial power because nonlinear effect is too small to balance diffraction effect.