Nonlocal Effects Research Articles

Expressions of nonlocal quantities and application to Stoneley waves in weakly nonlocal orthotropic elastic half-spaces

In this paper, we introduce a novel model of nonlocal elasticity, called the weakly nonlocal elasticity, and provide explicit expressions of nonlocal quantities for harmonic plane waves propagating in the weakly nonlocal elastic solids. Then, we apply these expressions to investigate the propagation of Stoneley waves along the interface between two weakly nonlocal orthotropic elastic half-spaces. The half-spaces may be compressible or incompressible, and they are in welded contact. Our main aim is to derive explicit dispersion equations of Stoneley waves. First, we derive the explicit dispersion equation for the compressible case (when two half-spaces are compressible) using the surface impedance matrices of half-spaces. Then, the explicit dispersion equations for the incompressible cases (at least one half-space is incompressible) are obtained using the incompressible limit method. The simple and immediate derivation of these equations proves the convenience of the incompressible limit method. Some numerical examples are carried out to examine the effect of nonlocality and incompressibility on the Stoneley wave velocity.

When functionally graded materials meet higher order simplified strain gradient elasticity theory

We investigate the constitutive equations when the functionally graded materials (FGMs) are considered under the strain gradient elasticity theory (SGET). The SGET considered includes both the Helmholtz and bi-Helmholtz types. The constitutive equations become more complicated and contain more terms due to the interaction between the material gradation and the nonlocal effect of the strain gradient. We also derive the governing partial differential equations (PDEs) by the balance law of linear momentum, and the PDEs also appear to be highly complicated. Under the assumption that material gradation is of the exponential form, a simpler set of governing PDEs can be reached. Solutions to those PDEs under the formulation of different modes of crack problems are discussed.

How Accurately Can DFT Describe Non-valence Anions?

Weakly bound non-valence anions are molecular systems where the excess electron stabilizes in a very diffuse orbital whose size, shape, and binding energy (∼1-100 meV) are governed by the long-range electrostatic potential of the molecule. Its binding energy comes mainly from charge-dipole or charge-multipole interactions or dispersion forces. While highly correlated methods, like coupled cluster methods, are considered to be the state of the art for describing anionic systems, especially when the electron lies in a very diffuse orbital, we consider here the possibility to use DFT-based calculations. In such molecular anions, the outer electron experiences long-range exchange and correlation interactions. We show that DFT can describe long-range bound states provided that a correct asymptotic exchange and correlation potential is used, namely, that from a range-separated hybrid functional. This opens an alternative to the computationally demanding highly correlated method calculations. It is also suggested that the study of weakly bound anions could help in the construction of new DFT potentials to study systems where nonlocal effects are significant.

Statistical analysis and Neural Network Modeling of functionally graded porous nanobeams vibration in an elastic medium by considering the surface effects

The natural frequency of a clamped–clamped functionally graded porous (FGP) nanobeam is predicted in this study. Material distribution is considered based on monotonous, symmetric, and non-symmetric patterns in the thickness direction. This paper deals with governing equations of nanobeams based on third-order shear deformation beam theory in conjunction with nonlocal strain gradient theory (NSGT) and surface effects. Artificial neural network (ANN) is utilized to predict the effect of eight parameters including temperature gradient, residual surface stress, porosity distribution pattern, porosity parameter, nonlocal and material length scale parameters, and elastic and shear coefficients of Pasternak foundation on the fundamental frequency of FGP nanobeam. Different training methods are selected to simulate input and output dependency. Results show that the dependency of the natural frequency is inverse to the temperature gradient and nonlocal parameter in the sense that increasing these factors will decrease the natural frequency. Also, increasing the material length scale parameter grows the effect of the nonlocal parameter. Residual surface stress, material length scale, and Pasternak foundation parameters have a direct effect on the output and among them; the material length scale parameter has a more noticeable effect. Finally, it was found that by increasing the porosity parameter value, the diversity of natural frequency levels up drastically

Minimal Molecular Building Blocks for Screening in Quasi-Two-Dimensional Organic-Inorganic Lead Halide Perovskites.

Layered hybrid organic-inorganic lead halide perovskites have intriguing optoelectronic properties, but some of the most interesting perovskite systems, such as defective, disordered, or mixed perovskites, require multiple unit cells to describe and are not accessible within state-of-the-art ab initio theoretical approaches for computing excited states. The principal bottleneck is the calculation of the dielectric matrix, which scales formally as O(N4). We develop here a fully ab initio approximation for the dielectric matrix, known as IPSA-2C, in which we separate the polarizability of the organic/inorganic layers into minimal building blocks, thus circumventing the undesirable power-law scaling. The IPSA-2C method reproduces the quasi-particle band structures and absorption spectra for a series of Ruddlesden-Popper perovskites to high accuracy, by including critical nonlocal effects neglected in simpler models, and sheds light on the complicated interplay of screening between the organic and inorganic sublattices.

Tunable Heat-Flux Rectification in Graded Nanowires in Non-Linear Guyer-Krumhansl Regime.

We study heat rectification in composition-graded nanowires, with nonlocal and nonlinear effects taken into account in a generalized Guyer-Krumhansl equation. Using a thermal conductivity dependent on composition and temperature, the heat equation is solved. Introducing a non-vanishing heat supply (as for instance, a lateral radiative heat supply), we explore the conditions under which either nonlocal or nonlinear effects or both contribute to heat rectification and how they may be controlled by means of the external radiative flux. The corresponding rectification coefficients are calculated as well, and the physical conditions under which the system becomes a thermal diode are pointed out.

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.

Revisiting Biophysical Impacts of Greening on Precipitation Over the Loess Plateau of China Using WRF With Water Vapor Tracers

AbstractThe Loess Plateau of China has witnessed a remarkable greening trend due to vegetation restoration in recent decades. However, the precipitation response to greening remains unclear, and the hydrological effect of greening is controversial. Here, we revisited biophysical effects of greening on precipitation over the plateau during 2002–2015 using the state‐of‐the‐art water vapor tracer embedded in a regional coupled model. We find that greening can promote the growing season precipitation (0.45 mm·day−1), with 15% and 85% of the precipitation increment resulting from increases in the local evapotranspiration and the water vapor inflow from outside the plateau, respectively. As a consequence, the enhanced precipitation can compensate for the terrestrial water loss driven by the increased evapotranspiration, leading to a slight increase in the water yield. This study highlights the dominant role of the nonlocal effect in precipitation responses to greening in this region.

Multipole Excitations and Nonlocality in 1d Plasmonic Nanostructures.

Efficient simulation methods for taking nonlocal effects in nanostructures into account have been developed, but they are usually computationally expensive or provide little insight into underlying physics. A multipolar expansion approach, among others, holds promise to properly describe electromagnetic interactions in complex nanosystems. Conventionally, the electric dipole dominates in plasmonic nanostructures, while higher order multipoles, especially the magnetic dipole, electric quadrupole, magnetic quadrupole, and electric octopole, can be responsible for many optical phenomena. The higher order multipoles not only result in specific optical resonances, but they are also involved in the cross-multipole coupling, thus giving rise to new effects. In this work, we introduce a simple yet accurate simulation modeling technique, based on the transfer-matrix method, to compute higher-order nonlocal corrections to the effective permittivity of 1d plasmonic periodic nanostructures. In particular, we show how to specify the material parameters and the arrangement of the nanolayers in order to maximize or minimize various nonlocal corrections. The obtained results provide a framework for guiding and interpreting experiments, as well as for designing metamaterials with desired dielectric and optical properties.

The surface-boundary layer connection across spatial scales of irrigation-driven thermal heterogeneity: An integrated data and modeling study of the LIAISE field campaign

Irrigation in semi-arid regions induces thermal heterogeneity across a range of spatial scales that impacts the partitioning of energy at the surface, the development of the atmospheric boundary layer, and the bidirectional interactions between the atmosphere and the surface. In this analysis, we use data from the Land Surface Interactions with the Atmosphere in the Iberian Semi-Arid Environment (LIAISE) experiment combined with a coupled land–atmosphere model to understand the role of the scales of irrigation-induced, thermal heterogeneity on the surface fluxes and consequently, the development of the diurnal convective boundary layer. The surface heterogeneity is characterized by Bowen ratios that range from ∼0.01 in the irrigated areas to ∼30 in the non-irrigated areas; however, the observed boundary-layers dynamics in both locations are similar. In this analysis, we address the questions of how the surface fluxes impact the development of the boundary-layer dynamics and how the boundary layer influences the diurnal cycle of surface fluxes. To interpret the observations, we introduce a heterogeneity scaling scheme where length scales range from local scale (∼100 m) to regional scale (∼10 km) to investigate the role of scale on surface representation in numerical models and to address the discrepancy between surface observations and their representation in weather and climate models.We find that at the surface, both the available energy and its partitioning depend on spatial scale. The observed boundary-layer properties can be explained through the composite of surface fluxes at the regional scale. Surface fluxes at the local scales are unable to replicate the observed boundary layer — even when including large-scale contributions. We find that non-local boundary layer processes like advection are important for partitioning energy at the local scale. We explore the connection between surface fluxes and the development of the boundary layer and the potential non-local effects on boundary-layer development.

The temporal dynamics of nonlocal plasmonic nanoparticle under the ultrashort pulses

Modern plasmonics plays a crucial role in photonics and optics, and paves a way for a variety of emerging applications. Since the stationary behavior of plasmonic nanoparticles is quite well studied, the quantum-driven ultrafast response of ultra-small particles in specific electromagnetic regimes attract ever-increasing attentions nowadays. In this paper, we investigate the temporal dynamics of the plasmonic nanoparticles involving nonlocal effect under the illumination by an external ultrashort pulse. We find that the intensity of the corresponding dipole moment can be globally suppressed and the magnitude of the time-shift decreases with the increase of nonlocality. In addition, we observe large decay rate and small oscillation period when the nonlocality is taken into account for quite small duration time near (or below) the surface plasmon resonant frequencies. Further discussion reveals that the time-shift can be either positive or negative because of the emergence of abnormal dispersion relationship. These reshaping on dipole moment in time domain may be applicable in the modulation on the ultrashort signals of nanophotonic devices.

Slope Deflection Method in Nonlocal Axially Functionally Graded Tapered Beams

In this study, the slope deflection method was presented for structures made of small-scaled axially functionally graded beams with a variable cross section within the scope of nonlocal elasticity theory. The small-scale effect between individual atoms cannot be neglected when the structures are small in size. Therefore, the theory of nonlocal elasticity is used throughout. The stiffness coefficients and fixed-end moments are calculated using the method of initial values. With this method, the solution of the differential equation system is reduced to the solution of the linear equation system. The given transfer matrix is unique and the problem can be easily solved for any end condition and loading. In this problem, double integrals occur in terms of the transfer matrix. However, this form is not suitable for numerical calculations. With the help of Cauchy’s repeated integration formula, the transfer matrix is given in terms of single integrals. The analytical or numerical calculation of single integrals is easier than the numerical or analytical calculation of double integrals. It is demonstrated that the nonlocal effect plays an important role in the fixed-end moments of small-scaled beams.

Nonlocal correlation effects due to virtual spin-flip processes in itinerant electron ferromagnets

We present an ab initio method for electronic structure calculations, which accounts for the interaction of electrons and magnons in ferromagnets. While it is based on a many-body perturbation theory we approximate numerically complex quantities with quantities from time-dependent density functional theory. This results in a simple and affordable algorithm which allows us to consider more complex materials than those usually studied in this context ($3d$ ferromagnets) while still being able to account for the nonlocality of the self-energy. Furthermore, our approach allows for a relatively simple way to incorporate self-consistency. Our results are in a good agreement with experimental and theoretical findings for iron and nickel. Especially the experimental exchange splitting of nickel is predicted accurately within our theory. Additionally, we study the half-metallic ferromagnet NiMnSb concerning its nonquasiparticle states appearing in the band gap due to spin-flip excitations.

An analytical model for predicting equivalent elastic moduli of micro/nano-honeycombs with nonlocal effects

When the structural size of honeycomb enters micro/nano scale, the influence of nonlocal effects on the mechanical responses becomes non-negligible, which should be taken into account when evaluate the mechanical properties of micro/nano-honeycombs. To this end, a novel method for predicting the equivalent elastic moduli of micro/nano-honeycombs is proposed. In this method, the two-phase local/nonlocal model is introduced into the constitutive equations and the analytical solution of the equivalent moduli is derived according to the energy equivalent principle. It is illustrated by the numerical examples that the results of the present method are lower than those of the classical elasticity theory, which is consistent with the phenomena observed in the experiment, effectively showing the nonlocal effects. The magnitude of nonlocal effects can be influenced by the geometrical size of the honeycomb. The smaller the geometric size of the honeycomb is, the more significant the nonlocal effects are. With the increase of the geometrical size of honeycomb, the nonlocal effects gradually weaken, and the numerical values predicted by the present method gradually approach the equivalent moduli values of the macro-scale honeycombs. Hence the present method has a good universality that can be used in both macro and micro/nano scale honeycombs.

Blow-up solutions of a chemotaxis model with nonlocal effects

In this paper, we investigate the radially symmetric solutions to the following chemotaxis system with nonlocal term (0.1)ut=△u−∇⋅(u∇v)+μu1−∫Ωuκdx,x∈Ω,t>0,0=△v−m(t)+u,x∈Ω,t>0,(u,v)(x,0)=(u0(x),v0(x)),x∈Ω,where Ω≔BR(0) is a ball whose center is the origin, n≥3, μ>0 and m(t)=1|Ω|∫Ωu(x,t)dx. We show that for any m0>0, there exists a nonnegative initial data u0∈C1(Ω̄) with 1|Ω|∫Ωu0dx=m0 such that the corresponding solution of (0.1) blows up in finite time under the assumption 0<κ<min{2,n2}.

Local–nonlocal stress-driven model for multi-cracked nanobeams

Exact closed-form solutions for multi-cracked Euler–Bernoulli nanobeams are provided by proposing two equivalent approaches. The considered multi-cracked nanobeams are modeled with a well-posed local–nonlocal stress-driven model and contain an arbitrary number n of isolated damaged cross-sections. In order to simulate the damaged sections, it is assumed that the nanobeam bending flexibility contains n Dirac delta functions, with a Dirac delta located at each damaged section: this representation of cracked sections, already used in local problem, is adopted for the first time here in the local–nonlocal stress-driven model. The first approach providing closed-form solutions is based on the integral definition of the local–nonlocal stress-driven model, where the bending curvature is given by the superposition of the local and nonlocal phases, and the nonlocal phase is an integral convolution of the bending moment. This approach provides an integro-differential equation, which is solved by taking firstly the Laplace transform and then the anti-transform. In the second approach, it is shown that the integral definition of the stress-driven multi-cracked nanobeam model is equivalent to a differential equation together with suitable constitutive boundary conditions. This equation is solved by making use of Laplace transform again. The two approaches provide the same solution, with the second one resulting computationally faster. Interesting results show that a jump of the rotation at the damaged cross-sections occurs in local beam, but does not occur in pure nonlocal nanobeams (i.e. local phase is absent): contrary to the local elasticity theory, the bending curvature of pure nonlocal nanobeams has no singularity at damaged sections. The typical stiffness increase, due to the increase in nonlocal fraction of the mixture or to the increase in the length-scale parameter, also appears in multi-cracked nanobeams and this stiffening nonlocal effect is more pronounced in more constrained nanobeams.

Transformable Metasurfaces Enabled by Twisting Induced Nonlocality (Advanced Optical Materials 8/2023)

In article number 2202363, Hongsheng Chen, Zuojia Wang, and co-workers reveal the nonlocal effect in twisted electric dipoles and demonstrate its capability of non-volatile transformation on scattering. The proposed polarizability circles theory can quantitatively analyze the nonlocal effect in this metasurface, indicating judicious spatial and spectral selectivity. The established wireless-controlled prototype verifies the reconfigurability for continuous electromagnetic response manipulation and beam steering.

Scattering of plane SH waves by a circular tunnel in nonlocal fractional-order viscoelastic half-space

This paper proposed a complex function solution to the scattering of plane SH waves by circular tunnels in nonlocal fractional-order viscoelastic half-space. The nonlocal theory and the fractional order viscoelastic model are used to describe the viscoelastic properties and nonlocal effects of the soil, respectively. The basic equations are expressed in the complex domain based on the theory of complex functions, and then the scattering displacement potential function of plane SH waves is obtained using the wave function expansion method. The correctness of the presented method is verified by degrading it to the classical local elastic solution. Finally, the effects of non-local parameters, soil viscosity and fractional order on the distribution of dynamic stress concentration factors inside the tunnel were analyzed, and it was found that they had significant effects on the dynamic stress concentration factors under high-frequency wave incidence.

Analytical solutions of peridynamic equations. Part II: Elastic wave propagation

We use the separation of variables technique to construct analytical solutions for peridynamic models of dynamic elasticity. We show that, similar to the case of peridynamic models for transient diffusion, infinite series nonlocal solutions for peridynamic elasticity can be obtained directly from the solutions of the corresponding classical model by inserting “peridynamic/nonlocal factors” in the time-exponential part of the solution. The analytical solutions show that wave dispersion, caused by nonlocality, is contained in the horizon-dependent nonlocal factor. We obtain formulas for wave dispersion and group velocities for 1D and 2D peridynamic elastic wave propagation with three commonly-used peridynamic kernels. We observe interesting complexity in nonlocal solutions, generated by nonlocal wave dispersion, and “proportional” to the size of the nonlocal interaction region. Different from the diffusion case, as time goes to infinity, the nonlocal solution for elasticity does not converge to the classical one for a fixed horizon size, meaning that nonlocal effects persist in time. We solve several examples of wave propagation with Dirichlet boundary conditions and smooth or discontinuous initial conditions and compare these analytical solutions with those corresponding to the classical model, which is seen as a particular case of the PD model for horizon equal to zero. Interestingly, we find that in PD solutions, initial discontinuities in space persist at the same location, in time. While most of the analytical solutions we present here are formal, for some of the cases, we are able to prove uniform convergence of the series solutions. This work is the first presentation of a systematic analytical treatment of peridynamic problems in 2D finite domains.

Kinetic theory of the nonlocal electrodynamic response in anisotropic metals: Skin effect in 2D systems

The electrodynamic response of ultrapure materials at low temperatures becomes spatially nonlocal. This nonlocality gives rise to phenomena such as hydrodynamic flow in transport and the anomalous skin effect in optics. In systems characterized by an anisotropic electronic dispersion, the nonlocal dynamics becomes dependent on the relative orientation of the sample with respect to the applied field, in ways that go beyond the usual, homogeneous response. Such orientational dependence should manifest itself not only in transport experiments, as recently observed, but also in optical spectroscopy. In this paper, we develop a kinetic theory for the distribution function and the transverse conductivity of two- and three-dimensional Fermi systems with anisotropic electronic dispersion. By expanding the collision integral into the eigenbasis of a collision operator, we include momentum-relaxing scattering as well as momentum-conserving collisions. We examine the isotropic 2D case as a reference, as well as anisotropic hexagonal and square Fermi-surface shapes. We apply our theory to the quantitative calculation of the skin depth and the surface impedance, in all regimes of skin effect. We find qualitative differences between the frequency dependence of the impedance in isotropic and anisotropic systems. Such differences are shown to persist even for more complex 2D Fermi surfaces, including the ``supercircle'' geometry and an experimental parametrization for ${\mathrm{PdCoO}}_{2}$, which deviate from an ideal polygonal shape. We study the orientational dependence of skin effect due to Fermi-surface anisotropy, thus providing guidance for the experimental study of nonlocal optical effects.