Power Law Parameters Research Articles

Entropy, thermal, and mass transportation optimization of magnetohydrodynamic power-law nanofluid over stretched sheet with chemical reaction effect

The power-law nanofluid’s heat and mass transmission over a stretched surface with magnetic field, entropy optimization, and chemical reaction effects is the main focus of the present study. The governing partial differential equations are reduced using similarity transformation into ODEs (ordinary differential equations), which are then numerically solved with the help of the Keller box and finite difference techniques. A substantial evaluation is conducted using the controlling flow factors, which include the Eckert number, chemical reaction factor, Brownian motion parameter, thermophoresis number, power-law index (n), and generalized Prandtl number (Pr), on the fluid velocity profile, flowing fluid temperature, and concentration profile. A decrease in the velocity profile is observed when the chemical reaction process is accelerated, leading to heat absorption. However, when the power-law parameter increases, the fluid’s temperature decreases, and the velocity profile increases at specific values of viscous dissipation (Ec = 0.1) and chemical reaction (γ = 0.01). The values of the coefficient of skin friction (Cf), Sherwood factor (Shx), and reduced local Nusselt number (Nux are also computed and presented in the form of a table for the generalized Prandtl number (Pr = 7.0). The coefficient of skin friction and mass transfer and heat transfer rates are quantitatively compared with those in the literature for particular circumstances, and the results demonstrate good agreement with each other. This research offers insightful information for designing and improving systems that use nanofluids exposed to external magnetic fields, which has ramifications in many technical uses, including heat exchange systems based on nanofluids and thermal management systems.

Quantum versatility in PageRank

Quantum mechanics empowers the emergence of quantum advantages in various fields, including quantum algorithms. Quantum PageRank is a promising tool for a future quantum internet. Recently, arbitrary phase rotations (APRs) have been introduced in the underlying Szegedy's quantum walk of the quantum PageRank algorithm. In this work we thoroughly study the role APR plays in quantum PageRank. We discover the versatility resulting from quantumness. Specifically, we discover the emergence of a cluster phenomenon in rankings considering the rotation phases, i.e., the existence of similar clusters in the distribution of the rankings and their fidelity with the corresponding classical PageRanks, the ranking distribution variance, the coherence and entanglement of PageRank states, and the power-law parameter in the ranking distributions on a scale-free network concerning the two rotation phases. Furthermore, we propose an alternate quantum PageRank with APR which provides an extra tunnel for the analysis of PageRank. We also study the PageRank on the trackback graph of a scale-free graph for the investigation of network information traffic tracking. We demonstrate the rich cluster diversity formed in our alternate quantum PageRank, which offers a novel perspective on the quantum versatility of PageRank. Our results present the quantum-enabled perspective for PageRanking and shed light on the design and application of practical quantum PageRank algorithms. Published by the American Physical Society 2024

Fatigue characterization and life prediction of flexible lattice structures based on DLP processes

This study investigated the effects of cell configuration and relative density on the fatigue performance of truss-like lattice structures. Among the lattice structures examined, simple cube cells exhibited the highest fatigue strength across all relative densities. Numerical simulation results indicated that the S-N curves of the structures demonstrated pronounced power-law behavior as the volume fraction changed. The influence of various geometric factors on the power-law model parameters is discussed in detail. The power-law coefficient is influenced by the unit cell configuration and relative density; however, the power-law index is not affected by relative density and depends solely on the unit cell configuration. A fatigue life prediction model based on the Ashby-Gibson model was proposed. Finally, the reliability of the numerical simulation results was experimentally verified, with the predicted results of the model showing good agreement with the test data.

Characteristic Analysis of Vertical Tidal Profile Parameters at Tidal Current Energy Site

Many mathematical models have been proposed to estimate vertical tidal current profiles. However, as previous studies have shown that tidal current energy sites have different characteristics in their vertical tidal current profiles, it is necessary to estimate the profiles from field-measured data for practical purposes. In this study, we measured layered tidal currents over two months using an acoustic Doppler current profiler (ADCP) to analyze the characteristics of vertical tidal current profiles at the Jangjuk Strait, a candidate site for tidal current energy. As a result, the power law parameter α and bed roughness β were estimated as 4.51–12.41 and 0.38–0.42, respectively. Additionally, the maximum roughness length representing seabed roughness in the logarithmic profile was estimated as 0.221 m, and the estimated friction velocity was 0.038–0.194 m/s. Furthermore, a high correlation was observed between the depth-averaged tidal current velocity and friction velocities at all sites during flood and ebb tide conditions. A high correlation was also found between the bed roughness, roughness length, and power law exponent at relatively deeper sites. Tidal current energy sites display distinct characteristics compared to other sea areas. Therefore, it is essential to account for field conditions when conducting numerical modeling and design.

Stroop task and practice effects demonstrate cognitive dysfunction in long COVID and myalgic encephalomyelitis / chronic fatigue syndrome.

The Stroop task was used to investigate differences in cognitive function between Long COVID (LC), Myalgic Encephalomyelitis / Chronic Fatigue Syndrome (ME/CFS) and healthy control subjects. Subjects viewed four color words or neutral (XXXX) stimuli with the same (congruent) or different color ink (incongruent). Cognitive conflict was inferred from response times for pairings of prestimuli and subsequent stimuli. Overall effects were assessed by univariate analysis with time courses determined for binned response times. LC and ME/CFS had significantly longer response times than controls indicating cognitive dysfunction. Initial response times were ranked LC > ME > HC, and decreased according to power functions. At the end of the task (900s), times were ranked LC = ME > HC. Response times were significantly slower for stimuli following an incongruent prestimulus. Time series for Stroop effect, facilitation, interference, surprise index and practice power law parameters were generally similar in LC, ME/CFS and HC suggesting comparable patterns for recruitment of cognitive resources. The prestimulus data were analyzed and generated positive Stroop and interference effects that were distinct from stimulus effects. LC and ME/CFS have global slowing of response times that cannot be overcome by practice suggesting impaired communications between network nodes during problem solving. Analysis of matched prestimulus - stimulus effects adds a new dimension for understanding cognitive conflict. Cognitive dysfunction in Long COVID and ME/CFS was demonstrated using the Stroop task which found global slowing of response times and limitations of practice effects.

Impact of fly-ash (silica) on amorphous phase formation ain NaNO3-Sr(NO3)2 composite solid electrolytes

In the current research, various weight percentages of flyash were incorporated into a mixed system of 85.32% NaNO3 and 14.68% Sr(NO3)2. The system was analyzed using the studies of conductivity, dielectric and electric modulus. An increase in DC conductivity was observed with the addition of flyash, peaking at 10% by weight. Beyond this concentration, the conductivity began to decrease. This increase in conductivity is attributed to the formation of an amorphous phase within the mixed sytem. XRD, FTIR, SEM, and DSC analyses of the flyash dispersed systems indicated the formation of an amorphous phase. The amorphous phase may be due to the surface interaction between fly-ash(silica)and phase of mixed system. The AC conductivity, which depends on frequency, adheres to universal power law. Power law parameter were determined.

Revisiting the effect of lens mass models in cosmological applications of strong gravitational lensing

Abstract Strong gravitational lens system catalogues are typically used to constrain a combination of cosmological and empirical power-law lens mass model parameters, often introducing additional empirical parameters and constraints from high resolution imagery. We investigate these lens models using Bayesian methods through a novel alternative that treats spatial curvature via the non-FLRW timescape cosmology. We apply Markov Chain Monte Carlo methods using the catalogue of 161 lens systems of Chen et al. (2019) in order to constrain both lens and cosmological parameters for: (i) the standard ΛCDM model with zero spatial curvature; and (ii) the timescape model. We then generate large mock data sets to further investigate the choice of cosmology on fitting simple power-law lens models. In agreement with previous results, we find that in combination with single isothermal sphere parameters, models with zero FLRW spatial curvature fit better as the free parameter approaches an unphysical empty universe, ΩM0 → 0. By contrast, the timescape cosmology is found to prefer parameter values in which its cosmological parameter, the present void fraction, is driven to fv0 → 0.73 and closely matches values that best fit independent cosmological data sets: supernovae Ia distances and the cosmic microwave background. This conclusion holds for a large range of seed values fv0 ∈ {0.1, 0.9}, and for timescape fits to both timescape and FLRW mocks. Regardless of cosmology, unphysical estimates of the distance ratios given from power-law lens models result in poor goodness of fit. With larger datasets soon available, separation of cosmology and lens models must be addressed.

Influence of printing orientation on power-law hardening and ductile damage parameters for 3D-printed SS316L steel: experimental and FEA approach

In the present investigation, the selective laser melting (SLM) technique has been utilized for the 3-dimensional printing (tensile test specimens) of SS316L steel powder at 00 (horizontal) and 900 (vertical) angles. Further, an experimental and finite element analysis approach has been made to analyse the effect of printed orientation or direction on the Hollomon power law parameters (strain hardening exponent (n) and strength coefficient (K)) and ductile damage parameters (fracture strain (εf), stress triaxiality (η) and strain rate ( ε ̇ )). The influence of printing orientation on plastic deformation behavior has also been analysed. The results revealed that 00 angle 3D-printed specimens exhibited 11.05%, 21.97% and 9.50% more yield strength, tensile strength and elongation than 900 angle 3D-printed tensile test specimens. Further, the strain hardening exponent (n) and strength coefficient (K) (Hollomon power law hardening model parameters) for 00 angle 3D-printed specimens are 35.80% and 32.47% more than the 900 angle 3D-printed tensile test specimens respectively. The fracture strain for 00 angle 3D-printed specimens is 37.82% less than the 900 angle 3D-printed tensile test specimens. The percentage difference between FEA and experimental results is less than 5% which shows the good prediction capability of estimated Hollomon power law parameters and ductile damage model parameters with developed FEA model for 00 and 900 3D printed specimens.

An empirical tool for predicting the presence or absence of coseismic displacements at GNSS stations

Unmodeled displacements in GNSS times series, induced by instrumental artifacts or geophysical events, create significant biases in station trajectory parameters that can propagate into the reference frame itself. While non-tectonic ‘jumps’, such as equipment changes, affect only a specific GNSS station, seismically-induced displacements can affect large numbers of sites, severely threatening the frame’s stability. Manually reviewing individual GNSS time series for such effects is highly impractical because there can be thousands of GNSS stations in a frame, and the total number of earthquakes Mw ≥ 6.0 since GPS became fully operational is + 5100. To avoid this time-consuming task, automated methods rely on empirical power-law functions to determine which earthquake-station pairs require coseismic displacement parameters. Still, ‘conservative’ power-law functions tend to add coseismic offsets to stations that do not need them, which can also threaten the stability of the frame. In this work, we present an empirical formulation that was obtained using 809 global seismic events to fit power-law parameters that do not overestimate the region of influence of earthquakes. Our method is based on a two-level selection process: level 1 is isotropic and only considers the epicentral distance between the stations and the earthquake, and level 2 uses the geophysical parameters of the earthquake to predict a ‘tighter’ displacement pattern to select which stations require coseismic trajectory parameters. We applied our level 2 method to a database of ~ 4700 event-station pairs and showed that it removed ~ 55% of the total pairs, all of which had been falsely selected by level 1.

Optical beam spread in seawater

We study the spatial and angular distribution of light in a narrow stationary beam propagating in a medium like seawater. For a power-law parametrization of the seawater phase function, using radiative transfer analysis, we derive analytical expressions that determine the radiance distribution in the medium. Both the case of intermediate source–receiver distances, where absorption only begins to affect spreading of the beam, and the asymptotic regime of beam propagation are examined. For the main characteristics of the radiance distribution (the total power, the variance of the angular and radial distributions), scaling relations involving the inherent optical parameters of seawater are found. To validate the expressions obtained we carry out Monte Carlo simulation for commonly adopted seawater scattering models (of Petzold and Morel et al) and their analytical parameterizations. For optical parameters typical to seawater, the predicted analytical laws are in excellent agreement with the results of the Monte Carlo computations.

Diversified characteristics of the dissipative heat on the radiative micropolar hybrid nanofluid over a wedged surface: Gauss-Lobatto IIIA numerical approach

The present examination focuses on the Falkner-Skan flow of micropolar hybridized nanofluid via a wedge surface. The proposed study examines thermal radiative fluxing and heat dissipation in hybridized nanoparticle aqueous solutions. Simulations of uni-directional radiative transport in optically dense fluids use Rosseland's diffusion model. This study created a Cu-TiO2/water hybrid nanofluid by mixing Cu and TiO2 nanomolecules with H2O. Partial differential equations from Naiver-Stokes theory are used to generate the regulating flow phenomena, then convert them into ordinary differentiation equations using an appropriate similarity approach. Additionally, the three-stage Lobatto IIIA method is used to compute the formulae. Calculations are done using MATLAB's built-in bvp5c function. We found that increasing material characteristics slows fluid flow because micropolar nanofluids minimize drag. These alterations alter fluid flow and boost temperature. However, boosting thermal radiation and Eckert number slows heat movement but improves temperature profiles. Much prior research ignored thermal radiative fluxing and heat dissipation in the aqueous solution of hybrid nanomolecules (Cu and TiO2) in Falkner-Skan micropolar flow via a wedge surface. Tables show wall frictional factor and Nusselt quantity results. Micropolar fluid characteristic decreases velocity but increases micro-rotational velocity. Power-law parameters, volume fractions, radiation, heat source, and Eckert amount affect thermal contours.

Modeling the thermo-oxidative aging effects on fatigue life of natural rubber using a continuum damage mechanics approach

Thermo-oxidative aging (TOA) significantly impacts the fatigue life of rubbers by reducing the fatigue strength and modifying the slope of the Wöhler curve, rendering traditional time-temperature superposition methods inadequate. In this work, we aim to develop a model capable of predicting the effect of TOA on the fatigue properties of rubbers. For this purpose, dumbbell specimens of natural rubber (NR) were subjected to aging in an air-vented oven at different temperatures prior to mechanical testing. Tensile tests were conducted to quantify the aging effects on a microscale network parameter known as elastically active chains (EAC) density, along with determining ultimate properties such as the stress and strain at break. By using a time-temperature equivalence and the Arrhenius shift factor, master curves were constructed for both EAC density and ultimate properties. Subsequently, the fracture properties of the aged material were predicted using an energy limiter approach whose evolution follows that of EAC density. Furthermore, a relationship between the parameters of the continuum damage mechanics (CDM) approach (specifically, the power law parameters of the Wöhler curve) and the fracture properties was proposed, resulting in accurate estimates of the fatigue life regardless of the aging conditions. Satisfactory agreement was observed between the model predictions and the data for nine aging conditions encompassing four different temperatures. The CDM approach also allows assessing the evolution of mechanical damage within the material influenced by TOA. The novelty of this approach lies in establishing a direct relationship between fatigue and fracture properties. Moreover, this is the first time to the best of our knowledge that TOA has been explicitly incorporated into a fatigue life prediction model via the evolution of the EAC density.

Artificial boundary method for the fractional second-grade fluid flow on a semi-infinite plate with the effects of magnetic field and a power-law viscosity

As a typical representative of viscoelastic fluids, second-grade fluids have many applications, such as paints, food products, and cosmetics. In this paper, the equation for describing the fractional second-grade fluid with the power-law viscosity on a semi-infinite plate under the influence of a magnetic field is studied. The numerical solution is obtained using the finite difference method. To handle the semi-unbounded region, the (inverse) z-transform is applied to establish the absorbing boundary condition (ABC) for the solution at the cut-off point. In addition, the numerical example analyzes the superiority of the ABC over the directly truncated boundary condition and the effects of different parameters on the velocity distribution. The conclusion is that the slip parameter, power-law exponent parameter, and power-law index parameter promote the fluid flow, while the magnetic field and fractional parameter hinder the fluid flow.

Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time

This study aims to develop second-order relativistic viscous magnetohydrodynamics (MHD) derived from kinetic theory within an extended relaxation time approximation (momentum/energy dependent) for the collision kernel. The investigation involves a detailed examination of shear stress tensor evolution equations and associated transport coefficients. The Boltzmann equation is solved using a Chapman-Enskog-like gradient expansion for a charge-conserved conformal system, incorporating a momentum-dependent relaxation time. The derived relativistic nonresistive, viscous second-order MHD equations for the shear stress tensor reveal significant modifications in the coupling with dissipative charge current and magnetic field due to the momentum dependence of the relaxation time. By utilizing a power law parametrization to quantify the momentum dependence of the relaxation time, the anisotropic magnetic field-dependent shear coefficients in the Navier-Stokes limit have been investigated. The resulting viscous coefficients are seen to be sensitive to the momentum dependence of the relaxation time. Published by the American Physical Society 2024

Incandescent Lamp from Black Body Perspective

The incandescent lamp from black body perspective was investigated using commercial lamps of various watts. The major component of the incandescent lamp is the tungsten filament. The resistance of the tungsten filament was measured using a digital multimeter at an initial laboratory temperature. Light produced from lamp was separated into visible colours by an equilateral triangular glass prism. Deduced resistances were used to obtain equivalent temperatures by power-law parameterization. The Wien’s displacement law was used to estimate Peak wavelengths at different temperatures. The diameter of the tungsten was measured after dissecting the lamp, and this was used to determine its cross-sectional area. Both Wien’s displacement law and Stefan-Boltzmann expressions were applied in determining the filament’s spectral emissive power (SEP) in comparison with that of the visible spectrum. Planck’s graph of intensity using peak wavelength of tungsten filament as reference was juxtaposed with the intensity of visible spectrum using OriginPro 2016 SR0 b9.3.226. The maximum temperature attained was 2852.87 K with (SEP) of 1478955.24 Wm-2 for the 200W lamp. For the 100W lamp, the (SEP) obtained was 749347.9078 Wm-2 at 2489.14 K. Both temperatures, and even as low as 1250 K, were in agreement with Wien’s displacement law. The percentage estimation of visible spectrum in the radiation was about fourteen percent (14 %) while the rest was infra red radiation. This low visible light produced may be as a result of the non-ideal black body nature of the tungsten filament; and so, the incandescent lamp may be considered a quasi-black body.

Rheology of Suspensions Thickened by Cellulose Nanocrystals.

The steady rheological behavior of suspensions of solid particles thickened by cellulose nanocrystals is investigated. Two different types and sizes of particles are used in the preparation of suspensions, namely, TG hollow spheres of 69 µm in Sauter mean diameter and solospheres S-32 of 14 µm in Sauter mean diameter. The nanocrystal concentration varies from 0 to 3.5 wt% and the particle concentration varies from 0 to 57.2 vol%. The influence of salt (NaCl) concentration and pH on the rheology of suspensions is also investigated. The suspensions generally exhibit shear-thinning behavior. The degree of shear-thinning is stronger in suspensions of smaller size particles. The experimental viscosity data are adequately described by a power-law model. The variations in power-law parameters (consistency index and flow behavior index) under different conditions are determined and discussed in detail.

Enhancing shale gas recovery: An interdisciplinary power-law model of hydro-mechanical-fracture dynamics

This study explores the efficiency of using carbon dioxide (CO2) to extract shale gas, highlighting its potential to enhance extraction while mitigating environmental CO2 pollution. Given the intricate microstructure of shale, CO2 injection inevitably induces deformation within the shale reservoir's internal microstructure, thereby impacting gas displacement efficiency. The organic matter (kerogen) network and fracture network in shale, serving as primary spaces for gas adsorption and migration, exhibit complex microstructural characteristics. Thus, we developed a dynamic coupled hydro-mechanics permeability model for binary gas displacement, and three novel, interdisciplinary fractal power-law parameters are proposed to represent the distribution of shale fractures, considering the adsorption–desorption strength of the kerogen network. Numerical simulations analyzed the changes in gas seepage, diffusion, shale stress, permeability, and factors influencing displacement efficiency during the CO2–EGR (enhanced gas recovery) projects. Key findings include (1) CO2 injection leads to a nonlinear increase in the number of shale fracture networks, thereby enhancing the CH4 output efficiency. (2) Compared to traditional fractal theory, the proposed power-law model is applicable to a wider range of reservoir fracture distributions and effectively characterizes the density (by α), size (by r), and complexity (by n) of the fracture network during the CO2–EGR process. (3) Changes in the proposed interdisciplinary power-law parameters significantly alter CO2 and CH4 adsorption capacities and, in turn, significantly affects displacement efficiency and shale deformation. According to calculations, these parameters have the greatest impact on the CO2–EGR process, ranging from 16.3% to 68.1%.

Numerical investigation of forced convective MHD tangent hyperbolic nanofluid flow with heat source/sink across a permeable wedge

The combined effect of wedge angle and melting energy transfer on the tangent hyperbolic magnetohydrodynamics nanofluid flow across a permeable wedge is numerically evaluated. Electronic gadgets produce an excessive amount of heat while in operation, so tangent hyperbolic nanofluid (THNF) is frequently used to cool them. THNF has the potential to dissipate heat more efficiently, thereby lowering the possibility of excessive heat and malfunctioning components. The effects of thermal radiation and heat source/sink are also examined on the flow of THNF. The flow has been formulated in the form of PDEs, which are numerically computed through the MATLAB solver BVP4c. The numerical results of BVP4c are relatively compared to the published work for validity purposes. It has been detected that the results are accurate and reliable. Furthermore, from the graphical results, it has been perceived that the rising impact of the Weissenberg number accelerates the velocity and thermal profile. The effect of the power-law index parameter drops the fluid temperature, but enhances the velocity curve. The variation in the wedge angle boosts the shearing stress and energy propagation rate, whereas the increment of Wi declines both the energy transfer rate and skin friction.

A Couple of Fresh New Perspectives on the Concatenation Model with Power-Law of Self-Phase Modulation

In this paper, we have secured new optical solitons for the concatenation model with power-law nonlinearity. The traveling wave hypothesis serves as the starting point. To retrieve optical soliton solutions, we have implemented two powerful techniques into the model: the Sardar Sub-Equation Method (SSEM) and the Tanh-Coth method. For power-law nonlinearity, we derived through the balancing principle that solitons would exist for different values of the power-law parameter. Therefore, we have secured a large variety of new soliton solutions for the model. This paper derives dark, bright, and singular soliton solutions for the value of n, as the first case was already covered in a previous report dedicated to addressing the model with Kerr law nonlinearity. Lastly, all the parametric existence conditions of the solitons and all solutions have been constructed.

Generalized vortex flow of nanoparticle shapes over a permeable disc surface with generalized slip conditions

This paper investigates the generalized vortex flow of nanofluid consisting of titanium dioxide (TiO2) with base fluid (H2O) over a permeable disk surface that generates a heat transfer process in the thermal boundary layer of the disk. Four types of non-spherical shapes of nanoparticles (blade, brick, cylinder and platelet) are considered for the research. The motion is produced when the fluid is far from the disk surface and rotates like a solid body with a constant angular velocity [Formula: see text]. The partial differential equations (PDEs) are obtained using boundary layer approximations and then converted into ordinary differential equations (ODEs) using suitable similarity transformations. These nonlinear ODEs are solved using the bvp4c MATLAB solver. The effect of different parameters (n, A, [Formula: see text], [Formula: see text], R and Pr) on the velocity components and temperature profile is shown graphically and in tabular results. This analysis concludes that for all non-spherical shapes, the velocity spectrum of all nanoparticles decreases when the values of factors such as power-law, suction, volume fraction and slip parameter increase. All non-spherical shapes of a nanofluid experience a decrease in fluid temperature due to the Prandtl number, while radiation numbers have the opposite effect.