Nonlocal Parameter Research Articles

Detecting hidden order in fractional Chern insulators

Topological phase transitions go beyond Ginzburg and Landau's paradigm of spontaneous symmetry breaking and occur without an associated local order parameter. Instead, such transitions can be characterized by the emergence of nonlocal order parameters, which require measurements on extensively many particles simultaneously—an impossible venture in real materials. On the other hand, quantum simulators have demonstrated such measurements, making them prime candidates for experimental confirmation of nonlocal topological order. Here, building upon the recent advances in preparing few-particle fractional Chern insulators using ultracold atoms and photons, we propose a realistic scheme for detecting the hidden off-diagonal long-range order (HODLRO) characterizing Laughlin states. Furthermore, we demonstrate the existence of this hidden order in fractional Chern insulators, specifically for the ν=1/2-Laughlin state in the isotropic Hofstadter-Bose-Hubbard model. This is achieved by large-scale numerical density matrix renormalization group (DMRG) simulations based on matrix product states, for which we formulate an efficient sampling procedure providing direct access to HODLRO in close analogy to the proposed experimental scheme. We confirm the characteristic power-law scaling of HODLRO, with an exponent 1/ν=2, and show that its detection requires only a few thousand snapshots. This makes our scheme realistically achievable with current technology and paves the way for further analysis of nonlocal topological orders, e.g., in topological states with non-Abelian anyonic excitations. Published by the American Physical Society 2024

Size-dependent effect on the interaction of surface waves in micropolar thermoelastic medium with dual pore connectivity

This research tackles a critical knowledge gap in Rayleigh surface wave propagation. It offers a comprehensive analysis that surpasses previous limitations. A size-dependent micropolar medium with unique void distributions and thermal effects is considered in this work. The constitutive relations and equations of motion for a nonlocal micropolar thermoelastic medium with double voids (MTMWDV) have been established by using Eringen’s nonlocal elasticity theory. Employing the three-phase-lag thermoelasticity theory (TPLTE), the study utilizes a wave-mode method to derive analytical solutions for Rayleigh waves in a nonlocal MTMWDV. To gain a comprehensive understanding of wave behavior, we solve the characteristic equation and analyze its roots, applying a filter based on the surface wave decay condition. A medium with stress-free and isothermal boundaries is explored through computational simulations to determine the attenuation coefficient and phase velocity. Furthermore, particle motion analysis is conducted to complement the analytical and computational approaches. Moreover, the influence of the nonlocal parameter and various thermoelastic models on these wave phenomena is investigated. The validity of the current mathematical model is confirmed through the derivation of particular scenarios.

Analysis to the dynamic response of a functionally graded spherical microshell in consideration of fractional-order dual-phase-lag heat conduction and nonlocal effect

Functionally graded materials (FGMs) stand as one of the most representative composite materials due to the superior thermal resistance in non-isothermal environment. On another front, the applicability of integer-order heat conduction models is increasingly questionable because the heat transfer shares the history-dependent property at time microscale. It is noted that the small-scale effect of elastic deformation has become significant due to the development of micro-devices. To capture the small-scale effect of elastic deformation and the memory-dependent effect of heat conduction in the FGM microstructures, as a first attempt, the present study focuses on developing a thermoelastic model by incorporating the fractional-order dual-phase-lag (FODPL) heat conduction model and the Eringen’s nonlocal model. Moreover, the extension of the Caputo definition, i.e., the Tempered-Caputo (TC) definition of fractional derivative ruling out singular kernel is adopted to depict the memory-dependent effect of the heat conduction. Then, the modified model is used to investigating the dynamic response of a FGM spherical microshell subjected to a sinusoidal thermal-mechanical loading. The corresponding governing equations are formulated and then solved by Laplace transform techniques. Some parametric results are demonstrated to display the influences of the fractional-order parameter, the nonlocal parameter and the power-law index on the considered physical quantities.

Temperature-dependent thermal buckling and free vibration behavior of smart sandwich nanoplates with auxetic core and magneto-electro-elastic face layers

This article addresses the thermomechanical thermal buckling and free vibration response of a novel smart sandwich nanoplate based on a sinusoidal higher-order shear deformation theory (SHSDT) with a stretching effect. In the proposed sandwich nanoplate, an auxetic core layer with a negative Poisson’s ratio made of Ti-6Al-4V is sandwiched between Ti-6Al-4V rim layers and magneto-electro-elastic (MEE) face layers. The MEE face layers are homogenous volumetric mixtures of cobalt ferrite (CoFe2O4) and barium titanate (BaTiO3). The mechanical and thermal material properties of the auxetic core and MEE face layers are temperature-dependent. Using Hamilton’s principle, governing equations are constructed. To characterize the size-dependent behavior of the nanoplate, governing equations are adapted with the nonlocal strain gradient theory (NSGT). By applying the principles of Navier’s technique, closed-form solutions are obtained. Parametric simulations are carried out to examine the effects of auxetic core parameters, temperature-dependent material properties, nonlocal parameters, electric, magnetic, and thermal loads on the free vibration and thermal buckling behavior of the nanoplate. According to the simulation results, it is determined that the auxetic core parameters, temperature-dependent material properties, and nonlocal factors significantly affect the thermomechanical behavior of the nanoplate. The outcomes of this investigation are expected to contribute to the advancement of smart nano-electromechanical systems, transducers, and nanosensors characterized by lightweight, exceptional structural integrity and temperature sensitivity. Also, the auxetic core with a negative Poisson’s ratio provides a metamaterial feature, and thanks to this feature, the proposed model has the potential to be used as an invisibility technology in sonar and radar-hiding applications.

WITHDRAWN: Accurate and efficient analytical simulation of free vibration for embedded nonlocal CNTRC beams with general boundary conditions

This study aims to evaluate the free vibrational response of restrained nanobeam enriched by nanocomposites based on an exact Fourier series approach. In order to capture the small size effects on the dynamical response, Eringen’s differential form of nonlocal elasticity is used which employs the one size (nonlocal) parameter. Within the framework of Rayleigh and Bernoulli-Euler beam theories to include the effect of nonlocality and by employing Fourier sine series together with Stokes’ transformation, a system of linear equations is obtained then solved by using the coefficient matrix. The combined effects of elastic boundary conditions, elastic medium, dispersion patterns and nonlocal effects are examined by solving this eigen-value problem constructed with Fourier infinite series. Free vibration frequencies are calculated for carbon nanotube reinforced nanobeam under different rigid or restrained boundary conditions, including an elastic medium Winkler-Pasternak type. A comprehensive parametric study is performed, with the particular focus on the influences of distribution pattern, elastic boundary and medium parameter on the free vibrational response of the composite nanobeam with different graded distributions. It is concluded that the addition of a small amount of carbon nanotube material can reinforce the stiffness of the nanobeam, and its free vibration performance is significantly affected by the distribution patterns, elastic medium and boundary conditions.

Dynamic stability of the euler nanobeam subjected to inertial moving nanoparticles based on the nonlocal strain gradient theory

This research studied the dynamic stability of the Euler-Bernoulli nanobeam considering the nonlocal strain gradient theory (NSGT) and surface effects. The nanobeam rests on the Pasternak foundation and a sequence of inertial nanoparticles passes above the nanobeam continuously at a fixed velocity. Surface effects have been utilized using the Gurtin-Murdoch theory. Final governing equations have been gathered implementing the energy method and Hamilton's principle alongside NSGT. Dynamic instability regions (DIRs) are drawn in the plane of mass-velocity coordinates of nanoparticles based on the incremental harmonic balance method (IHBM). A parametric study shows the effects of NSGT parameters and Pasternak foundation constants on the nanobeam's DIRs. In addition, the results exhibit the importance of 2T-period DIRs in comparison to T-period ones. According to the results, the Winkler spring constant is more effective than the Pasternak shear constant on the DIR movement of nanobeam. So, a 4 times increase of Winkler and Pasternak constants results in 102 % and 10 % of DIR movement towards higher velocity regions, respectively. Furthermore, the effect of increasing nonlocal and material length scale parameters on the DIR movement are in the same order regarding the magnitude but opposite considering the motion direction. Unlike nonlocal parameter, an increase in material length scale parameter shifts the DIR to the more stable region.

Thermal wave reflection and propagation in temperature rate-dependent non-local diffusive solids

The propagation and reflection of thermo-elastic waves through diffusive nonlocal isotropic medium had been studied in this paper. The Green–Lindsay model of thermo-elasticity is incorporated in the context of Temperature Rate Dependent Theory. Using Helmholtz vector decomposition rule, the system of governing equations has been transformed to their respective components. The dispersion relation in frequency indicates the existence of three coupled waves and one independent wave propagating through the medium. The coupled waves are affected by non-locality, temperature field and diffusivity in the medium; anyhow, un-coupled shear vertical wave is only affected by the non-local parameter. The reflection of [Formula: see text]-wave is also studied at the free boundary of the solid and their corresponding amplitude ratios are computed using set of suitable boundary conditions. The obtained results are further discussed graphically for significant physical parameters of interest. The results in the literature are obtained as a special case after ignoring the diffusivity in the solid.

A Nonlocal Numerical Solution Based on Carrera Unified Formulation for Static and Free Vibration Analysis of Laminated Composite Nanoplate

This paper presents an advanced numerical model based on Carrera unified formulation (CUF) and isogeometric analysis (IGA), the size-dependent finite element unified formulation model is proposed to investigate the static bending and free vibration of laminated composite nano-plate. The CUF type of trigonometric function with nine degrees of freedom is used to simulate the displacement fields of laminated nano-plate. The size effect of nano-plate structures is included through the Eringen’s nonlocal elastic theory. The size-dependent governing equations for static bending and free vibration of laminated are established based on CUF, IGA and nonlocal theory. The correctness of the presented numerical model is verified by comparison with existing solutions. Furthermore, with the addition of a nonlocal effect, the plate’s stiffness decreases correlating to an increase in nonlocal parameter. Through different calculations, the changes in the static and free vibration responses of laminated composite nano-plate are effected by nonlocal parameter, plate length-to-thickness ratio, and boundary conditions including Young’s modulus ratio.

On the development of a constitutive model for steel subjected to fire and explosion

The behavior of steel under thermal and mechanical loading including high transient temperatures and strain rates (e.g., fire, creep or explosion) is extremely complex. To study this behavior, we propose a constitutive model accordance with the laws of thermodynamic, the principle of virtual power and experimental results. The thermodynamic framework considers the Clausius-Duhem inequality and maximum dissipation rate principle, as well as the theory of finite deformations, linear isotropic viscoelasticity, nonlinear isotropic and kinematic hardening, local and non-local viscoplasticity, local and non-local anisotropic viscodamage and parameters associated to material behavior dependent on loadings. The components of the thermodynamic conjugate forces are defined from the Helmholtz free energy function and the rate of energy dissipation, which are postulated considering the creep phenomenon, thermal-mechanical transient phenomenon, cyclic phenomenon and plastic wave propagation phenomenon. The balance of microforces is defined based on the principle of virtual power. A novel rule of non-associated thermo-viscoplastic flow of the Perzyna type and a novel rate dependent local and non-local damage evolution law are introduced from constitutive model. The verification of the model was carried out in two benchmark studies composed of fire tests. The predictions of the model have shown in according with the results of the experiments. A sensitivity study was also performed with a view to analysis the influence of the parameters in achieved results. From this study a simplified constitutive model is presented. Benchmark studies composed of explosion tests are part of future work.

On the stability analysis of a restrained functionally graded nanobeam in an elastic matrix with neutral axis effects

Abstract In this work, a general eigenvalue solution of an arbitrarily constrained nonlocal strain gradient nanobeam made of functionally graded material is presented for the first time for the stability response by the effect of the Winkler foundation. Elastic springs at the ends of the nanobeam are considered in the formulation, which have not been considered in most studies. In order to analyze deformable boundary conditions, linear equation systems are derived in terms of infinite power series by using the Fourier sine series together with the Stokes’ transform. The higher-order force boundary conditions are used to obtain a coefficient matrix including different end conditions, power-law index, elastic medium, and small-scale parameters. A general eigenvalue problem of technical interest, associated with nonlocal strain gradient theory, is mathematically evaluated and presented in detail. Parametric results are obtained to investigate the effects of material length scale parameter, Winkler stiffness, power-law index, nonlocal parameter, and elastic springs at the ends. In addition, the effects of the other higher-order elasticity theories simplified from nonlocal strain gradient theory are also investigated and some benchmark results are presented.

Enhancing the Mechanical Performance of Concrete Slabs through the Incorporation of Nano-sized Iron Oxide Particles (Fe2O3)

The utilization of recycled iron in durable concrete production has gained attention for enhancing sustainability and resource efficiency. Simultaneously, incorporating nanoparticles as supplementary cementitious materials (SCMs) offers significant benefits. Introducing nano-sized iron particles (Fe2O3) into the cement paste results in a compact microstructure, improving strength, and durability. In this study, we investigate the bending behavior of concrete slabs reinforced with Fe2O3 nanoparticles using the non-local quasi-3D shear deformation theory based on Eringen's non-local differential constitutive relations. To characterize the elastic material properties of the nanocomposite, we employ Eshelby's homogenization model. In order to extend the applicability of our findings, we assume that the concrete plate rests on Kerr's foundation, which includes a shear layer connected to upper and lower springs. By deriving the equations of motion using the principle of virtual work, we establish a comprehensive framework for analyzing the bending of the concrete plate. To solve the equilibrium equations for a simply supported concrete plate, we present Navier's analytical solutions. Our investigation considers various influential parameters, such as the concentration of Fe2O3 nanoparticles in the concrete matrix, the elastic constants of the soil medium, different types of bending loads, and size-dependent nonlocal parameters. One of the most captivating findings of this study is that the incorporation of 30 wt% of iron nanoparticles in concrete leads to a remarkable improvement of 60% in the elastic properties of the material. Additionally, this same amount of iron nanoparticles has shown the potential to reduce the deflection of thin plates by over 60%.

Renormalisable Non-Local Quark–Gluon Interaction: Mass Gap, Chiral Symmetry Breaking and Scale Invariance

We derive a Nambu–Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique of Bender, Milton and Savage applied to non-local theories, providing a set of Dyson–Schwinger equations in differential form. In the local case, we obtain closed-form solutions in the simplest case of the scalar field and extend it to the Yang–Mills field. In general, for non-local theories, we use a perturbative technique and a Fourier series and show how higher-order harmonics are heavily damped due to the presence of the non-local factor. The spectrum of the theory is analysed for the non-local Yang–Mills sector and found to be in agreement with the local results on the lattice in the limit of the non-locality mass parameter running to infinity. In the non-local case, we confine ourselves to a non-locality mass that is sufficiently large compared to the mass scale arising from the integration of the Dyson–Schwinger equations. Such a choice results in good agreement, in the proper limit, with the spectrum of the local theory. We derive a gap equation for the fermions in the theory that gives some indication of quark confinement in the non-local NJL case as well. Confinement seems to be a rather ubiquitous effect that removes some degrees of freedom in the original action, favouring the appearance of new observable states, as seen, e.g., for quantum chromodynamics at lower energies.

Examining the critical speed and electro-mechanical vibration response of a spinning smart single-walled nanotube via nonlocal strain gradient theory

In this study, the stability and vibration analyses of a spinning smart nanotube under electrical loads are examined for the first time. The smart nanotube structure is made from a single-walled zinc oxide nanotube (SWZnONT) due to its extraordinary piezoelectric and magnetic properties, which have great potential for use as a rotating component in nanoelectromechanical systems (NEMS). To achieve this aim, nonlocal strain gradient theory and Maxwell’s electrostatic equations are used to capture the structure’s small-scale and piezoelectric effects, respectively. In addition, the nanotube’s structural model is based on the Euler–Bernoulli beam theory, deriving governing equations and boundary conditions via the Hamilton principle. A technique employing Galerkin-based closed-form solutions is utilized to solve the equations of motion and get the vibration response of the spinning smart nanotube. Finally, the effects of the material length scale, nonlocal parameter, rotating speed, external voltage, and boundary conditions on natural frequency and critical rotational speed are investigated. The study results indicate that applying an external voltage to spinning SWZnONT effectively adjusts the critical speed and enhances structural stability.

Analysis on reflected waves through semiconductor nanostructure medium with temperature dependent properties

The article is about the study of reflected waves through the surface of an elastic solid. The medium considered for the propagation of waves is homogeneous isotropic with semiconductor properties. The thermoelastic properties of the medium are a function of temperature. The governing equations are formulated by using non-local elastic theory. The conduction process of heat is studied by using the concept of three-phase lag along with fractional order time derivative. After reflecting through the surface one transverse and three longitudinal waves travel back into the media. The reflection coefficients and their energy ratios are computed analytically. Numerically simulated results are obtained for the intrinsic semiconductor material Silicon to depict the effect of temperature dependency parameters, nonlocal parameters, and time derivative fractional order on the different reflection coefficients. Some published results are also discussed as special cases.

Photothermoelastic interaction in a two-dimensional semiconductor with nonlocal stress theory

The present contribution enlightens a viable simulation which describes the photothermoelastic interactions for a two-dimensional thermoelastic transversely isotropic thick semiconducting plate due to the presence of a varying heat source. The upper surface of the semiconductor is traction-free, subjected to prescribed surface temperature and prescribed carrier density flux while the lower surface of the plate rests on a rigid foundation and is thermally insulated. In this new model, the conventional Fourier law has been modified assimilating the memory-dependent derivative within a slipping interval in association with the nonlocal stress theory. On utilizing Laplace and Fourier transformation mechanism, the governing equations for displacement, carrier density and temperature have been obtained in the Laplace–Fourier transform domain. In order to have the solutions in the space-time domain, the inversion of the double transform have been carried out numerically based on the method of Fourier series expansion. From the graphical representations corresponding to the numerical results, the significance of effective parameters such as nonlocality parameter, delay-time parameter is discussed. Noteworthy differences in the results have been demonstrated for different kernel functions. Also, the superiority of a nonlinear kernel function and its effectiveness is also reported in the study.

Size effect on vibration properties of axially moving nanoplates under different boundary conditions

The nonlocal strain gradient theory is employed to investigate the transverse free vibration characteristics of two-dimensional nano-plates with axial velocities. A generalized Hamiltonian principle has been used to establish the vibration governing equations for the system as well as the corresponding boundary conditions. By applying complex modal analysis to three boundary conditions, the plate’s natural frequency is determined, including four-end simply supported, four-end clamped, and opposite-edge simply supported and clamped, and comparing the effect of the size parameters on the natural frequency in relation to the boundary conditions; based on different theories, the effects of changing boundary conditions on natural frequencies are systematically compared. In the numerical study, it is demonstrated that the size effect significantly influences only the self-oscillation frequency at the nanoscale, whereas the nonlocal parameter as well as the material characteristic parameter have “softening” and “hardening” effects on the equivalent stiffness of the nanoplates, respectively, which are directly related to their natural frequencies. Compared to simple supports, clamped boundary conditions are more significantly affected by size parameters. In addition, higher order frequencies exhibit greater sensitivity and are susceptible to changes in boundary conditions and size parameters.

Application of the Green's function method for static analysis of nonlocal stress-driven and strain gradient elastic nanobeams

This paper focuses on the static analysis of a generally restrained Euler-Bernoulli nanobeam (GRNB), which is subjected to arbitrary distributed or concentrated loads. The small length scale effect is introduced through a strongly nonlocal integral elastic law called the stress-driven nonlocal Euler-Bernoulli beam model, and a weakly nonlocal elastic law called the strain-gradient Euler-Bernoulli beam model. The stress-driven nonlocal theory and the strain gradient elasticity theory are both employed, to formulate the differential equation governing the Euler-Bernoulli nanobeams. Both theories are ruled by a similar 6th order differential equation, with distinct higher-order boundary conditions. The paper demonstrates that the strain gradient theory can be also reformulated as a stress-driven nonlocal theory with unsymmetrical kernel, in contrast to the initial stress-driven nonlocal theory which has symmetrical exponential kernel. Additionally, some theoretical backgrounds about both nonlocal elasticity theorems are provided. Exact solutions for both nanobeam models are presented, using Green's function method. The parameters of the Green's functions are derived for each beam theory, and then utilized to establish the static displacement function of both nanobeam theories. Exact solutions are provided for the bending of both nanobeams with various end boundary conditions, that account for the small length scale effects. The paper also compares the responses of the stress-driven Euler-Bernoulli beam and the strain gradient Euler-Bernoulli beam, showing close deflections and similar effects of increasing the nonlocal parameter on beam stiffness. A major difference highlighted between the two theories is that the strain gradient theory predicts a homogeneous strain state for homogeneous stress state, as opposed to the stress-driven theory.

Effects of positional disorder upon the nonlocal effective parameters of a metamaterial composed of coated spheres

An electromagnetic characterization of a bianisotropic medium based on nonlocal homogenization theory with small positional disorders has been presented. The proposed theory is general and can be used for any type of random positional disorders provided that the probability density functions associated with these positional disorders are known. Later, the proposed general theory was used for a nonlocal metamaterial composed of coated spheres with Gaussian types of positional disorder in the microwave and infrared range of frequencies. It is studied that by increasing the positional disorder, the epsilon negative, mu negative and double negative bandwidths of a metamaterial reduce and even vanish for some special cases. It is found that the bandwidths of absorption peaks associated with the imaginary parts of effective permittivity and effective permeability become wider with the increase in positional disorder. It is also concluded that magnetoelectric coupling arising due to lattice effects become almost negligible for the relatively large positional disorder for a weak nonlocal or spatially dispersive metamaterial. The proposed findings are helpful in the designing of nonlocal disordered metamaterials.

Impact of weak nonlocal nonlinearity on modulational instability and chirp-free soliton trains in parabolic law optical fiber

This study considers the generation and evolution of chirp-free soliton trains in a focusing cubic-quintic nonlinear optical fiber media (by utilizing experimental parameters), under the influence of weak nonlocal nonlinearity. Analysis of modulational instability (MI) reveals that the MI gain exist only in the anomalous dispersion regime, with the quintic nonlinear term increasing the maximum gain and sideband frequencies. The nonlocal nonlinearity parameter generally suppresses the impact of MI, because the maximum gain is greatly reduced with increase in nonlocality. By using the subsidiary ordinary differential equation method, stationary periodic soliton trains are obtained; with the intensity of the optical beam greatly reduced and frequency increased as nonlocality is gradually stepped up. However, an increase in nonlocality instead reduces the frequency of the traveling optical signals; derived via an efficient transformation method. Our results strongly suggest that nonlocal nonlinearity has potential applications in the control of laser beams; as nonlinear periodic optical signals can be easily transformed to very weak quasi-plane waves.

A nonlocal higher-order shear deformation approach for nonline ar static analysis of magneto-electro-elastic sandwich Micro/Nano-plates with FG-CNT core in hygrothermal environment

In this study, the nonlocal static analysis of Magneto-Electro-Elastic (MEE) sandwich micro/nano-plates with Functionally Graded Carbon Nanotubes (FG-CNTs) core in a hygrothermal environment is studied. The nonlocal static formulation is developed based on Reddy's High-order Shear Deformation theory (HSDT). The von Kármán nonlinear strains are used and the governing equations of the HSDT are derived accounting for Eringen's nonlocal stress-gradient model. The governing equations are solved using the Galerkin method, which involves expanding the displacement field based on orthogonal functions. The variation of the volume fractions through the thickness of FG-CNTs core layer has been computed using two different homogenization techniques: the rule of mixtures and the Mori–Tanaka scheme. A detailed parametric study to show the characteristics of the FG-CNTs core, nonlocal parameters, thermal and moisture changes, types of CNT reinforcement and volume fraction, electric and magnetic potentials, and geometric parameters. The results are compared with the first-order shear deformation theory (FSDT) and classical plate theory to show the accuracy of nonlocal High-order Shear Deformation theory(NHSDT) formulation.