Phase Lag Parameters Research Articles

Synchronization transitions in adaptive Kuramoto-Sakaguchi oscillators with higher-order interactions.

Coupled oscillators models help us in understanding the origin of synchronization phenomenon prevalent in both natural and artificial systems. Here, we study the coupled Kuramoto oscillator model having phase lag and adaptation in higher-order interactions. We find that the type of transition to synchronization changes from the first-order to second-order through tiered synchronization depending on the adaptation parameters. Phase lag enables this transition at a lower exponent of the adaptation parameters. Moreover, an interplay between the adaptation and phase lag parameters eliminates tiered synchronization, facilitating a direct transition from the first to second-order. In the thermodynamic limit, the Ott-Antonsen approach accurately describes all stationary and (un)stable states, with analytical results matching those obtained from numerical simulations for finite system sizes.

Domain of influence on generalized thermoelastic diffusion theory

The aim of this research work is to establish the theory of the domain of influence of diffusion disturbance with potential-temperature disturbance under the theory of generalized thermo-elastic diffusion using Lord and Shulman model. For a finite time t > 0, it has been proved that the potential due to displacement, temperature and diffusion effect does not produce any disturbances outside a bounded domain and the domain of influence is dependent on the support of thermo-elasto-diffusive load, the thermo-elasto-diffusive coupling constant and the phase-lag parameters. It has been shown that the domain of influence of the present case reduce to the domain of influence for classical thermo-elasticity theory with or without diffusion and the thermo-elasticity theory with one relaxation parameter without diffusion. Also, the effect of diffusion on thermal wave propagation is shown. This theorem will be applicable to analyze the deformation occur in elastic solids due to internal and external loads for the thermo-elasto-diffusive models and problems based on it in the field of engineering physics like solid-state-physics, physical metallurgy (fabrication of semi-conductor devices in mixture metals and molten semi-conductor), material engineering (separation of polymers), aircraft engineering, mechanical engineering and also in the industries like oil extraction from hydrocarbon and manipulation of macro-molecules like DNA etc.

Effect of thermal diffusivity on Rayleigh waves in human tissue

This work examines the nature of human tissue under the context of dual phase lag thermoelastic diffusion theory using the principle of propagation of Rayleigh wave along the stress free, thermally insulated/isothermal, and impermeable/isoconcentrated conditions. The governing equations for the tissue are formed by considering the third-order approximation of Taylor’s expansion for the modified Fourier’s law of heat conduction and modified Fick’s law of mass diffusion in terms of phase lag parameters. The irrational secular equations of Rayleigh waves are derived, which are then rationalized to extract their complex roots. The phase speeds and the attenuation coefficients are evaluated from these complex roots. The variation of these phase speeds and attenuation coefficients are plotted graphically against angular frequency for two significant modes. The behavioral patterns of displacement components, temperature, and concentration fields are computed and are expressed graphically. The paths of the particle motion are represented graphically. Some results of published articles are recovered from the present formulation to validate our results.

Effect of higher-order interactions on chimera states in two populations of Kuramoto oscillators.

We investigate the effect of the fraction of pairwise and higher-order interactions on the emergent dynamics of the two populations of globally coupled Kuramoto oscillators with phase-lag parameters. We find that the stable chimera exists between saddle-node and Hopf bifurcations, while the breathing chimera lives between Hopf and homoclinic bifurcations in the two-parameter phase diagrams. The higher-order interaction facilitates the onset of the bifurcation transitions at a much lower disparity between the inter- and intra-population coupling strengths. Furthermore, the higher-order interaction facilitates the spread of breathing chimera in a large region of the parameter space while suppressing the spread of the stable chimera. A low degree of heterogeneity among the phase-lag parameters promotes the spread of both stable chimera and breathing chimera to a large region of the parameter space for a large fraction of the higher-order coupling. In contrast, a large degree of heterogeneity is found to decrease the spread of both chimera states for a large fraction of the higher-order coupling. A global synchronized state is observed above a critical value of heterogeneity among the phase-lag parameters. We have deduced the low-dimensional evolution equations for the macroscopic order parameters using the Ott-Antonsen Ansatz. We have also deduced the analytical saddle-node and Hopf bifurcation curves from the evolution equations for the macroscopic order parameters and found them to match with the bifurcation curves obtained using the software XPPAUT and with the simulation results.

Implementation of a Robust PMAE Algorithm to Limit Large Gain Variation in a Fuel-Cell Integrated EV Charging Architecture

This paper proposes an adaptive error convergence technique to improve the charging dynamics of an electric vehicle (EV) charging system in a grid-integrated proton-exchange membrane fuel cell (PEMFC) architecture. The fuel cell is most often characterized by its slow dynamics during multiple load transients and preferably operated as an auxiliary energy source in EV charging architecture. The delayed response affects the overall charging dynamics with further controller phase lag and non-linear system parameters to induce a significant convergence error during reference command tracking. To effectively control multi-source integrated charging dynamics in an EV charging architecture, a projection-modified adaptive estimation (PMAE) algorithm is proposed in this paper. The control algorithm establishes a variable gain adaptation within a bounded error contour and updates the controller gains based on the tracking error dynamics gradient. The fuel cell, supporting other energy resources, provides a stronger charging resiliency with a duty-modified control technique at the EV charging station. To validate the effectiveness of the controller implementation, a grid-integrated multi-objective EV charging prototype is designed and developed for grid-to-vehicle (G2V) and vehicle-to-grid (V2G) at variable operating conditions.

The Effect of Nonlocal Scale Value and Phase Lags on Thermoelastic Waves in a Multilayered LEMV/CFRP Composite Cylinder

In this study, the effect of nonlocal scale value and two phase lags on the free vibration of generalized thermoelastic multilayered LEMV (Linear Elastic Material with Voids)/CFRP (Carbon Fiber Reinforced Polymer) composite cylinder is studied using nonlocal form of linear theory of elasticity. The governing equation of motion is established in longitudinal axis and variable separation model is used to transform the governing equations into a system of differential equations. To investigate vibration analysis from frequency equations, the stress free boundary conditions are adopted at the inner, outer and interface boundaries. The graphical representation of the numerically calculated results for frequency shift, natural frequency, and thermoelastic damping is presented. A special care has been taken to inspect the effect of nonlocal parameter on the aforementioned quantities. The results suggest that the nonlocal scale and the phase lag parameters alter the vibration characteristics of composite cylinders significantly.

Effect of Nonlocal Elasticity and Phase Lags on the Magneto Thermoelastic Waves in a Composite Cylinder with Hall Current

In this study, the effect of nonlocal scale value and two phases lags on the free vibration of generalized magneto thermoelastic multilayered LEMV (Linear Elastic Material with Voids)/CFRP (Carbon Fiber Reinforced Polymer) composite cylinder is studied using nonlocal form of linear theory of elasticity. The governing equation of motion is established in longitudinal axis and variable separation model is used to transform the governing equations into a system of differential equations. To investigate vibration analysis from frequency equations, the stress free boundary conditions are adopted at the inner, outer and interface boundaries. The graphical representation of the numerically calculated results for frequency shift, natural frequency, and thermoelastic damping is presented. A special care has been taken to inspect the effect of nonlocal parameter on the aforementioned quantities. The results suggest that the nonlocal scale and the phase lag parameters alter the vibration characteristics of composite cylinders significantly.

Study the effects of temperature and strain rates on transient thermomechanical responses on multilayer skin tissue

The present study is focused on understanding the effects of strain and temperature rates on heat transport mechanisms and the related thermo-mechanical interaction with skin tissue, which are essential for the effective application of thermal therapeutic techniques. The goal of this article is to develop a mathematical framework to investigate the thermo-mechanical phenomena occurring on triple-layered skin tissue using the Modified Green-Lindsay model (MGL) by taking into consideration of two thermal relaxation parameters. This model takes into consideration the effect of strain and temperature rate factors in thermoelastic behaviour which was neglected in several other thermoelastic models. The problem is formulated in a unified way to derive the governing equations and constitutive relations under the present model and also the thermoelasticity with two phase-lag parameters. A comprehensive assessment of solution is discussed for MGL model and compared the results with the corresponding results predicted by dual phase lag generalized thermoelastic model that involves two phase-lags. The effect of strain rate term in heat transport on skin tissue are especially highlighted.

Chimera states in multiplex networks: Chameleon-like across-layer synchronization.

Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators' mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups' position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.

Elastic Thermal Deformation of an Infinite Copper Material Due to Cyclic Heat Supply Using Higher-Order Nonlocal Thermal Modeling

Thermoelastic modeling at nanoscale is becoming more important as devices shrink and heat sources are more widely used in modern industries, such as nanoelectromechanical systems. However, the conventional thermoelastic theories are no longer applicable in high-temperature settings. This study provides an insight into the thermomechanical features of a nonlocal viscous half-space exposed to a cyclic heat source. Using a novel concept of fractional derivatives, introduced by Atangana and Baleanu, it is assumed that the viscoelastic properties follow the fractional Kelvin–Voigt model. The nonlocal differential form of Eringen’s nonlocal theory is employed to consider the impact of small-scale behavior. It is also proposed that the rule of dual-phase thermal conductivity can be generalized to thermoelastic materials to include the higher-order time derivatives. The numerical results for the examined physical variables are presented using the Laplace transform technique. Furthermore, several numerical analyses are performed in-depth, focusing on the effects of nonlocality, structural viscoelastic indicator, fractional order, higher-order and phase-lag parameters on the behavior of the nanoscale half-space. According to the presented findings, it appears that the higher-order terms have a major impact on reactions and may work to mitigate the impact of thermal diffusion. Furthermore, these terms provide a novel approach to categorize the materials based on their thermal conductivities.

Heating process analysis for microplate subjected to moving laser pulse source

The moving laser pulse has been widely employed in microstructure processing and manufacturing, while its influence on the dynamic response of microplates is still unclear. This paper aims to propose a thermo-mechanical coupling model to reveal the transverse response of a microplate subjected to a three-dimensional (3D) moving laser heat source. Herein, not only the 3D heat conduction of the moving laser but also the size-dependent behavior of the microplate are taken into account, in which the former is described by the dual-phase-lag (DPL) heat transfer model and the latter is captured by using the modified couple stress theory. Firstly, the governing equations of the microplate are derived with the aid of Hamilton's principle, which are analytically solved by employing the Green's function method, and they are also validated by comparing with FE simulation and previous studies. Subsequently, influences of phase-lag parameters, pulse duration, laser moving speed and size-scale parameter on the thermo-dynamic response of microplate are examined. It is demonstrated that the size-scale parameter and pulse duration both can reduce the deflection amplitude of the microplate, while the effect of laser moving speed is coupled with the phase-lag parameters. The quantitative results obtained in this study can be adopted to deeply understand the heating process during the actual laser-assisted micro-manufacturing and to provide some effective guidelines on this process.

Thermoelastic Coupling Response of an Unbounded Solid with a Cylindrical Cavity Due to a Moving Heat Source

The current article introduces the thermoelastic coupled response of an unbounded solid with a cylindrical hole under a traveling heat source and harmonically altering heat. A refined dual-phase-lag thermoelasticity theory is used for this purpose. A generalized thermoelastic coupled solution is developed by using Laplace’s transforms technique. Field quantities are graphically displayed and discussed to illustrate the effects of heat source, phase-lag parameters, and the angular frequency of thermal vibration on the field quantities. Some comparisons are made with and without the inclusion of a moving heat source. The outcomes described here using the refined dual-phase-lag thermoelasticity theory are the most accurate and are provided as benchmarks for other researchers.

Nonlocal thermoelasticity: Transient heat conduction effects on the linear and nonlinear vibration of single-walled carbon nanotubes

This novel study presents a framework to investigate the effects of transient heat conduction on the nonlinear deflection and vibration of single-walled carbon nanotubes (SWCNTs) based on Eringen’s nonlocal elasticity and nonlocal heat conduction theories. The first phase of this research involves modifying the hyperbolic heat conduction theory by including a nonlocality term, in which the scale of energy transport is taken into account. The next phase includes a thermoelasticity solution for carbon nanotubes (CNTs), which is developed by Eringen’s nonlocal theory and implementing the obtained temperature. The differential quadrature method (DQM) is used to solve the transversely induced nonlocal heat conduction. We have shown the effect of thermal waves on the mode shapes and nonlinear vibration of a SWCNT by considering phase lag parameters. All boundaries are considered under a temperature-jump at the nanometer scale to consider the boundary phonon scattering. The effects of several parameters, including time-dependent boundary conditions, time lag, nonlocal parameter, length and radius, and end supports on the frequency response of SWCNTs are investigated.

Fractional Dual-Phase Lag Equation—Fundamental Solution of the Cauchy Problem

In the paper, a fundamental solution of the fractional dual-phase-lagging heat conduction problem is obtained. The considerations concern the 1D Cauchy problem in a whole-space domain. A solution of the initial-boundary problem is determined by using the Fourier–Laplace transform technique. The final form of solution is given in a form of a series. One of the properties of the derived fundamental solution of the considered problem with the initial condition expressed be the Dirac delta function is that it is symmetrical. The effect of the time-fractional order of the Caputo derivatives and the phase-lag parameters on the temperature distribution is investigated numerically by using the method which is based on the Fourier-series quadrature-type approximation to the Bromwich contour integral.

A Thermoelastic Piezoelectric Fixed Rod Exposed to an Axial Moving Heat Source via a Dual-Phase-Lag Model

Piezoelectric ceramics are used more in the active control of noise and vibration with sensors and actuators. As a result, a one-dimensional homogeneous thermoelastic fixed piezoelectric rod subjected to a moving heat flow has been considered. The heating rod is affected by three fields, namely, thermal, mechanical, and electric potential. In order to design a reliable smart structure, this study is necessary and the thermopiezoelectric behavior of piezoelectric ceramics must be understood clearly. The Laplace transform method is applied to acquire the distributions of stress, deformation, and temperature fields. The effect of heat source velocity and phase lag parameters on the considered physical fields is displayed graphically, and the results are compared with other models of thermoelasticity. The present findings could find possible applications for designing receiving portions of transformers of Rosen type for voltage magnification.

Photothermoelastic Investigation of Semiconductor Material Due to Distributed Loads

A dynamic mathematical model of photothermoelastic (semiconductor) medium is developed to analyze the deformation due to inclined loads. The governing equations for photothermoelastic with dual phase lag model are framed for two dimensional case and are further simplified by using potential function. Appropriate transforms w.r.t time (Laplace) and w.r.t space variables (Fourier) are employed on the resulting equations which convert the system of equations into differential equation. The problem is examined by deploying suitable mechanical boundary conditions. Specific types of distributed loads as uniformly distributed force and Linearly distributed force are taken to examine the utility of the model. The analytic expressions like displacements, stresses, temperature distribution and carrier density are obtained in the new domain (transformed).To recover the quantities in the physical domain, numerical inversion technique is employed. Numerical computed results with different angle of inclination vs distance are analyzed with and without dual phase lag theories of thermoelasticity in the form of visual representations. It is seen that physical field quantities are sensitive towards photothermoelastic and phase lag parameters.

Waves at the imperfect boundary of elastic and bio-thermoelastic diffusive media

The present investigation deals with the reflection and transmission phenomena in isotropic elastic half-space (ES) and bio-thermoelastic diffusive half-space (BDS) for the study of plane harmonic waves. The two half-spaces are separated by an imperfect interface and the governing equations for BDS are modified by introducing phase lag parameters in Fourier’s law of heat conduction and Fick’s law of mass diffusion. After expressing the equations in two-dimension, the potential functions are used to simplify the equations for further calculation. The plane P or SV wave is incident from ES which results in two reflected waves in ES and four transmitted waves in BDS. The amplitude ratios are obtained for these reflected and transmitted waves concerening the incident P or SV wave for stiffness forces. The obtained amplitude ratios are further used to drive the energy ratios of various reflected and transmitted waves. These ratios are impacted by the characteristics of the wave and material properties of the media. The resulting energy ratios are computed numerically by developing a numerical algorithm and displayed in the form of graphs to show the effects of blood perfusion rate, lagging times, and stiffness parameters.

Vibrations of Inhomogeneous Viscothermoelastic Nonlocal Hollow Sphere under the effect of Three-Phase-Lag Model

Herein, the free vibrations of inhomogeneous nonlocal viscothermoelastic sphere with three-phase-lag model of generalized thermoelasticity have been addressed. The governing equations and constitutive relations with three-phase-lag model have been solved by using non-dimensional quantities. The simple power law has been presumed to take the material in radial direction. The series solution has been established to derive the solution analytically. The relations of frequency equations for the continuation of viable modes are developed in dense form. The analytical results have been authenticated by the reduction of nonlocal and three–phase–lag parameters. To investigate the quality of vibrations, frequency equations are determined by applying the numerical iteration method. MATLAB software tools have been used for numerical computations and simulations to present the results graphically subject to natural frequencies, frequency shift, and thermoelastic damping. The numerical results clearly show that the variation of vibrations is slightly larger in case of nonlocal elastic sphere in contrast to elastic sphere.

Response of deflection and thermal moment of Timoshenko microbeams considering modified couple stress theory and dual-phase-lag heat conduction model

The present work focuses on the vibration analysis of Timoshenko microbeams considering the effects of the modified couple stress theory (MCST) and the dual-phase-lag (DPL) heat conduction model. The explicit expressions for equations of motion and corresponding boundary conditions of microbeam are constructed using the Hamilton’s principle and DPL heat conduction theory. For the simply supported microbeam, the deflection and thermal moment are obtained subjected to a constant impulsive force per unit length. A comparison of results between classical theory and the MCST under DPL model is specifically taken into consideration. The obtained results are also compared to the existing results for Lord-Shulman (LS) and Fourier heat conduction models. Besides, the influences of some parameters, such as the aspect ratios of length to thickness and material length-scale parameter to thickness on deflection and thermal moment of the microbeam, are analyzed in a detailed manner. The effects of phase-lag parameters associated with the DPL heat conduction model on deflection and thermal moment are also discussed. For a short time range, the present results show a good agreement with the corresponding results under LS and Fourier heat conduction models. But for a large time range, the present results show a lower rate of energy dissipation in comparison to LS and Fourier heat conduction models. In addition, the size-dependency of microbeam under the DPL model has been observed which plays an important role on the response of deflection and thermal moment. It is also revealed that there is a significant influence of phase-lags on the variation of microbeam’s deflection and thermal moment.

Optimal cost tuning of frustration: Achieving desired states in the Kuramoto-Sakaguchi model.

There are numerous examples of studied real-world systems that can be described as dynamical systems characterized by individual phases and coupled in a networklike structure. Within the framework of oscillatory models, much attention has been devoted to the Kuramoto model, which considers a collection of oscillators interacting through a sinus function of the phase differences. In this paper, we draw on an extension of the Kuramoto model, called the Kuramoto-Sakaguchi model, which adds a phase lag parameter to each node. We construct a general formalism that allows us to compute the set of lag parameters that may lead to any phase configuration within a linear approximation. In particular, we devote special attention to the cases of full synchronization and symmetric configurations. We show that the set of natural frequencies, phase lag parameters, and phases at the steady state is coupled by an equation and a continuous spectra of solutions is feasible. In order to quantify the system's strain to achieve that particular configuration, we define a cost function and compute the optimal set of parameters that minimizes it. Despite considering a linear approximation of the model, we show that the obtained tuned parameters for the case of full synchronization enhance frequency synchronization in the nonlinear model as well.