Power-law Type Research Articles

The dynamical stability and instability of Rayleigh–Bénard problem for non-Newtonian fluids with power law type

We conduct a mathematical investigation into the dynamical stability and instability of the Rayleigh–Bénard (abbr. RB) problem for incompressible non-Newtonian fluids exhibiting power law type behavior, with p ⩾ 1 . We establish a critical threshold, denoted as R c , and endeavor to demonstrate that the RB problem exhibits exponential stability through the energy method when the Rayleigh number R (which is influenced by the non-Newtonian component) falls within the interval [ 0 , R c ) . Additionally, we formulate an instability criterion, R > R c , under which the RB problem is deemed unstable, we aim to prove this instability by employing a modified variational method. Our results show that non-Newtonian part has the stabilizing effect for thermal instability.

FLOW ANALYSIS IN A ROLLER DRILL BIT DURING DRILLING USING WATER-BASED AND HYDROCARBON-BASED MUD

Drilling is the main type of increase in hydrocarbon production. Bits of various types are used as a rock-destroying tool during drilling. When drilling any wells for oil and gas, drilling fluids are used as a working fluid. The flow of these types of liquids differs from the flow of water, which is an incompressible medium. The purpose of this work is to study the flow of the Newtonian fluid of water and two types of water-based drilling fluids, which is described by the power-law model of a non-Newtonian fluid and the hydrocarbon-based fluid of the Herschel-Bulkley type. In the work, the construction of the geometric model of the square bit was carried out, and the estimated unstructured grid of the liquid volume filling the internal area of the bit and the space behind the bit was constructed. Calculations of the three-dimensional flow of water, drilling fluids on water and hydrocarbon bases were carried out using the open platform OpenFOAM. It was found that during the flow of liquids described by non-Newtonian models, the kinematic viscosity of the liquid changes depending on the velocities and shear stresses. Another important factor in the use of non-Newtonian fluids when drilling wells is the reduction of hydraulic losses during their flow. This is achieved due to the presence of a certain structure of the liquid, non- zero values of shear stresses, lubricating properties even with their viscosity, which is ten times higher than the viscosity of water. Visualization of the flow of three types of fluids: Newtonian, non-Newtonian power-law and non-Newtonian Herschel-Bulkley type is presented. The use of non- Newtonian fluids makes it possible to reduce the formation of vortices and, as a result, also affects the amount of hydraulic losses in the direction of their reduction.

High-temperature magneto-structural coupling in the Sr(Fe1/2Nb1/2)O3 system

We report the high-temperature phase transitions in the technologically important lead (Pb-) free B-site disordered Sr(Fe1/2Nb1/2)O3 (SFN) perovskite using dc magnetization and x-ray/neutron diffraction measurements. Our dc magnetization M (T) study reveals two magnetic transitions around 620 K and 708 K for the first time. The magnetic transition occurring around 620 K is linked with the structural phase transition, as confirmed by the temperature-dependent x-ray diffraction studies. Interestingly, the octahedral tilt angle (φ) and the integrated intensity of the superlattice reflection (ISL) decrease continuously with increasing temperature and vanishes across the structural phase transition. We have modeled the temperature variation of both φ and ISL using the power law type functional dependence which suggests the tricritical nature of the phase transition. Another transition occurring around 708 K in the M (T) plot is driven by oxygen vacancies. Neutron powder diffraction analysis of SFN at 295 K shows no sharp magnetic Bragg peaks, which are characteristic of long-range magnetic order. Instead, it reveals diffuse scattering, suggesting the presence of short-range magnetic ordering.

Research on the Rheological Properties and Diffusion Law of Coal-Based Solid Waste Geopolymer Grouting Material.

The rheological properties and diffusion law of coal-based solid waste geopolymer grouting material (CGGM) slurry were investigated by rheological property test and diffusion theory model derivation. Based on the power-law fluid constitutive equation, a theoretical model of slurry diffusion in an inclined fissure aquifer was established, and the effect of slurry grouting time on the slurry diffusion distance under different fissure widths, fissure inclination angles, and grouting pressures were analyzed. The results show that when coal gangue:cement:fly ash = 5:4:1, sodium silicate modulus 2.0, sodium silicate content is 10%, CGGM slurry's bleeding rate of 1%, the liquidity of 227 mm, the initial and final setting time is 412 min and 825 min, respectively, to meet the requirements of the grouting project. CGGM slurry is a typical viscosity time-varying power-law type fluid, and the slurry diffusion distance is positively correlated with the grouting pressure, fissure width, fissure inclination angle, and negatively correlated with the rheological index. The established theoretical model can provide a reference for the parameter design of CGGM slurry in grouting construction.

Heat Transfer and Entropy Generation in Vibrational Flow: Newtonian vs. Inelastic Non-Newtonian Fluid

A computational method is employed to solve heat transfer and entropy generation within a circular pipe. The thermal boundary condition assumes a constant wall temperature, while viscosity is taken to be dependent on temperature. A power-law type shear-thinning fluid is utilized in the analysis, with sinusoidal vibration applied horizontally perpendicular to the flow direction. Temperature distributions across the pipe are illustrated. Additionally, the entropy generation rate over the entire fluid volume under vibration was examined, comparing the results between steady flow and vibrational flow for both types of fluids. It was found that radial mixing is more pronounced in non-Newtonian fluids as vibration increases the strain rate, which is higher for low Reynolds numbers. The research provides a quantitative analysis of heat transfer and entropy generation for both Newtonian and shear-thinning fluids at different Reynolds numbers. It was observed that the effectiveness of superimposed vibrational flow is limited, especially for low Reynolds numbers and flow behavior index characteristic of shear-thinning fluids.

Freezing of short-range ordered antiferromagnetic clusters in the CrFeTi2O7system.

We report on the CrFeTi2O7(CFTO) system using a combination of x-ray diffraction, dc magnetization, ac susceptibility, specific heat and neutron diffraction measurements. CFTO is seen to crystallize in a monoclinic P21/a symmetry. It shows a glassy freezing at Tf ~ 22 K, characterized by the observation of bifurcation between ZFC and FC χ (T) curves, frequency dispersion across Tf in ac susceptibility, and follows Vogel-Fulcher and power law type critical dynamics, very slow relaxation of iso-thermal remanent magnetization with time and the absence of an anomaly in the temperature dependence of specific heat measurements. The microscopic neutron diffraction analysis of CFTO not only confirms the absence of long-range antiferromagnetic ordering but also exhibits diffuse scattering due to the presence of short-range ordered antiferromagnetically correlated spin clusters.&#xD.

Strongly Different Adhesion Reduction for 1D or 2D Random Fractal Roughness, and an Extension of the BAM Model to Anisotropic Surfaces

The influence of roughness on adhesion has been studied since the time of Fuller and Tabor, but recently there has been debate about how roughness exactly seems to kill (but sometimes enhance!) adhesion, particularly with reference to the accepted model of fractal roughness. We show that the Persson–Tosatti criterion does not depend on anisotropy of the surface for a typical power law PSD if written in terms of rms roughness and magnification. Instead, a very simple extension of the Bearing Area Model (BAM) of Ciavarella to anisotropic fractal surface shows a weak but clear dependence on the anisotropy, with higher adhesion in the 1D case, showing better agreement than the Persson–Tosatti criterion to actual numerical results of Afferrante Violano and Dini. However, neither of the two models permit to capture the strong hysteresis found in experiments between loading and unloading, which is very likely to enhance adhesion more as we move from the isotropic to the full 1D case. This suggests the mechanism of load amplification along contact lines and the associated elastic instabilities, is not captured by either the Persson–Tosatti or the BAM model applied to anisotropic surfaces.

Inference of the Gutenberg-Richter b-value: New insights and results

The size-frequency distribution of many geological and geophysical variables, in relation to fractures, faulting and seismicity, is well described by a statistical distribution of the power law type which is characterized by its exponent. For earthquake magnitudes, the exponent is the well-known b-parameter of the Gutenberg-Richter scaling law. In this paper we:•provide a strict statistical derivation of the distribution law of earthquake magnitudes,•show that the maximum likelihood estimator of the b-parameter is unbiased,•demonstrate that the maximum likelihood estimator is invariant to the value chosen as the minimum magnitude threshold in so far as it is larger than the magnitude of completeness of the earthquake catalogue, and•provide a new estimator based on the minimization of the Kolmogorov-Smirnov statistic and provide a strategy for detecting and mapping the spatio-temporal variation of the b-parameter in seismic swarms.The findings are illustrated with simulated data and a case study with real data.

Study of [formula omitted] dimensional fractional order non-linear Benney equation using an analytical technique

The area related to fractional order partial differential equations (FOPDEs) has also attracted attention. Therefore, we focuss our attention to study nonlinear Benney equations of using power law type Caputo derivative of fractional order. To compute a series-type solution for the problem under consideration, we combine the Adomian approach with the Laplace transform. Our findings are supported by graphical representations and numerical interpretations, illustrating the applicability and insights gained from this approach in solving complex real-world problems.

Bi-modal COVID-19 transmission with Caputo fractional derivative using statistical epidemic cases

The progression of the still ongoing COVID-19 epidemic must be studied in the world of differential operators other than those specified with integer-order temporal derivatives, according to ongoing scientific studies in the fields of fractional calculus, mathematical modeling, and epidemiology. Infectious diseases leave behind a historical footprint because of their long memory. With this in mind, the article below makes an effort to probe an epidemiological model using a Caputo differential operator with a singular kernel of power-law type. The ability of the Caputo operator to capture the evolution of complicated phenomena has been demonstrated in a number of studies, prompting us to conduct the analysis presented here. The analysis contains solid reasons while using the fractional operator for the COVID-19 epidemiological paradigm and presents the fixed point concept for the existence and uniqueness of its solutions. Hyers–Ulam–Rassias stability aids in finding model equilibrium, and the nonlinear least squares method yields the unknown parameters that also include the model’s fractional order. The actual cases of the infection support the superiority of the Caputo concept with evidence of smaller residuals. The numerical simulations are run to see how varying important parameters affect the disease’s spread.

Dynamic embedding of effective harmonic normal mode vibrations in all-atomistic energy gap fluctuations: Case study of light harvesting 2 complex.

Environmental effects in excitation energy transfer have mostly been modeled by baths of harmonic oscillators, but to what extent such modeling provides a reliable description of actual interactions between molecular systems and environments remains an open issue. We address this issue by investigating fluctuations in the excitation energies of the light harvesting 2 complex using a realistic all-atomistic simulation of the potential energy surface. Our analyses reveal that molecular motions exhibit significant anharmonic features, even for underdamped intramolecular vibrations. In particular, we find that the anharmonicity contributes to the broadening of spectral densities and substantial overlaps between neighboring peaks, which complicates the meaning of mode frequencies constituting a bath model. Thus, we develop a strategy to construct a minimally underdamped harmonic bath that has a clear connection to all-atomistic dynamics by utilizing actual normal modes of molecules but optimizing their frequencies such that the resulting bath model can best reproduce the all-atomistic simulation results. By subtracting the underdamped contribution from the entire fluctuations, we also show that identifying a residual spectral density representing all other contributions with overdamped behavior is possible. We find that this can be fitted well with a well-established analytic form of a spectral density function or, alternatively, modeled as explicit time dependent fluctuations with muti-exponential or power law type correlation functions. We provide an assessment and the implications of these possibilities. The approach presented here can also serve as a general strategy to construct a simplified bath model that can effectively represent the underlying all-atomistic bath dynamics.

A Three-Dimensional Velocity Field Related to a Generalized Third-Grade Fluid Model

In this work, we propose a new three-dimensional constitutive equation related to a third-grade fluid. This proposal is based on experimental work for which the viscosity term and the terms related to viscoelasticity may depend on the shear rate, in accordance with a power-law type model. The numerical implementation of this fluid model is rather demanding in terms of computational calculation and, in this sense, we use the Cosserat theory related to fluid dynamics, which makes the transition from the three-dimensional fluid model to a one-dimensional fluid model for a specific geometry under study which, in this case, is a straight tube with constant circular cross-section. Based on this approximation theory, the one-dimensional fluid model is solved by assuming an ordinary differential equation involving: an unsteady mean pressure gradient; an unsteady volume flow rate; the Womersley number; and the viscosity and viscoelasticity parameters. Consequently, for specific data, and using the Runge–Kutta method, we can obtain the solution for the unsteady volume flow rate and we can present simulations to the three-dimensional velocity field.

Vibrational response of a sandwich microplate considering the impact of flexoelectricity and based on a novel porous-FGM formulation

Flexoelectricity indicates a unique characteristic of insulators and dielectric materials that results in electrical polarization induction in response to the non-uniform strain gradient. The impact of this property is bolder on the microscale and nanoscale rather than the macroscale. This article is conducted to derive the governing equations of motion for a flexoelectric-multilayer structure and evaluate its vibrational behavior in response to various variable variations. The model includes a functionally graded (FG) porous core which is confined between two flexoelectricity-based face sheets at both sides and a Vlasov type of foundation. To gain the governing equations, the new type of power law for porous material beside Hamilton’s principle (HP) and modified couple stress theory (MCST) is implemented. Capturing the effects of length scale parameter, different materials, aspect and thickness ratios, porosity index, foundation parameter and boundary conditions (B.C.s) on the normalized natural frequency (NNF) of such a multilayer model based on the novel FG porous material formulation serve as the main novelty of this article. According to the results, it is revealed that the lateral ratio enhancement causes NNF and stiffness reduction in the model. Furthermore, among all considered B.C.s, simply support (SSSS) and clamped support (CCCC) refer to the lowest and the highest NNF respectively. The content of the recent article serves as a good source to provide a better understanding of the vibrational response of high stiffness-to-weight ratio structures to different variable variations.

A multi-material topology optimization approach to hybrid material structures with gradient lattices

In this paper, we present a novel approach for designing hybrid material structures that incorporate solid, void, and spatially-varying lattices. This approach extends the recursively defined power-law type multi-material interpolation model by incorporating additional gradient material phases. Unlike conventional models, the new extended model considers the secondary ``solid'' material phase as a type of lattice, enabling adjustment of lattice geometry and mechanical behavior with gradient control variables such as density or size. By means of numerical homogenization and interpolation, we explicitly express the effective mechanical behavior of the gradient lattice in relation to the gradient control variable. This approach enhances design freedom by allowing for flexible control of individual material volumes, and also the lower and upper bounds of gradient variables. By using implicit geometrical modeling techniques, the resulting gradient control variable field can be interpreted to create spatially-varying and smoothly-connected lattices at any arbitrary resolution. The effectiveness and flexibility of the proposed approach have been demonstrated through a series of benchmark design tests considering various lattice material types.

On the existence, uniqueness, stability, and numerical aspects for a novel mathematical model of HIV/AIDS transmission by a fractal fractional order derivative

In this study, we explore a mathematical model of the transmission of HIV/AIDS. The model incorporates a fractal fractional order derivative with a power-law type kernel. We prove the existence and uniqueness of a solution for the model and establish the stability conditions by employing Banach’s contraction principle and a generalized α-ψ-Geraghty type contraction. We perform stability analysis based on the Ulam–Hyers concept. To calculate the approximate solution, we utilize Gegenbauer polynomials via the spectral collocation method. The presented model includes two fractal and fractional order derivatives. The influence of the fractional and fractal derivatives on the outbreak of HIV is investigated by utilizing real data from the Cape Verde Islands in 1987–2014.

TWO PHASE SLIP FLOW OF BLOOD IN HEPATIC ARTERY WITH SPECIAL REFERENCE TO HEPATITIS B

In this paper, we have presented a model of two-phased arterial hepatic blood flow in hepaticarteries remote from the heart and proximate to the Liver keeping in view the nature of hepatic blood circulation in the human body. Blood is supposed to be non-Newtonian of the power-law type. Solutions of the constitutive equations are obtained in analytical as well as in numerical forms. The role of hematocrit is explicit in the determination of blood pressure drop in the case of Hepatic disease Hepatitis B.

Existence, uniqueness and decay rates of a certain type of 3D Hall-MHD equations with power-law type

Existence, uniqueness and decay rates of a certain type of 3D Hall-MHD equations with power-law type

Features of the photophoretic motion of an evaporating droplet in a viscous non-isothermal binary gas medium

A theoretical description of the photophoretic motion in a viscous nonisothermal binary gas mixture of a large evaporating spherical droplet with significant relative temperature differences in its vicinity is carried out in the quasi-stationary approximation for small Reynolds and Pecle numbers. When describing the properties of a gaseous medium, a power-law type of dependence of the coefficients of molecular transport (viscosity, diffusion and thermal conductivity) and density on temperature was taken into account. Numerical estimates have shown the nonlinear nature of the dependence of the photophoretic force and velocity on the average temperature of the droplet surface.

Skin Factor Consideration in Decline Curve Analysis

Summary This paper introduces an approach for the impact of skin factor on the decline curve analysis of hydraulically fractured reservoirs. The objective is to consider this impact in the production forecasting and the ultimate recovery estimation. The approach focuses on reducing the uncertainties that could be raised from this impact on the production history and increasing the accuracy of the predicted flow rates. It proposes an easy and promising tool for the decline curve analysis that could be applied confidently to different oil- and gas-producing wells and different reservoirs. This approach utilizes the rate-normalized flow rate derivative β behavior of the fractured reservoirs. This derivative demonstrates a constant behavior with time for each flow regime when the production history has not undergone the impact of the skin factor. However, the constant behavior no longer exists when this impact has influenced the production history. Instead, a power-law type model governs the relationship between the flow rate derivative and production time. New analytical flow rate decline curve models, exponential-type, are derived from the flow rate derivative power-law type models for the flow regimes. Different models for calculating the skin factor are developed for the three linear flow regimes that could be observed during the transient state flow conditions. The proposed flow rate models are used to simulate the production history and forecast the future performance. Moreover, the hydraulic fracture conductivity can be calculated using these models as well as the flow rate loss caused by skin factor. Several case studies are examined by the proposed approach where the production history is used to characterize the dominant flow regimes. The study has reached several observations and conclusions. The impact of skin factor is seen clearly throughout transient state flow regimes; however, this impact declines sharply before reaching pseudosteady-state flow (boundary-dominated flow regime). The impact of the skin factor alternates the constant behavior of the flow rate derivative with time to a power-law type relationship. A straight line of a slope (0.5) is diagnosed during hydraulic fracture and formation linear flow regime on the log-log plot of the flow rate derivative β and time, while the bilinear flow regime demonstrates a straight line of a slope (0.25). Because of the skin factor, exponential decline curve models replace the power-law type models of the flow rate during the abovementioned flow regimes. These models exhibit an excellent match between the calculated flow rate and the production history. The maximum flow rate loss occurs during very early production time even though the skin factor during this time is less than the intermediate production time. This study presents a novel approach for the decline curve analysis taking into account the impact of skin factor. The novelty is represented by considering the flow regimes in the production forecasting of hydraulically fractured reservoirs. This approach is smoothly applied to predict the future performance with no need to know the wellbore and reservoir parameters. It can be used to predict the declining flow rate for a constant or varied bottomhole flowing pressure.

Micro Rain Radar and Radiometric Measurements to Unravel Contrasting Features of Rain Microstructure Below and Above the Boundary Layer

AbstractKa‐band Micro rain Doppler radar is an effective tool to investigate the profiles of precipitation microstructure in terms of the raindrop size distribution (DSD). The DSD parameters that vary appreciably with height are indicative of the associated atmospheric phenomena. Hence the present investigation endeavors to put light on the underlying physical processes responsible for the evolution of varied rain microstructure profiles using micro rain radar (MRR), and radiometric measurements complemented with re‐analysis outputs over an urban tropical location, Kolkata (22.57°N, 88.37°E), India. MRR unravels the prevalence of significant biases in the typical power law relationship (Dm = aRb) between rain rate (R) and mass‐weighted mean drop diameter (Dm) along the rain height, especially during intense convective rain events, above the atmospheric boundary layer (ABL). Consequently, an alternative empirical relation appropriate to account for the R‐Dm variability above the ABL is proposed. Further, radiometric measurements and re‐analysis outputs reveal that the presence of atmospheric instabilities coupled with wind shear impacts above the ABL contributes to the enhanced breakup of raindrops and the deviations in the usual R‐Dm relationship. Thus, the present study intends to highlight the applicability of ground‐based radar measurements over the tropics to devise quantitative precipitation algorithms for reliable rain estimates.