Power Law Parameters Research Articles

Advanced frequency of thick FGM cylindrical shells with fully homogeneous equation

The effects of shear deformation theory and improved shear correction factors on the advanced computation of frequencies by using the fully homogeneous equation for thick functionally graded material (FGM) circular cylindrical shells are studied. It is quite reasonable to consider the extra advanced effect of third-order shear deformation theory (TSDT) of displacements on the varied shear correction coefficient. The values of advanced nonlinear shear correction coefficient are usually functions of the nonlinear coefficient term in TSDT, power-law exponent parameter, and environment temperature. The main achievements in the nonlinear case of displacements and with the varied value of shear correction coefficients, the non-dimensional fundamental frequencies are estimated, investigated, and compared with the values in the linear case. This paper aims to study the fundamental frequencies of very thick FGM cylindrical shells under the advanced effects of shear deformation theory and improved shear correction factors.

Bright soliton of the third-order nonlinear Schrödinger equation with power law of self-phase modulation in the absence of chromatic dispersion

In this article, we are interested in two principal topics. First, the bright optical soliton solutions of the third-order (1+1)-nonlinear Schrödinger equation including power law nonlinearity with inter-modal and spatio-temporal dispersions are perused by taking advantage of the new Kudryashov method. Second, the impacts of power law nonlinearity parameters on soliton attitude are investigated for acquired bright soliton form. With the proposed technique, the bright optical soliton solution is acquired, and 3D, contour, and 2D plots are depicted. Then, the impact of power law nonlinearity parameters on the soliton attitude has been successfully demonstrated. As is clear from this perusal power law parameters have an important impact on the soliton attitude, and this impact alters based on the soliton form. As regards our investigation, this form of the equation has not been studied with the power law nonlinearity in the absence of the chromatic dispersion for nonlinear models and the proposed method has not been applied the introduced equation before. It is expected that the consequences which are acquired in this study will shed light on the studies in this field.

Advanced numerical simulation techniques in MHD fluid flow analysis using distributed fractional order derivatives and Cattaneo heat flux model

AbstractThis study investigates the flow and heat transfer characteristics of a second‐grade fluid over a flat surface with variable heat flux. Utilizing a mathematical model based on distributed order fractional derivatives, we offer a more precise representation of non‐Newtonian fluid behavior. The associated highly nonlinear equations are tackled numerically through an innovative amalgamation of the finite difference scheme and the technique. Our investigation thoroughly evaluates the influence of several critical parameters on the fluid's motion and thermal characteristics. Notably, the magnetic parameter significantly inhibits the fluid's velocity, illustrating the impact of magnetic forces. Additionally, the power law parameter leads to a decrease in both velocity and temperature profiles, highlighting its influence on fluid dynamics. Furthermore, changes in the Reynold number and the second‐grade fluid parameter are observed to cause a substantial increase in skin friction, by approximately 40% to 50%. These simulation results provide valuable insights into the complex interaction between fluid flow and heat transfer characteristics, enhancing our understanding of such systems in industrial applications.

Effect of incidence angle on PV soiling loss

The effect of light incidence angle is crucial for accurate interpretation of soiling sensor readings and soiling loss data. In this study, the effect of incidence angle on soiling loss is investigated under a solar simulator using artificially and naturally produced soiling samples on different types of glass substrates. It was found that the incidence angle dependence of soiling loss can be described satisfactorily using a two-parameter model, which has one power-law parameter associated with dust morphology and a fraction parameter dependent on the substrate’s angular transmittance. These results are applicable to beam radiation; further research is needed to apply them to field conditions in which diffuse solar radiation is significant. Findings from this study may provide an approach for more accurately calculating PV soiling loss based on optical sensor readings and for more meaningful soiling loss comparison across different locations.

Experimental validation of the power law hemolysis model using a Couette shearing device.

The study of blood trauma, such as hemolysis in blood-carrying devices, is crucial due to the high incidence of adverse events like alteration of blood function, bleeding, and multi-organ failure. The extent of flow-induced hemolysis, predominantly influenced by stress duration and intensity, is described by established model parameters based on the power law approach. In recent years, various parameters were determined using different Couette shearing devices and donor species. However, they have not been validated due to limited experimental data. This study provides hemolysis measurements in a Couette shearing device and evaluates the suitability of different power law parameters. The revised Couette shearing device generates well-defined dynamic stress loads that are repeatedly applied to blood samples at a defined temperature. Human blood samples with an adjusted hematocrit of 30%, were tested with varying repetitions (20 to 80 times). The half-sinusoidal stress loads had amplitudes of 73 to 140 Pa and exposure times of 24 msec per repetition. The parameters of five common power law hemolysis approaches were then compared with the experimental data. The prediction with the power law model parameters C = 3.458 × 10-6, α = 0.2777 and β = 2.0639 showed a good agreement with the experimental results. The effect of multiple short-time stresses on hemolysis was investigated to validate the power law hemolysis model with the Couette shearing device of this study.

Diffusion Coefficients of Variable-Size Amphiphilic Additives in a Glass-Forming Polyethylene Matrix.

Diffusion of additives in polymers is an important issue in the plastics industry since migratory-type molecules are widely used to tune the properties of polymeric composites. Predicting the diffusional behavior of new additives can minimize the need for repetitive experiments. This work presents molecular dynamics simulations at the microsecond time scale and uses the MARTINI force field to estimate self-diffusion coefficients, D, of six monounsaturated amides and their analogs carboxylic acids in polyethylene matrices (PE, MW = 5600 Da). The results are strongly influenced by the glass-forming properties of the PE matrix, which we characterize by three distinct temperatures. The metastability region (T < 325 K), the glass transition temperature (Tg = 256-260 K), and the end of the transition (T ≅ 200 K). Self-diffusion mechanisms are inferred from the results of the dependence of D on the molecular mass of the additive, observing a Rouse-like behavior at high temperatures and deviations from it within the metastability region of the matrix. Interestingly, D values are nonsensitive to the nature of the considered polar head for additives of similar size. The temperature-dependent behavior of D follows, at fixed additive size, a linear Arrhenius pattern at high temperatures and a super Arrhenius trend at lower temperatures, which is well represented with a power law equation as predicted by the Mode Coupling Theory (MCT). We offer a conceptual explanation for the observed super-Arrhenius behavior. This explanation draws on Truhlar and Kohen's interpretation of the available energies at both the initial and the transition states along the diffusion pathway. The matrix's mobility significantly affects solute self-diffusion, yielding equal activation enthalpies for the Arrhenius region or the same power law parameters for the super-Arrhenius regime. Finally, we establish a one-to-one time-equivalence of the self-diffusion processes between CG and all-atom systems for the largest additives and the PE matrix in the high-temperature regime.

Optical Solitons for the Dispersive Concatenation Model with Power-Law Nonlinearity by the Complete Discriminant Approach

The present paper is a sequel to the paper on the topic with Kerr law nonlinearity. For power-law nonlinearity, it was derived through balancing principle that the solitons would exist for two values of the power-law parameter, namely n = 1 or n = 2. The current paper derives dark and singular solitons for the latter value of n since the first case was already covered in a previous report that was dedicated to address the model with Kerr law.

Advanced Frequency Study of Thick FGM Cylindrical Shells by Using TSDT and Nonlinear Shear

For the advanced frequency study of thick functionally graded material (FGM) circular cylindrical shells, it is interesting to consider the extra effects of nonlinear coefficient term in third-order shear deformation theory (TSDT) of displacements on the calculation of varied shear correction coefficient. The formulation for the advanced nonlinear shear correction coefficient are based on the energy equivalence principle. The values of nonlinear shear correction coefficient are usually functions of nonlinear coefficient term of TSDT, power-law exponent parameter and environment temperature. The free vibration frequencies of thick FGM circular cylindrical shells are investigated with the simply homogeneous equation by considering that simultaneous effects of the TSDT, the nonlinear shear correction coefficient of transverse shear force and the two direction of mode shapes. The novelty is more important and reasonable for the thick FGM circular cylindrical shells, especially for the ratio of length to thickness is five by considering the effects of advanced nonlinear shear correction coefficient and nonlinear coefficient term of TSDT on the advanced calculation of fundamental first natural frequencies.

Bright Optical Solitons for the Concatenation Model with Power-Law Nonlinearity: Laplace-Adomian Decomposition

This paper is a numerical study of the bright optical solitons that emerge from the concatenation model which is considered with power-law nonlinearity. The Laplace-Adomian decomposition scheme is the integration methodology adopted in the paper. The surface plots are exhibited for a range of values of the power-law parameter.

Rheological Properties and Kinetics of Gelation of Binary Polymers between Xanthan Gum and Locust Bean Gum.

The synergistic interaction and gelling kinetics between xanthan gum (XG) and locust bean gum (LBG) at different mass ratios (XG/LBG 9:1, 7:3, 5:5, 3:7, 1:9) were investigated using a rheometer. The results showed that the mixtures of XG and LBG induced gel formation, and the strongest gel structure was found for the mixture of XG/LBG 3:7 according to the yield stress, storage modulus (G'), and power law parameters. Temperature ramp studies indicated that heating destroyed the gels at 55~60 °C, while cooling induced the sol-gel transition at around 52 °C for all mixtures. Structure developing rate (SDR) curves showed that XG/LBG 3:7 exhibited the highest SDR during the cooling ramp among all the samples. Non-isothermal kinetic analysis demonstrated that the gelation process of XG/LBG mixtures during cooling included two steps: a high-temperature region (55~39 °C) needing higher activation energy (Ea, 111.97 to 199.20 kJ/mol for different mixtures) and a low-temperature region (39~20 °C) needing lower Ea (74.33 to 85.31 kJ/mol), which indicated higher energy barriers to overcome at the initial stage of gel formation. The lowest Ea of 74.33 kJ/mol was found for XG/LBG 3:7 in the low-temperature region. Scanning electron microscopy (SEM) showed that the gel of XG/LBG 3:7 presented the densest entanglements. These results indicated the strongest synergism interaction occurred in XG/LBG 3:7 to form gel network structures. This study will help promote the application of XG-LBG blends to design novel food structures.

Numerical investigation of heat source induced thermal slip effect on trihybrid nanofluid flow over a stretching surface

The fluid flow model is evaluated with the mass and energy transfer through the trihybrid nanofluid (Thnf) past a stretching permeable sheet. The proficiency of the nanofluid could be more effective, improved and stable by introducing nanoparticles with various thermal and rheological properties. The trihybrid nanoliquid has been prepared by the dispersion of silver (Ag), cobalt ferrite (CoFe2O4), and magnesium oxide (MgO) nanocomposites in water. The consequences of Darcy-Forchheimer are engaged in the momentum equation, to evaluate the permeability effect. The fluid flow is expressed in the form system of PDEs with effect of natural convection, magnetic field and heat source. Which are converted into a non-dimensional set of ODE by using similarity variables substitutions. Moreover, the numerical approach PCM (parametric continuation method) is used to deal the derived set of ODEs. The results are relatively compared to the existing study for accuracy purposes. It has been noted that the Thnf has higher thermal conductivity than ordinary and hybrid nanoliquid. The velocity field rises with the mounting values of the thermal Grashof number. The velocity curve drops with the effect of a power law, Forchheimer's, and porosity parameters.

A modified decomposition method for the analysis of porous triangular fin with a power exponent of thermal properties and magnetic effect

A closed-form solution of the triangular porous fin with a simultaneous variation of power law-dependent heat transfer coefficient, internal heat generation, and surface emissivity parameters under the influence of external magnetic and electric fields is carried out. Darcy’s model has been used to simulate flow in the porous triangular fin with insulated boundary conditions. The governing singular value equation is nondimensionalized and solved by modified Adomian decomposition method (MADM) and the results of MADM are compared with the numerical solution obtained from the finite difference method (FDM) in the limiting conditions. The graphical analysis of the significant power law variation of thermophysical parameters, Hartmann number and important design parameters such as the half-thickness parameter of the triangular fin are performed and physically interpreted. A comparative study has been carried out with multiple power law parameters at different values while other thermophysical parameters were kept at a fixed level and it has been found that fin temperature is highest at higher values of power index parameters. From this study, it has been found that with the increasing value of the Hartmann number as well as the porosity parameter, the efficiency of the triangular porous fin increases rapidly.

Lidar-Derived Rockfall Inventory—An Analysis of the Geomorphic Evolution of Rock Slopes and Modifying the Rockfall Activity Index (RAI)

Rockfall presents a significant risk to the safety and economy of communities and infrastructure in mountainous regions. The recently-developed Rockfall Activity Index (RAI) utilizes high-resolution terrestrial lidar-derived digital elevation models (DEMs) of rock slopes to categorize a slope face into seven distinct morphological units, or “RAI classes”. This paper focuses on a comprehensive study conducted at four sites in Alaska, USA, where a robust lidar-based five-year inventory of 4381 rockfall events was analyzed. The primary objective was to investigate variations in failure characteristics, such as cumulative magnitude–frequency distributions, non-cumulative power–law parameters, average annual failure rates, and average failure depths, among the different RAI classes. The findings demonstrate that the seven RAI classes effectively differentiate the rock slope based on unique mass-wasting characteristics. Furthermore, the research explores spatial and temporal variations in these failure characteristics. Based on the study’s outcomes, recommendations are provided for modifying the RAI parameters for each RAI class, specifically the annual failure rate and average failure depth. These modifications aim to enhance the accuracy and effectiveness of rockfall hazard assessments.

Rheological Modeling of 7075 Aluminum Alloy Semi-Solid Slurry and its Application in the Simulation of SEED Rheocasting Process

Rheocasting technology has been successfully applied to produce aluminum alloy parts of automobile and communication equipment. However, its application scope is still limited. One reason is that the strength of the applied alloys is limited. In recent years, lots of researchers have tried to use 7075 aluminum alloy in the rheocasting process because this alloy has excellent mechanical properties. In this work, the rheological behavior of 7075 aluminum alloy semi-solid slurry is studied through shear stress-controlled test and shear rate-controlled test. Then the constitutive parameters in Power-Law (PL) model or Carreau-Yasuda (CY) model of non-Newtonian fluid are determined. The models are used to simulate the flow behavior of 7075 aluminum alloy semi-solid slurry in Swirled Enthalpy Equilibration Device (SEED) rheocasting process. The simulation results indicate that the CY model derived from the shear rate sweep test is more suitable for simulating the flow behavior of 7075 aluminum alloy semi-solid slurry during rheocasting than the other models.

Frequency-dependent diffusion kurtosis imaging in the human brain using an oscillating gradient spin echo sequence and a high-performance head-only gradient

Measuring the time/frequency dependence of diffusion MRI is a promising approach to distinguish between the effects of different tissue microenvironments, such as membrane restriction, tissue heterogeneity, and compartmental water exchange. In this study, we measure the frequency dependence of diffusivity (D) and kurtosis (K) with oscillating gradient diffusion encoding waveforms and a diffusion kurtosis imaging (DKI) model in human brains using a high-performance, head-only MAGNUS gradient system, with a combination of b-values, oscillating frequencies (f), and echo time that has not been achieved in human studies before. Frequency dependence of diffusivity and kurtosis are observed in both global and local white matter (WM) and gray matter (GM) regions and characterized with a power-law model ∼Λ*fθ. The frequency dependences of diffusivity and kurtosis (including changes between fmin and fmax, Λ, and θ) vary over different WM and GM regions, indicating potential microstructural differences between regions. A trend of decreasing kurtosis over frequency in the short-time limit is successfully captured for in vivo human brains. The effects of gradient nonlinearity (GNL) on frequency-dependent diffusivity and kurtosis measurements are investigated and corrected. Our results show that the GNL has prominent scaling effects on the measured diffusivity values (3.5∼5.5% difference in the global WM and 6∼8% difference in the global cortex) and subsequently affects the corresponding power-law parameters (Λ, θ) while having a marginal influence on the measured kurtosis values (<0.05% difference) and power-law parameters (Λ, θ). This study expands previous OGSE studies and further demonstrates the translatability of frequency-dependent diffusivity and kurtosis measurements to human brains, which may provide new opportunities to probe human brain microstructure in health and disease.

Analysis of Blood Flow in Human Brain Vessels for Newtonian and Non-Newtonian Blood Properties

The cerebral artery system can be affected by various diseases such as stroke, carotid stenosis, vertebral stenosis, intracranial stenosis, aneurysms, and vascular malformations. Understanding the blood flow specific to each patient's cerebral arteries can provide crucial information about how these diseases progress and guide potential treatment options. A patient-specific Magnetic Resonance Imaging (MRI) scan of a human brain was utilized to create a 3D model of the arterial system. Blood flow simulations were conducted using the ANSYS (Fluent) R2021 software package. The ICEM meshing tool within the ANSYS software was employed to prepare the models. The velocity rise and pressure drop were observed in the branching of the basilar artery. This can provide valuable patient specific information on various cerebral diseases, and drug delivery cases. The non-Newtonian properties of blood were established by inputting the Power Law parameters into the ANSYS Fluent system. It was observed that the effects of non-Newtonian properties of blood are relatively negligible for the large vessels studied (&gt; 200 um).

Impact of Joule heating on magnetohydrodynamic dissipative flow above a slendering surface with thermophoresis and Brownian movement with slip/no-slip conditions

ABSTRACT Purpose Hybrid nanofluids meet the necessities of several technological and production industries. Owing to these ample applications, a numerical investigation is accomplished to examine the thermal transmission feature of magneto-hybrid nanofluid flow due to an extending surface of varied thickness with multiple slip effects. Design/methodology The arising system of Partial Differential equations (PDEs) are exercised by adopting suitable similarities to attain the non-dimensional Ordinary Differential equations (ODEs) and the solutions are obtained by implementing bvp5c built in MATLAB package. The energy equation is loaded with Brownian motion, thermophoresis and Joule heating effects. The implication of pertinent constraints upon the flow features is discussed graphically. Findings The outcomes imply that the energy transmission rate is considerably high in no-slip case as equated with the slip case. Further, the power-law index parameter effectively uplifts the thermal and concentration gradients in both the situations. Originality The prime motive of this research is to present the relative analysis of heat transmission of hybrid nanoliquid in two different situations, namely slip and no-slip cases.

Parametrization of electron sheath expansion for Langmuir probe I-V traces

The Langmuir probe is a common plasma diagnostic widely utilized in various fields of plasma physics, and its associated methods of data analysis remains in active development. In this work, we present an attempt using a power law parametrization model similar to Sheridan's empirical formulation is to describe the sheath expansion effect on electron current in an argon plasma. The fitting results using the power law parametrization method show observably better consistency compared to those using conventional interception method and inflection method. It is also observed that when used to fit the electron saturation current at probe bias voltages well beyond the plasma potential plus the argon ionization energy, resultant curve fitted by power law parametrization, as with that by linear fitting, deviates significantly from the curve fitted at lower bias voltages, albeit the saturation obtained fitted using the power law method remained consistent with that fitted at lower probe bias voltages. Probable causes of this deviation include anode glow or spots near the probe and the changes of the global plasma parameters via electron absorption at very high probe bias. The fact that the resultant electron saturation current remained consistent hints that these non-trival effects can also be approximated by power law parametrization.

Comparing Tear Film Viscosity between Sjögren and Non-Sjögren Dry Eye Disease.

This study aimed to compare tear film viscosity (TFV) in Sjögren and non-Sjögren dry eye diseases (DEDs). This was a cross-sectional observational study. A total of 68 DED patients were enrolled, including 32 patients with Sjögren syndrome (SS) and 36 without SS. TFV was assessed by a tear film analyzer and determined by the momentary moving speed (MMS; MMS (t) = α × t-β, t = time (s)) with its power-law fitting-derived parameters (α and β). Among the four indices of TFV (MMS (0.1 s), MMS (2.0 s), α, and β), the SS-DED patients had significantly lower MMS (0.1 s) (p = 2.01 × 10-5), α (p = 0.0375), and β (p = 0.0076). The SS-DED group also had significantly higher OSDI, lower central and nasal tear meniscus height (TMH), and higher OSS. MMS (0.1 s) was significantly correlated with nasal TMH and OSS (ρ = 0.2520, p = 0.0381 in nasal TMH; ρ = -0.3487, p = 0.0036 in OSS). Index β was not correlated with any non-TFV tests. In conclusion, MMS (0.1 s), α, and β are promising TFV indices in distinguishing SS-DED from non-SS-DED patients early. Among these TFV indices, lower MMS is the best alternative clue for detecting SS-DED.

Comparison of methodologies for creating spread-out Bragg peaks in proton therapy using TOPAS and MCNP codes

In proton beam treatments, the superposition of several weighted Bragg curves with different incident energies is required to homogeneously irradiate a large tumor volume, creating a spread-out Bragg peak (SOBP). This paper confirms on the suitability of two different methods to create SOBPs – Bortfeld/Jette's and MCMC (Monte Carlo calculations and Matrix Computations), using Monte Carlo simulations performed with TOPAS and MCNP6.1. To generate the SOBPs, algorithms were developed for implementation of the two methods, which enabled to find the weights for thirty variations of SOBPs, categorized according to their width and maximum depths. The MCMC method used weight optimization in designing SOBPs to avoid negative values. In contrast, the Bortfeld/Jette's method yielded the SOBPs according to the variation of a power-law parameter (p) introduced by the range-energy relationship. Optimal values of p, from MCNP and TOPAS, were selected in order to retrieve SOBPs with the best smoothness and then related to those obtained from the literature. In comparing both methods and codes, dose homogeneity parameters (HOM) were used to examine the SOBP flatness and gamma analyses were employed to assess the dose deposition along its full extension. The results showed that the SOBPs designed using the MCMC method had better HOM values and computational performance for both codes when compared to the Bortfeld/Jette's method. The gamma analyses highlighted significant differences between the entrance doses comparing the two different methods, for SOBPs with intermediate and high depths and small width. This evaluation was not possible with the HOM values alone, which stresses the relevance of a broad analysis to avoid unintended doses in healthy tissues.