Perturbation Technique Research Articles

Nonlinear Energy Harvesting From a Base Excited Size-Dependent Flexoelectric Nanostructure with Off-Center Rigid Tip Mass Subjected to Axial Pulsating Excitation

This study explores the incorporation of flexoelectricity and size-dependence effects in electricity harvesting from a novel nanostructure. This nanostructure, featuring a cylindrical-shaped rigid tip mass, is stimulated at the base with axial pulsating excitation. Designed with a nanobeam material, the energy harvester accounts for structural nonlinearity, flexoelectricity, and the presence of an off-center rigid mass, operating under multiple excitations. The eigenanalysis is employed to delve into the dynamic characteristics of the system, providing engineers with insights to identify safe operating regions and operational constraints. Additionally, perturbation techniques are utilized to estimate steady-state voltage and power characteristics, with a focus on maximizing voltage and power generation. The study underscores the impact of size dependence on nanoscale design, flexoelectricity, asymmetric tip mass, and various excitation parameters within a constrained operating range. Analysis reveals how saddle-node and pitchfork bifurcations can disrupt energy harvesting performance and suggests strategies for mitigating these issues by adjusting operational parameters. Moreover, the study emphasizes the significant role of the off-center rigid tip mass in energy estimation compared to conventional microstructure-based energy harvesters. Analytical findings are rigorously validated against numerical results under different resonant scenarios, showcasing the accuracy of the analytical approach in capturing nonlinear sources and optimizing energy harvesting from nanostructures.

Enhancement of Mine Images through Reflectance Estimation of V Channel Using Retinex Theory

The dim lighting and excessive dust in underground mines often result in uneven illumination, blurriness, and loss of detail in surveillance images, which hinders subsequent intelligent image recognition. To address the limitations of the existing image enhancement algorithms in terms of generalization and accuracy, this paper proposes an unsupervised method for enhancing mine images in the hue–saturation–value (HSV) color space. Inspired by the HSV color space, the method first converts RGB images to the HSV space and integrates Retinex theory into the brightness (V channel). Additionally, a random perturbation technique is designed for the brightness. Within the same scene, a U-Net-based reflectance estimation network is constructed by enforcing consistency between the original reflectance and the perturbed reflectance, incorporating ResNeSt blocks and a multi-scale channel pixel attention module to improve accuracy. Finally, an enhanced image is obtained by recombining the original hue (H channel), brightness, and saturation (S channel), and converting back to the RGB space. Importantly, this image enhancement algorithm does not require any normally illuminated images during training. Extensive experiments demonstrated that the proposed method outperformed most existing unsupervised low-light image enhancement methods, qualitatively and quantitatively, achieving a competitive performance comparable to many supervised methods. Specifically, our method achieved the highest PSNR value of 22.18, indicating significant improvements compared to the other methods, and surpassing the second-best WCDM method by 10.3%. In terms of SSIM, our method also performed exceptionally well, achieving a value of 0.807, surpassing all other methods, and improving upon the second-place WCDM method by 19.5%. These results demonstrate that our proposed method significantly enhanced image quality and similarity, far exceeding the performance of the other algorithms.

Effect of slip boundary conditions on unsteady pulsatile nanofluid flow through a sinusoidal channel: an analytical study

A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number.

Comparative Study of the MPPT Control for the Photovoltaic Water Pumping System between FSS-P&O and VSS-P&O

This paper describes the implementation of a renewable energy system that operates independently. It comprises a photovoltaic generator (PV) that supplies power to a solar pumping system, driven by a permanent magnet direct current motor (PMDC) via a DC-DC Buck converter. Consequently, the objective is to maintain steady operation with continuous power supply despite changes in two environmental parameters, including solar irradiation and absolute temperature. The maximal power extraction of the PV panel using the usual perturbation and observation (P&O) technique achieves this objective. This method must provide appropriate duty cycle control for the DC-DC buck converter when the user-selected Fixed-Step Size (FSS) is used, unfortunately, selecting an insufficient fixed-step size led to a power ripple issue with the PV panel. Incorporating a new Variable Step-Size (VSS) into the traditional P&O algorithm shows the occurrence of the enhanced P&O-MPPT control approach. The proposed technique is validated by utilizing the PROTEUS/ISIS software. For various climatic situations, the results demonstrate that the proposed control technique is preferable to the one based on the standard P&O-MPPT.

Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials

Abstract The calendering process is pivotal in enhancing various materials’ surface properties and characteristics, making them indispensable for achieving desired product quality and performance. Also, this process holds significant relevance in various industrial applications, such as polymer processing, food production, and the manufacturing of composite materials. So, the aim of this study is to theoretically examine the calendering process applied to third-grade materials. It specifically explores how temperature variations impact material behavior during passage through two counter-rotating heated rolls. Particular consideration is given to the influence of temperature-dependent viscosity via Reynold’s model. The complexities of mass, momentum, and energy balance equations are reduced through the application of the Lubrication approximation theory. Solutions to these equations for variables such as velocity, flow rate, and temperature fields are accomplished by combining perturbation and numerical techniques. In relation to the calendering process, the thickness of the exiting sheet is specifically explored. Furthermore, this study quantifies substantial engineering parameters such as roll-separating force, pressure distribution, and power transferal from the rolls to the fluid. The governing equations belong to three key dimensionless parameters, namely, the Brinkman number, which is a product of Eckert number and Prandtl number, the temperature-dependent consistency index μ \mu , and a parameter η \eta correlating to non-Newtonian behavior. The outcomes of this study are presented both graphically and in tabular form. It has been observed that a rise in the third-grade parameter decreases detachment point and sheet thickness due to increased material rigidity. Furthermore, established results in the literature regarding the calendering of Newtonian fluids are validated.

Identification and Control of Flexible Joint Robots Based on a Composite-Learning Optimal Bounded Ellipsoid Algorithm and Prescribe Performance Control Technique

This paper presents an indirect adaptive neural network (NN) control algorithm tailored for flexible joint robots (FJRs), aimed at achieving desired transient and steady-state performance. To simplify the controller design process, the original higher-order system is decomposed into two lower-order subsystems using the singular perturbation technique (SPT). NNs are then employed to reconstruct the aggregated uncertainties. An adaptive prescribed performance control (PPC) strategy and a continuous terminal sliding mode control strategy are introduced for the reduced slow subsystem and fast subsystem, respectively, to guarantee a specified convergence speed and steady-state accuracy for the closed-loop system. Additionally, a composite-learning optimal bounded ellipsoid algorithm (OBE)-based identification scheme is proposed to update the NN weights, where the tracking errors of the reduced slow and fast subsystems are integrated into the learning algorithm to enhance the identification and tracking performance. The stability of the closed-loop system is rigorously established using the Lyapunov approach. Simulations demonstrate the effectiveness of the proposed identification and control schemes.

Consequences of Thermal Diffusion and Chemical Reaction on Mixed Convection MHD Casson Fluid through Porous Media with Inclined Plates

In this present article, we analyzed the effects of Thermal diffusion and chemical reaction on nonlinear mixed convection MHD flow of viscous, incompressible and electrically conducting fluid past an inclined porous channel under the influence of thermal radiation and chemical reaction. The transformed conservation equations are solved analytically subject to physically appropriate boundary conditions by using two term perturbation technique. The numerical values of fluid velocity, fluid temperature and species concentration are displayed graphically whereas those of skin friction coefficient, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. It is observed that the velocity is decreased with increasing magnetic field parameter. The resultant velocity and concentration has enhances with increasing thermal diffusion parameters. The study is relevant to chemical materials processing applications.

Identification of lyophilized avocado powder adulteration using the cavity perturbation technique at microwave frequencies

In this paper, we propose the cavity perturbation technique using a high Q cylindrical cavity at 2.4 GHz to identify adulteration of dry-freeze avocado powder with two of the most common adulterants (chickpea powder and green color). Three different adulteration conditions are explored, namely, avocado powder mixed with color, avocado powder mixed with chickpea powder, and avocado powder mixed with 50% colour–50% powder, at various contamination ratios (100, 90, 77, 62, 50, and 0%). For all cases, the perturbation technique shows clear linear quadratic regression trends that make adulteration identification possible.

Cosmographic and matter bounce scenario in modified torsion gravity

In this manuscript, we investigate the matter bounce cosmological implications in the context of f(T,τ) gravity (T represents the torsion scalar whereas τ is the trace of the energy–momentum tensor). We construct the field equations for spatially flat homogeneous and isotropic space–time with perfect fluid configuration. We consider the two particular forms of scale factor inspired by loop-quantum cosmology to investigate the matter bounce mechanism. In this regard, we examine the graphical behavior of cosmological as well as dynamical parameters at and in the neighborhood of bounce point. Furthermore, the stability via perturbation technique and energy conditions are also discussed. It is concluded that all the cosmographic tests favor the bouncing cosmology for an appropriate choice of model parameters. It is worth mentioning that considered models are stable and energy conditions are violated at the bouncing point as well as in its vicinity leading to a successful bouncing scenario.

Analysis of free convective flow of nanofluid due to inclined surface with thermos-diffusion effects and chemical reaction

An unsteady free convective flow of nanofluid is studied due to inclined surface in presence of thermos-diffusion effects. The chemical reaction, radiative phenomenon and heat source features are also utilized to discuss the transport phenomenon. The properties of nanomaterials are endorsed with interaction of copper, titanium oxide and aluminum oxide nanoparticles. The dimensionless system is achieved for the governing model. The analysis solution with perturbation technique is suggested. The illustration of thermal flow problem is visualized with variation of parameters graphically. The numerical outcomes are also computed and illustrated.

Evolution of Subsonic Shock Waves Associated with Reconnection Jets in Earth’s Magnetotail

Motivated by the signatures of nonlinear electrostatic waves observed by the Magnetospheric Multiscale spacecraft mission in reconnection jet regions of Earth's magnetotail, we have explored the dynamical features of ion-acoustic shock waves in the magnetotail. In this investigation, we have examined the dynamics and characteristics of ion-acoustic subsonic shock waves in non-Maxwellian space plasma comprising of two counterstreaming ion beams with suprathermal electrons, assumed to follow a kappa (κ) distribution. A reductive perturbation technique has been adopted to establish an evolution equation for small amplitude electrostatic shock structures. Importantly, subsonic waves only exist when the beam velocity exceeds a certain threshold, beyond which supersonic and subsonic waves may coexist. The combined effects of the beam velocity and the non-Maxwellian electron statistics have been analyzed to examine the characteristics of subsonic shock waves. Both symmetric and asymmetric (in relative beam density) models have been considered, leading to distinct possibilities in the evolution of subsonic shock waves. The findings of the investigation will help unfold the relatively unexplored dynamical characteristics of subsonic shock waves that may form and propagate in the magnetosphere.

A multi-region analysis of unsteady Oseen's equation for accelerating flow past a circular cylinder

It is difficult to find a valid high-order (of Reynolds number) analytical approximation to the uniform viscous flow past an infinite circular cylinder by applying perturbation techniques. In this study, we show that by accelerating flow past a circular cylinder with taking unsteady Stokes' solution as an initial approximation, higher-order approximation solutions to unsteady Oseen's equation can be obtained by an iteration scheme of perturbation, which exactly satisfy the boundary conditions. As a matter of fact, the nonlinear (convective) term linearized by Oseen's approximation is overweighted especially near the body surface. To eliminate the overweight, a multi-region analysis is proposed in this study to improve analytical unsteady Oseen's solution so as to extend the valid range of Reynolds numbers. In other words, the flow region is hypothetically divided into several annular regions, and the linearized convective term in each region is modified by multiplying with a Carrier's coefficient c (0 < c ≤ 1). The results show that, when the accelerating parameter in the range of 0.5 ≤ a ≤ 4, the maximum effective Reynolds number Reeff of the fourth-order five-region solution is both much larger than that of Stokes' and Oseen's ones. For example, when a = 0.5, Reeff = 22.26 is roughly eight times that of Stokes' solution (Reeff = 2.67), and nine times that of Oseen's solution (Reeff = 2.41). Moreover, when the instantaneous Reynolds number Re(t) is smaller than the Reeff, the flow separation angle and the wake length are both consistent with the numerical results obtained by accurately solving the full Navier-Stokes equations. In addition, the flow properties, including the drag coefficients, streamline patterns, and the pressure coefficients, as well as the vorticity distributions also agree well with the numerical results. This study represents a significant extension of our previous study for unsteady Stokes' equation [Xu et al., Phys. Fluids 35, 033608 (2023)] to unsteady Oseen's equation and its generalization.

Microwave thermal pre-treatment and calcination of biomineralised sorbents for calcium looping

Waste eggshells have been investigated as biomineralised CO2 sorbents for the calcium looping cycle due to their high Ca content, low cost, availability, and high CO2 uptake. This work investigates a novel heat-pre-treatment using eggshells as raw material. The eggshells were simultaneously calcined and thermally pre-treated via microwave heating using different powers and times whilst maintaining the same input energy in a single mode cavity reactor. The calcined eggshells were characterised using standard characterisation techniques such as TGA and isotherms of N2 adsorption at 77 K. The dielectric properties were measured using the cavity perturbation technique at 2.45 GHz. Numerical electromagnetic simulations were performed using COMSOL Multiphysics and results were used to optimise the experimental setup. The treated materials were subjected to carbonation/calcination cycles in order to assess their suitability as a calcium-looping sorbent. The sorbent that exhibited a more stable CO2 uptake was the one treated at the highest power (800 W) 4.5 mmol CO2/g sorbent after 20 cycles under mild calcination conditions. Adsorbents prepared at 400, 600 and 800 W displayed similar CO2 uptake after 20 cycles when the calcination conditions were under more realistic conditions.

Isospectral graphs via spectral bracketing

In this article, we develop a perturbative technique to construct families of non-isomorphic discrete graphs which are isospectral for the standard (also called normalised) Laplacian and its signless version. We use vertex contractions as a graph perturbation and spectral bracketing with auxiliary graphs which have certain eigenvalues with high multiplicity. There is no need to know explicitly the eigenfunctions of the corresponding graphs. In principle, one only needs to know the multiplicity of the eigenvalues of the auxiliary graphs, and that these eigenvalues are all different. We illustrate the method by presenting several families of examples of isospectral graphs including fuzzy balls, complete bipartite graphs and subdivision graphs obtained from the previous examples. All the examples constructed turn out to be also isospectral for the standard (Kirchhoff) Laplacian on the associated equilateral metric graph.

Modified Korteweg–de Vries solitons with quartic nonlinearity in a dusty plasma

The present multicomponent dusty plasma with ions, Cairns distributed electrons and immobile dusts has been investigated first time through modified Korteweg–de Vries (mKdV) equation of quartic nonlinearity derived by reductive perturbation technique. In this new investigation, it is found that the dust ion-acoustic (DIA) solitary waves have smaller amplitudes compared to the amplitudes of mKdV-DIA compressive solitons of our previous investigation []. Roles of non-thermal parameter (β), dust to ion density ratio (σ), number of dust charge (Z d ) and initial streaming speed of ion (u i0) in the growth of amplitudes and widths of this new mKdV-DIA solitons are investigated.

Free vibration analysis of the geometrically nonlinear functionally graded porous curved panels in deterministic and stochastic domains considering various boundary conditions

This study focuses on the analysis of free vibrations in functionally graded (FG) panels with characteristics such as porosity, curvature, and geometric nonlinearity. The analysis encompasses both deterministic and stochastic domains while considering a range of boundary conditions. The nonlinear finite element formulation adopted in this study is based on a higher-order nonlinear shell theory that incorporates the von Karman geometric nonlinearity. The material properties of the FG curved panels are graded using a power law distribution. The investigation includes four different boundary conditions and various types of curved panels, namely spherical, hyperbolic paraboloidal, elliptical, and cylindrical. Stochastic analysis employs the first-order perturbation technique (FOPT), while Monte Carlo simulation (MCS) is employed solely for validating the FOPT model. The study explores the influence of boundary conditions, panel types, porosity distribution, volume fraction index, and other factors in both deterministic and stochastic domains, taking into account randomness in material properties. The stochasticity in the geometric properties like dimensions, and boundary conditions can be the potential future scope of this study.

Coupled circularly polarized electromagnetic soliton states in magnetized plasmas

The interaction between two co-propagating electromagnetic pulses in a magnetized plasma is considered, from first principles, relying on a fluid-Maxwell model. Two circularly polarized wavepackets by same group velocities are considered, characterized by opposite circular polarization, to be identified as left-hand- or right hand circularly polarized (i.e. LCP or RCP, respectively). A multiscale perturbative technique is adopted, leading to a pair of coupled nonlinear Schrödinger-type (NLS) equations for the modulated amplitudes of the respective vector potentials associated with the two pulses. Systematic analysis reveals the existence, in certain frequency bands, of three different types of vector soliton modes: an LCP-bright/RCP-bright coupled soliton pair state, an LCP-bright/RCP-dark soliton pair, and an LCP-dark/RCP-bright soliton pair. The value of the magnetic field plays a critical role since it determines the type of vector solitons that may occur in certain frequency bands and, on the other hand, it affects the width of those frequency bands that are characterized by a specific type of vector soliton (type). The magnetic field (strength) thus arises as an order parameter, affecting the existence conditions of each type of solution (in the form of an envelope soliton pair). An exhaustive parametric investigation is presented in terms of frequency bands and in a wide range of magnetic field (strength) values, leading to results that may be applicable in beam-plasma interaction scenarios as well as in space plasmas and in the ionosphere.

Pulsatile nanofluid flow with variable pressure gradient and heat transfer in wavy channel

This research contributes to the comprehension of nanofluid behaviour through a wavy channel, emphasizing the significance of considering diverse influences in the modelling process. The study explores the collective influence of pressure gradient variation, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat transfer on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research assuming a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient, significantly influencing several associated parameters. The mathematical model characterizing nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameters values. The findings obtained for differing parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, volume fraction of nanoparticles, radiation parameter, Prandtl number, and the suction/injection parameter on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with higher permeability. Additionally, the temperature is observed to escalate with a rising nanoparticle volume fraction and radiation parameter, while it declines with increasing Prandtl number.

Uncertain damage identification methods based on residual force vector under the influence of measurement noise

This paper proposes probabilistic and interval methods, grounded in the residual force vector technique, to quantify measurement uncertainties and effectively integrate them into the identification process. In the probabilistic method, the measurement noise is assumed to be a zero-mean normal distribution, while the stiffness parameters of structural elements are assumed to follow a normal distribution, represented by mean values and standard deviations. In the interval method, the measurement noise is modelled as interval numbers, and the interval perturbation technique is employed to derive interval bounds for elemental stiffness parameters. A two-step model updating strategy is implemented, separately addressing pristine and damaged structures, to mitigate modeling errors. By using the results of probabilistic damage identification, a novel damage index termed damage expectation capable of capturing both the extent and probability of damage is introduced. Furthermore, an interval damage index is introduced to quantify the damage based on interval damage identification results. The impact of noise levels on the statistical properties of uncertain damage indices is also investigated. Numerical examples reveal that deterministic indexes exhibit a monotonic increase in average values with increasing noise levels. Particularly, as noise levels rise, the standard deviation of the combination index initially surpasses the deterministic damage index but eventually diminishes. Through the proposed methodology, structural damage can be identified even in the presence of uncertainties. The efficacy of the proposed damage identification technique is also validated by experimental data.

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.