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The Cattaneo-Christov double diffusion theory extends the classical Fourier and Fick laws by introducing a relaxation time, accounting for thermal and mass diffusion at finite speeds rather than assuming instantaneous diffusion. This theory works especially well for explaining how non-linear mixed convection and chemical reactions over a stretching surface behave and boost heat and mass transfer of Sutterby nanofluid. Using the proper similarity transformations, the governing model is converted into a non-dimensional form. It is then numerically solved using the Runge-Kutta-Fehlberg (RK-45) method in conjunction with shooting procedures. The impact of the heat transport rate on the significant variables (Brownian motion, Biot number and thermal relaxation time parameter) is addressed vis sensitivity studied using response surface methodology (RSM). It is concluded that Forchheimer number and Deborah number on velocity profile is quite similar. The influence of temperature difference parameter on the thermal distribution and mass transport rate is reverse. The opposite behavior of nanoparticle concentration and mass transport rate is viewed for thermophoretic parameter. Furthermore, the heat transport rate is more sensitive to the impact of Brownian motion comparing with Biot number and thermal relaxation time parameter. • Simulating the heat transfer enhancement for non-Darcian Sutterby nanofluid flow. • This study views the behavior of heat and mass transport toward a stretchy surface. • Cattaneo-Christov double diffusion theory discussed in θ (η) and ϕ (η) equation. • The Roseland approximation is adopted for Brownian and thermophoretic diffusion. • Optimization approach employed via (RSM) for the important parameters. [ABSTRACT FROM AUTHOR]

The simplified general perturbations 4 (SGP4) orbital propagation model is one of the most widely used methods for rapidly and reliably predicting the positions and velocities of objects orbiting Earth. Over time, SGP models have undergone refinement to enhance their efficiency and accuracy. Nevertheless, they still do not match the precision offered by high-precision numerical propagators, which can predict the positions and velocities of space objects in low-Earth orbit with significantly smaller errors. In this study, we introduce a novel differentiable version of SGP4, named ∂ SGP4. By porting the source code of SGP4 into a differentiable program based on PyTorch, we unlock a whole new class of techniques enabled by differentiable orbit propagation, including spacecraft orbit determination, state conversion, covariance similarity transformation, state transition matrix computation, and covariance propagation. Besides differentiability, our ∂ SGP4 supports parallel propagation of a batch of two-line elements (TLEs) in a single execution and it can harness modern hardware accelerators like GPUs or XLA devices (e.g. TPUs) thanks to running on the PyTorch backend. Furthermore, the design of ∂ SGP4 makes it possible to use it as a differentiable component in larger machine learning (ML) pipelines, where the propagator can be an element of a larger neural network that is trained or fine-tuned with data. Consequently, we propose a novel orbital propagation paradigm, ML- ∂ SGP4. In this paradigm, the orbital propagator is enhanced with neural networks attached to its input and output. Through gradient-based optimization, the parameters of this combined model can be iteratively refined to achieve precision surpassing that of SGP4. Fundamentally, the neural networks function as identity operators when the propagator adheres to its default behavior as defined by SGP4. However, owing to the differentiability ingrained within ∂ SGP4, the model can be fine-tuned with ephemeris data to learn corrections to both inputs and outputs of SGP4. This augmentation enhances precision while maintaining the same computational speed of ∂ SGP4 at inference time. This paradigm empowers satellite operators and researchers, equipping them with the ability to train the model using their specific ephemeris or high-precision numerical propagation data. • Developed ML-dSGP4, integrating differentiable propagation with neural networks. • ML-dSGP4 bridges the gap between simulated/observed data and SGP4 predictions. • ML-dSGP4 outperforms baseline SGP4 and hybrid SGP4 in prediction accuracy. • dSGP4 leverages hardware acceleration (e.g. GPU) for efficient batch propagation. • Released the model and tutorials as open-source under the ESA Github organization. [ABSTRACT FROM AUTHOR]

The current study investigates the effects of thermal radiation and Lorentz's force on heat and mass flow in a nanofluid with a magnetic field and free convection, as it passes over a vertical permeable sheet. The dominant PDEs are turned into linked nonlinear ODEs using an appropriate similarity transformation. Using the MATLAB ODE45 tool, dimensionless ODEs are numerically computed using the finite difference procedure. Four different water-based nanofluids are considered, including copper, titanium dioxide, aluminum oxide, and silver. The influence of emerging dimensionless numbers and other parameters, such as the magnetic force parameter, the radiation parameter, the suction parameter, the Prandtl number, the Schmidt number, the Dufour number, as well as for constant values of the modified local Grashof number and local Grashof number on the concentration, velocity, and temperature profiles is emphasized and mentioned. Moreover, the visual representation of the effects of a volume percentage of up to 4% copper nanoparticles on the distributions of concentration, temperature, and velocity is also shown. The temperature profile, concentration profile, and velocity profile all grow with an increase in the volume percent of copper nanoparticles between 0.00 and 0.04. Furthermore, numerous scenarios are investigated for the distributions of the local Sherwood number, the local Nusselt number, and the local skin friction coefficient. The local Nusselt number decreases, and the local skin friction coefficient and Sherwood number increase about by 30 %, 45 %, and 60 % respectively due to increasing the value of volume fraction from 0 % to 4 %. The local skin friction coefficient increases and the local Nusselt number decreases by about 15 % and 39 % respectively for rising values of the thermal radiation number from 0.5 to 3.5. In addition, for magnetic force parameter values between 0.5 and 4.0, the local skin friction coefficient drops by about 13 %. [ABSTRACT FROM AUTHOR]

In the current study, authors have studied the heat transfer through ternary hybrid nanofluid (THNF) between the gap of a disk and cone, where both are co-rotating with regard to the other. The authors have developed a mathematical model of THNF flow inside a gap between a cone and a disk with the effects of magnetic field, Hall effects, and radiation parameters. The unique aspect of this study is the implementation of a powerful artificial neural network (ANN) that exhibits improved robustness and accurate predictive performance for the Nusselt number at the surface of both the cone and disk. Through the use of proper similarity transformations, the model equations are transformed into a collection of nonlinear ODEs. Using MATLAB and an inbuilt bvp4c function, these equations are numerically solved. The main objective of this research is to examine the impacts of cone and disk rotation within the co-rotation system. The heat transfer rate is seen to be higher at the surface of the disk. It is followed from the analysis of the ANN model that the regression value for each case varies between 0.99574 and 1, and in many cases, it is exactly equal to 1. In addition, the mean square error (MSE) for every dataset is notably very close to zero. The effect of the angle of the conical gap is also one of the noteworthy subjects due to the significance of its effects in several engineering sector applications. [ABSTRACT FROM AUTHOR]

Current artifact aims to investigate attributes of nanofluidic transport mechanism developed for dynamics of Williamson liquid over an extendable cylinder with novel physical aspects of magnetic field. Additionally, Newtonian heating is accounted at cylinder surface and Reynold viscosity model is implemented to delineate the aspects of temperature dependent viscosity. Thermophoresis, Brownian motion, and variable viscosity effects have been studied for heat and mass transfer analysis. Formulation of problems characterized by governing physical laws is conceded in the form of dimensional partial differential setup by executing boundary layer approach. Conversion of attained differential system into ODE's is engrossed by capitalizing similarity transformations. Numerical procedures (Runge-Kutta and shooting) are implemented to resolve the problem and to attain solution. Effectiveness of sundry variables on associated distributions is revealed through graphical and tabular manner. Quantities of interest are also manipulated against the involved variables. Comparison of results to certify the numerical code is checked by making assessment with existing studies and found remarkable agreement. [ABSTRACT FROM AUTHOR]

This paper presents a linear parameter varying (LPV) interpolation modeling method and modal-based pole placement (PP) control strategy for the ball screw drive (BSD) with varying dynamics. The BSD is modeled as a global LPV model with position-load dependence by selecting position and load as scheduling variables. The global LPV model is obtained from local subspace closed-loop identification and LPV interpolation modeling. A modal-based global LPV model is obtained through the similarity transformation. Based on this model, a modal-based LPV PP control strategy is proposed to achieve various modal control. Specifically, a state feedback control structure with an LPV state observer is designed to realize online state estimation and real-time state feedback control of modal state variables which cannot be measured directly. The steady-state error is minimized by introducing an error state space (SS) model with the integral effects. Moreover, the stability of the closed-loop system is analyzed according to the controllable decomposition and principle of separation. It is experimentally demonstrated that the proposed modal-based LPV PP control strategy can effectively achieve precise tracking and outstanding robustness meantime. • A global LPV model of the BSD is built by interpolation modeling. • A modal-based LPV pole placement control is proposed to achieve modal control. • The proposed modeling and control achieve precise tracking and excellent robustness. [ABSTRACT FROM AUTHOR]

This article explores the influence of activation energy and microorganisms on the flow of Jeffrey nanofluid over an electrically conducting stretching surface, considering key factors such as Brownian motion, thermophoresis, Joule heating, and thermal radiation. The fluid dynamics entail a stretching surface subjected to prescribed surface temperature and constant wall surface temperature. Through similarity transformations, the governing equations are solved using MATLAB's bvp4c function. Employing a numerical and perturbative approach, the study examines critical parameters' effects on flow distribution, heat transfer, mass transport, and microorganism density. Graphical illustrations and tabulations are utilized to illustrate these effects, including the elucidation of Nusselt, Sherwood, friction coefficient, and motile microbe. The study's findings hold promise for optimizing processes in environmental remediation, bioengineering, and nanotechnology. It is seen that thermophoresis reduced the coefficients of motile density number, Sherwood number, and Nusselt number. Peclet and bio-convective Schmidt numbers enhanced the spread of microorganisms. CWT profile exhibits greater dominance compared to PST profile. • The influence of activation energy and microorganisms on the flow of Jeffrey nanofluid over an electrically conducting stretching surface is explored. • A stretching surface subjected to prescribed surface temperature and constant wall surface temperature is analyzed. • Through similarity transformations, the governing equations are solved using MATLAB's bvp4c function. • Employing a numerical and perturbative approach, the study examines critical parameters' effects. • The study's findings hold promise for optimizing processes in environmental remediation, bioengineering, and nanotechnology. [ABSTRACT FROM AUTHOR]

Our study delves into the dynamics of a convective Magneto-Hydrodynamic Bioconvective Nanofluid model (MHD-BCNFM) flowing over a convectively heated stretched sheet. To accomplish this, we utilize the distinctive capabilities of the Supervised Stochastic Approach for Computational Analysis (SSACA). By integrating similarity transformations, we convert the partial differential equations (PDEs) governing the system into coupled ordinary differential equations (ODEs). We generate the dataset for our approach using the Adam numerical technique specifically tailored for the (MHD-BCNFM). Achieving this involves systematic modulation of parameters such as λ , bioconvection Péclet number P e , Bioconvection constant σ , Brownian motion parameter N b , and thermophoresis parameter N t. "Moreover, we utilize a reference dataset to compute numerical values of various physical quantities in the (MHD-BCNFM) employing SSACA-based Artificial Intelligence methods. The effectiveness of our devised SSACA approach is demonstrated by a negligible mean squared error, ranging from approximately 10−8 to 10−10. Histograms exhibit a maximum error range of 10−5, closely aligning with optimal correlation/regression measures. Outstanding performance metrics in terms of Mean Squared Error (MSE) are attained at levels such as l 9.93E−12, 1.07E−11, 6.28E−10, 1.43E−11, 2.09E−09, 3.65E−11, 2.97E−11, and 2.80E−13 against 320, 430, 209, 85, 356, 295, 66, and 136 epochs. A comparative study between the proposed and reference datasets underscores the authenticity and precision of SSACA, supported by error analyses ranging from E-05 to E-09 across all scenarios. [ABSTRACT FROM AUTHOR]

In the present analysis, tangent hyperbolic fluid is assumed to be flowing over a stretching cylinder. The thermophysical characteristics of fluids are assumed to be variable. The thermal and solutal rates are investigated by using viscous dissipation, activation energy, and thermal radiation. The governing equations occur in the form of partial differential equations, and then these equations are transformed into ordinary differential equations by using similarity transformations. Then, by using the BVP4C method, we obtain the numerical solution to the equations. The impacts of the involved parameters, such as Prandtl, Weissenberg, Schmidt, Eckert number, viscosity coefficient, and thermal radiation parameters, are presented through the graphs. The velocity profile decreases due to the power law index, Weissenberg number, and temperature-dependent viscosity. However, it increases due to the Darcy-Forchheimer number and curvature parameter. The temperature distribution rises with the Eckert number, curvature parameter, and radiation parameter. On the other hand, it declined for the Prandtl number and power law index. Similarly, the concentration profile increases for the activation energy, reaction rate, and temperature difference parameter, but it decreases for the curvature parameter and Schmidt number. • Darcy-Forchheimer and temperature dependent viscosity of tangent hyperbolic fluid. • Viscous dissipation, activation enrgy and thermal radiation is assumed. • The MATLAB programme is used to graphically analyze the behavior. • Stretching cylinder is considered. [ABSTRACT FROM AUTHOR]

Primary objective of this examination is to discover hybridized nanofluid flowing and heat transport that flows between a rotatable cone positioned above an expandable disc. Hybridized nanofluid contains Cadmium telluride (CdTe) as first nanoparticle and Silicon carbide (SiC) as second nanoparticle in ethylene glycol as base fluid. Electromagnetic impact and Darcy-Forchheimer model are considered with thermal radiative fluxing. By using appropriate similarity transformation, physical phenomena may be illustrated by a collection of nondimensional equations. An in-depth analysis is conducted to examine how the expansion of the surface affects the motion and temperature layers, as well as the swirl angle from the disc surface, and heat transfers from the cone and disc walls. Results demonstrate that expanding the wall varies flowing and heat dynamics within the conical gap. Boost CdTe nanoparticles without SiC nanoparticles lower disc Nusselt numbers while increasing it in a cone. In absence of CdTe nanoparticles, SiC nanoparticles increase Nusselt numbers in disc and cone. Nusselt numbers peak for rotating cone and expanded disk at φ 1 = φ 2 = 0.04. When gap angles are modest, faster wall expansion rate cools disk surface and heats cone surface. These findings have important medical and pharmacological implications in blood component separation and drilling machine cooling. [ABSTRACT FROM AUTHOR]

Hybrid ferrofluids have exhibited enhanced heat transfer results in numerous applications. Industry demands like inclination sensors and solar water heaters give a new insight into heat transfer problems on the angle of inclination problems. Thus, this paper is motivated to analyse the effect of inclination angle towards mixed convection hybrid ferrofluid flow, including heat sources and convective boundary conditions, on a porous shrink surface. By utilising a similarity transformation, the intricate nature of the partial differential equations (PDEs) is simplified, transforming it into a set of ordinary differential equations (ODEs) and numerically solved in the bvp4c (MATLAB). A positive correlation was obtained between the current model and past researchers. Besides that, the increase in nanoparticle volume fraction improved the skin friction by approximately 14.79% and 15.00% for opposing and assisting flow regions, accordingly. Altering the inclination angle positively impacted growth by approximately 3.28% and 0.0068% on the skin friction and the heat transfer rate, accordingly. The inclusion of a heat source reduced the heat transfer rate by approximately 0.20% and 0.19% for both opposing and assisting flow regions, respectively. Meanwhile, a greater rise in heat transfer rate by approximately 174.48% when the Biot number, Bi rose. [ABSTRACT FROM AUTHOR]

In this paper, we extend the definition of phases of sectorial matrices to those of semi-sectorial matrices, which are possibly singular. Properties of the phases are also extended, including those of the Moore-Penrose generalized inverse, compressions and Schur complements, matrix sums and products. In particular, an interlacing relation is established between the phases of A + B and those of A and B combined. Also, a majorization relation is established between the phases of the nonzero eigenvalues of AB and the phases of the compressions of A and B , which leads to a generalized matrix small phase theorem. For the matrices which are not necessarily semi-sectorial, we define their (largest and smallest) essential phases via diagonal similarity transformation. An explicit expression for the essential phases of a Laplacian matrix of a directed graph is obtained. [ABSTRACT FROM AUTHOR]

The objective of this manuscript is to model the fully fractional unsteady Casson nanofluid flow between two parallel plates influenced by magneto hydrodynamic forces and Darcian effects in both slip and no-slip case. Casson nanofluid model is fractionally transformed through mixed similarity transformations into a non-dimensional fully fractional model. In modeled fluid problem the continuity equation is identically satisfied and fractional order highly non-linear momentum equation is obtained. The obtained fractional model is further validated by putting α = 1 and obtaining the integer order Casson fluid model already existing in literature. In order to solve the flow problem, a hybrid of homotopy perturbation method and Laplace transform, namely He-Laplace method (HLM) is utilized. The obtained results are validated with existing results in literature and through residual errors and average error plots with increasing order of approximation. It is observed that results obtained through HLM are better in terms of accuracy than existing results. Moreover, the errors reduce substantially as order of approximation in HLM increases, depicting the convergence of proposed scheme. Graphical analysis is also performed to analyze the behavior of normal and radial velocity. Furthermore, contour plots are presented for flow rate and skin friction of Casson nanofluid. It is observed that fluid parameters present different behavior incase of fractional environment when compared with existing integer order results. Also, the behavior of velocity profile in no-slip case is in contrast to the behavior noted in slip case of Casson nanofluid. These finding confirm the importance of fractional modeling in terms of capturing more generalized physical phenomena. [ABSTRACT FROM AUTHOR]

In this study, the mixed convective stagnation-point flow of a Al 2 O 3 - C u / H 2 O hybrid nanofluid towards a stretched disc with a convective boundary and zero mass flux condition is described with mass suction and viscous dissipation effects. The process is accomplished by using thermophoretic and Brownian motion physical phenomena. After performing a similarity transformation on the PDEs in order to convert them into an ODE system, the bvp4c solver is then employed in order to carry out a numerical solution. In the study that was described above, the flow, heat, and mass transfer characteristics were investigated with the assistance of the Buongiorno model and the Devi and Devi model. The following characteristics were brought up as points of contention: ϕ 1 , ϕ 2 , λ , S , N t , N b , L e , E c , B i and B. There is a very good consonance among the existing and antecedent results in undeniable cases, as well as a connection error of approximately 0%. The velocity and temperature profiles upsurge with the increment of the nanoparticle volume fraction and mixed convection parameter, while the velocity increases with the addition of the suction parameters. As a result of this study, we are able to estimate the flow and thermal behavior of Al 2 O 3 - C u / H 2 O when the physical parameters are embedded. [ABSTRACT FROM AUTHOR]

Coal-rock recognition is vital for mining safety and efficiency. Traditional methods are labor-intensive and error-prone, while machine learning and deep learning improve accuracy but are hindered by limited, inconsistent datasets due to challenging mining conditions. To address these issues, this research introduces a novel image synthesis approach leveraging Neural Style Transfer with the VGG-19 model to overcome data scarcity. The style images are derived from 200 real coal face images, while the content images are represented as synthetic grayscale images. Furthermore, the Regional Similarity Transformation Function and the Dragonfly Algorithm are employed to enhance the quality of coal-rock style images. Results from 1,000 iterations indicate that the proposed method substantially improves the quality and diversity of coal-rock images, with interfaces and textural details becoming significantly clearer and more closely resembling the expected coal-rock interfaces seen in the original content images. Additionally, an automated machine learning-based approach is used to generate coal-rock content images, thereby further enhancing the efficiency of the synthesis process. This methodology notably enriches the coal-rock image dataset, bolstering the robustness and accuracy of recognition models and contributing to more efficient mining operations. Synthetic images simulating low-light and dusty environments were created to enhance model robustness. These synthetic images were used to train a coal-rock recognition model, which achieved an impressive 92% accuracy. The findings underscore the effectiveness of synthetic images in overcoming data limitations and strengthening coal-rock recognition systems for real-world applications. [ABSTRACT FROM AUTHOR]

A recent paper by Wang et al. (2023) A generalized weighted total least squares-based, iterative solution to the estimation of 3D similarity transformation parameters, Measurement 210 (2023) 112563, https://doi.org/10.1016/j.measurement.2023.112563 on 3D symmetric similarity coordinate transformations based on a generalized weighted total least squares. I found the results were not entirely accurate. For control purposes, 3 separate data sets in the article (Table 2, Table 5 and Table 8) were solved according to Bektas (2024). The results are exactly the same as Bektas (2024) and Mercan et al. (2018). Wang et al. (2023) results contain minor differences. The transformation parameters found were not completely correct and there were significant differences, especially in the residuals. My guess is that the differences in Wang et al.'s (2023) results are due to poor convergence, the authors should have looked for ways to deal with poor conditioning, but they didn't. [ABSTRACT FROM AUTHOR]

• The algorithms can generate a Matrix-Geometric (MG) representation of the system lifetime distribution from its components lifetime distributions for any structures. • The resulting MG representation of the system lifetime distribution can be used to calculate several functional reliability measures at once. • The algorithms can be applied for any structures with discrete-time components. • The algorithms can reduce computation time and memory significantly. • The model can be generated using simple algorithms in MATLAB codes. • It applies to dynamic reliability analysis for many engineering systems. • The computation method is simple and fundamentals that they can be used to enrich course material on applied computations and system reliability. System reliability analysis in discrete phase-type (DPH) distributions requires longer computation time as the matrix order increases with the number of components and the complexity of the system structure. This paper presents a method to reduce the computation time by performing a similarity transformation on the DPH distribution model of the component lifetimes. Similarity transformation produces a matrix-geometric (MG) distribution whose generator matrix is in Jordan canonical form with fewer non-zero elements, so the computation time is faster. We modified the algorithms for system reliability in DPH distributions to make them applicable to MG distributions. Our experiments using several Jordan canonical forms show significant reductions in computation times. [ABSTRACT FROM AUTHOR]

This paper presents computational studies aimed at quantifying 2D effects in opposed jet counterflow non-premixed flames. The principal aim is to explain the variation of global extinction strain rate (a g) with the ratio of nozzle separation distance to its diameter (L / D o ). The limited experiments available in literature shows that a g decreases with an increase in L / D o . On the other hand, 1D models, widely used to interpret data and perform optimization and validation of kinetic mechanisms, show the opposite trend – a g increases with an increase in L / D o and quickly asymptotes. While this issue has been discussed in the literature, to the best of our knowledge, a conclusive resolution of the issues has not come about till now. Towards this, a computational methodology is developed. Two 2D configurations are constructed with boundary conditions in such a way that the results from one mimic experiments and the other mimics 1D models. Corresponding terms in the conservation equations are compared between the two configurations and the reasons for the discrepancy are identified. The assumption of plug flow boundary condition at fuel and oxidizer nozzles exit is shown to be the main reason for the discrepancy between experiments and 1D models. The data showed that this discrepancy in global extinction strain rate trends arise due to coupling of ρ u z (d u z / d z) term (momentum of axial velocity in the axial direction or Term 1) of axial momentum equation with ρ F (z) 2 term (momentum of radial velocity in the radial direction or Term 3) of radial momentum equation through d u z / d z value at reactant nozzles exit, where F (z) represents a similarity transformation variable. It was found that for L / D o ≥ 1, 1D computations can be used as long as the global extinction strain rate is in the range of 300–350 s − 1. General prescription for choice of L / D o as a function of a g is outlined. The new insights gained provide a framework to understand the combustion and emission characteristics of new fuels using an opposed jet counterflow configuration. • Conflicting trends in extinction strain rate (a g) data vs models clarified with CFD. • Plug flow assumption is not valid for all burner configurations and a g range. • 1D model predictions reasonable for burner aspect ratio L/D 0 ≥ 1 & 300 ≤ a g ≤ 350 s-1. • Coupling of axial–radial terms in conservation equations significant for L/D 0 ≤ 0.5. a g ≤ 350 s-1. • 2D model is essential for data interpretation and kinetic studies beyond this range. [ABSTRACT FROM AUTHOR]

The flow of third-grade nanofluid over a stretched surface is analyzed with a particular focus on the transport of heat due to melting by taking into account both homogeneous and heterogeneous reactions. To account for various effects, the energy equation incorporating viscous dissipation, Joule heating and radiation is considered, as well as the influence of thermophoresis and Brownian motion. A similarity transformation is used to simplify the expressions such that the model is analyzable. Utilizing the homotopic technique, series solutions are obtained, and a convergence result is established. Our investigation based on this series solution explores the impact of different factors on the flow model, and demonstrates that increasing the melting parameter leads to a decrease in temperature, entropy rate and concentration, while to an increase in velocity. [Display omitted] • The study examines melting in non-Newtonian nanomaterials in third grade. • Investigation into chemical reactions in nanofluid flow. • Melting enhances velocity but reduces temperature and concentration. • Thermophoresis raises temperature; concentration influenced by thermophoresis. • Entropy rises with Brinkman number and magnetic parameter; decreases with melting. [ABSTRACT FROM AUTHOR]

In this paper, an extended (3+1)-dimensional nonlinear Schrödinger equation is studied. By using similarity transformation, some exact solutions of this equation are obtained, which include soliton solutions and periodic function solutions, its nonlinear spatial modulation and external potential are affected by time and space. Based on the solution obtained previously, some figures are displayed. [ABSTRACT FROM AUTHOR]

We study the self-similar transmission of optical beams inside an inhomogeneous birefringent tapered graded-index nonlinear fiber amplifier within the framework of generalized coupled Schrödinger equations with spatially inhomogeneous nonlinearity, group velocity dispersion, tapering and gain or loss. New kinds of similariton solutions for the governing model are constructed by means of the similarity transformation method. Especially, the M-shaped and W-shaped similariton pulses are found successfully for the first time, which do not exist in single-mode waveguide amplifier. In addition, bright–dark similaritons are found in the presence of tapering effect. It is shown that these waveforms exhibit a quadratic phase structure, which leads to chirped self-similar pulses. In addition, we determine the relationships among the tapering profile, gain or loss distribution, nonlinearity, and similariton width, which provide the required conditions for controlling the self-similar wave dynamics. Moreover, we discuss the dynamical evolution of the similariton pulses under the influence of special tapering profiles, which are of physical importance in practical applications. The results show that through selecting the appropriate tapering, dispersion and nonlinearity profiles, we can control the dynamics of similaritons effectively. • We have analyzed similaritons in birefringent tapered graded-index nonlinear fiber amplifiers. • The M-shaped and W-shaped similariton pulses are found successfully for the first time. • New kinds of similariton solutions are constructed by means of the similarity transformation method. [ABSTRACT FROM AUTHOR]

[Display omitted] This study inspected the impacts of thermophoresis and electrophoresis on the rate of aerosol particle deposition through cone, plate, wedge geometries in a Marangoni convective flow. The proposed mathematical model becomes more innovative by taking into account the effects of elastic deformation, variable thermal conductivity and mixed convection. It uses a trihybrid nanofluid composed of water-based fluid, Silver (A g) , Titanium dioxide (T i O 2) , and Magnesium oxide (M g o) nanoparticles. One important area of use is in the design and improvement of trihybrid nanofluid-based materials with specialized thermal, electrical, and mechanical properties. Improvements in heat transmission in microfluidic and nanofluidic devices are critical for chemical reactions, electronics cooling, and biological applications. Improved materials processing methods, precise drug administration mechanisms, and more effective cooling systems can all result from an understanding of the interactions between fluid flow, elastic deformation, and nanoparticle dynamics under the impact of electrical and temperature gradients. The equations corresponding to the suggested PDEs (particle differential equations) are converted into ODEs (ordinary differential equations) by choosing suitable similarity transformation. The semi-analytical technique HAM (Homotopy analysis method) is executed to drive the solution of the proposed problem. When the values of the elastic deformation parameter increase, the thermal and velocity profiles decline. With higher values of electrophoretic parameter, the concentration profile becomes augmented. [ABSTRACT FROM AUTHOR]

The topic of fluid flow through disks is important due to a broad range of its applications in industries, engineering, and scientific fields. The objective of the current article is to analyze the bioconvective micropolar nanofluid flow between the coaxial, parallel, and radially stretching double disks in the occurrence of gyrotactic motile microorganisms with convective thermal boundary conditions. Darcy–Forchheimer medium is considered between the double disks that allow the flow horizontally with additional effects of porosity and friction. The flow is also considered under the impacts of thermal conductivity and thermal radiations. The influence of gyrotactic microorganisms is accommodated through the bioconvection, which increases the strength of thermal transportation. Furthermore, the Cattaneo-Christov heat flux theory is also accounted. The flow model is trans moved into a system of ordinary differential equations (ODEs) utilizing appropriate similarity transformation functions. The bvp4c technique has been used to solve the transformed flow model. The implication of some prominent physical and bioconvection parameters on velocities, microrotation, thermal field, volumetric concentration of nanoparticles, and microorganisms' fields are presented through graphs and tabular ways. It is observed that the stretching ratio parameter of the disks accelerates the axial and micro rotational velocities of the nanofluid. In contrast, the stretching Reynolds number slows down the radial velocity near the plane's center. The temperature profile goes high against the Brownian motion, thermal radiation, and thermal conductivity parameters, while an inverse trend has been observed for increasing magnitudes of Prandtl number. The nanoparticles concentration profile is upsurged against the thermophoresis parameter. The density profile of gyrotactic motile microorganisms is de-escalated by the Peclet number and the bioconvection Lewis number. Micropolar parameters cause an increase of couple stresses and a decrement in shear stresses. A comparison with published work is provided under certain limitations to test the validity of numerical scheme accuracy. [ABSTRACT FROM AUTHOR]

The current analysis aims to find the solution to the buoyancy effect on time-dependent flow and heat transfer induced by a hybrid micropolar nanofluid over a permeable shrinking or stretching vertical flat plate. A novel hybrid nanofluid is utilized, which consists of the agglomeration of water (pure fluid) and two dissimilar nanoparticles like silver (Ag) and titanium dioxide (TiO 2). Initially, the model is developed in the form of the non-linear partial differential equations (PDEs) with three independent variables, which are transformed to the set of dimensionless ordinary differential equations (ODEs) using the appropriate similarity transformations. These dimensionless ODEs are solved numerically via the bvp4c package in MATLAB software. The consequence of various involved controlling parameters on the velocity, microrotation, friction drag, temperature, and heat transfer characteristics for the upper branch solution (UPBS) and the lower branch solution (LOBS) are thoroughly inspected. In physical engineering quantities of interest, it is deeply observed that for the case of stretching, the solution of the stable (upper) branch is possible for the entire negative and positive selected values of the stretching/shrinking parameter. In contrast, the lower branch solution exists only for negative values of the stretching/shrinking parameter for the shrinking case. [ABSTRACT FROM AUTHOR]

The (2 + 1) dimensional Konopelchenko–Dubrovsky equation (2D-KDE) is an integro differential equation which describes two-layer fluid in shallow water near ocean shores and stratified atmosphere. In this respect, the solutions of (2D-KDE) describe two dual functions which represent two-layer fluid. Here, we are concerned with deriving self-similar (similarity) solutions of the inhomogeneous-nonautonomous (2D-KDE). In this context, the model equations are nonlinear partial differential equations (NLPEs) with space and time dependent coefficients. It is worth noticing to mention that, the (2D-KDE) with space and time dependent coefficients was not considered in the literature up to date. So that, the present work is novel. In fact, only the study of (NLPDEs) with space dependent or time dependent coefficients was carried. This was done by using Lie symmetry. Here, we use a different technique together with introducing similarity transformations. The similarity solution are obtained via the extended unified method (EUM), which is an alternative technique to the use of Lie group symmetries of (NLPDEs). It is worthy to mention that the (EUM) is of low cost time in symbolic computations and it provides a wide class of solutions. The solutions presented here, are classified to hyperbolic and elliptic functions.The results are obtained via symbolic computations and they are evaluated numerically and displayed in graphs. Multiple solutions structures are observed. Among them dromian pattern, bridge shape, lumps vector and interaction between longitudinal and lateral complex waves. These results are completely new. A unified approach for analyzing the stability of the steady state solution is established. The stability of the is determined against varying the relevant parameters. It is found that stability holds against the dispersion coefficient, while instability holds against the nonlinearity coefficient and the phase velocity. [ABSTRACT FROM AUTHOR]

Most existing 3D geometry copy detection research focused on 3D watermarking, which first embeds "watermarks" and then detects the added watermarks. However, this kind of methods is non-straightforward and may be less robust to attacks such as cropping and noise. In this paper, we focus on a fundamental and practical research problem: judging whether a point cloud is plagiarized or copied to another point cloud in the presence of several manipulations (e.g., similarity transformation, smoothing). We propose a novel method to address this critical problem. Our key idea is first to align the two point clouds and then calculate their similarity distance. We design three different measures to compute the similarity. We also introduce two strategies to speed up our method. Comprehensive experiments and comparisons demonstrate the effectiveness and robustness of our method in estimating the similarity of two given 3D point clouds. [ABSTRACT FROM AUTHOR]

The existing compound-fault diagnosis methods of rolling bearings have their own defects, which makes their accuracy of fault diagnosis impossible to be guaranteed. Therefore, this paper attempts to combine symplectic similarity transformation with Ramanujan subspace theory, and then a periodic impulse extraction method called symplectic Ramanujan mode decomposition (SRMD) method is proposed. SRMD separates the components with different fault features through symplectic similarity transformation and hierarchical clustering method to obtain symplectic clustering components (SCCs). At the same time, SRMD uses the Ramanujan subspace theory to extract the major periodic impulse components of each component to be extracted, and then obtains symplectic Ramanujan components (SRCs). The results show that SRMD is a resultful method in compound-fault diagnosis of bearings with excellent periodic impulse extraction ability. • A novel periodic impulse extraction method, called SRMD, is proposed for composite fault diagnosis of rolling bearings. • Symplectic similarity transformation and Ramanujan subspace theory are introduced into composite fault diagnosis of rolling bearings. • The proposed method not only has excellent signal separation ability, but also has excellent periodic impulse extraction ability. [ABSTRACT FROM AUTHOR]

The current research aims to study the heat transfer rate in mixed convection flow of viscous fluid along a vertical cylinder containing swimming microorganisms and velocity slip effects. The thermal and solutal processes are examined using gyrotactic microorganisms, chemical reaction and slip conditions. The non-linear (PDEs) of the governing flow are transformed into set of highly nonlinear (ODEs) by employing appropriate similarity transformations, which are then resolved computationally by Runge-Kutta-Fehlberg 4 th order toward with shooting approach. The predicted solution is derived using the Levenberg-Marquardt scheme combined with a backpropagation neural network (LMS-BPNN). The labelled data sheet is divided into three parts: 80 % data is used for training, 10 % for validation and 10 % for testing. The performance of the proposed AI-based LMS-BPNN is examined in term of MSE for considered scenarios. An optimal solution is achieved at 675 , 397 , 727 , 647 , and 711 , epochs, while performance in terms of MSE for these epochs is to be 1.06 × E − 9 , 8.47 × E − 10 , 9.20 × 10 − 9 , 9.94 × E − 10 ,and 9.09 × 10 − 10 . The assigned computational valuations and ANN valuations are in excellent alignment than those existing studies on numerous special cases. The predicted solution with AI-based technique LMS-BPNN is reliable, well-organized, and easy to handle the thermal and solutal transport analysis of flow across a stretchable cylinder. The validity of proposed LMS-BPNN algorithm is examined with absolute error analysis and error is found to be approximately 10 − 4. [ABSTRACT FROM AUTHOR]

The aim of this research work is to estimate and analyze the solution of rheological chemical reactive Carreau nanofluid (CNRFM) induced by exponentially extended surface (EES) subject to variable physical attributes by using stochastic analysis on Levenberg Marquardt backpropagation neural networks (SALMBNNs). The non-linear Partial Differential Equations (PDEs) are transformed by using the similarity transformation variables into their corresponding ODEs. The reference values are created with ARK (adaptive Runge-Kutta) scheme. The ensuing results are explained for the variable viscosity, Weissenberg number (material number), Brownian movement factor, LRF (local rotation factor), LN (Lewis number) and activation energy with chemical reaction in addition. Numerical calculations of different physical quantities are approximated with artificial intelligence based SALMBNNs from dataset created with ARK method. The convergence, accuracy, and efficiency of the proposed stochastic analysis on Levenberg Marquardt backpropagation neural network (SALMBNNs) are established and endorsed through iterative learning curves at each incremental step in epoch, statistical instance distribution studies of error-histograms, analysis of adaptive controlling parameters of SALMBNNs, and evaluation of regression metric. [ABSTRACT FROM AUTHOR]

We study the existence of localized matter waves in Bose Einstein condensate (BEC) loaded into variable shape optical lattice (OL) potential. Similarity transformation is used to solve Gross-Pitaevskii equation (GPE) with space and time dependent coefficients. Bright and dark soliton solutions are obtained depending on the nonlinearities being focusing or defocusing. We analyze how the parameters of OL affect the properties of the soliton solutions. We also employ direct numerical simulations to prove the stability of the solutions and determine the parameter region in which the solutions are stable. • Soliton formation is highly affected by optical lattice properties. • Stable solitons can be formed with variable shape optical lattices. • Optical lattices are important tools for quantum simulations. [ABSTRACT FROM AUTHOR]

Exploring and identifying a good feature representation to describe high-dimensional datasets is a challenge of prime importance. However, plenty of feature selection techniques and distance metrics exist, which entails an intricacy for identifying the one best suited to the task. This paper provides an algorithm to design high-order distance metrics over a sparse selection of features dedicated to classification. Our approach is based on Conditional Random Field (CRF) energy minimization and Dual Decomposition, which allow efficiency and great flexibility in the considered features. The optimization technique ensures the tractability of high-dimensionality problems using hundreds of features and samples. Our approach is evaluated on synthetic data as well as on Covid-19 patient stratification. Comparisons with state-of-the-art baselines and our proposed method on different classification results prove the learned metric's relevance. [Display omitted] • Novel higher-order metric learning algorithm with Conditional Random Fields. • Leverage graph and hyper-graph structures. • Semi-supervised feature selection and weighting. • Dedicated classification principle. [ABSTRACT FROM AUTHOR]

The problem of network attacks is a primary focus in the domain of intrusion detection. Models face significant challenges in recognizing intrusion behaviors, particularly when dealing with high-dimensional and sparse datasets. Traditional machine learning methods often struggle with these dimensionality issues. In contrast, deep learning, a crucial technology in intrusion detection, excels at managing high-dimensional data. However, traditional image coding methods do not adequately address data sparsification and often overlook the spatial continuity among features. The Fourier transform is a promising solution for data sparsity issues, as it effectively mitigates the impact by converting data into a different domain. Inspired by the Fourier transform, this paper proposes a lightweight intrusion detection model called TFTKD, based on Convolutional Neural Networks (CNN) and knowledge distillation. The model applies a two-dimensional Fourier transform to convert grayscale images from the time domain to the frequency domain. This transformation enhances the similarity between neighboring pixels, effectively addressing data sparsification. During the training phase, a teacher network, comprising an 8-layer CNN, is pre-trained. In the distillation phase, a one-layer CNN serves as the student network, employing Self-adaptive Temperature Knowledge Distillation to enhance the student's generalization capabilities. This approach results in a compact student network model with a constrained parameter count, demonstrating superior learning efficiency and accuracy compared to state-of-the-art methods. Experimental validation was conducted using four publicly accessible intrusion detection datasets, demonstrating the effectiveness of the proposed method. • Use a two-dimensional Fourier transform to address the problem of image sparsity. • Propose a self-adaptive temperature knowledge distillation method. • Develop a high-accuracy, lightweight intrusion detection model. [ABSTRACT FROM AUTHOR]

The goal of this work is to present the numerical results of MHD flow of nanofluid with Cattaneo-Christov heat flux model and thermally radiation by a stretching surface with melting boundary conditions. Nanofluids are a new kind of nanofluid but their commercial application is still in the works. It is also expected that hybrid nanomaterials should be used in more effective related technologies. These nanofluids would be used in cancer treatment, electronic systems, packaging materials and scientific research. It was established that the physical illustration exists for the examined boundary value problem. For a stretching surface, it was realized that a nanofluid with γ - A l 2 O 3 nanoparticles mechanism is a cooler on growing some of the examined flow parameters. Blood, water and C 2 H 6 O 2 are used as base fluids and nanoparticles γ - A l 2 O 3 were measured as a nanofluid. By employing appropriate similarity transformations, the main governing PDEs are composed to a set of nonlinear ODEs which are then numerically solved in the computational tool MATLAB by a three-stage Lobatto III-A formula. The velocity is declined for the greater estimations of the permeability parameter. The temperature is boomed up for the greater estimations of Biot number and radiation parameter. Moreover, the flow ranges for each flow parameter, such as 0.1 ⩽ λ ⩽ 1.0 , 0.1 ⩽ ϕ ⩽ 0.3 , 0.1 ⩽ K ⩽ 1.0 , - 0.5 ⩽ α ⩽ 0.5 , 0.1 ⩽ R d ⩽ 1.0 , 0.4 ⩽ M e ⩽ 1.2 , 1.0 ⩽ Ω ⩽ 1.2 , 0.4 ⩽ B i ⩽ 1.0 and 1.5 ⩽ θ w ⩽ 1.7 are scrutinized. In this research work, a numerical scheme was used to explore the aspects of γ - A l 2 O 3 nanomaterials across a starching surface. The authenticity of the aforementioned research work guarantees that the new study was never identified before and is wholly new; thus, in the case of results authenticity, a Lobatto III-A formula is designed to simulate in mathematical software MATLAB by built-in routine bvp4c (shooting) method and it is observed to be in good agreement with the previous works of literature. [ABSTRACT FROM AUTHOR]

The problem of two phase bio-convective nano fluid flow past a vertical stretching flat surface in presence of volume fraction of the dust particles has been investigated. Governing partial differential equations of the problem for both fluid and dust phases are transformed into ordinary differential equations using suitable similarity transformations. The resulting non-linear differential equations are solved numerically using MATLAB built-in bvp4c solver scheme. The velocity, temperature of fluid motion and concentration of micro-organisms are presented graphically for various flow parameters. Coefficient of local skin friction, local Nusselt number and local density number of the micro-organisms are calculated and presented in tables for various parameters. [ABSTRACT FROM AUTHOR]

In this study, the dual solutions for mixed convection flow of an Oldroyd-B fluid containing alumina nanoparticles over a shrinking sheet are investigated taking into account the effects of magnetic field and heat source/sink. By utilizing the similarity transformations, the governing equations are reduced to ordinary differential equations which have been solved by the well-known shooting method. The present investigation reveals that some published results are not realistic. It is remarkable that for higher Deborah numbers for relaxation and retardation times, suction parameter and magnetic field parameter, the domain of the occurrence of dual solutions becomes wider and the local skin friction coefficient and local Nusselt number are found to increase. On the other hand, dual solutions exist in a broader domain as long as the volume fraction of alumina nanoparticles is less than or equal to 0.05 and after that it decreases. The critical values of the shrinking parameter relating to the existence of dual solutions are rendered in approximate functions. These characteristics of an Oldroyd-B nanofluid are not reported yet and might be useful in the development of the existing technology. [ABSTRACT FROM AUTHOR]

Wide-area 3D data generation for complex urban environments often needs to leverage a mixed use of data collected from both air and ground platforms, such as from aerial surveys, satellite, and mobile vehicles. On one hand, such kind of data with information from drastically different views (ca. 90° and more) forming cross-view data, which due to very limited overlapping region caused by the drastically different line of sight of the sensors, is difficult to be registered without significant manual efforts. On the other hand, the registration of such data often suffers from non-rigid distortion of the street-view data (e.g., non-rigid trajectory drift), which cannot be simply rectified by a similarity transformation. In this paper, based on the assumption that the object boundaries (e.g., buildings) from the over-view data should coincide with footprints of façade 3D points generated from street-view photogrammetric images, we aim to address this problem by proposing a fully automated geo-registration method for cross-view data, which utilizes semantically segmented object boundaries as view-invariant features under a global optimization framework through graph-matching: taking the over-view point clouds generated from stereo/multi-stereo satellite images and the street-view point clouds generated from monocular video images as the inputs, the proposed method models segments of buildings as nodes of graphs, both detected from the satellite-based and street-view based point clouds, thus to form the registration as a graph-matching problem to allow non-rigid matches; to enable a robust solution and fully utilize the topological relations between these segments, we propose to address the graph-matching problem on its conjugate graph solved through a belief-propagation algorithm. The matched nodes will be subject to a further optimization to allow precise-registration, followed by a constrained bundle adjustment on the street-view image to keep 2D-3D consistencies, which yields well-registered street-view images and point clouds to the satellite point clouds. Our proposed method assumes no or little prior pose information (e.g. very sparse locations from consumer-grade GPS (global positioning system)) for the street-view data and has been applied to a large cross-view dataset with significant scale difference containing 0.5 m GSD (Ground Sampling Distance) satellite data and 0.005 m GSD street-view data, 1.5 km in length involving 12 GB of data. The experiment shows that the proposed method has achieved promising results (1.27 m accuracy in 3D), evaluated using collected LiDAR point clouds. Furthermore, we included additional experiments to demonstrate that this method can be generalized to process different types of over-view and street-view data sources, e.g., the open street view maps and the semantic labeling maps. [ABSTRACT FROM AUTHOR]

Deep cross-modal hashing which integrates deep learning and hashing into cross-modal retrieval, achieves better performance than traditional cross-modal retrieval methods. Nevertheless, most previous deep cross-modal hashing methods only utilize single-class labels to compute the semantic affinity across modalities but overlook the existence of multiple category labels, which can capture the semantic affinity more accurately. Additionally, almost all existing cross-modal hashing methods straightforwardly employ all modalities to learn hash functions but neglect the fact that original instances in all modalities may contain noise. To avoid the above weaknesses, in this paper, a novel multi-label enhancement based self-supervised deep cross-modal hashing (MESDCH) approach is proposed. MESDCH first propose a multi-label semantic affinity preserving module, which uses ReLU transformation to unify the similarities of learned hash representations and the corresponding multi-label semantic affinity of original instances and defines a positive-constraint Kullback–Leibler loss function to preserve their similarity. Then this module is integrated into a self-supervised semantic generation module to further enhance the performance of deep cross-modal hashing. Extensive evaluation experiments on four well-known datasets demonstrate that the proposed MESDCH achieves state-of-the-art performance and outperforms several excellent baseline methods in the application of cross-modal hashing retrieval. Code is available at: https://github.com/SWU-CS-MediaLab/MESDCH. [ABSTRACT FROM AUTHOR]

We have investigated the nanofluid flow in a converging and diverging channel of heated and inclined plane walls. The wellknown Buongiorno model has been undertaken for the transport of nanoparticles in a base fluid. The upper (lower) wall of the channel has the geometry and it is presented by an equation of the straight line y = mx + a 0 (y = - mx - a 0 ), in which m is the slope of the upper wall, a 0 is the half width of the channel inlet (exit) for diverging (converging) flow, x and y are representing the Cartesian Coordinates. Note that the walls of the channel are uniformly and equally heated and the nanoparticle concentration at the walls is also constant. On the contrary, the flow problem is strictly described in Cartesian Coordinates. The problem is formulated for the upper half of the channel and later on the results are generalized for the lower half. The new observations are shown in different graphs. The four governing PD E' s are simplified with the help of proper and appropriate similarity transformations and they constituted a system of ODE's, whereas, it is equipped with several dimensionless parameters. Note that the convective terms in energy and concentration equations are disappeared in view of these similarity variables. The effects of all parameters are investigated on flow, heat and mass transfer characteristics. Moreover, effects of all parameters are seen on skin friction, rates of heat and mass transfer. In addition, classical models of nanofluid flow inside a converging and diverging channel in plane polar coordinates will be the special cases of the current modeled problem. Furthermore, the perturbation solution of the modeled equations is also determined for small values of the parameter. Note that slope m and Pr number are used as a perturbation parameters for the momentum equation and energy, species concentration equations and these solutions are valid for small values of all other parameters involved in the problem. In addition, exact solutions of the final ODE are also found for special ranges of parameters value. Moreover, the comparison is shown between the different solutions of the problem and classical solutions in tables and graphs. The temperature (concentration) profiles are increased (decreased) with the increasing of Nb , and Nt , however, both of them are increased with m. Moreover, the linear (non-linear) profiles of skin friction (rate of heat transfer) are decreased(increased) with the increasing of both Re (Pr , m) and m (Nb). In addition, the rate of mass transfer is increased linearly (non-linearly) against the increasing value of Nt (Pr) and Nb (Nb = Nt). Note that the temperature (concentration) profiles are effectively improved (declined) with the increase of thermophoretic forces, moreover, it is also rapidly increased (decreased) with the increase of concentration of nanoparticles (and their rapid fluctuations) in a converging and diverging channel. [ABSTRACT FROM AUTHOR]

A number of commercial fluids, including synthetic automotive oils, food and consumer products containing polymer additives exhibit weakly rate-thickening responses in the final stages of capillarity-driven thinning, where a large accumulated strain and high extensional strain rate alter the thinning dynamics of the slender liquid filament. Consequently, measurements of capillarity-driven thinning dynamics typically feature two distinct regions at the early and late stages of the filament breakup process, each dominated by distinct mechanisms. These features have been incorporated in a simple Inelastic Rate-Thickening (IRT) model with linear and quadratic contributions to the constitutive stress–strain rate relationship, in which the apparent extensional viscosity slowly thickens at high strain rates. We numerically compute the thinning dynamics of the IRT model assuming an axially-slender axisymmetric filament and no fluid inertia. The computational results motivate a similarity transformation and we obtain a new self-similar solution in which the second-order stress is balanced by capillarity. The new asymptotic solution leads to a self-similar filament shape that is more slender than the Newtonian counterpart and, close to singularity, results in a quadratic dependence of the mid-point radius of the filament with time to breakup. A new and distinct asymptotic geometric correction factor, X ≈ 0. 5827 is derived and we show that a more accurate value of the true extensional viscosity in a rate-thickening fluid can be recovered from an interpolated time-varying geometric correction factor based on the magnitudes of different stress components. Finally, we propose a statistically data-driven protocol to select the best-fit constitutive model using a parameter-free information criterion. This enables us to more accurately quantify the extensional rheological behavior of complex rate-thickening viscoelastic fluids using capillarity-driven thinning dynamics. • The filament thinning dynamics predicted by the IRT model are studied numerically. • An asymptotic X value from the second-order stress contribution is calculated. • A data-fitting protocol incorporating time-varying X (t) values is presented. • A rheoinformatic method is proposed to obtain the best-fit model from measurements. [ABSTRACT FROM AUTHOR]

Magnetic resonance (MR) images can be corrupted by artifacts and noise, potentially leading to misinterpretation of the images. In this paper, we propose a novel approach based on the discrete shape space of images (DSSI) to jointly reduce artifacts and noise in MR images. The proposed method restores MR images in multiple domains based on the distinct generation mechanisms of noise and artifacts. The images in multiple domains are analyzed in a non-Euclidean space. The DSSI is constructed as a Riemannian manifold to measure the intrinsic properties of images. Images are considered shapes from a geometric perspective, and the impact of similarity transformations (e.g., rotation, scaling, and translation) on image analysis is eliminated. The patch-based rank-ordered difference (PROD) detector is defined in k-space within the framework of DSSI to detect and remove sparse outliers that cause artifacts. In addition, a novel similarity function for images is defined using the DSSI and be used to design the improved filter. Finally, the convergence of the improved filter is theoretically analyzed, indicating that our method offers an effective estimator of the ideal image. The experimental results of various MR images demonstrate that the proposed approach outperforms classical and state-of-the-art methods for artifact correction and noise removal, both qualitatively and quantitatively. • We propose a method for enhancing MR image quality by reducing artifacts and noise simultaneously. Motivated by the properties of these undesired components, our method combines the advantages of both k-space and image space to enhance images. • We construct the discrete shape space of images (DSSI) to measure the intrinsic image similarity in Riemannian manifold by treating images as shapes from a geometric view. Therefore, image similarity is independent of similarity transformations. • The patch-based rank-ordered difference (PROD) is defined under the framework of the DSSI to detect and remove MR artifacts in k-space. The PROD is defined by a signed distance between patches as artifacts usually appear as sparse outliers with prominent features. • We design an improved filter using the similarity function of images defined in the DSSI to reduce noise in the image space. This is an interesting advantage when compared with the similarity function used in the classical NLM, which is rather sensitive to rotation. • We theoretically investigate the convergence of our improved filter and find that using the geometric information of images to measure the similarity between images can ensure that the restored image is an effective estimator of the ideal image. [ABSTRACT FROM AUTHOR]

• A study on the behavior of non-Newtonian Jeffrey fluid with viscous dissipation on a three-dimensional stretching surface is conducted. • Both homogeneous and heterogeneous reactions in magnetohydrodynamic (MHD) Jeffrey fluid are considered. • Governing equations and boundary conditions are derived and transformed into nondimensional forms using similarity transformations. • Graphical representations and tables are utilized to investigate the impact of various physical parameters. The rheological properties of the non-Newtonian fluids make them highly beneficial for various industrial and engineering applications because their unique characteristics offer advantages in a wide range of fields. A study on the behavior of Jeffrey fluid with viscous dissipation on a bi-directional stretching surface is conducted. Homogeneous and heterogeneous reactions in electrically conducting Jeffrey fluid are considered. Governing equations and boundary conditions are derived and transformed into nondimensional forms using similarity transformations. MATLAB's bvp4c solver is employed to solve and analyze these equations. Graphical representations and tables investigate the impact of various flow parameters, including temperature, concentration, velocity, skin friction, heat, and mass transfer rates. Results indicate that with an increase in the Prandtl number, temperature field decline. The velocity, thermal, and solutal profiles drop when the Deborah number increases. Moreover, comparing homogeneous and heterogeneous parameters reveals a decrease in the surface's heat and mass transfer rate in the presence of thermal transport and concentration profile variations at different values of dimensionless variables. [ABSTRACT FROM AUTHOR]

An investigation of the influence that the Cattaneo–Christov heat and mass flux have on the whirling flow that occurs across a stretchable cylinder is being carried out in this study. This model takes into consideration the impact of a magnetic field, in addition to also taking into account heat and the diffusion of solutes. During the process of developing this mathematical model, the Navier-Stokes equation was employed to illustrate the flow that was predicted. Under the flow assumptions, the partial differential equations were derived from an approximation of the Navier-Stokes equation using the boundary layer approach. In order to make advantage of the ordinary differential equations formalism, the system is transformed via the application of similarity transformations. The Runge Kutta Felberg-45 (RKF-45) method gives an explanation of a system that does not have any dimensions. Both quantitatively and visually, the impacts of the key physical variables are shown. It is noticed that, the Swirl velocity profile decayed for higher values of magnetic parameter and Reynolds Number. Further we noticed that, the temperature fields strengthen with enhanced values of Eckert numbers (E c 1 and E c 2). [ABSTRACT FROM AUTHOR]

The hybrid nano-composite fluid transportation in Jaffery-Hemal flow (JHF) has important uses in various technologies, like converging dies, hydrology, automobiles, etc. Such significant applications motivated us to work on the current problem. Therefore, the purpose of the current work is to inspect the energy efficiency analysis of hybrid nanofluids via convergent/divergent channels using porous space. The hybrid nanofluid consists of polyethylene glycol water, nanoparticles Zr O 2 and MgO. To understand the porosity features, the Darcy-Forchheimer law is used. Solar radiation is considered for a more comprehensive analysis of the thermal field. The strong ODEs are obtained using a suitable similarity transformation. The NDSolve technique is used to simulate numerical results, which are then compared with previous published results. Plots and tables are used to report physical investigations of the related parameters. For higher solid volume fractions, the divergent channel's velocity drops. Whereas it increases for a convergent channel. In the presence of variables, Eckert number, and porosity parameter, skin friction increases in divergent channels and decreases in convergent channels for both nanofluids and hybrid nanofluids. Furthermore, it is noticed that hybrid nanocomposite has more dominant features than nanocomposite for both scenarios of narrowing/expanding channels. [ABSTRACT FROM AUTHOR]

In this research, we explore the flow dynamics of micropolar Casson fluids over curved surfaces, while incorporating prescribed heat and surface fluxes, as well as heat generation effects. By applying similarity transformation to the governing model, we derive individual differential equations which are then reduced to general differential equations. This transformation yields a mathematical structure conducive to problem analysis. Through the use of numerical methods, we solve ordinary differential equations to investigate the fluid dynamics and heat transfer phenomena in this specific flow configuration. The main aim of this study is to offer a comprehensive understanding of the intricate behavior displayed by micropolar Casson fluids on curved surfaces under the influence of prescribed heat and surface fluxes, along with heat generation. By employing numerical methods, this study aims to contribute to the advancement of theoretical understanding by addressing the complex interactions between fluid dynamics and thermal properties. [ABSTRACT FROM AUTHOR]