Perturbation Technique Research Articles

Impacts of radiative heat flux and heat acquisition on steady Magneto hydrodynamics with viscous and ohmic dissipation, Free convection casson fluid flow between porous plates

An investigation was conducted on a steady magnetohydrodynamic (MHD) free convection flow of a Casson fluid across a parallel vertical plate immersed in a porous medium with viscous and magnetic dissipation. In addition, the energy equation contains terms for radiational heat flow, heat injection, and suction. The perturbation approach provides an analytical solution to the governing nonlinear partial differential equations underlying this phenomenon. The numerical approach in the Maple program was used to verify the correctness of the outcomes produced by the perturbation technique. The Grashof and Prandtl numbers, Casson fluid, magnetic field, and porosity parameters as well as radiation parameter, and heat injection/suction parameter impact on the flow is discussed graphically. Skin friction coefficient and Nusselt number are tabulated for a range of magnetic and radiative parameter values. The other physical factors listed above accelerate the fluid velocity, but the magnetic field decreases it. Furthermore, the wall shear stress and heat transfer were significantly impacted by the magnetic and radiative factors.

Resonant Frequency Analysis using Perturbation and Resonant Cavity Method in Printed Dual Band Antenna for WiMAX Application

A printed dual-band antenna is designed to resonate at 3.5 GHz with the measured gain of 6.38 dBi and at 5.5 GHz with that of 5.84 dBi for the WiMAX application. The bandwidth of this antenna at 3.5 GHz and 5.5 GHz is 8% and 5%, respectively. The radiation efficiency of 91.45% is obtained at 3.5 GHz and that of 89.56% at 5.5 GHz. A novel approach based on the perturbation technique is used to relate the resonant frequency to the electromagnetic energy stored and the volume of the proposed antenna’s structure. The dual resonant length of this antenna is determined by a parameter named as the length reduction factor, which is computed by the curve fitting method. A polynomial equation connects the length reduction factor and resonance frequency. The resonant cavity model has been used to derive the resonant frequency equations for dual bands. The simulation and measured results are used to validate the analytically predicted resonant frequency caused by the structure perturbation and cavity technique and show good agreement. This antenna is fed by a balanced parallel plane, which conveniently facilitates the PCB’s integration.

On the modulational of Schamel nonlinear Schrödinger equation and the associated envelope excitations in a degenerate relativistic quantum complex plasma

The modulational instability (MI) of Schamel/modified nonlinear Schrödinger equation (SNLSE) or (mNLSE) and the associated envelope excitations, including bright solitons in a multicomponent dense plasma consisting of relativistically degenerate electrons, trapped ions, and non-degenerate dust species are reported. A conventional multiple scales perturbative technique is utilized to get a SNLSE. This equation is different from the standard NLSE which the SNLSE has a nonlinear term with fractional order (3/2). The MI criteria are derived in detail. Also, the occurrence of envelope solitary wave and the effects of the different physical parameters on its profile are briefly discussed. The current results are advantageous to understand the mechanism of the propagation of the envelope excitations in complex plasmas with trapped ions and relativistically degenerate electrons, such as those observed in space observations and laboratory complex plasma.

Existence and Global Asymptotic Behavior of Positive Solutions for Superlinear Singular Fractional Boundary Value Problems

In this paper, we provide sufficient conditions for the existence, uniqueness and global behavior of a positive continuous solution to some nonlinear Riemann-Liouville fractional boundary value problems. The nonlinearity is allowed to be singular at the boundary. The proofs are based on perturbation techniques after reducing the considered problem to the equivalent Fredholm integral equation of the second kind. Some examples are given to illustrate our main results.

A Mathematical Investigation of Flow of Third Grade Fluid in Channel Filled with Porous Media with Heat Source

In this study on flow of third grade fluid in channel filled with porous media in the presence of heat generation, the researcher considered and analyzed the effects thermo-physical parameters involved the momentum and energy equations. The nonlinear momentum and energy equations arising from the flow regime is solved analytically using perturbation technique. Explicit expression for the velocity field and energy balance have been obtained Results show that a little increase in the third grade parameterß , Grashof number,G, and the magnetic field parameter,M, reduces the velocity of fluid flow but enhances the temperature of the system greatly.

Influence of variable viscosity and gravity fluctuation on double diffusive convection in a fluid layer with boundary slab of finite conductivity

The linear stability analysis is carried out for the onset of double-diffusive convection in a fluid layer with a boundary slab along with temperature-dependent viscosity and gravity fluctuation. The authors proposed three types of gravity fluctuation. We considered three cases of gravity field fluctuation: (a) linear and (b)parabolic and (c) cubic. An analytical solution for the subsequent problem is acquired through the perturbation technique. The findings demonstrate that the viscosity variation parameter, the thermal conductivity ratio, the gravity parameter, the depth ratio, and the soret parameter accelerate the start of convection, while the increasing Lewis number slow down the convective motion. Additionally, the system was found to be more stable for the linear type of gravity field fluctuation and more unstable for the cubic type of gravity field fluctuation.

Linear and nonlinear kinetic Alfvén waves at Venus

Space observations show that Venus suffers significant atmospheric erosion caused by the solar wind forcing. Plasma acceleration is found to be one of the main mechanisms contributing to the global atmospheric loss at Venus through its magnetotail. Motivated by these observations, we propose that kinetic Alfvén waves (KAW) may be a possible candidate for charged particle energization at the upper atmosphere of Venus. To test this hypothesis, we explored the basic features of both linear and nonlinear KAW structures at Venus. We considered a low-but-finite β plasma consisting of ionospheric populations (consisting of hydrogen H+, oxygen O−, and isothermal ionospheric electrons) and solar wind populations (protons and isothermal electrons). In the linear regime, we obtain a linear dispersion relation that exhibits a dependence on the intrinsic plasma configuration at Venus. The linear analysis predicts wave structures with wavelengths of ~10–102 km and frequencies of up to ~5 Hz. In the nonlinear regime, small-but-finite-amplitude solitary excitations with their corresponding bipolar electric field are obtained through the reductive perturbation technique. We discuss the influence of the intrinsic plasma parameters (the ionic concentration, solar wind electron temperature, magnetic field strength, and obliqueness) on the nature of the structures of the solitary KAWs and their corresponding electric field. We find that the ambipolar field is amplified with increasing propagation angle, magnetic field strength, and relative temperature of electrons. Our theoretical analysis predicts the propagation of elliptically polarized ultra-low-frequency (ULF) solitary structures with a maximum magnitude of ~0.01–0.034 mV m−1 and a time duration of 20–30 s. The result of the fast Fourier transform (FFT) power spectra of the ambipolar parallel electric field is broadband electromagnetic noise in the frequency range of ~0.5–2 Hz.

A non-standard computational method for stochastic anthrax epidemic model

This study employing a non-standard computational method for a stochastic anthrax epidemic model can enhance accuracy, evaluate control measures, and identify critical factors. The mathematical modeling of an anthrax disease includes the four-compartment of the population as susceptible animals (s), infected animals (i), carcasses animals (c), and grams spores of animals in the environment (a). The continuous model analysis (equilibria, reproduction number, and local stability of equilibria) is studied rigorously. The stochastic model is based on transition probabilities and parametric perturbation techniques. The fundamental properties of the model with standard computational methods such as Euler Maruyama, stochastic Euler, and stochastic Runge Kutta are studied. Unfortunately, these methods are time-dependent and even valid for short-period analysis of the disease. In comparison, the non-standard computational method, like the non-standard finite difference method nonstandard finite difference in the sense of stochastic, is designed for the given model. The non-standard computational method and its dynamical properties (positivity, boundedness, and dynamical consistency) are studied thoroughly. In the end, numerical results of the non-standard computational method with the existing standard computational methods are provided. These benefits contribute to a more comprehensive understanding of anthrax epidemiology and support effective decision-making in public health interventions.

On the propagation of cnoidal wave and overtaking collision of slow shear Alfvén solitons in low β magnetized plasmas

The overtaking collisional phenomenon of slow shear Alfvén solitons are studied in a low beta (β = kinetic pressure/magnetic pressure) collisionless, magnetized plasma consisting of electron and ion fluids. By employing a reductive perturbation technique, the Korteweg–de Vries (KdV) equation is deduced for investigating the nonlinear slow shear Alfvén wave. Before embarking on the study of the overtaking collisions, the stability analysis of the KdV equation is studied using the bifurcation theory. Also, a nonlinear periodic solution of the KdV equation is derived for the first time in the Weierstrass elliptic function formula. Moreover, the condition for converting the Weierstrass elliptic function expression to soliton is discussed. Furthermore, it is found that only density dip (rarefactive) solitons are formed in the super-Alfvénic regime. The next step includes the use of the Hirota bilinear method, which results in two and three shear Alfvén soliton solutions and their subsequent phase shifts. The influence of the plasma parameters on the amplitude as well as width of the slow shear Alfvén wave solitons are examined analytically and numerically. We also find out the profiles of overtaking interaction of slow shear Alfvén dip solitons having different amplitudes and speeds numerically. This study is important for understanding the phenomena of nonlinear slow shear Alfvén wave structures both in space and in laboratory plasmas.

Flow and heat transfer analysis on micropolar fluid through a porous medium between a clear and Al2O3−Cu/H2O in conducting field

The current study is focused on the flow of micropolar liquid in a saturated permeable medium sandwiched between clear and hybrid nanofluid filled in an inclined channel, with radiation and dissipation effects. Copper and Aluminium oxide nanoparticles is considered along with base (water) fluid. The solution for velocity, micro rotational velocity, and temperature are determined by applying the regular perturbation technique to the dimensionless version of the governing equations. The heat transport rate at the left y=−1 and right y=2 plate is also calculated, as well as shear stress expressed in terms of skin-friction coefficient and Nusselt number. The result obtained for various physical parameters are analyzed through several graphs and tables. Results reveal that an increase in the material parameter of micropolar fluid, the motion of the fluid flow decreases. The heat transport rate is enhanced and the velocity is degraded by the magnetic parameter. The Hybrid nanofluid temperature is greater when compared to clear and binary hybrid nanofluid. This work establishes the mechanisms for heat transport enhancement on micropolar liquid through a porous medium between a clear and hybrid nanofluid in conducting field.

Investigating the parametric impacts on dust-ion-acoustic solitary waves in magnetized rotating plasmas

This article examines the combined effect of plasma rotation, magnetic field, and several parameters on the dust-ion-acoustic solitary waves (DIASWs). A rotating plasma system is assumed that comprises positive ions (mobile and adiabatic), negative light ions (trapped), isothermal electrons, and dust particles (stationary and positively or negatively charged). Using the reductive perturbation technique (RPT), the mKdV equation is obtained to investigate the variations in wave nature caused by different forces and parameters. It is found that the external magnetic field, oblique rotation, electron and dust concentrations play a key role in varying wave amplitude, width as well as phase speed. Depending on whether the dust is positively or negatively charged, the rotational frequency increases (decreases) the phase speed (amplitude and width). Moreover, the magnetic field enhances the wave amplitude but reduces the width. The results obtained from the study are expected to be useful in describing rotating flows of magnetized plasmas observed in white dwarfs, neutron stars, pulsar radiations, etc.

Understanding contributing neurons via attribution visualization

Understanding contributing neuron features is crucial to explaining convolutional neural network (CNN) decisions. The attribution research provides an effective way to detect contributing neuron features and numerically assign them attribution scores. However, a method to clearly and intuitively represent the implications hidden in neuron attributions is lacking. Attribution scores show the numerical importance of contributing neurons, but the meanings implied by these numerical scores are still not available. To mitigate this gap, we propose an optimization-based visualization method named attribution visualization, which enables an intuitive understanding of neuron attributions. Our approach is distinguished from existing visualization methods by its ability to produce noise-free result, i.e., the ability to remove irrelevant regions from visualizations. We achieve this by introducing an optimizable mask into the visualization process and designing an objective function that simultaneously optimizes the area-constrained mask and visualization. Furthermore, we propose the fractal noise pyramid with diverse and natural frequency spectra as our mask perturbation technique which is key to removing unrelated noise in visualization. We implement several comparisons and user studies with other visual explanations to demonstrate the unique properties of our attribution visualization. We also apply our attribution visualization on two representative CNNs, showcasing its ability to intuitively understand contributing neuron features.

Thermoelastic resonance analysis of BNNT-reinforced nanocomposite beams heated by internal thermal source

The nanocomposite structures due to excellent chemical and thermal resistant have considerable potential for use in an aggressive environment with high corrosion and temperature gradient. This study analyzes subharmonic (Ω/ωL=2 and 3) and superharmonic (Ω/ωL=1/2 and 1/3) resonance behavior of boron nitride nanotube-reinforced composite (BNNT-RC) beams under harmonic excitation and internal thermal source. The thermal analysis is carried out for determining the temperature change using the two-dimensional heat conduction equation with the assumption of an arbitrary variation in the thickness direction. In the framework of adjacent equilibrium configurations and Galerkin method, the modified couple stress Timoshenko beam equations are reduced to one nonlinear decoupled equation. Next, closed-form relations of vibration amplitude (a) and detuning parameter (σ∼) are developed for subharmonic and superharmonic excitations using the multiple-scale perturbation technique. The nonlinear frequency and resonance responses are verified by comparison with the existing ones in the literature. Finally, parametric studies are presented to discuss the effects of length scale parameter, temperature change, energy rate of thermal source, detuning parameter, and geometric ratios. The snap-through buckling behavior is observed in the curves of ωNL/ω∗-ΔT and different unstable paths exist after the occurrence of instability. The thermoelastic effect can increase the stability range of harmonic load amplitude for various values of detuning parameter and it is more pronounced for the temperature variation induced by an internal thermal source.

Adapting Geo-Indistinguishability for Privacy-Preserving Collection of Medical Microdata

In the era of the Fourth Industrial Revolution, the increasing demand for data collection and sharing for analysis purposes has raised concerns regarding privacy violations. Protecting individual privacy during the collection and dissemination of sensitive information has emerged as a critical concern. In this paper, we propose a privacy-preserving framework for collecting users’ medical microdata, utilizing geo-indistinguishability (Geo-I), a concept based on well-known differential privacy. We adapt Geo-I, originally designed for protecting location information privacy, to collect medical microdata while minimizing the reduction in data utility. To mitigate the reduction in data utility caused by the perturbation mechanism of Geo-I, we propose a novel data perturbation technique that utilizes the prior distribution information of the data being collected. The proposed framework enables the collection of perturbed microdata with a distribution similar to that of the original dataset, even in scenarios that demand high levels of privacy protection, typically requiring significant perturbations to the original data. We evaluate the performance of our proposed algorithms using real-world data and demonstrate that our approach significantly outperforms existing methods, ensuring user privacy while preserving data utility in medical data collection.

SORET AND DUFOUR EFFECTS IN A THREE-DIMENSIONAL MHD FLOW PAST A SEMI-INFINITE UNIFORMLY MOVING VERTICAL PLATE WITH CONSTANT HEAT FLUX

In this paper, we have considered the three-dimensional MHD flow past a semi-infinite uniformly moving porous plate with Soret and Dufour effects. The plate is subjected to a sinu-soidal suction velocity and constant heat flux. It is assumed that a uniform magnetic field is applied normal to the plate and directed into the fluid region. But the induced magnetic field is neglected in the study on the assumption that the magnetic Reynolds number is very small. The analytic solutions are obtained by adopting the method of perturbation technique. The influence of magnetic field parameter, thermal diffusion and diffusion-thermo effects on the flow, heat and mass transfer characteristics are mainly focused on the study. It is found from our study that fluid velocity increases under the influence of Soret and Dufour effects.

Temperature and frequency dependencies of the permittivities of selected pyrometallurgical reaction mixtures

High temperatures are required in pyrometallurgical processes and consequently they are extremely energy intensive. Microwaves can offer several potential thermal energy efficiency advantages such as selective and/or rapid internal heating. The fundamental parameters which determine the interaction of microwaves with any given non-magnetic material are the real and the imaginary permittivities. In the current research, the permittivities of various mixtures of several pyrometallurgical raw materials plus carbonaceous reducing agents were determined as a function of both temperature and frequency, using the cavity perturbation technique. The raw materials investigated were an oolitic iron ore, an electric furnace dust and a chromite ore. As the temperature of a mixture increased, the permittivities began to increase rapidly, at temperatures lower than for the raw material alone. Subsequently, as the temperatures increased even further, the permittivities began to decrease and consequently peaks were typically observed in both the real and the imaginary permittivities. The changes in the permittivities of the mixtures were interpreted in terms of reduction reaction information available in the literature and also the amounts of the various species present as calculated by the Equilibrium Module of HSC Chemistry® 7.1. The initial rapid rise in the permittivities of the mixtures was attributed to the presence of the carbonaceous reducing agent, while the decrease was ascribed to the consumption of the carbonaceous reducing agent and also the reduction of metal oxides to metal. The permittivity data can be utilized to better understand the heating behaviour of the mixtures and also can be employed in numerical modelling.

Peristaltic transportation of thermally radiative Sutterby fluid in a tapered microfluidic vessel with convective conditions

Fluid transport from one place to another place by peristaltic pumping is being employed to design the advanced pumping device widely applied in biomedical and industrial applications. Therefore, the peristaltic motion of electrically conducting Sutterby fluid in a tapered channel with slip velocity and convective conditions has been analyzed in this examination. The heat transfer mechanism is also scrutinized in conjunction with thermal radiation and viscous dissipation. The governing expressions of the proposed model are followed under the assumptions of the small Reynolds number hypothesis and long wavelength. The perturbation technique has been implemented to yield the outcome for velocity, energy, and streamlining. The pumping characteristic has been estimated by the Weddles rule. The impressions of numerous pertinent parameters on the flow fields are highlighted via graphs. It is observed from the current flow analysis that the velocity of the flow increases by increasing the Sutterby fluid parameter while it declines with the magnetic parameter. Furthermore, the thermal radiation parameter decreases the temperature distribution of fluid. The current model has been used in bio-engineering processes, industrial fluid mechanics, thermal processing, and cooling systems.

Blockwise acceleration of alternating least squares for canonical tensor decomposition

AbstractThe canonical polyadic (CP) decomposition of tensors is one of the most important tensor decompositions. While the well‐known alternating least squares (ALS) algorithm is often considered the workhorse algorithm for computing the CP decomposition, it is known to suffer from slow convergence in many cases and various algorithms have been proposed to accelerate it. In this article, we propose a new accelerated ALS algorithm that accelerates ALS in a blockwise manner using a simple momentum‐based extrapolation technique and a random perturbation technique. Specifically, our algorithm updates one factor matrix (i.e., block) at a time, as in ALS, with each update consisting of a minimization step that directly reduces the reconstruction error, an extrapolation step that moves the factor matrix along the previous update direction, and a random perturbation step for breaking convergence bottlenecks. Our extrapolation strategy takes a simpler form than the state‐of‐the‐art extrapolation strategies and is easier to implement. Our algorithm has negligible computational overheads relative to ALS and is simple to apply. Empirically, our proposed algorithm shows strong performance as compared to the state‐of‐the‐art acceleration techniques on both simulated and real tensors.

Temperature and frequency dependencies of the permittivities of ferroalloys and reaction mixtures

Ferroalloys, such as ferrochromium, ferromanganese and ferrosilicon are pyrometallurgically produced in energy intensive submerged arc furnaces. In turn, these materials can be used as reagents in a number of pyrometallurgical processes, where the energy requirements are typically supplied by electricity or by the combustion of hydrocarbons. Presently, there are significant incentives to develop more efficient processes, which utilize renewable energy. The electricity from these renewable sources can be converted into electromagnetic radiation, such as microwaves, which in turn can be used as a thermal energy source. The amount of energy absorbed from the electromagnetic field and the amount converted into heat are determined by the real and the imaginary permittivities, respectively. These permittivity results are needed for process development, in particular for numerical modelling. In this research, the permittivities of selected ferroalloys and reaction mixtures were determined as a function of temperature and frequency using the cavity perturbation technique. Also, the limitations of the cavity perturbation technique for these types of measurements are highlighted. In order to interpret the permittivity changes for the reaction mixtures, HSC Chemistry®7.1 was utilized to model the compositional changes as a function of temperature. The results indicate that microwaves are a potential heating source for ferroalloy production and also in processes which utilize ferroalloys as a reagent.

SelfCF: A Simple Framework for Self-supervised Collaborative Filtering

Collaborative filtering (CF) is widely used to learn informative latent representations of users and items from observed interactions. Existing CF-based methods commonly adopt negative sampling to discriminate different items. That is, observed user-item pairs are treated as positive instances; unobserved pairs are considered as negative instances and are sampled under a defined distribution for training. Training with negative sampling on large datasets is computationally expensive. Further, negative items should be carefully sampled under the defined distribution, in order to avoid selecting an observed positive item in the training dataset. Unavoidably, some negative items sampled from the training dataset could be positive in the test set. Recently, self-supervised learning (SSL) , has emerged as a powerful tool to learn a model without negative samples. In this paper, we propose a self-supervised collaborative filtering framework (SelfCF) , that is specially designed for recommender scenario with implicit feedback. The proposed SelfCF framework simplifies Siamese networks and can be easily applied to existing deep-learning based CF models, which we refer to as backbone networks. The main idea of SelfCF is to augment the latent embeddings generated by backbone networks instead of the raw input of user/item ids. We propose and study three embedding perturbation techniques that can be applied to different types of backbone networks including both traditional CF models and graph-based models. The framework enables learning informative representations of users and items without negative samples, and is agnostic to the encapsulated backbones. We conduct experimental comparisons on four datasets, one self-supervised framework, and eight baselines to show that our framework may achieve even better recommendation accuracy than the encapsulated supervised counterpart with a 2×–4× faster training speed. The results also demonstrate that SelfCF can boost up the accuracy of a self-supervised framework BUIR by 17.79% on average and shows competitive performance with baselines.