Nonlocal Conductivity Research Articles

A PROBLEM IN FRACTIONAL ORDER THERMO-VISCOELASTICITY THEORY FOR A POLYMER MICRO-ROD WITH AND WITHOUT ENERGY DISSIPATION

A new study has been developed that considers the size-dependent interaction between viscoelastic deformation and thermal fields, incorporating the fractional heat conduction law with and without energy dissipation. The model is used for a particular one-dimensional problem involving a polymer micro-rod of arbitrary length experiencing three different types of thermal loading without the presence of any heat source. The study uses Laplace transforms and numerical inversion to examine how fractional order, nonlocal elasticity, and nonlocal thermal conduction impact thermal dispersion and thermo-viscoelastic response. Comparative numbers demonstrate the effects of various parameters. Findings demonstrate that nonlocal thermal and viscoelastic characteristics have a significant impact on all recorded field values, offering possible suggestions for the creation and assessment of thermal-mechanical attributes in nanoscale devices.

Reflection of plane waves in a non-local viscothermoelastic half-space under variable thermal conductivity and microelongation effects

The present work is implicated with the investigation of wave propagation in a homogeneous, isotropic, non-local microelongated viscothermoelastic solid half space with variable thermal conductivity under the dual phase lag (DPL) model. It is found analytically that three coupled longitudinal waves and one independent transverse wave exist in the medium which travel with distinct speeds. Reflection coefficients and energy ratios of various reflected waves are obtained analytically and presented graphically for aluminum epoxy-like material. The variations of these reflection coefficients are analyzed for different values of non-local parameter, microelongational parameter, viscosity and variable thermal conductivity. The expressions of energy ratios acquired in explicit form are also represented graphically as functions of the angle of incidence in accordance with the defined rule of conservation of energy.

Elasto-Thermodiffusion in a Slim Strip Revisited with New Definition of Nonlocal Heat Conduction

Elasto-Thermodiffusion in a Slim Strip Revisited with New Definition of Nonlocal Heat Conduction

Nonlocal conductivity, continued fractions, and current vortices in electron fluids

Nonlocal conductivity, continued fractions, and current vortices in electron fluids

Thermal analysis of 3D viscoelastic micropolar nanofluid with cattaneo-christov heat via exponentially stretchable sheet: Darcy-forchheimer flow exploration

This article presents a comprehensive study on the thermal behavior of a three dimensional viscoelastic micropolar nanofluid under the inspiration of Cattaneo-Christov heat conduction model. The nanofluid is subject to an exponentially stretchable sheet and the flow is characterized by Darcy-Forchheimer formulation. Similarity variables are used to convert viscoelastic nanofluids PDEs into ODEs. MATLAB platform with bvp4c command is used to solve resulting ODE. The impact of involving parameters such that velocity ratio, Schmidt number, Prandtl number, Peclet number, Forchheimer number, buoyancy ratio parameter, Brownian motion, Heat source, Magnetic parameter on velocity profiles, rotation, temperature concentration and density profiles via graphs and tables. Temperature curve is improved up for magnetic parameters, temperature exponent parameter and thermopherosis parameter while significance loss is noted for increasing value of Prandtl number Pr and relaxation time λT. This research bears significance in applications related to advanced heat exchangers, microfluidic systems, and other emerging technologies where the interplay of nanofluids, viscoelasticity, and non-local heat conduction is of paramount importance.

Scale-Dependent Heat Transport in Dissipative Media via Electromagnetic Fluctuations.

We develop a theory for heat transport via electromagnetic waves inside media, and use it to derive a spatially nonlocal thermal conductivity tensor, in terms of the electromagnetic Green's function and potential, for any given system. While typically negligible for optically dense bulk media, the electromagnetic component of conductivity can be significant for optically dilute media, and shows regimes of Fourier transport as well as unhindered transport. Moreover, the electromagnetic contribution is relevant even for dense media, when in the presence of interfaces, as exemplified for the in-plane conductivity of a nanosheet, which shows a variety of phenomena, including absence of a Fourier regime.

Electromagnetic thermo-viscoelastic response of piezoelectric rods considering memory dependent effects

Based on the theory of nonlocal elasticity and nonlocal heat conduction, a new dual-phase-lag heat conduction model with memory dependent effect is proposed in this article to explore the thermodynamic behavior of functionally graded rotating piezoelectric rods under the action of moving heat sources. Assuming that the material properties of functionally graded piezoelectric rods vary exponentially along the length direction, the end of the rod is rigid and fixed without voltage. Use Laplace transform to transform the problem into the spatial domain and perform analytical solutions, then use inverse Laplace transform to obtain the time-domain solution. Numerical solutions were performed for dimensionless displacement, temperature, electric potential, and stress, and the variation patterns of the physical quantities involved were described in graphical form. The calculation provides the effects of functional gradient non-uniformity index, thermal nonlocal parameters, kernel function, and viscoelastic parameters on the physical quantities involved.

A new constitutive theory of nonlocal piezoelectric thermoelasticity based on nonlocal single-phase lag heat conduction and structural transient thermo-electromechanical response of piezoelectric nanorod

Thermo-electromechanical coupling analysis at micro and nano temporal and spatial scales becomes significantly important with extensive application of ultrafast heating technology to micro/nano-machining and manufacturing of piezoelectric micro/nano-devices, where the size effects in heat conduction and elastic deformation remarkably increase. This article aims to establish a new nonlocal piezoelectric thermoelasticity theory based on newly developed model of Eringen-type nonlocal single-phase-lag heat conduction via Eringen’s nonlocal continuum mechanics. The proposed model is applied to analyze the thermo-electromechanical responses of piezoelectric nanorod by Laplace transformation technique. The effects of nonlocal characteristic lengths on wave propagations and structural transient response are evaluated and discussed.

Nonlocal dual-phase-lag thermoelastic damping analysis in functionally graded sandwich microbeam resonators utilizing the modified coupled stress theory

Functionally graded (FG) sandwich structures stand as one of the most representative composite structures owing to the thermal resistance and the energy absorption property in non-unfiorm thermal environment. Additionally, accurately estimating thermoelastic damping (TED) is of great importance for the design of high-performance micro/nano-resonators. Nevertheless, the classical TED models fail on the micro/nano-scale structures due to without considering the influences of the spatial size-dependent effects related to heat transfer and elastic deformation. The nonlocal heat conduction model and modified coupled stress theory are responsible for the size-dependent effects. To address this issue, present study aims to conduct the size-dependent TED model of FG sandwich microbeam resonators for TED analysis by incorporating the nonlocal dual-phase-lag (NDPL) heat conduction model and the modified coupled stress theory (MCST). 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 formulated, and then, the analytical solution is solved by complex frequency method. Exact and closed-form expressions for TED can be obtained through the complex frequency method. The results are validated, and the parameter effects of the nonlocal thermal parameter, the material length-scale parameter, the power-law index and the vibration modes on the TED are analyzed. The results show that the energy dissipation can be reduced by the size-dependent effects resulting in improving the quality factor of microstructures. It is expected that these results may provide a theoretical basis for predicating TED in the design of FG sandwich micro/nano-resonators with high quality factor in extreme heat transfer environment.

Numerical solutions of nonlocal heat conduction technique in tumor thermal therapy

The heat transport that takes place in living tissue during magnetic tumor hyperthermia is described in this study using the nonlocal bioheat model in spherical coordinates. In magnetic fluid hyperthermia, it is crucial to regulate the therapeutic temperature. This paper suggests a hybrid numerical approach that employs the Laplace transforms, change of variables, and modified discretization techniques, coupled with nonlocal hyperbolic shape function, to tackle the present problem. This study investigates the impacts of nonlocal parameter and the disparity in thermophysical properties between diseased and healthy tissue. A graph is displayed to represent the numerical temperature results. The validity of the numerical findings is demonstrated by comparing them with the results reported in previous literature.

Nonlocal Spin Correlation as a Signature of Ising Anyons Trapped in Vacancies of the Kitaev Spin Liquid.

In the Kitaev chiral spin liquid, Ising anyons are realized as Z_{2} fluxes binding Majorana zero modes, which, however, are thermal excitations with finite decay rates. On the other hand, a lattice vacancy traps a Z_{2} flux even in the ground state, resulting in the stable realization of a Majorana zero mode in a vacancy. We demonstrate that spin-spin correlation functions between two vacancy sites exhibit long-range correlation arising from the fractionalized character of Majorana zero modes, in spite of the strong decay of bulk spin correlations. Remarkably, this nonlocal spin correlation does not decrease as the distance between two vacancy sites increases, signaling Majorana teleportation. Furthermore, we clarify that the nonlocal correlation can be detected electrically via the measurement of nonlocal conductance between two vacancy sites, which is straightforwardly utilized for the readout of Majorana qubits. These findings pave the way to the measurement-based quantum computation with Ising anyons trapped in vacancies of the Kitaev spin liquid.

Dynamic behavior of nanoplate on viscoelastic foundation based on spatial-temporal fractional order viscoelasticity and thermoelasticity

The nanodevices often work in a thermal environment and lead to the viscoelastic and thermoelastic coupling which becomes more complicated when further coupled with the size effects. A spatial-temporal fractional order model is proposed to study the dynamic behavior of thermoelastic nanoplate in the present work. The integer order differential is extended to the fractional order differential with the integer order differential as a special case. This extension makes the modeling of small-scale effects of mechanical behavior and generalized heat conduction more flexible. Non-local strain gradient elasticity and non-local heat conduction are used to describe the spatial non-local effects while the fractional order differential to describe the complicated history-dependent effects or the temporal nonlocal effects. The standard solid viscoelastic model and generalized heat conduction model with the fractional order differentials lead to the fractional-order differential governing equations. The fractional order differential equation is solved by the Laplace transform method, and the analytical solution of the response is expressed in terms of the Mittag-Leffler function. In order to verify the reliability of the analytical solution, the numerical solution is also provided for comparison. Based on the numerical results of dynamic response under the step load, the effects of thermoelastic fractional order parameters, viscoelastic fractional order parameters, and small-scale parameters are discussed. The new spatial-temporal fractional order model is a natural extension of the traditional integer order model which can be recovered from the present model.

Non-classical theory of electro-thermo-elasticity incorporating local mass displacement and nonlocal heat conduction

A non-classical local gradient theory of nonferromagnetic thermoelastic dielectrics is presented, incorporating both the local mass-displacement process and the heat-flux gradient effect. The process of local mass displacement is related to the changes in material microstructure. The nonlocal heat conduction law is also addressed in the model. Thus, the generalized relationship between the higher-grade heat and entropy fluxes is adopted. The gradient-type constitutive relations and governing equations are derived using the fundamental principles of continuum mechanics, non-equilibrium thermodynamics, and electrodynamics. Due to the contribution of higher-grade flux, the nonlocal law of heat conduction is obtained. The constitutive relations for isotropic materials with the corresponding additional material constants are derived. To illustrate the local gradient theory and to show the electro-thermo-mechanical coupling effect in isotropic materials, a straightforward problem is analytically solved for a layered non-piezoelectric structure under non-uniform temperature distribution. The analytical results reveal that the thermal polarization effect can also be pronounced in isotropic materials. To illustrate the model considering the effect of nonlocal heat conduction, the propagation of spherical thermoelastic harmonic waves in a homogeneous and isotropic elastic medium with non-classical heat conduction law is studied.

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.

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.

A reduced-order peridynamic model for predicting nonlocal heat conduction in nanocomposites

A reduced-order peridynamic model is developed for predicting transient heat conduction in nanocomposites. Peridynamics is utilized to describe the nonlocal heat conduction process in the nanoscale. An implicit numerical scheme is constructed for numerical discretization, and the proper orthogonal decomposition is employed to establish the reduced-order model. The performance of the proposed method is verified quantitatively with benchmark problems. Discontinuities, such as cracks and interfacial thermal resistance, can be successfully captured with the computation time significantly reduced. The reduced-order peridynamics provides an alternative solution to balance the flexibility of peridynamics and the urgency of computation efficiency.

A nonlocal theory of heat transfer and micro-phase separation of nanostructured copolymers

Directed self-assembly of block copolymer (BCP) has shown promise as a nano-patterning technology for various applications such as microelectronics, semiconductor manufacturing and biotechnology. In this paper, we present a thermodynamically consistent nonlocal model of phase transformation and heat transfer for BCP via the continuum theory of mixtures. Our model is developed based on the mass and energy balances of each phase and a set of microforce balances to describe the dynamics of microphase separation during self-assembly and the size and memory effects of heat conduction in BCP thin films. We derive constitutive relations for coupling the phase field and temperature through upscaling the self-consistent field theory of polymers, and present the connections between the derived nonlocal heat conduction model and the phonon Boltzmann transport equation. We provide a finite element solution of the proposed model that includes unconditionally stable time-stepping schemes, and we perform various numerical experiments that showcase different features of the model. Furthermore, we conduct three-dimensional numerical experiments of laser zone annealing process to qualitatively investigate the effect of laser velocity on the self-assembly behavior of BCP thin films. Our results show that the proposed model can simulate essential features of thermally induced phase responses of BCPs, consistent with experimental observations and high-fidelity simulations.

Effects of changing thermal conductivity on photothermal excitation in non-local semiconductor material subjected to moisture diffusion and laser pulses

A novel model is presented in this study for the situation of wave interference in a non-local stimulated semiconductor medium, including thermal, plasma, and elastic waves. Moisture diffusion in one dimension (1D) has been included in the governing equations by varying the non-local medium's thermal conductivity under the impact of laser pulse according to the non-Gaussian temporal profile. The dimensionless model was characterized by linear transformations. Analytical solutions were obtained by applying Laplace transforms to a description of the governing equations based on the photo-thermoelasticity theory based on moisture diffusivity and variable thermal conductivity. When applying certain of the circumstances (thermal ramp type and non-Gaussian plasma shock), linear solutions are achieved in the time domain using various numerical techniques based on inverse Laplace transforms. Some of the physical variables being studied are visually shown via numerical simulation. The present investigation has produced numerous important concrete instances. Using graphs and theoretical descriptions, several contrasts are drawn, while certain physical factors, such as relaxation durations, changing thermal conductivity, non-local parameters, and reference moisture values, are in play.

Topological Andreev rectification

Quantized transport is a powerful probe of topological phases, and metals are topologically classified by the Euler characteristic of the Fermi sea. Here, the authors demonstrate analytically and numerically that a 2D metal proximitized by a Josephson $\ensuremath{\pi}$ junction exhibits rectification for current along the junction. They introduce the rectified nonlocal conductance and show it is quantized by the Fermi sea topology. InAs-based heterostructures, as well as monolayer and bilayer graphene, are identified as promising platforms for demonstrating this effect.

Signatures of nonlocal electrical conductivity in near-field microscopy

We propose and theoretically substantiate a method to study the nonlocal conductivity of two-dimensional electron systems (2DESs) using the tools of near-field microscopy. We show that the height-dependent polarizability of an illuminated near-field probe is substantially different for various transport regimes of charge carriers in a 2DES. For the hydrodynamic transport regime, the polarizability scales as ${z}_{0}^{\ensuremath{-}2}$, where ${z}_{0}$ is the elevation of the probe above the 2DES. Both for Drude and for classical ballistic regimes of conduction, the polarizability scales as ${z}_{0}^{\ensuremath{-}3}$. In the former case, the polarization is carrier density independent, while in the latter it largely depends on carrier density. More generally, we find that the polarizability of the probe is proportional to the Laplace transform of the wave-vector-dependent conductivity and the inverse dielectric function of the 2DES over the wave vectors $q$. Our results should provide a simple tool for studies of nonlocal conductivity in solids, which is challenging to address with other techniques.