Nonlocal Effects Research Articles

Impacts of nonlocal fear effect and delay on a reaction–diffusion predator–prey model

In this research, we examine a predator–prey model in which nonlocal fear plays a role alongside delay in a reaction–diffusion framework. We integrate two delays into the model to account for the lag between when fear starts affecting the growth rate of prey and when it starts affecting the growth rate of the predator through feedback. The first step is to investigate local and global stability and bifurcations in the equilibrium states of the nondelayed model. We explore the Hopf bifurcation in the delayed model using the delay as the bifurcation parameter. Our theoretical findings are then backed up by certain simulations. It reveals how the system, depending on its level of anxiety and the time delays involved, displays a wide range of spatiotemporal patterns.

An accelerated novel meshless coupled algorithm for Non-local nonlinear behavior in 2D/3D space-fractional GPEs

In this work, an accelerated novel meshless coupled algorithm is first presented for the numerical study of high-dimensional space-fractional nonlinear Schrödinger or Gross-Pitaevskii equations (SFNLS/GPEs). The proposed meshless method is motivated by the novel coupled concepts: (a) a time splitting-step is adopted to decompose the NLSE; (b) the spatial Riesz fractional derivative under the Riemann-Liouville operator is discretized by the combination of numerical integration and meshless weighted-least-square schemes; (c) an accurate absorbing boundary condition is employed to treat the unbounded domain. Meanwhile, a parallel algorithm based on the above approximated schemes is designed to reduce the computing cost on a CUDA-program-based GPU card. Subsequently, the validation and numerical convergence rate of the proposed method for SFNLSE are discussed and illustrated by solving two 2D/3D examples. Furthermore, the proposed parallel meshless algorithm is extended to predict the nonlinear dynamic behaviors dominated by the space-fractional Gross-Pitaevskii equations (SFGPEs), and the influence of nonlocal effect on the nonlinear phenomena is also discussed. The presented numerical results illustrate that the proposed algorithm for multi-dimensional SFNLSEs is reliability and high-efficient.

Nonlinear nonlocal damping effects under magnetic loads of a ferromagnetic-viscoelastic nanotube exposed to a nonlinear elastic medium with nonlocal viscosity

This study presents innovative results on a nonlinear dynamic model of a ferromagnetic-viscoelastic nanotube (FVN) whose dissipation effects are captured by material behavior with a linear dissipation law operating in a nonlinear geometric regime. It investigates a possible system derived from a Kelvin–Voigt type dissipation model that describes internal viscoelastic damping in the form of a parallel spring and a dashpot. In addition, a class of losses by linear viscous media in local and nonlocal damping is presented in the modeling. Magnetic load effects are studied using axial rod theory regardless of rotational inertia and shear effects. The governing equation is derived by Hamilton's principle for the FVN subjected to a transverse magnetic field resting on a nonlinear elastic foundation with viscose effects. Formulas have been developed to obtain the nonlinear damping characteristics of a single-walled nanotube. Then, multiple scale method (MSM)-based solutions and Eringen elasticity theory are applied to demonstrate the aforementioned effects on a narrow clamped-clamped (CC) nanotube in detail. The approximate analytical solution is verified by numerical integration methods and a good agreement between the approximate analytical and numerical results is observed. The effect of all important parameters such as local and nonlocal viscosity damping, nonlinear damping coefficient, linear and nonlinear stiffness of the elastic medium due to changes in amplitude vibration of the magnetic field (AVMF) and displacement responses (DR) have been investigated. The original research proposed in this paper may enable the systematic study of nonlinear damping in nanomechanical oscillators, which may help to reveal the underlying physical mechanism.

Correlated Electronic Structure of La_{3}Ni_{2}O_{7} under Pressure.

Recently, superconductivity with a T_{c} up to 78K has been reported in bulk samples of the bilayer nickelate La_{3}Ni_{2}O_{7} at pressures above 14GPa. Important theoretical tasks are the formulation of relevant low-energy models and the clarification of the normal state properties. Here, we study the correlated electronic structure of the high-pressure phase in a four-orbital low-energy subspace using different many-body approaches: GW, dynamical mean field theory (DMFT), extended DMFT (EDMFT) and GW+EDMFT, with realistic frequency-dependent interaction parameters. The nonlocal correlation and screening effects captured by GW+EDMFT result in an instability toward the formation of charge stripes, with the 3d_{z^{2}} as the main active orbital. We also comment on the potential relevance of the rare-earth self-doping pocket, since hole doping suppresses the ordering tendency.

Magnetoelectric Energy in Electrodynamics: Magnetoelectricity, Bi(an)isotropy, and Magnetoelectric Meta‐Atoms

AbstractMagnetoelectricity denotes the relationship between electric polarization and magnetization. In materials with an intrinsic magnetoelectric (ME) effect, the energy density comprises the polarization, magnetization, and ME energy densities. These three components of energy define local (subwavelength) characteristics of electromagnetic (EM) responses in multiferroic materials. In a subwavelength domain, coupling between the electric and magnetic dipole oscillations forms the ME field structures that are characterized by the violation of both spatial and temporal symmetry. Unlike multiferroics, bi(an)isotropic metamaterials are associated with an EM response characterized only by spatial symmetry breaking. This also applies to chiral materials. Since no “intrinsic magnetoelectricity” is assumed in such structures, any concepts about the stored ME energy are not applicable. This clearly points to the effect of nonlocality. That is why the basic concepts of bi(an)isotropy can only be analyzed by the EM far‐field characteristics. In this paper, it is argued that in the implementation of local (subwavelength) ME meta‐atoms and systems for near‐field probing of chirality, the concept on ME energy is crucial. Real ME energy can occur when ME fields in a singular subwavelength domain are characterized by a violation of both the symmetry of time reversal and spatial reflection.

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.

Torsional Dynamics of Axially Graded Viscoelastic Carbon Nanotubes

Torsional vibration analysis of the axially functionally graded carbon nanotubes has been carried out. Nonlocal stress gradient elasticity theory has been used in continuum mechanics model of the carbon nanotube. Variation of the material properties of the axially graded nanostructure has been assumed in exponential form. Differently from the majority of literature works, viscous damping and nonlocal parameters have been assumed in grading form. Energy functional for the carbon nanotube has been achieved with minimum potential energy principle and weak form solution has been obtained with the Ritz Method. Effects of material grading, nonlocality and viscoelasticity to the torsional dynamics of axially graded carbon nanotube have been investigated. Results of the present work could be useful in modeling and production of axially functionally graded nanostructures.

Recent Developments in Terahertz Nanosensors

Terahertz (THz) waves occupy the electromagnetic spectrum between microwave and infrared radiation, with frequencies typically ranging from 0.1 to 10 THz. Compared with other optic and electronic tools, this frequency range allows for unique sensing applications such as nondestructive, label‐free, and fast detection. Despite the promising features of THz sensing applications, the dimensional mismatch between THz wavelength and nanoscale agents hinders practical applications, especially in biosensing and chemical sensing. Several recent studies propose that engineered THz resonators, such as split ring resonators, linear dipole and slot antennas, and nanogap loop antennas, enhance the sensitivity for detecting trace amounts of target molecules, such as viruses and explosives. When combined with near‐field imaging techniques in the THz range, these THz nanosensors may revolutionize our understanding of complex nanoscale systems, including 2D materials, as researchers can observe quantum dynamics directly in molecules, mobile carriers in semiconductors, THz quantum nonlocal effects, and dynamics of excitons and polaritons at THz frequencies. Additionally, THz biomolecular sensors are also discussed, where the sensor platforms will lead to a great impact in the advancement of ultrasmall‐quantity characterization of proteins, label‐free diagnosis of Alzheimer's disease, and conformational dynamics of biomolecules in their aqueous environment.

Accuracy Assessment of Atomistic Neural Network Potentials: The Impact of Cutoff Radius and Message Passing.

Atomistic neural network potentials have achieved great success in accelerating atomistic simulations in complicated systems in recent years. They are typically based on the atomic decomposition of total properties, truncating the interatomic correlations to a local environment within a given cutoff radius. A more recently developed message passing (MP) neural network framework can, in principle, incorporate nonlocal effects through iteratively correlating some atoms outside the cutoff sphere with atoms inside, a process referred to as MP. However, how the model accuracy depends on the cutoff radius and the MP process has rarely been discussed. In this work, we investigate this dependence using a recursively embedded atom neural network method that possesses both local and MP features, in two representative systems: liquid H2O and solid Al2O3. We focus on how these settings influence predictions for structural and vibrational properties, namely, radial distribution functions (RDFs) and vibrational density of states (VDOSs). We find that while MP lowers test errors of energy and forces in general, it may not improve the prediction for RDFs and/or VDOSs if direct interatomic correlations in the local environment are insufficiently described. A cutoff radius exceeding the first neighbor shell is necessary, beyond which involving MP quickly enhances the model accuracy until convergence. This is a potentially more efficient way to increase the model accuracy than directly increasing the cutoff radius, especially with more memory savings in the GPU implementation. Our findings also suggest that using the mean test error as the measure of the model accuracy alone is inadequate.

Combined Effects of Surface Energy, Initial Stress and Nonlocality on Vibration of Carbon Nanotubes Conveying Fluid Resting on Elastic Foundations in a Thermo-Magnetic Environment

This paper scrutinizes the simultaneous impacts of surface elasticity, initial stress, residual surface stress and nonlocality on the nonlinear vibration of carbon nanotube conveying fluid resting while resting on linear and nonlinear elastic foundations and operating in a thermo-magnetic environment. The derived partial differential equation is decomposed into spatial and temporal equations using Galerkin method of decomposition. Thereafter, the temporal differential equation is solved with the aid of method of homotopy perturbation. Studies of the significance of the model parameters reveal that the negative value of the surface stress enhances the frequency ratio while the positive value of the surface stress abates the ratio. At any given value of nonlocal parameters, the surface effect is lessened for enhancing value of the length of the nanotube. The frequency ratio is abated as strength of the magnetic field, nonlocal parameter and the length of the nanotube are increased. The nonlocality lessens the surface effects and ratio of the frequencies. At high values of nonlocal parameter and nanotube length, the natural frequency of the structure gradually approaches nonlinear Euler–Bernoulli beam limit. The ratio of the frequencies is heightened when the temperature change is reduced at high temperature while at room/low temperature, such ratio is enhanced as the temperature change is augmented. Also, the frequency ratio at low temperatures is lower than at high temperatures. The present work will be very useful in the design and control of carbon nanotubes in thermo-magnetic environment while resting on elastic foundations.

Analysis of the Influence of Quantum Effects on Optical Characteristics of Plasmonic Nanoparticles Based on the Discrete Sources Method

The discrete sources method is adapted to the study of surface quantum effects based on mesoscopic boundary conditions with Feibelman parameters. A comparative analysis of the influence of bulk nonlocal effects and surface effects on optical characteristics of gold and silver nanoparticles is carried out using the generalized nonlocal optical response model. It is established that allowance for the nonlocal effect in the noble metals always leads to a reduced amplitude of the surface plasmon resonance (SPR) and its blue shift, while the surface effect depends substantially on the geometry of the particles. To a large degree, the mesoscopic boundary conditions recover the SPR amplitude as compared with the bulk nonlocal effect. This difference is especially noticeable in the field enhancement factor on the surface of the particles. Additionally, substantial differences in the SPR behavior for gold and silver particles are found in the case of mesoscopic boundary conditions.

Nonlocal effect on shear wave propagation in a fiber-reinforced poroelastic layered structure subjected to interfacial impulsive disturbance

The present study illuminates the influence of impulsive line source on Horizontally polarized shear (SH) waves propagating in a stratified structure consisting of two distinct nonlocal fiber-reinforced layers with voids over a foundation with nonlocal functionally graded fiber-reinforced substrate with voids. The governing equations for a nonlocal fiber-reinforced poroelastic medium are established. The proposed mathematical model incorporates the Green’s function technique and the Fourier transformation to yield the complex dispersion relation of the propagating wave. The study discloses the existence of two wave fronts of SH-waves propagating with different speeds through the layered structure. The second wave front arises as a result of existence of void pores, while the first wave front defines SH-wave propagation in a nonlocal fiber-reinforced layered structure. Each wave front possesses individual critical frequency beyond which they fail to propagate. Speeds of both wave fronts are influenced by the appearance of nonlocality parameter. Using MATHEMATICA, several graphs have been plotted to demonstrate the impact of key parameters on the dispersion and attenuation of both wave fronts. Some notable cases have been derived which validate the present mathematical model.

Synthesis of Polarization-Independent Perfect Anomalous Reflectors via Modulated Metasurfaces and an Analytical Design Model

A systematic approach to the synthesis of polarization-independent metasurfaces for anomalous reflection is presented. A fast analytical procedure is laid out to analyze the electromagnetic (EM) behavior of an impedance-modulated metasurface for arbitrary angles of incidence and reflection, subsequently serving as a means to provide the necessary impedance profile for reflection toward a specific direction, while capturing all propagation mechanisms, including surface waves (SWs) and nonlocal effects. We apply this procedure to design a metasurface for reflecting a normal incident wave to a different reflection angle, where the synthesized impedance is approximated by a discrete design, based on orthogonal metallic patches. This is done to provide control of both cases of incident wave polarization, while the unit cell analysis and extraction of equivalent impedance is easily performed by a full-wave computational eigenmode analysis of the unit cell. The unit cell design is performed by a simple fine-tuning process with minimal geometric modifications, and the actual discrete metasurface design is proven to agree well with the continuous model. The validity of the synthesis approach is perfectly demonstrated by the fabrication and experimental verification of a model design.

Light scattering from the metallic nanowires with radially anisotropic cloaks

We discuss the scattering properties of the core–shell nanowires containing metallic core with nonlocal effects and radially anisotropic shell based on the nonlocal full-wave theory. The tunable extinction spectrum could be obtained by adjusting the anisotropy parameter and geometric size of the core–shell nanowires. The main peak resulted from transverse mode would be enhanced with the optimal anisotropy parameter. The subsidiary peaks due to the longitudinal mode become dense for the coated nanowires with thin anisotropic shell. Moreover, S-shaped and Z-shaped Fano resonances in the core–shell nanowires are presented under weak dissipation. These results will have potential applications in optical communications and ultra-sensitive detections.

Dynamics of a diffusive predator–prey model with nonlocal fear effect

The fear effect on prey populations due to the presence of a predator’s sound or smell can be more impactful than direct predation. In this paper, we formulate a diffusive predator–prey model incorporating the nonlocal fear effect. The existence and boundedness of solutions are showed. We also study the stability of constant steady states by using the characteristic equation and Lyapunov functionals. Steady-state bifurcations are carried out in detail by the Lyapunov-Schmidt method. The analyses demonstrate that the fear effect in the system can change the stability of the constant steady state and there exist spatially nonhomogeneous steady states. Hopf bifurcations are also investigated and the results show that high levels of fear can stabilize the model by excluding the existence of periodic solutions. Finally, numerical simulations are sketched to illustrate our theoretical findings. This work can help us further understand the impact of fear effect on the stability of constant steady states, steady-state bifurcations and Hopf bifurcations of predator–prey models.

On the nonlocal Newtonian cosmology

In the absence of an exact development of the cosmological models based on the Mashhoon nonlocal gravity, the Newtonian regime clarifies some aspects of it. To improve this model more reliable, going through some semi-Post-Newtonian considerations may be useful. One important feature to consider is the formation of horizons, which can be understood as a consequence of the finite interaction velocity. This highlights the importance of extending the integration across the entire space–time, rather than solely focusing on the spatial sector. In this context, we show that the density of effective dark matter would increase, while the density of Baryonic matter decreases, during the deep matter-dominated era. This finding is in contradiction with the predictions of the standard model of cosmology and it raises concerns about the compatibility of using Tohline–Kuhn kernel and considering the nonlocal effects as an effective dark matter in ΛCDM.

Tuning nonlocal effects in grooved cylindrical plasmons by hydrodynamic model: A competing mechanism

Using the linearized hydrodynamic equations, we explore the optical characteristics of grooved cylinders of different groove numbers and widths, which have a strong impact on the corresponding resonance peaks. The number of grooves is an important new variable parameter to tune the energy of the dipolar plasmon without appreciable broadening of the plasmonic peak. As the groove number and width increase, the excitation and interesting anomalous redshifts of plasmonic higher-order modes are found, which can be unraveled by a competing mechanism between nonlocal effects and surface electron scattering. These findings are of importance for further apprehending the optical belongings of nanoscale complex structures and play a significant guiding role in the design of tunable plasmonic devices.

Fractional view analysis of the diffusion equations via a natural Atangana-Baleanu operator

In this article, the natural transform decomposition method (NTDM) is applied to evaluate the fractional-order diffusion equations utilizing the Atangana-Baleanu operator. The method offers an efficient analytical solution by combining the natural transform methodology with a decomposition strategy. The suggested method incorporates non-local effects and memory qualities introduced by the Atangana-Baleanu operator while demonstrating adaptability and applicability to various fractional-order diffusion equations. In comparison to previous analytical techniques, the NTDM has demonstrated the lowest calculation volume and the highest rate of convergence. The obtained results are presented illustratively by using graphical simulations. The suggested method is therefore easily adaptable to other non-linear issues. The NTDM includes comparative analysis capabilities, practicality, and accurate results for researchers and practitioners. In order to solve fractional-order phenomena, particularly diffusion equations, NTDM is regarded as the best analytical technique.

Thermal control of polarization of light with nonlocal plasmonic anisotropic metamaterials

Plasmonic nanostructures have demonstrated significant potential for engineering the intensity and polarization state of light with further opportunities to actively manipulate them by external stimulation using nonlinear effects. Plasmonic metamaterials composed of arrays of vertically oriented metallic nanorods have shown a dynamically tunable optical response based on the change of the electron temperature. The modulation of the optical properties is particularly pronounced in the epsilon-near-zero regime and can be further enhanced by nonlocal effects. Here, we experimentally study the optical properties of gold nanorod metamaterials with a strong nonlocal response under optically-induced heating, exploiting temperature dependence of the metal permittivity. Recovering the Stokes parameters of light transmitted through the metamaterial, we demonstrate the change in the polarization of the transmitted light by more than 20% for temperature changes under hundred degrees. Combined with a numerical analysis, this shows the possibility of controlling transmission and polarization state of light by using metamaterial-assisted thermal modulation.

Analytic inclined flow rule for determining granular rheology under strong non-local effects

This study theoretically establishes a flow rule for a granular flow down a rough inclined plane, capable of determining granular rheology in the presence of strong non-local effects resulting from grain cooperativity. To describe the non-local rheology, a Landau–Ginzburg model is formulated in terms of the fluidisation parameter represented by the granular inertial number. The exact solutions of the inertial-number field are solved and provide physical insights into the evolution of the internal rheology and the flow arrest process controlled by the flow height. Through asymptotic analysis in the regime dominated by strong non-locality, the exact solutions are further reduced to yield an analytical flow rule for the mean flow velocity. A comparison between the prediction of the flow rule and experimental data from the literature for sand grains determines the underlying rheology law and the relevant rheological parameters. Thus, the proposed flow rule serves as an effective tool for inferring granular rheology from strongly non-local inclined flow data, surpassing the limitations of the classical flow rule deduced from the local rheology framework.