Nonlocal Effects Research Articles

Dynamic Analysis of a Timoshenko–Ehrenfest Single-Walled Carbon Nanotube in the Presence of Surface Effects: The Truncated Theory

The main objective of this paper is to study the free vibration of a Timoshenko–Ehrenfest single-walled carbon nanotube based on the nonlocal theory and taking surface effects into account. To model these effects on frequency response of nanotubes, we use Eringen’s nonlocal elastic theory and surface elastic theory proposed by Gurtin and Murdoch to modify the governing equation. A modified version of Timoshenko nonlocal elasticity theory—known as the nonlocal truncated Timoshenko beam theory—is put forth to investigate the free vibration behavior of single-walled carbon nanotubes (SWCNTs). Using Hamilton’s principle, the governing equations and the corresponding boundary conditions are derived. Finally, to check the accuracy and validity of the proposed method, some numerical examples are carried out. The impacts of the nonlocal coefficient, surface effects, and nanotube length on the free vibration of single-walled carbon nanotubes (SWCNTs) are evaluated, and the results are compared with those found in the literature. The findings indicate that the length of the nanotube, the nonlocal parameter, and the surface effect all play important roles and should not be disregarded in the vibrational analysis of nanotubes. Finally, the results show how effective and successful the current formulation is at explaining the behavior of nanobeams.

Thermoelastic response analysis of a functionally graded rotating piezoelectric rod considering nonlocal effects and Kelvin–Voigt viscoelastic model

This article proposes a new formulation of Fourier’s heat conduction law by considering the size effect of functionally graded piezoelectric materials. Which contains the Caputo–Fabrizio type fractional-order heat transfer equation. The Kelvin–Voigt model was used to characterize the viscoelastic behavior of the material. The model is applied to the study of the thermodynamic behavior of functionally graded piezoelectric rods under thermal shock. It is assumed that the ends of the functionally graded piezoelectric rod are fixed and insulated, that there is no electric potential between the ends, and that the physical properties of the rod vary exponentially along the axial direction of the rod. The control equation is solved by the Laplace integral transformation and its numerical inverse transformation, and the distribution of the studied physics field is obtained, which is illustrated graphically. Finally, the effects of nonhomogeneity index, fractional-order derivatives, nonlocal parameters, and viscoelastic coefficients on the characteristics of the physical variables are investigated and discussed.

Thermoelastic damping analysis of functionally graded sandwich microbeam resonators incorporating nonlocal and surface effects

Functionally graded (FG) sandwich microstructures/nanostructures stand as one of the most promising composite structures due to the capability to resist thermal shock and high noise in extreme thermal environments. Meanwhile, accurately prediction quality-factor based on thermoelastic damping (TED) is of great significance for the design of high-performance microresonators /nanoresonators. However, the classical TED models fail to explain the size-dependent thermo-mechanical behavior. The nonlocal elasticity and surface elasticity are responsible for the size-dependent phenomenon. In this article, a modified TED model is proposed to estimate the impact of the size-dependent effect on the TED of FG sandwich microbeam resonators in unsteady heat transfer processes by combining the nonlocal elasticity model, surface elasticity model, and dual-phase-lag (DPL) heat conduction model. It is assumed that the FG sandwich microbeam resonators consist of a ceramic core and FG surfaces. The energy equation and the transverse motion equation are derived. The analytical expression of TED is obtained by the complex frequency method. The influences of the factors including the nonlocal parameter, the surface effect, the power-law index, and the vibration modes on the TED are analyzed. These results provide a reasonable theoretical analysis to predicate TED in the design of FG sandwich microresonators/nanoresonators with high performance.

Enhancement and quenching of plasmon-enhanced spectroscopy of single molecule confined in metallic nanoparticle dimers

We present a theoretical analysis of plasmon-enhanced fluorescence (PEF) and Raman scattering (PERS) spectroscopy of a single molecule confined in the laser-irradiated metallic nanoparticles (NPs) dimer, focusing on the origin of the spectral enhancement and quenching effects. The theoretical method of D-parameters has been used to calculate the dimer distance-dependent nonlocal dielectric effect in Ag and Au NPs. Meanwhile, other damping rates and electric field enhancements are quantitatively computed by finite element method. Moreover, PEF and PERS spectra of rhodamine 6G are obtained within the density-functional theory. Our calculated results show that the PERS mainly depend on the excitation and emission field enhancements, and thus it occurs at the narrower dimer gap due to the stronger localized plasmon coupling. The PEF is related to fluorescence rate caused by the competition between excitation electric field and quantum efficiency, and the increase of former may enhance the fluorescence intensity while the lower latter lead to reduce the intensity as decreasing the dimer distance. The contribution of nonlocal dielectric effect can significantly reduce the quantum efficiency at smaller distance so that it overcomes the excitation field enhancement, leading to the fluorescence quenching for Au NPs dimer. Furthermore, by optimizing the dimer distance and NPs size, the maximum PERS and PEF cross sections reach 10−14 and 10−15 under 2.45 eV laser excitation for Ag NPs dimer, and 10−18 for Au NPs. Our study finely explains the experiment results showed either fluorescence enhancement or quenching with the change of molecule-NPs distance, and better guidance for optimizing the experiments.

Vibrational analysis of transversely isotropic hollow cylinder based on fractional generalized thermoelastic diffusion models with nonlocal effects

Vibrational analysis of transversely isotropic hollow cylinder based on fractional generalized thermoelastic diffusion models with nonlocal effects

The ultrashort pulse laser ablation model of silicon based on the generalized thermoelastic theory with spatio-temporal nonlocal effect

The present work is devoted to establishing the ultrashort pulse laser ablation generalized thermoelastic model with spatio-temporal nonlocal effect and investigating the transient responses of the process of silicon ablated by the picosecond pulse laser. The research is divided into three cases. 1) The solid silicon before the target surface melting is studied, and the transient responses of the final state of this case are taken as the initial conditions of the Case Two. 2) The liquid silicon after the target surface melting is researched, and the heat flux taken away by vaporization is considered in the boundary condition. 3) The solid silicon after the target surface melting is discussed, and the moving solid-liquid interface is regarded as the coordinate origin. The coupled governing equations containing spatial nonlocal parameter, time delay factor, and kernel function are established and solved by the Laplace transform together with its numerical inversion. The melting time and depth of target are emphatically discussed. The temperature, displacement and stress with different laser intensity, spatial nonlocal parameter, time delay factor, kernel function as well as time are obtained and illustrated graphically.

Analysis of nonlocal effects on plane waves in a transversely isotropic visco-thermoelastic medium with variable thermal conductivity

PurposeThis study aims to analyse the behaviour of plane waves within a nonlocal transversely isotropic visco-thermoelastic medium having variable thermal conductivity.Design/methodology/approachThe concept of enunciation is used in the generalized theory of thermoelasticity in accordance with the Green–Lindsay and Eringen’s nonlocal elasticity models. The linear viscoelasticity model developed by Kelvin–Voigt is used to characterize the viscoelastic properties of transversely isotropic materials.FindingsIt has been noticed that three plane waves, which are coupled together, travel through the medium at three different speeds. The derivation of reflection coefficients and energy ratios for reflected waves is carried out by incorporating suitable boundary conditions. Numerical computations are performed for the amplitude ratios, phase speeds and energy partition and displayed in graphical form.Originality/valueThe outcomes of the numerical simulation demonstrate that the amplitude ratios are significantly influenced by variable thermal conductivity, nonlocal parameters and viscosity. It is further observed from the plots that the phase speeds in a transversely isotropic medium depend on the angle of incidence. In addition, it has been established that the energy is preserved during the reflection phenomenon.

Broadband unidirectional surface plasmon polaritons with low loss.

Unidirectional surface plasmon polaritons (SPPs) have been proven to truly exist at an interface between a magnetized semiconductor and an opaque isotropic material, however, they suffer rather serious leakage loss (with propagation length shorter than two wavelengths) caused by nonlocality. In this work, we investigate an alternative category of unidirectional SPPs existing on a nonreciprocal plasmonic platform with a cladding composed of a dielectric heterostructure transversely terminated by metal. This unidirectional SPP mode exists for small wavenumbers within the entire upper bulk-mode bandgap of the magnetized semiconductor, hence it is robust against nonlocal effects over a broad band. In contrast to previous unidirectional SPPs, the leakage loss of the present unidirectional SPPs is significantly reduced by more than five times, since the portion of modal energy distributed in the cladding is substantially increased. A similar reduction in absorption losses associated with semiconductor dissipation is observed. Though the nonlocality induces a backward-propagating SPP with extremely large wavenumbers, it can be suppressed even at very small level of dissipation. Therefore, our proposed plasmonic waveguide actually exhibits exceptional unidirectional characteristics.

Localized microbially induced inflammation influences distant healthy tissues in the human oral cavity

Variation in human immune response to the same bacterial or viral pathogen is well established in the literature. Variation in immune response to microbial challenge has also been observed within the human oral cavity. Our recent study focused on characterizing observed variations in microbially induced gingival inflammation-resulting in three distinct clinical Inflammatory Responder Types (IRTs): High-IRT, Low-IRT, and Slow-IRT. Here, we applied a high-resolution temporal multiomic analysis during microbially induced inflammation in order to characterize the effects of localized oral inflammation on distant healthy tissues in young healthy adults. Our results highlight a nonlocalized subclinical effect with alterations in proinflammatory host mediators and an ecological shift toward dysbiosis within the subgingival microbiome in an IRT-dependent manner-despite maintained oral hygiene. Our results provide mechanistic insight into how healthy tissues within humans are influenced by distant localized inflammation and may ultimately become susceptible to disease.

Thermoelastic response of an elastic rod under the action of a moving heat source based on fractional order strain theory considering nonlocal effects

In this paper, based on fractional order strain theory and nonlocal heat conduction theory, the thermoelastic response of an elastic rod rigidly fixed at both ends and subjected to a moving heat source is investigated. The nonlocal fractional order strain control equation is established, and the analytical expressions of dimensionless temperature, displacement, and stress are solved using the Laplace integral transformation and numerical inverse transformation. The distribution law of physical quantities such as temperature, displacement, and stress when the fractional parameters, heat source moving speed, and thermal nonlocal parameters change is obtained. The results show that strain parameters and thermal nonlocal parameters have less influence on thermal–mechanical waves, while heat source velocity has a significant influence on thermal–mechanical waves.

Dynamics of a predator–prey model with mutation and nonlocal effect

The global dynamics of a nonlocal predator–prey model with mutation are investigated in this paper. First, by building a new comparison principle and constructing monotone iterative sequences, we give the existence of the solution for the corresponding initial boundary value problem. Then the uniqueness and uniformly boundedness of the solution are established by using the fundamental solution and quasi-fundamental solution of the heat equation, Grönwall’s inequality and auxiliary functions. Finally, under the truncation function method, we discuss the asymptotic behavior of the solution. It is worth mentioning that the asymptotic behavior here is different from the conclusion of the classical model and we use more refined analysis and estimation in the research process.

A Buckling Analysis of Thermoelastic Micro/Nano-Beams Considering the Size-Dependent Effect and Non-Uniform Temperature Distribution.

Thermoelastic buckling of micro/nano-beams subjected to non-uniform temperature distribution is investigated in this paper. The mechanical governing equation is derived based on the surface effect and mechanical non-local effect. The non-local heat conduction model is used to predict temperature distribution in micro/nano-beams. Therefore, the obtained analytical solution can be used to analyze the influence of both the mechanical and thermal small scale effects on buckling of thermoelastic micro/nano-beams. In numerical simulations, a critical thickness is proposed to determine the influence region of both mechanical and thermal small scale effects. The influence of a small scale effect on buckling of micro/nano-beams must be considered if beam thickness is less than the critical thickness. In the influence region of a small scale effect, a surface effect has strong influence on the size-dependent buckling behavior, rather than mechanical and thermal non-local effects. Moreover, combined small scale effects, i.e., a surface effect and both mechanical and thermal non-local effects, lead to a larger critical load. Additionally, the influence of other key factors on buckling of the micro/nano-beams is studied in detail. This paper provides theoretical explanation to the buckling behaviors of micro/nano-beams under a non-uniform temperature distribution load.

Two-temperature generalized magneto-thermic-viscoelastic response problem considering non-local and memory effects

Based on the two-temperature generalized magneto-thermal-viscoelastic theory considering scale effects and fractional time derivatives, the dynamic response of generalized magneto-thermal-viscoelastic theory in homogeneous isotropic semi-infinite elastic media with infinite conductivity is studied. Laplace Fourier integral transform and numerical inverse transform are used to solve the general solution of dimensionless physical equations. Based on the numerical results, the effects of time factor, fractional parameter and scale effect on the transient magneto thermic viscoelastic response of the structure are discussed respectively. The above results are visually expressed in the form of graphs. The results show that the temperature and displacement are less affected by each parameter, the stress increases with the increase of time, non-local and viscosity parameters, and decreases with the increase of fractional order parameters. This result is of great significance to the application of different physics fields, and provides some theoretical guidance for solving practical engineering problems.

Rate of accelerated expansion of the epidemic region in a nonlocal epidemic model with free boundaries

This paper is concerned with the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators, and the epidemic region is represented by an evolving interval enclosed by the free boundaries in the model. In Wang and Du (2022 J. Differ. Eqn. 327 322–81), it was shown that the model is well-posed, and its long-time dynamical behaviour is governed by a spreading-vanishing dichotomy. The spreading speed was investigated in a subsequent work of Wang and Du (2023 Discrete Contin. Dyn. Syst. 43 121–61), where a threshold condition for the diffusion kernels J 1 and J 2 was obtained, such that the asymptotic spreading speed is finite precisely when this condition is satisfied. In this paper, we examine the case that this threshold condition is not satisfied, which leads to accelerated spreading; for some typical classes of kernel functions, we determine the precise rate of accelerated expansion of the epidemic region by constructing delicate upper and lower solutions.

Reflection, transmission, and dissipation of plane waves in sandwiched functionally graded thermo- electro-elastic nanoplates via nonlocal integral elasticity theory

On account of the Lord-Shulman thermo-electric-elastic (TEE) theory and the nonlocal integral elasticity effect, the propagation of the plane wave in sandwiched functionally graded material (FGM) nanoplates, especially its energy dissipation, is investigated. A mathematical model is established by using the extended Legendre polynomial series approach. After imposing the mechanical, electrical and thermal boundary conditions by using the Legendre series, the reflection and transmission as well as the dissipation energy ratios are obtained. The influences of the nonlocal effect, relaxation time, gradient index, and electric filed are discussed. It is found that the nonlocal effect on the reflection of P waves is consistent with their transmission, but opposite to reflection of SV waves. Meanwhile, the nonlocal effect increases the dissipation. Besides, the dissipation variation in the normal incidence mainly comes from the transmission waves. The study is beneficial for the design of wave characteristics in TEE FGM nanoplates.

Thermal damage analysis in tissue caused by electromagnetic radiation using space–time collocation method

Over the past half-century, the usage of external heat sources in medical applications has increased substantially. Controlling heat damage is essential for ensuring the efficacy of the treatment. Living tissues are highly non-homogeneous; hence, it is important to take into account the effects of local non-equilibrium on their thermal behavior. In the present study, two- and three- space dimensional time-space fractional single-phase-lag (SPL) and dual-phase-lag (DPL) models for bio-heat transfer in tissue are considered to study the thermal damage and temperature in tissue caused by electromagnetic radiation as an external heat source. The considered mathematical models are more general and consider non-Fourier as well as non-local effects. We obtain the numerical solution for the models by combining Gaussian RBFs and shifted Chebyshev polynomials in the space and time directions, respectively. The RBFs depend on Euclidean distance, so they can easily be used in multidimensional space domain, and the use of Chebyshev polynomials gives spectral accuracy in time direction. It is also explored how different parameters, such as blood perfusion rate Wb, phase lags τq, τt, and fractional derivatives α, β, affect the temperature distribution and thermal damage in the tissue.

Imperfect and multilayered magneto-electro-elastic nanoplates bending response analysis based on the nonlocal state-space approach

The present article is about the 3D static responses of the multilayered magneto-electro-elastic (MEE) nanoplates with imperfect interfaces and nonlocal effect analytically by the state-space method. To model the imperfect interfaces, which have been assumed to be electro-magnetically weakly conducting, the spring type layer model has been used. The nonlocal effect is taking into account in the modeling through to the Eringen nonlocal elasticity theory. The propagator matrix technique is utilized to derive the solution at any position in the transverse direction of the MEE nanoplates. The nonlocal length effect on the whole amount state variables has been highlighted in numerical examples. It has been carried out that, this parameter influences weakly the stresses, the electric and the magnetic displacements, respectively; but it has a strong influence on the elastic displacements, the electric and the magnetic potentials. Furthermore, the effects of the staking sequence and the interface parameters have been clearly illustrated.

Critical travelling waves of a vector-host disease model with spatio-temporal nonlocal effect

This paper is concerned with the existence of travelling wave solution (TWS) with critical speed c∗ for a nonlocal reaction–diffusion vector-host disease model. When the basic reproduction ratio R0 at the disease-free equilibrium is greater than one, we adopt the limiting arguments and contradictory approach to show the existence of critical TWS. Furthermore, it is observed that R0 at the final size of susceptible hosts and vectors is less than one, which indicates that the disease will not eventually break out.

Stabilized state-based peridynamics for elasticity emanating from constrained Lagrangian

State-based peridynamics for elasticity paves the way to bridge the local theory with the inherent capabilities of general elasticity with non-local effects. However, the original non-ordinary state-based peridynamics with correspondence materiel models suffers from high-frequency oscillations due to zero-energy mode instability. To address this issue, we start from the fundamental Lagrangian with the introduction of a constraint potential energy that minimizes the numerical error and suppresses the zero-energy mode oscillations. A stabilized non-ordinary state-based peridynamics is then derived from this constrained Lagrangian that forms an integral–differential–algebraic system. In specifics, the equation of motion for particles is described by integral-differential equations while the constraint suppressing the zero-energy mode instability is expressed as algebraic equations (zero-error constraint). An energy–momentum conserving implicit time-stepping scheme for this integral–differential–algebraic system is then derived. End-to-end 2D and 3D simulations, including scalar wave propagation, crack path, and large deformation problems, are presented to show that the proposed method is promising for these applications in terms of accurately capturing the crack path and large deformation, efficiently eliminating the numeral oscillations, conserving the total energy for long duration simulations, and preserving the zero-error constraint.

Nonlocal Soft Plasmonics in Planar Homogeneous Multilayers

Plasmonics is the study of resonant oscillations of free electrons in metals caused by incident electromagnetic radiation. Surface plasmons can focus and steer light on the subwavelength scale. Apart from metals, plasmonic phenomena can be observed in soft matter systems such as electrolytes which we study here. Resonant charge oscillations can be induced for ions in solution, however, due to their larger mass, they are plasmon-active in a lower frequency regime and on a larger wavelength scale. Our investigation focuses on spatial confinement which allows increasingly strong charge interactions and gives rise to nonlocality or spatial dispersion effects. We derive and discuss the nonlocal optical response of ionic plasmons using a hydrodynamic two-fluid model in a planar homogeneous three-layer system with electrolyte-dielectric interfaces. As in metals, we observe the emergence of additional longitudinal propagation modes in electrolytes which causes plasmonic broadening. Studying such systems enables us to identify and understand plasmonic phenomena in biological and chemical systems.