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This article introduces a, possibly damage‐enhanced, pressure‐dependent‐based incremental‐secant mean‐field homogenization (MFH) scheme for two‐phase composites. The incremental‐secant formulation consists on a fictitious unloading of the material up to a stress‐free state, in which a residual stress is attained in its phases. Then the secant method is performed in order to compute the mean stress fields of each phase. One of the main advantages of this method is the natural isotropicity of the secant tensors that allows defining the linear‐comparison‐composite (LCC). In this work, we show that this isotropic nature is preserved for a non‐associated pressure dependent plastic flow, making possible the direct definition of the LCC. This model is thus able to represent the physics of real polymeric composites. The MFH scheme is then verified by testing its prediction capabilities in several cases, including cyclic and nonproportional loading involving perfectly elastic phases, elasto‐plastic and damage‐enhanced elasto‐plastic phases in random representative volume elements (RVE) of uni‐directional (UD) composites and of composites reinforced with spherical inclusions. [ABSTRACT FROM AUTHOR]

• Modeling multi-physical behaviors of a piezoelectric nanoribbon used as a self-powered component in medical nanorobots. • Quantifying both nonlocal and strain gradient effects where gradient types of normal strain and bending moment are defined. • Demonstrating coupling phenomena of internal parameters but independence between internal scale and external parameters. This paper is contributed to the studies of dynamic behaviors of a piezoelectric nanoribbon subjected to thermal-mechanical-electrical fields that is used as an approximate model for the self-powered component in medical nanorobots. Both the nonlocal and strain gradient effects are taken into account, and a gradient type of normal strain is introduced and applied instead of the classical normal strain. By combining the theoretical constitutive relations with nonlocal strain gradient piezoelectric equations, the governing equations and boundary conditions under the nonlocal strain gradient theory are derived, respectively, by means of Hamilton's principle and a new definition of nonlocal strain gradient bending moment. The differential quadrature method is used to solve the governing equations numerically and the influences of internal characteristic scales and external physical parameters on dynamic behaviors are discussed. It is demonstrated that the stiffness weakening and strengthening are, respectively caused by the nonlocal and strain gradient effects. The classical results are recovered in case of the same magnitudes for the nonlocal parameter and strain gradient characteristic parameter. There is a coupling between two internal characteristic scales and the peak value of strain gradient characteristic parameter may exist, but effects of internal characteristic parameters and external physical parameters on dynamic behaviors are independent. Additionally, the self-powered nanoribbon may lose its stability with a certain critical external parameter. The work could be useful for the design and realization of self-powered nanostructures. [ABSTRACT FROM AUTHOR]

This paper is devoted to study the dynamical behavior of a Belousov–Zhabotinsky reaction–diffusion system with nonlocal effect and find the essential difference between it and classical equations. First, we prove the existence of the solution by using the comparison principle and constructing monotonic sequences. Furthermore, the uniqueness is given by using fundamental solution and Gronwall's inequality. Then we obtain the uniform boundedness of the solution by means of auxiliary function. Finally, we investigate the states of the solution as the parameters change and show some new and interesting phenomena about nonlocal Belousov–Zhabotinsky reaction–diffusion system by using stability analysis and numerical simulations. [ABSTRACT FROM AUTHOR]

This study investigates thermal effect on free vibration of cracked single-walled carbon nanotubes (SWCNTs) embedded in an elastic medium under different boundary conditions. The nonlocal Euler–Bernoulli beam equations are derived using the Hamiltonian principle. The interaction of the elastic medium and the SWCNT is modeled using Winkler-type foundation. The effect of low and high temperatures, crack severity, crack position, scale coefficient, and elastic medium are investigated. The results show that the temperature at some cases have the significant effects on the frequencies. The elastic medium has a great influence on the frequencies of cracked and non-cracked beams at any temperature. [ABSTRACT FROM AUTHOR]

The aim of this article is to critique the contemporary scientific reduction of mind to brain, a dogma which is shown to be philosophically unsound and empirically unproven. The world of physical phenomena is understood to be encompassed by other subtle transphysical worlds accessed after death of the physical body., (Copyright © 2024. Published by Elsevier Inc.)

This paper concerns a nonhomogeneous singular fractional order system, with two frictional damping terms. This system can be considered as a generalization of the so-called Timoshenko system. Results on the existence, uniqueness, and continuous dependence on the solution were obtained via an energy approach, which mainly relies on a priori bounds and density arguments. The approach relies on functional analysis tools and operator theory. Very few results concerning the well-posedness of fractional order Timoshenko systems can be found in the literature. Our results generalize and improve the previous ones and significantly boost the development of the used method.

In this paper, we are dedicated to studying the global dynamics of a nonlocal predator–prey model with double mutation. First, by defining a pair of upper and lower solutions, we build a new comparison principle. Furthermore, based on the new comparison principle, we get the existence of the solutions by constructing monotone iterative sequences. Finally, using the quasi-fundamental solution, Gronwall's inequality and auxiliary functions, the uniqueness and uniform boundedness of the solutions are given. It is worth noting that this paper is the first to introduce the double mutation into the system and obtain the well-posedness and the uniform boundedness of the solutions by more detailed analysis and estimation. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study plane wave propagation in a homogeneous isotropic nonlocal magneto-thermoelastic medium under the effect of Hall current applied to multi-dual-phase lag heat transfer. For a 2-D assumed model, three types of coupled longitudinal waves (quasi-longitudinal, quasi-transverse and quasi-thermal) exist. The wave characteristics, such as phase velocity, specific loss, attenuation coefficients, energy ratios, penetration depth and amplitude ratios of transmitted and reflected waves, are computed numerically and depicted graphically. The energy ratios have been calculated by taking the ratio of the share of energy in the different scattered waves to the incident wave. The impact of nonlocal parameter and Hall current parameter has been represented graphically by taking different values. Some particular cases have also been discussed. [ABSTRACT FROM AUTHOR]

In this paper the authors develop the governing equations for a finite element model of micro-cracking based on a novel approach, eschewing differential equations and continuum mechanics. Instead of first stating the continuum balance laws and constitutive relations followed by discretization, the body is discretized first and then the equations of equilibrium are directly stated for the discretized body. It is shown that, as a result, the balance laws and constitutive relations can be entirely stated in terms of edge forces and lengths rather than strains. Furthermore, by ensuring that microcracks always propagate along the dual mesh which represents the possible fracture microplanes in the element, the need for creating additional nodes, gap elements or cohesive zones is avoided. Finally, the notion of the survival probability of a fracture microplane is introduced and the transition probability evolution is described by using probabilistic notions from population models. Thus the resulting governing equations can be solved by a conventional elastic predictor, followed by a nonlocal fracture corrector, making this convenient to augment conventional elements with fracture abilities. [ABSTRACT FROM AUTHOR]

Torsional surface wave propagation in an elastic half-space with void pores is investigated within the context of Eringen's nonlocal theory of elasticity. Three types of torsional surface waves are found to travel with distinct speeds, which are frequency dependent and hence dispersive in nature. All the three kind of torsional surface waves are affected by the presence of non-locality present in the medium, where as torsional surface wave of second and third kind also depend on the presence of voids in the medium. To attain more clarity about the behavior of all the three kind of waves, results are simulated numerically. The dispersion curves are plotted and the effect of the presence of voids and non-locality is noticed and analyzed. [ABSTRACT FROM AUTHOR]

In this article, we formulate and implement a computational multiphase periporomechanics paradigm for unguided fracturing in unsaturated porous media assuming passive pore air pressure. The same governing equation for the solid phase applies on and off cracks. Crack formation in this framework is autonomous, requiring no prior estimates of crack topology. As a new contribution, an energy‐based criterion for arbitrary crack formation is formulated using the peridynamic effective force state for unsaturated porous media. Unsaturated fluid flow in the fracture space is modeled in a simplified way in line with the nonlocal formulation of unsaturated fluid flow in the bulk. The formulated unsaturated fracturing periporomechanics is numerically implemented through an implicit fractional step algorithm in time and a two‐phase mixed meshless method in space. The two‐stage operator split converts the coupled periporomechanics problem into an undrained deformation and fracture problem and an unsaturated fluid flow in the deformed skeleton configuration. Numerical simulations of in‐plane open and shear cracking are conducted to validate the accuracy and robustness of the fracturing unsaturated periporomechanics model. Then numerical examples of wing cracking and nonplanar cracking in unsaturated soil specimens are presented to demonstrate the efficacy of the proposed multiphase periporomechanics paradigm for unguided cracking in unsaturated porous media. [ABSTRACT FROM AUTHOR]

We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in the determination of the potential by the exterior Dirichlet-to-Neumann map. The main tools are the qualitative and quantitative unique continuation properties for the fractional Laplacian. For the stability, we also prove that the log type stability estimate is optimal. The log type estimate shows the striking difference between the inverse problems for the fractional and classical wave equations in the stability issue. The results hold for any spatial dimension n ∈ ℕ. [ABSTRACT FROM AUTHOR]

Neuronal dynamics is driven by externally imposed or internally generated random excitations/noise, and is often described by systems of random or stochastic ordinary differential equations. Such systems admit a distribution of solutions, which is (partially) characterized by the single-time joint probability density function (PDF) of system states. It can be used to calculate such information-theoretic quantities as the mutual information between the stochastic stimulus and various internal states of the neuron (e.g., membrane potential), as well as various spiking statistics. When random excitations are modeled as Gaussian white noise, the joint PDF of neuron states satisfies exactly a Fokker-Planck equation. However, most biologically plausible noise sources are correlated (colored). In this case, the resulting PDF equations require a closure approximation. We propose two methods for closing such equations: a modified nonlocal large-eddy-diffusivity closure and a data-driven closure relying on sparse regression to learn relevant features. The closures are tested for the stochastic non-spiking leaky integrate-and-fire and FitzHugh-Nagumo (FHN) neurons driven by sine-Wiener noise. Mutual information and total correlation between the random stimulus and the internal states of the neuron are calculated for the FHN neuron. [ABSTRACT FROM AUTHOR]

In this paper, we prove some existence results of solutions for a class of nonlocal initial value problem for nonlinear fractional hybrid implicit differential equations under generalized Hilfer fractional derivative. The result is based on a fixed point theorem on Banach algebras. Further, examples are provided to illustrate our results.

• A well-posed stress-driven nonlocal model for sensors with multiple eccentric masses. • New results on frequency shifts and mode shapes of the first four vibrational modes. • The effect of the eccentricity of attached masses on frequencies is studied. • Studying the inverse problem of detecting the location and mass of attached particles. Studying the dynamics of small-scale beams with attached particles is crucial for sensing applications in various fields, such as bioscience, material science, energy storage devices, and environmental monitoring. Here, a stress-driven nonlocal model is presented for the free transverse vibration of small-scale beams carrying multiple masses taking into account the eccentricity of the masses relative to the beam axis. The results show excellent agreement with the experimental and numerical data in the literature. New insights into the frequency shifts and mode shapes of the first four vibrational modes of stress-driven nonlocal beams with up to three attached particles are presented. The study investigates the inverse problem of detecting the location and mass of an attached particle based on natural frequency shifts. The knowledge acquired from the present study provides valuable guidance for the design and analysis of ultrasensitive mechanical mass sensors. [ABSTRACT FROM AUTHOR]

• We proposed the mechanical model predicting microstructure-induced non-uniform deformation (micro-NUD). • Parameters quantifying micro-NUD are determined using experimentally measured strain field. • Nonlocal finite element model established could predict the strain field of the fine and coarse grain specimens. Engineering materials have a heterogeneous microstructure that induces non-uniform deformations (NUDs) even under uniform stress. Therefore, the development of NUDs in heterogeneous materials under a macroscopically non-uniform stress is characterized by the interactions between micro- and macroscopic NUDs. In this study, we attempt to directly describe microscopic NUDs by introducing a constitutive equation for the strain field. Using polycrystalline metal, which is a well-known heterogeneous material, we performed the uniaxial tensile tests on specimens with curved gauge sections. During modeling, the constitutive equation without nonlocal effect was first fitted based on the distribution of the local equivalent stress and strain. The strain calculated using the fitted equation was regarded as the strain for the homogeneous material, whereas the strain deviating from the fitted equation was assumed to be induced by the microscopic heterogeneity of the material. The respective strains were represented using different constitutive models, and the parameters employed in the models were fitted separately using the experimentally measured strain field. The plastic compliance gradient was employed as a material parameter quantifying the microscopic NUDs. Subsequently, a multiaxial elastoplastic nonlocal constitutive equation was formulated based on the nonlocally extended J 2 flow theory. Finite element method simulations introducing the proposed nonlocal effect indicated that a scale-dependent NUD characterized by the interactions between micro- and macro-NUDs could be represented using the proposed model. Furthermore, the proposed model could predict the experimentally observed strain field characterized by a polycrystalline microstructure, such as the dispersion of the strain concentration at the curved gauge section and the appearance of NUDs even under uniform stress. [Display omitted] [ABSTRACT FROM AUTHOR]

• Alternative proof of variational consistency of the wryness measure is furnished. • A finite deformation micropolar peridynamics (PD) theory is developed. • A new bond breaking criterion is proposed for PD micropolar materials. • Quasi-static and dynamic simulations reveal the effect of micropolarity on the response. This paper concerns developments in both classical and peridynamic (PD) finite deformation micropolar elasticity theory. The first part presents an alternative proof of a theorem that demonstrates variational consistency of the wryness measure in classical finite deformation micropolar elasticity which is one of the novel contributions of this work. The linearized version of the proposed wryness measure is compared with the wryness measure of small deformation micropolar elasticity. In the second part of this work, a finite deformation micropolar PD theory is presented. After proposing an additional integro-differential equation along with the standard PD equation of motion, the global balance of angular momentum is proved to be satisfied. The balance of virtual work is derived for the micropolar PD theory. Next, constitutive correspondence approach is used to relate PD force and moment states with their classical counterparts. The nonlocal versions of the strain and the proposed wryness measure are used in the constitutive correspondence. The constitutive equations of the classical micropolar theory are presented and how they can be incorporated in PD framework is discussed. We introduce a new bond breaking criterion for PD micropolar materials based on critical stretch and critical relative rotation. Quasi-static numerical simulations on deformations of plate with a hole and fracture of a double notched sheet are presented. Dynamic simulations concern wave propagation through a solid specimen and plate with a hole. Validation of the simulation results with the finite element solutions, boundary element solutions, and experimental observations demonstrate the potential of our approach. [Display omitted] [ABSTRACT FROM AUTHOR]

This article considers an inverse problem of time fractional parabolic partial differential equations with the nonlocal boundary condition. Dirichlet-measured output data are used to distinguish the unknown coefficient. A finite difference scheme is constructed and a numerical approximation is made. Examples and numerical experiments, such as man-made noise, are provided to show the stability and efficiency of this numerical method. [ABSTRACT FROM AUTHOR]

The present paper deals with Rayleigh wave propagation in a homogeneous isotropic nonlocal magneto-thermoelastic solid with hall current and rotation. The considered thermoelastic solid is subjected to multi-dual-phase lag heat transfer. The Secular equations of Rayleigh waves are derived mathematically at the stress-free and thermally insulated boundaries. The values of stress components, temperature change, phase velocity, attenuation coefficient, penetration depth and specific loss have been computed numerically and depicted graphically. The effects of hall current and nonlocal parameter have been depicted on the various wave quantities. Some particular cases have also been deduced from the present investigation. [ABSTRACT FROM AUTHOR]

A nonlocal Dynamic Stiffness Model (DSM) for free vibration analysis of Functionally Graded Material (FGM) stepped nanostructures based on the Nonlocal Elastic Theory (NET) is proposed. An exact solution to the equation of motion of a nanobeam element according to the Timoshenko beam theory, NET, and taking into account position of the neutral axis is constructed. Nondimensional frequencies and mode shapes of complete FGM stepped nanostructures are easily obtained using the nonlocal DSM. Numerical results are presented to show significance of the material distribution profile, nonlocal effect, and boundary conditions on free vibration of nanostructures. [ABSTRACT FROM AUTHOR]

In this paper, the Fokas–Lenells (FL) equations are investigated via bilinear approach. We bilinearize the unreduced FL system, derive double Wronskian solutions, and then, by means of a reduction technique we obtain variety of solutions of the reduced equations. This enables us to have a full profile of solutions of the classical and nonlocal FL equations. Some obtained solutions are illustrated based on asymptotic analysis. As a notable new result, we obtain solutions to the FL equation, which are related to real discrete eigenvalues and not reported before in the analytic approaches. These solutions behave like (multi)periodic waves or solitary waves with algebraic decay. In addition, we also obtain solutions to the two‐dimensional massive Thirring model from those of the FL equation. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of nonlocal equations where the convolution kernel is given by a Bessel potential symbol of order α for α > 1. Based on the properties of the convolution operator, we apply a global bifurcation technique to show the existence of a highest, even, 2 π -periodic traveling-wave solution. The regularity of this wave is proved to be exactly Lipschitz. [ABSTRACT FROM AUTHOR]

Hyperspectral–multispectral image (HSI-MSI) fusion relies on a robust degradation model and data prior, where the former describes the degeneration of HSI in the spectral and spatial domains, and the latter reveals the latent statistics of the expected high-resolution (HR) HSI. In practice, the degradation model is often unknown, and the data prior is usually too complicated to be expressed analytically. In this study, we propose a variational network for HSI-MSI fusion (VaFuNet), in which the degradation model and data prior are implicitly represented by a deep learning network and jointly learned from the training data. A variational fusion model regularized by deep prior is first proposed, and then, it is optimized via a half-quadratic splitting and unfolded into a deep network. The deep prior is implicitly represented by a proximity operator. Due to the structural self-similarity, HSI possesses structural recurrences across different scales. To exploit such nonlocal prior and enhance the representability of network, we also propose a multiscale nonlocal attention and embed it into the deep prior proximity. The degradation model and deep prior proximity are jointly learned via end-to-end training. Experimental results on simulated and real-life HSI datasets demonstrate the effectiveness of the proposed VaFuNet HSI-MSI fusion method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the lateral vibration of fully clamped beam-like microstructures subjected to an external transverse harmonic excitation. Eringen's nonlocal theory is applied, and the viscoelasticity of materials is considered. Hence, the small-scale effect and viscoelastic properties are adopted in the higher-order mathematical model. The classical stress and classical bending moments in mechanics of materials are unavailable when modeling a microstructure, and, accordingly, they are substituted for the corresponding effective nonlocal quantities proposed in the nonlocal stress theory. Owing to an axial elongation, the nonlinear partial differential equation that governs the lateral motion of beam-like viscoelastic microstructures is derived using a geometric, kinematical, and dynamic analysis. In the next step, the ordinary differential equations are obtained, and the time-dependent lateral displacement is determined via a perturbation method. The effects of external excitation amplitude on excited vibration are presented, and the relations between the nonlocal parameter, viscoelastic damping, detuning parameter, and the forced amplitude are discussed. Some dynamic phenomena in the excited vibration are revealed, and these have reference significance to the dynamic design and optimization of beam-like viscoelastic microstructures. [ABSTRACT FROM AUTHOR]

Based on one recent abstract critical point result for differentiable and parametric functionals which was recently proved by Ricceri, we establish the existence of three weak solutions for a class of degenerate nonlocal singular sub-linear problems when the nonlinear term admits some hypotheses on the behavior at infinitely or perturbation property. [ABSTRACT FROM AUTHOR]

Linear theory of nonlocal elastic material with double porosity structure is developed within the context of Eringen's theory of nonlocal elasticity. Energy density function is constructed from the basic variables, and then, constitutive relations are derived, which are used to develop the field equations for an isotropic homogeneous nonlocal elastic material with double porosity. It is found that there may exist four basic plane waves in an unbounded medium consisting of three sets of coupled dilatational waves and an independent transverse wave. The major impact of the presence of nonlocality in the medium is that all the four propagating plane waves face cut-off frequencies. The coupled dilatational waves are dispersive and attenuating in nature, while the transverse wave is dispersive and non-attenuating in nature below their respective cut-off frequencies and beyond which they disappear. It is also noticed that coupled waves are affected by the presence of voids, while the transverse wave is independent of the presence of voids in the medium. In the case of non-Voigt model, the coupled dilatational waves face critical frequencies in the low-frequency range. The effect of nonlocality and voids is shown graphically on the dispersion curve of the plane waves for a particular model. [ABSTRACT FROM AUTHOR]

Actively tunable and reconfigurable wavefront shaping by optical metasurfaces poses a significant technical challenge often requiring unconventional materials engineering and nanofabrication. Most wavefront-shaping metasurfaces can be considered “local” in that their operation depends on the responses of individual meta-units. In contrast, “nonlocal” metasurfaces function based on the modes supported by many adjacent meta-units, resulting in sharp spectral features but typically no spatial control of the outgoing wavefront. Recently, nonlocal metasurfaces based on quasi-bound states in the continuum have been shown to produce designer wavefronts only across the narrow bandwidth of the supported Fano resonance. Here, we leverage the enhanced light-matter interactions associated with sharp Fano resonances to explore the active modulation of optical spectra and wavefronts by refractive-index tuning and mechanical stretching. We experimentally demonstrate proof-of-principle thermo-optically tuned nonlocal metasurfaces made of silicon and numerically demonstrate nonlocal metasurfaces that thermo-optically switch between distinct wavefront shapes. This meta-optics platform for thermally reconfigurable wavefront shaping requires neither unusual materials and fabrication nor active control of individual meta-units.

Abstract This paper is concerned with the following nonlocal fourth-order elliptic problem: { Δ 2 u − m ( ∫ Ω | ∇ u | 2 d x ) Δ u = a ( x ) | u | s − 2 u + f ( x , u ) , x ∈ Ω , u = Δ u = 0 , x ∈ ∂ Ω , $$\begin{aligned} \textstyle\begin{cases} \Delta ^{2}u-m(\int _{\varOmega } \vert \nabla u \vert ^{2} \,dx)\Delta u=a(x) \vert u \vert ^{s-2}u+f(x,u), \quad x\in \varOmega , \\ u=\Delta u=0,\quad x\in \partial \varOmega , \end{cases}\displaystyle \end{aligned}$$ by using the mountain pass theorem, the least action principle, and the Ekeland variational principle, the existence and multiplicity results are obtained.

We study positive solutions to the fractional Lane-Emden system

Under voluntary vaccination, a critical role in shaping the level and trends of vaccine uptake is played by the type and structure of information that is received and used by parents of children eligible for vaccination. In this article we investigate the feedbacks of spatial mobility and the spatial structure of information on vaccination dynamics, by extending to a continuous spatially structured setting existing behavioral epidemiology models for the impact of vaccine adverse events (VAEs) on vaccination choices. We considered the simplest spatial setting, namely classical 'Fickian' diffusion, and focused on the noteworthy case where the infection is absent. This scenario mimics the important case of a population where a previously endemic vaccine preventable infection was successfully eliminated, but the re-emergence of the disease must be prevented. This is, for example, the case of poliomyelitis in most countries worldwide. In such a situation, the dynamics of VAEs and of the related information arguably become the key determinant of vaccination decision and of collective coverage. In relation to this 'information issue', we compared the effects of three main cases: (ⅰ) purely local information, where agents react only to locally occurred events; (ⅱ) a mix of purely local and global, country-wide, information due e.g., to country-wide media and the internet; (ⅲ) a mix of local and non-local information. By representing these different information options through a range of different spatial information kernels, we investigated: the presence and stability of space-homogeneous, nontrivial, behavior-induced equilibria; the existence of bifurcations; the existence of classical and generalized traveling waves; and the effects of awareness campaigns enacted by the Public Health System to sustain vaccine uptake. Finally, we analyzed some analogies and differences between our models and those of the Theory of Innovation Diffusion.

In this article, we discuss the existence of solutions of a fractional boundary value problem of order m ∈ (1, 2], with nonlocal non-separated type integral multipoint boundary conditions. Shaefer type and Krasnoselskii’s fixed point theorems are used to prove existence results for the given problem. To establish the uniqueness of solutions Banach contraction principle is used. The criteria for HyersUlam stability of the given boundary value problem is also discussed. Some examples are included for the illustration of our results.

We discuss in this note the stickiness phenomena for nonlocal minimal surfaces. Classical minimal surfaces in convex domains do not stick to the boundary of the domain, hence examples of stickiness can be obtained only by removing the assumption of convexity. On the other hand, in the nonlocal framework, stickiness is ''generic''. We provide various examples from the literature, and focus on the case of complete stickiness in highly nonlocal regimes.

Nonlocal metasurfaces, exemplified by resonant waveguide gratings (RWGs), spatially and angularly configure optical wavefronts through narrow-band resonant modes, unlike the broad-band and broad-angle responses of local metasurfaces. However, forward design techniques for RWGs remain constrained at lower efficiency. Here, we present a topology-optimized metasurface resonant waveguide grating (MRWG) composed of titanium dioxide on a glass substrate capable of operating simultaneously at red, yellow, green, and blue wavelengths. Through adjoint-based topology optimization, while considering nonlocal effects, we significantly enhance its diffraction efficiency, achieving numerical efficiencies up to 78% and Q -factors as high as 1362. Experimentally, we demonstrated efficiencies of up to 59% with a Q -factor of 93. Additionally, we applied our topology-optimized metasurface to color selectivity, producing vivid colors at 4 narrow-band wavelengths. Our investigation represents a significant advancement in metasurface technology, with potential applications in see-through optical combiners and augmented reality platforms.

This paper is devoted to studying the Cauchy problem corresponding to the nonlocal bistable reaction diffusion equation. It is the first attempt to use the method of comparison principle to study the well-posedness for the nonlocal bistable reaction-diffusion equation. We show that the problem has a unique solution for any non-negative bounded initial value by using Gronwall's inequality. Moreover, the boundedness of the solution is obtained by means of the auxiliary problem. Finally, in the case that the initial data with compactly supported, we analyze the asymptotic behavior of the solution. [ABSTRACT FROM AUTHOR]

In this article we formulate a stable computational nonlocal poromechanics model for dynamic analysis of saturated porous media. As a novelty, the stabilization formulation eliminates zero‐energy modes associated with the original multiphase correspondence constitutive models in the coupled nonlocal poromechanics model. The two‐phase stabilization scheme is formulated based on an energy method that incorporates inhomogeneous solid deformation and fluid flow. In this method, the nonlocal formulations of skeleton strain energy and fluid flow dissipation energy equate to their local formulations. The stable coupled nonlocal poromechanics model is solved for dynamic analysis by an implicit time integration scheme. As a new contribution, we validate the coupled stabilization formulation by comparing numerical results with analytical and finite element solutions for one‐dimensional and two‐dimensional dynamic problems in saturated porous media. Numerical examples of dynamic strain localization in saturated porous media are presented to demonstrate the efficacy of the stable coupled poromechanics framework for localized failure under dynamic loads. [ABSTRACT FROM AUTHOR]

This work is concerned with the reflection and transmission of quasi-longitudinal displacement wave incident at an imperfect interface between two nonlocal orthotropic micropolar half-spaces. The linear spring model is used to describe the imperfection of bonding behavior at the interface. Reflection, transmission coefficients and energy ratios of waves have been derived analytically for when a longitudinal displacement wave strikes for both imperfect and perfect interfaces. Finally, numerical examples are provided to show the effect of the imperfect interface, nonlocal parameter and incident angle on the reflection and transmission coefficients. [ABSTRACT FROM AUTHOR]

Reflection behavior of a set of coupled longitudinal/transverse waves incident obliquely at the flat boundary surface of a nonlocal micropolar thermoelastic half-space containing voids is investigated. Appropriate boundary conditions are setup for mechanically stress-free and thermally insulated boundary surface of the half-space. The equations yielding the reflection coefficients and the expressions of corresponding energy ratios of various reflected waves are presented. The nature of dependence of the reflection coefficients and their corresponding energy ratios against the angle of incidence is studied numerically for a specific model. Effect of several parameters on the reflection coefficients as well as on the corresponding energy ratios is noticed and depicted graphically. It is found that the sum of the energy ratios is approximately equal to unity at each angle of incidence. Some earlier known results are also recovered as special cases of the present formulation. [ABSTRACT FROM AUTHOR]

In this paper, we establish a scale invariant Harnack inequality for the fractional powers of parabolic operators (∂ t − ℒ) s , 0 < s < 1 , where ℒ is the infinitesimal generator of a class of symmetric semigroups. As a by-product, we also obtain a similar result for the nonlocal operators − ℒ s . Our focus is on non-Euclidean situations. [ABSTRACT FROM AUTHOR]

This research work studies the effect of variable thermal conductivity on transversely isotropic thermoelastic (TIT) homogeneous nonlocal clamped-free beam. The beam undergoes forced vibrations due to two types of heat sources i.e. exponential time-varying and time-harmonic load. The mathematical model has been formed for a 2-D problem using a heat equation with two temperature (2T) involving memory-dependent derivatives (MDD) and Euler Bernoulli beam theory (EBBT). Laplace transforms are used to solve the problem. The dimensionless expressions for a thermal moment, axial stress, lateral deflection, and temperature change are calculated for these two types of forced vibrations. MATLAB software is used for programming and numerical data for cobalt nanobeam has been considered. The influence of variable thermal conductivity and kernel function of MDD has been depicted graphically on the physical quantities such as temperature change, lateral deflection, axial stress thermal moment, for the forced vibrations. Specific cases have also been mentioned.