Spatial Nonlocal Effects Research Articles

Dynamic behavior of nanoplate on viscoelastic foundation based on spatial-temporal fractional order viscoelasticity and thermoelasticity

The nanodevices often work in a thermal environment and lead to the viscoelastic and thermoelastic coupling which becomes more complicated when further coupled with the size effects. A spatial-temporal fractional order model is proposed to study the dynamic behavior of thermoelastic nanoplate in the present work. The integer order differential is extended to the fractional order differential with the integer order differential as a special case. This extension makes the modeling of small-scale effects of mechanical behavior and generalized heat conduction more flexible. Non-local strain gradient elasticity and non-local heat conduction are used to describe the spatial non-local effects while the fractional order differential to describe the complicated history-dependent effects or the temporal nonlocal effects. The standard solid viscoelastic model and generalized heat conduction model with the fractional order differentials lead to the fractional-order differential governing equations. The fractional order differential equation is solved by the Laplace transform method, and the analytical solution of the response is expressed in terms of the Mittag-Leffler function. In order to verify the reliability of the analytical solution, the numerical solution is also provided for comparison. Based on the numerical results of dynamic response under the step load, the effects of thermoelastic fractional order parameters, viscoelastic fractional order parameters, and small-scale parameters are discussed. The new spatial-temporal fractional order model is a natural extension of the traditional integer order model which can be recovered from the present model.

Tumor Evolution Models of Phase-Field Type with Nonlocal Effects and Angiogenesis

In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on diffusive interface models and follow the phase-field approach that describes the tumor as a collection of cells. Such systems are based on a multiphase approach that employs constitutive laws and balance laws for individual constituents. In mathematical oncology, numerous biological phenomena are involved, including temporal and spatial nonlocal effects, complex nonlinearities, stochasticity, and mixed-dimensional couplings. Using the models, for instance, we can express angiogenesis and cell-to-matrix adhesion effects. Finally, we offer some methods for numerically approximating the models and show simulations of the tumor's evolution in response to various biological effects.

Spatial nonlocality effect on the surface plasmon propagation in plasmonic nanospheres waveguide

Spatial nonlocality affects the plasmonic characteristics of nanostructures. We used the quasi-static hydrodynamic Drude model to obtain the surface plasmon excitation energies in various metallic nanosphere structures. The surface scattering and radiation damping rates were phenomenologically incorporated into this model. We demonstrate that spatial nonlocality increases the surface plasmon frequencies and total plasmon damping rates in a single nanosphere. This effect was amplified for small nanospheres and higher multipole excitation. In addition, we find that spatial nonlocality reduces the interaction energy between two nanospheres. We extended this model to a linear periodic chain of nanospheres. Then we obtain the dispersion relation of surface plasmon excitation energies using Bloch’s theorem. We also show that spatial nonlocality decreases the group velocities and energy decay lengths of the propagating surface plasmon excitations. Finally, we demonstrated that the effect of spatial nonlocality is significant for very small nanospheres separated by short distances.

Quantum mechanics with spatial non-local effects and position-dependent mass

A new higher order Schrödinger equation characterized by a position-dependent mass is introduced based on long-range spatial kernel effects and von Roos arguments. The extended Schrödinger equation depends on the sign of the moments M k , k = 0 , 1 , 2 , … and a stabilized quantum dynamic is realized for M 2 > 0 and M 4 > 0 . We have discussed its implications in several quantum mechanical systems where more than a few were raised, mainly the emergence of the quantum Pais-Uhlenbeck and the relativistic quantum harmonic oscillators besides the complex periodic potential characterized by a PT symmetry.

Effects of Spatial Nonlocality versus Nonlocal Causality for Bound Electrons in External Fields.

Using numerically exact solution of the time-dependent Schrödinger equation together with time-dependent quantum Monte Carlo (TDQMC) calculations, here we compare the effects of spatial nonlocality versus nonlocal causality for the ground state and for real-time evolution of two entangled electrons in parabolic potential in one spatial dimension. It was found that the spatial entanglement quantified by the linear quantum entropy is predicted with good accuracy using the spatial nonlocality, parameterized naturally within the TDQMC approach. At the same time, the nonlocal causality predicted by the exact solution leads to only small oscillations in the quantum trajectories which belong to the idler electron as the driven electron is subjected to a strong high frequency electric field, without interaction between the electrons.

On governing equations for a nanoplate derived from the 3D gradient theory of elasticity

The paper is concerned with the asymptotically consistent theory of nanoscale plates capturing the spatial nonlocal effects. The three-dimensional (3D) elasticity equations for a thin plate are used as the governing equations. In the general case, the plate is acted upon by dynamic body forces varying in the thickness direction, and by variable surface forces. The thickness of the plate is assumed to be greater than the characteristic micro/nanoscale measure and much smaller than the in-plane characteristic dimension (e.g., the wave or deformation length). The 3D constitutive equations of gradient elasticity are used to link the fields of nonlocal stresses and strains. Using the asymptotic approach, a sequence of relations for stresses and displacements in the form of polynomials in the transverse coordinate with coefficients depending on time and in-plane coordinates was obtained. The asymptotically consistent 2D differential equation governing vibration (or static deformation) of a plate accounting for both transverse shears and the spatial nonlocal contribution of the stress and strain fields was derived. It was revealed that capturing nonlocal effects in all directions leads to an increase in the correction factor compared with the well-known 2D theories based on kinematic hypotheses and the Eringen-type gradient constitutive equations. The effect of the internal length scales parameters on free low-frequency vibrations and displacements of a plate is discoursed.

On a Space-Fractional Generalization of the Black Oil Model

Classical multiphase filtration models, which are based on Darcy's law, are well studied and actively used in modern oil engineering. However, such models do not allow efficient describing of processes with power-law memory effects or with spatial non-locality effects. In recent years, there has been a significantly increasing interest in models with fractional derivatives and integrals that allow such effects to be taken into account.The article considers the space-fractional generalization of the two-phase Black Oil model. This model is built on the basis of a fractional modification of the Darcy’s law with the Riesz potential, which is one of the possible generalizations of a fractional integral to the case of a multidimensional space. The use of such a modification of Darcy's law allows efficient describing of filtration processes in heterogeneous fractured porous media with the effects of spatial non-locality.For the numerical solution of the system of equations from the obtained model, the use of the IMPES method is proposed. For this purpose, from the presented system of equations, one equation is selected that describes the evolution of pressure. This equation is written provided that the capillary pressure variation within the time step is neglected.A special case of the pressure equation with the Riesz potential of radial function is considered, which describes the pressure variation in the case of a radial plane flow. For this equation, a self-similar solution is constructed using the Mellin integral transform method. A representation of this solution in the form of the Mellin-Barnes contour integral was obtained, which made it possible to write it in terms of the Fox functions. It is shown that in the limiting case of a zero degree of the Riesz potential, this solution coincides with the self-similar solution of the classical heat equation. The constructed self-similar solution can be further used in the software implementation of the numerical solution of the model presentedThe main line of further research is to develop and implement a software computing system based on the proposed fractional generalization of the two-phase Black Oil model.

Photonic topological Weyl degeneracies and ideal type-I Weyl points in the gyromagnetic metamaterials

As a new topological phase in three-dimensional momentum space, Weyl semimetals extend the repertoire of exotic topological states. In this paper, we find the existence of photonic Weyl points in electromagnetic continuous gyromagnetic metamaterials. The dispersion of the longitudinal mode of one of the two bands forming the Weyl point is flat; thus, the Weyl degeneracy point of the system is exactly at the critical transition between the type-I and type-II Weyl points. The Fermi arc connects the projections of the Weyl points with opposite chirality at the interface between the gyromagnetic metamaterial and vacuum. Full-wave simulation results show that surface waves can bypass sharp defects and achieve robust, unidirectional optical transmission without reflection. Furthermore, taking the spatial nonlocal effects into account, the ideal type-I Weyl points can exist in this class of metamaterials. This paper sheds light on fundamental understanding of topological physics, and the study of Weyl points in metamaterials will greatly enrich the field of topological photonics.

Discrete sources method for investigation of near field enhancement of core-shell nanoparticles on a substrate accounting for spatial dispersion

Quantum nanoplasmonics attracts increasing interest of researchers since its innovations have great potential for practical applications. Over the past decades, the use of core-shell nanoparticles has gained huge popularity due to the ability to manipulate the materials and sizes of both core and shell to control their plasmonic properties. This circumstance favorably distinguishes them from its homogeneous counterparts. In this paper, based on the Discrete Sources Method, we investigate the effect of spatial nonlocality in a metal shell of a nonspherical core-shell nanoparticle deposited on a glass prism. Our primary goal is to examine the impact of the nonlocal effect on the near-field enhancement and the absorption cross section of the particle. We found that accounting for the interaction of a particle with a prism has a larger influence on the optical characteristics of the near field than on the intensity in the far zone. For excitation of the core-shell particle, both a propagating and an evanescent wave, have been considered. It was found that evanescent wave excitation provides a larger near field enhancement than an exciting propagating wave. Taking into account the nonlocality effect in the metal shell leads to a significant damping of the plasmon resonance amplitude accompanied by a small blue shift.

Nonlocal theory of thermoelastic diffusive materials and its application in structural dynamic thermo-elasto-diffusive responses analysis

With the rapid development of ultrafast heating technologies and its application in the micro-machining of micro/nano-electromechanical devices, where the nonlocal effects on elastic deformation and heat/mass transfer will increase and classical/generalized theory of thermoelastic diffusion coupling does not hold any more. In this work, a nonlocal theory of thermoelastic diffusive materials is developed, and the spatial nonlocal effects of heat and mass transport are both considered for the first time. With the aid of thermodynamic principles, the constitutive relations involving size-dependent characteristic lengths are derived. In the aspect of the application, the proposed theoretical model is further used to investigate the dynamic thermo-elasto-diffusive responses of a one-dimensional semi-infinite medium with one end subjected to time-dependent shock loads, and the semi-analytical techniques based on Laplace transform methods are applied to obtain the transient solutions. The effects of nonlocal parameters on structural dynamic thermo-elasto-diffusive responses are also evaluated and discussed to be expected to provide new insights on the thermoelastic diffusion coupling at the micro/nanoscale.

Simulation of light scattering and electron energy loss (EELS) by small spatially dispersive plasmonic nanodimers

Despite the tremendous progress in the field of nanoplasmonics, complex plasmonic nanostructures such as dimers still present a significant challenge for proper numerical characterization. In particular, for the particles which size is smaller than electron mean free path in metals it is necessary to account for effects of spatial nonlocality in simulations. To address these problems a new mathematical model based on the Discrete Sources Method was developed and corresponding computer model was implemented. It enables one to successfully resolve the problem of accounting for spatial dispersion effects, which is especially important in the systems with very small gap and particle size, and it retains all key features of the Discrete Sources numerical approach including flexibility and a posteriori error estimation. We compute such scattering characteristics as electron energy loss probability and total scattered field intensity of nanodimers as one typically has to rely on methods of both optical and electron spectroscopy to experimentally investigate these structures. The developed model also allows to simultaneously consider several external excitations of the plasmonic system, including both electron and plane wave, in order to obtain more information about the system and to significantly speed up computational performance.

Attenuation of waves in a viscoelastic peridynamic medium

The effect of spatial nonlocality on the decay of waves in a dissipative material is investigated. The propagation and decay of waves in a one-dimensional, viscoelastic peridynamic medium is analyzed. Both the elastic and damping terms in the material model are nonlocal. Waves produced by a source with constant amplitude applied at one end of a semi-infinite bar decay exponentially with distance from the source. The model predicts a cutoff frequency that is influenced by the nonlocal parameters. A method for computing the attenuation coefficient explicitly as a function of material properties and source frequency is presented. The theoretical results are compared with direct numerical simulations in the time domain. The relationship between the attenuation coefficient and the group velocity is derived. It is shown that in the limit of long waves (or small peridynamic horizon), Stokes’ law of sound attenuation is recovered.

Nonlocal diffusion-elasticity based on nonlocal mass transfer and nonlocal elasticity and its application in shock-induced responses analysis

The instantaneous change of concentration in the rapid charging of Li-ions batteries can result in the Li-ions diffusion and diffusion-induced stresses. In such situation, the accurate description of the interaction mechanism between mass diffusion with matter is of great importance for the fabrication and exploitation of nano-electrochemical devices under non-uniform concentration in-service environment. To deal with such problems, this paper aims to establish a size-dependent diffusion-elasticity model is with the consideration of spatial nonlocal effects of concentration and strain fields. The proposed model is then applied to investigate the dynamic responses of a thick nanoplate under transient concentration loads.

Enhanced asymmetric transmission in hyperbolic epsilon-near-zero slabs

We investigate the asymmetric transmission for forward and backward propagation of tilted circular polarized optical waves in subwavelength epsilon-near-zero (ENZ) hyperbolic slabs. This chiral-optical effect is solely triggered by anisotropy without resorting to any breaking of reciprocity and chiral symmetries or spatial nonlocal effects. Remarkably, we show that the asymmetric transmission undergoes a dramatic enhancement near the ENZ condition. This happens since, close to the zero-crossing point, the extraordinary waves can accumulate the desired propagation phase even though the slab is ultrathin and, by varying excitation angles and slab thickness, we engineer this phase thus achieving a huge asymmetric transmission. The proposed strategy holds promise for realizing ultra-compact and efficient polarization devices in different frequency range even at very high frequencies (ultraviolet) since the effect is merely due to anisotropy and it is available without resorting to nanofabrication processes.

Studies on spatial nonlocal optical absorption properties in AlGaAs/GaAs three-step quantum well

To investigate the nonlocal linear intersubband optical absorption properties in AlGaAs/GaAs three-step quantum well (3SQW) nanostructures for a p-polarized states, we deduced the expression of the optical absorption coefficient in the two-level 3SQW system by using Green’s function method and the nonlocal relation between electron and photoelectric field. For the given 3SQW nanostructure, we performed numerical calculations of the optical absorption spectra for different parameters such as angles of incidence, the well width, and the height of the step barrier potential. The numerical results show that spatial nonlocal linear optical response of electrons to light field can induce the radiation shift. It is also demonstrated that the radiation shift and optical absorbance can be controlled by the structure of the 3SQW. These results may bring about a helpful impact in designing nanomaterials with multifarious nonlocality and observing the spatial nonlocal effects in experiment.

Investigation on plasmonic responses in multilayered nanospheres including asymmetry and spatial nonlocal effects

In this work, we present a rigorous approach for analyzing the optical response of multilayered spherical nano-particles comprised of either plasmonic metal or dielectric, when there is no longer radial symmetry and when nonlocality is included. The Lorenz–Mie theory is applied, and a linearized hydrodynamic Drude model as well as the general nonlocal optical response model for the metals are employed. Additional boundary conditions, viz., the continuity of normal components of polarization current density and the continuity of first-order pressure of free electron density, respectively, are incorporated when handling interfaces involving metals. The application of spherical addition theorems, enables us to express a spherical harmonic about one origin to spherical harmonics about a different origin, and leads to a linear system of equations for the inward- and outward-field modal coefficients for all the layers in the nanoparticle. Scattering matrices at interfaces are obtained and cascaded to obtain the expansion coefficients, to yield the final solution. Through extensive modelling of stratified concentric and eccentric metal-involved spherical nanoshells illuminating by a plane wave, we show that, within a nonlocal description, significant modifications of plasmonic response appear, e.g. a blue-shift in the extinction / scattering spectrum and a broadening spectrum of the resonance. In addition, it has been demonstrated that core–shell nanostructures provide an option for tunable Fano-resonance generators. The proposed method shows its capability and flexibility to analyze the nonlocal response of eccentric hybrid metal–dielectric multilayer structures as well as adjoined metal-involved nanoparticles, even when the number of layers is large.

Local thickness-dependent permittivity model for nonlocal bounded wire-medium structures

A local thickness-dependent permittivity is derived in closed form for bounded nonlocal wire-medium structures. The model takes into account spatial dispersion (as an average per length of the wires) and the effect of the boundary, and shows that an effective local model of a nonlocal medium is thickness dependent. The permittivity is comprised of a local bulk (Drude) term and a boundary- and thickness-dependent term, the latter including the effect of spatial nonlocality. Results are obtained for different wire-medium topologies which possess strong spatial dispersion, demonstrating good agreement with a nonlocal homogenization model and full-wave simulation results.

Stability and bifurcation of a predator–prey model with disease in the prey and temporal–spatial nonlocal effect

In this paper, we consider the dynamics of a predator–prey model with disease in the prey and ratio-dependent Michaelis–Menten functional response. The model is a reaction–diffusion system with a nonlocal term representing the temporal–spatial weighted average for the prey density. The limiting case of the system reduces to the Lotka–Volterra diffusive system with logistic growth of the prey. We study the linear stability of the two non-trivial steady states either with or without nonlocal term. The bifurcations to three types of periodic solutions occurring from the coexistence steady state are investigated for two particular kernels, which reveal the important significance of temporal–spatial nonlocal effects.

Spatial nonlocality in the infrared absorption spectra of polar semiconductor nanospheres

The absorption of infrared radiation by a polar semiconductor nanosphere is investigated, using a new extension of the Mie theory. The theory takes into account the spatial dispersion or nonlocality and determines the generalized Mie coefficients using an additional boundary condition of the continuity of the normal component of the displacement field at the surface of the system. Examples of calculated infrared absorption spectra are presented, by employing the typical values of doped InAs and InSb nanospheres. In the presence of the spatial nonlocal effects, the blue shift of the main absorption peaks, due to the coupled surface plasmon-optical phonon modes, are found to occur, while two groups of subsidiary peaks, due to coupled bulk plasmon-optical phonon excitations, appear in the optical spectra of the polar semiconductor nanospheres.

Spatially nonlocal effects on optical absorption properties in coupled quantum wells with an applied electric field

Based on the microscopic nonlocal optical response theory, the intersubband optical absorption properties in AlGaAs/GaAs couple quantum wells (CQWs) are investigated for p-polarized states. The numerical results show that spatial nonlocality of optical responses can induce a radiation shift on optical absorption spectra due to nonlocal effects. The dependence of the radiation shift on the CQW structure and the applied electric field is clarified. It is also demonstrated that the maximal radiation shift and the least optical absorbance can be obtained by adopting an appropriate CQW structure and a suitable applied electric field. This work may provide some methods of designing the nanomaterials with controllable nonlocality and observing the spatial nonlocal effects in experiment.