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This study focuses on the analysis of peristaltic transport of a hybrid nanofluid comprising deionized water as a base fluid and the multi-walled carbon nanotubes (MWCNTs) and copper oxide (CuO) as nanoparticles within a sinusoidal wavy porous duct, taking into consideration the influence of heat generation or absorption. The inaugural literature piece addresses the utilization of hybrid nanofluid in the context of peristaltic flow within ducts. To simplify the analysis, we have converted the non-dimensional equations into a two-dimensional (2D) coordinate system using the assumptions of a very long wavelength (δ < 1) and low Reynolds number (Re). The non-dimensional equations governing the behavior of the hybrid nanofluid are then solved numerically using the finite volume method. Numerical solutions for temperature and the 2D peristaltic flow are obtained with the assistance of the Mathematics software MATLAB. These solutions are subsequently represented graphically using MATLAB software. The graphical results highlight several key findings for important parameters. First, it is observed that the pressure rise, temperature profile, and pressure gradient in the hybrid nanofluid (CuMWCNTs/H2O) flow increases as heat generation increases. Furthermore, an increase in the nanoparticle volume fraction of both nanoparticles leads to a decrease in the pressure rise and pressure gradient in the hybrid nanofluid flow. Additionally, the widening of the channel reduces the pressure gradient and pressure rise in the CuMWCNTs/H2O hybrid nanofluid. The analysis also includes the visualization of streamlines for peristaltic transport. These streamlines reveal that an increase in amplitude results in larger bolus sizes, while heightened heat generation has the opposite effect, decreasing bolus sizes. The results of this investigation can be found in various cooling devices as flows in the ducts are very frequently utilized for the cooling process of engines. A further topic is common in applications related to microfluidics, heat exchangers, and biomedical devices where peristaltic pumping is employed. Our results are in 100% agreement with the existing literature in special cases. [ABSTRACT FROM AUTHOR]

The aim of the present work is to discuss the fractional mass-spring system with damping and driving force, considering a simple modification to the fractional derivatives with a non-singular kernel of the Atangana–Baleanu and Caputo–Fabrizio types. We introduce two novel modified fractional derivatives that offer advantages when the fractional differential equations involve higher-order fractional derivatives of order 1 + α or α + 1 , with 0 < α < 1 . Previous definitions of fractional derivatives with non-singular kernel do not have a unique definition, leading to significant inconsistencies. One of the main results of the present work is that the proposed modifications provide a unique result for the fractional-order derivatives 1 + α and α + 1 . Additionally, we apply these two novel fractional derivatives to the fractional mass-spring system with damping and driving force. In the case of the modified Caputo–Fabrizio fractional derivative, novel analytical solutions have been constructed, showing interesting oscillating time evolution with a transient term not previously reported. This transient term features an initial nonzero oscillating return away from the equilibrium position. For the modified Atangana–Baleanu fractional derivative, the numerical solutions also exhibit this nonzero oscillating return away from the equilibrium position. These results are not present when using the Caputo singular kernel derivative, as demonstrated in the comparison figures reported here. [ABSTRACT FROM AUTHOR]

We compute the numerical solution of Bratu's boundary value problem (BVP). To achieve this, we apply a new and useful approach to solve Bratu's boundary value problem by using Green's function and a new integral operator, along with a modified version of the Adomian decomposition method. This process produces solutions that call for the boundary conditions to be applied explicitly. Statistical results demonstrating the robustness and efficiency of the proposed scheme are included. An exact and approximate solution comparison is made with known results. The quantitative outcomes showcase our novel approach's high numerical precision and consistency across a range of parameter configurations. [ABSTRACT FROM AUTHOR]

This paper presents a new method for obtaining approximate closed-form solutions for crack propagation problems. In general, it is not possible to obtain explicit solutions of the parameters and elementary functions of these problems, due to their terms complexity, present in their definitions. In this way, we used numerical methods to obtain approximate numerical solutions. The method presented in this article provides a proposal, which, when defined by differential equations, is applicable and extensible to other problems. The approximate solutions are obtained as an exact solution of a modified initial value problem. The performance is evaluated in relation to problems with known exact solution. [ABSTRACT FROM AUTHOR]

In this study, we investigate the behavior of the Dirac–Born–Infeld (DBI) scalar field as a candidate for the nature of dark energy in a non-minimal coupling scenario with the scalar torsion within the framework of teleparallel gravity. We present numerical solutions for the equations of motion and analyze the behavior of various cosmological parameters for different values of the parameter ṽ and f̃. Our findings reveal that the DBI scalar field can contribute significantly to the energy density of the universe and drive the late-time acceleration of the universe, with a transition from deceleration to acceleration occurring within a redshift range consistent with recent observational bounds. We show that the present-day value of the deceleration parameter is consistent with recent observational constraints, and the DBI scalar field behaves like a cosmological constant model. Our results suggest that the DBI scalar field can play a significant role in driving the late-time acceleration of the universe and that it has the potential to be a viable alternative to the cosmological constant model. Further investigations are necessary to better understand the nature of the dark energy component and its implications for cosmology within the framework of teleparallel gravity. [ABSTRACT FROM AUTHOR]

The nonlinear Semilinear Dispersive-Fisher (SDF) model is an important equation describing wave dynamics in dispersive media influenced by nonlinear and diffusive effects. This study enhances both analytical and numerical methods to solve the SDF model and validate the solutions. We utilize the Modified Khater (MKhat) and Unified (UF) methods for analytical solutions, and He’s Variational Iteration (HVI) scheme for numerical approximations. Our investigation connects the SDF model to other nonlinear equations like the Korteweg–de Vries (KdV) and Fisher–Kolmogorov (FK) equations, demonstrating the consistency between analytical and numerical solutions. This research contributes to the understanding and modeling of wave phenomena in dispersive media with nonlinear and diffusive dynamics, offering refined analytical and numerical techniques specific to the SDF model. Key contributions include introducing the MKhat and UF methods for analytical solutions and employing the HVI scheme for numerical approximations, which are less represented in current literature. This work is positioned in mathematical physics, focusing on nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

The Navier–Stokes equations and the energy equation are used to investigate a fluid flow between two stretching rectangular surfaces subjected to a temperature difference that affects the dynamic viscosity and thermal conductivity of the fluid. The wall stretching process enhances the momentum boundary layer thickness which slows the axial motion of the fluid away from the flow boundaries. When the stretching parameter γ is equal to 1, that is the case corresponding to symmetric stretching, the minimum of the axial velocity is located at the midplane of the channel y = 0.5 if the viscosity variational parameter α equals 0. This minimum moves towards the region 0.5 < y < 1 for α > 0, but migrates towards the region 0 < y < 0.5 for α < 0. Moreover, in the case of symmetric stretching corresponding to γ = 1, the growth in Reynolds number Re tends to increase the axial velocity around the middle of the channel for α ≥ 0 in the attempt to counteract the effects of enhancing the momentum boundary layer thickness leading to the flattening of axial velocity profiles for Re ≥ 100. While the conductivity variational parameter β does not influence enough the fluid dynamics and heat transfer, the Reynolds number Re and the Péclet number Pé can increase or decrease the temperature distribution inside the channel depending on the sign of the parameter α. Practical applications related to the present study include lubrification, food manufacturing, paint industries, extrusion processes in plastic and metal industries. [ABSTRACT FROM AUTHOR]

A method is presented to demonstrate the application of computer simulations in the kinematic analysis of planar mechanisms, emphasizing its use in teaching the latter topic in a corresponding undergraduate course. Concepts of rigid-body dynamics are utilized in the kinematics of machines to analyze the motions (and forces in dynamics) transmitted within multiple interconnected links that make a mechanism, such as a car engine, airplane landing gear, press machine, door closer, and so on. Due to the tediousness of the analytical solutions, most textbooks limit the derivation of the equations to four-bar linkages like crank-rocker and crank-slider mechanisms. Benefiting from the advancements in computer programs, such as MATLAB, and their efficiency in solving large systems of linear and nonlinear equations, a method is proposed to facilitate teaching kinematic analysis of multi-bar linkages to undergraduate students while fostering the application of computational engineering via real-life examples. The results obtained from this method are shown to be in excellent agreement with the algebraic solution of the relative motion equations for each element in the mechanism. [ABSTRACT FROM AUTHOR]

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The object of this research is to examine the combined effects of mass and thermal Biot numbers on the properties of a Powell-Erying fluid flow that is two-dimensional, constant, viscous, incompressible, and non-Newtonian. In the direction of the flow is an extending sheet encircled by a porous medium. Further consideration is given to the existence of a chemical reaction, thermophoresis, Brownian motion, and velocity lapse, among other factors. Utilizing the Powell-Erying Cauchy non-Newtonian model, the viscoelastic effect is accounted for. When establishing concentration and temperature boundary conditions, thermal and mass Biot numbers are incorporated. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge–Kutta method. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge–Kutta method. Furthermore, the Nusselt number, Skin-friction, and Sherwood number coefficients are evaluated and shown in a tabular format utilizing the same parameters. In the end, the numerical outcomes obtained from this investigation are substantiated and considered to be highly consistent with the findings that were previously documented. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the stability and Hopf bifurcation of the fractional-order logistic equation with two different delays τ 1 , τ 2 > 0 : D α y (t) = ρ y (t - τ 1) 1 - y (t - τ 2) , t > 0 , ρ > 0 . We describe stability regions by using critical curves. We explore how the fractional order α , ρ , and time delays influence the stability and Hopf bifurcation of the model. Then, by choosing ρ , fractional order α , and time delays as bifurcation parameters, the existence of Hopf bifurcation is studied. An Adams-type predictor–corrector method is extended to solve fractional-order differential equations involving two different delays. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of theoretical results. [ABSTRACT FROM AUTHOR]

This paper primarily focused on analyzing a stochastic $ \mathcal{SVIR} $ epidemic model that incorporates Levy noises. The population may be divided into four distinct compartments: vulnerable class ($ \mathcal{S} $), vaccinated individuals ($ \mathcal{V} $), infected individuals ($ \mathcal{I} $), and recovered individuals ($ \mathcal{R} $). To achieve this, we chose existing and unique techniques as the most feasible solution. In the nexus, the stochastic model was theoretically analyzed using a suitable Lyapunov function. This analysis broadly covered the existence and uniqueness of the non-negative solution, as well as the dynamic properties related to both the disease-free equilibrium and the endemic equilibrium. In order to eradicate diseases, a stochastic threshold value denoted as "$\textbf{R}_0$" was used to determine if they may be eradicated. If $ \textbf{R}_0 < 1, $ it means that the illnesses have the potential to become extinct. Moreover, we provided numerical performance results of the proposed model using the artificial neural networks technique combined with the Bayesian regularization method. We firmly believe that this study will establish a solid theoretical foundation for comprehending the spread of an epidemic, the implementation of effective control strategies, and addressing real-world issues across various academic disciplines.

SUMMARY: Thermal convection in planetary solid (rocky or icy) mantles sometimes occurs adjacent to liquid layers with a phase equilibrium at the boundary. The possibility of a solid–liquid phase change at the boundary has been shown to greatly help convection in the solid layer in spheres and plane layers and a similar study is performed here for a spherical shell with a radius-independent central gravity subject to a destabilizing temperature difference. The solid–liquid phase change is considered as a mechanical boundary condition and applies at either or both horizontal boundaries. The boundary condition is controlled by a phase change number, Φ, that compares the timescale for latent heat exchange in the liquid side to that necessary to build a topography at the boundary. We introduce a numerical tool, available at https://github.com/amorison/stablinrb, to carry out the linear stability analysis of the studied setup as well as other similar situations (Cartesian geometry, arbitrary temperature and viscosity depth-dependent profiles). Decreasing Φ makes the phase change more efficient, which reduces the importance of viscous resistance associated to the boundary and makes the critical Rayleigh number for the onset of convection smaller and the wavelength of the critical mode larger, for all values of the radii ratio, γ. In particular, for a phase change boundary condition at the top or at both boundaries, the mode with a spherical harmonics degree of 1 is always favoured for Φ ≲ 10−1. Such a mode is also favoured for a phase change at the bottom boundary for small (γ ≲ 0.45) or large (γ ≳ 0.75) radii ratio. Such dynamics could help explaining the hemispherical dichotomy observed in the structure of many planetary objects. [ABSTRACT FROM AUTHOR]

New transition curves from straight paths to circular paths are proposed for the first time in this study. The paths enable the vehicles to maintain constant normal acceleration components when the vehicle has a given tangential deceleration component. The differential equation describing the path for an arbitrary tangential deceleration component is given first. Several special cases corresponding to different deceleration functions in terms of velocity and position are derived. The path equations are third order ordinary differential equations with high nonlinearities. The equations are cast into a non-dimensional form which enables to define the dimensionless parameters affecting the curves. Two of the special cases are numerically treated: (1) Deceleration proportional to the velocity, (2) Deceleration exponentially decaying with path length. The effects of dimensionless parameters on the solutions are exploited in the figures. The transition curves may be employed in determining the paths of land, aerial and marine vehicles. [ABSTRACT FROM AUTHOR]

This paper primarily focused on analyzing a stochastic SVIR epidemic model that incorporates Levy noises. The population may be divided into four distinct compartments: vulnerable class (S), vaccinated individuals (V), infected individuals (I), and recovered individuals (R). To achieve this, we chose existing and unique techniques as the most feasible solution. In the nexus, the stochastic model was theoretically analyzed using a suitable Lyapunov function. This analysis broadly covered the existence and uniqueness of the non-negative solution, as well as the dynamic properties related to both the disease-free equilibrium and the endemic equilibrium. In order to eradicate diseases, a stochastic threshold value denoted as "R0" was used to determine if they may be eradicated. If R0 < 1; it means that the illnesses have the potential to become extinct. Moreover, we provided numerical performance results of the proposed model using the artificial neural networks technique combined with the Bayesian regularization method. We firmly believe that this study will establish a solid theoretical foundation for comprehending the spread of an epidemic, the implementation of effective control strategies, and addressing real-world issues across various academic disciplines. [ABSTRACT FROM AUTHOR]

AbstractIncorporating slip conditions into computational fluid dynamics (CFD) simulations and experiments helps engineers predict and improve the effectiveness of superhydrophobic surfaces in reducing drag. This optimization approach leads to significant enhancements in fuel efficiency and performance across a range of fluid-flow systems, including marine vessels and aircraft. This study models the phenomena of velocity and temperature slip, coupled with MHD, within the context of nanofluid flow undergoing bioconvection over a stretching sheet. Subsequently, the study seeks to analyze the resulting effects on heat and mass kinematics. The bvp4c solver effectively calculates analytical solutions for the reduced problem obtained through similarity transformation from the underlying partial differential equations. Velocity and temperature slip both impact temperature, with velocity slip increasing heat transfer rates and temperature slip decreasing them. The thermal radiation parameter enhances nanoparticle concentration, although it’s offset by an increased Lewis number. Brownian motion amplifies mass transfer, but the thermal radiation parameter hampers it. The escalation in the microorganism density profile correlates with the increase in both the Bioconvection Lewis number and the Peclet number. Likewise, as thermophoresis parameters and the bioconvection constant increase, the microorganism density along the profile also rises. [ABSTRACT FROM AUTHOR]

A five-dimensional hyperchaotic system is a dynamical system with five state variables that exhibits chaotic behavior in multiple directions. In this work, we incorporated a 5D hyperchaotic system with constant- and variable-order Caputo and the Caputo–Fabrizio fractional derivatives. These fractional 5D hyperchaotic systems are solved numerically. Through simulations, the chaotic behavior of these fractional-order hyperchaotic systems is analyzed and a comparison between constant- and variable-order fractional hyperchaotic systems is presented. [ABSTRACT FROM AUTHOR]

Modelling seismic wavefields in complex 3-D elastic media is the key in many fields of Earth Science: seismology, seismic imaging, seismic hazard assessment and earthquake source mechanism reconstruction. This modelling operation can incur significant computational cost, and its accuracy depends on the ability to take into account the scales of the subsurface heterogeneities varying. The theory of homogenization describes how the small-scale heterogeneities interact with the seismic waves and allows to upscale elastic media consistently with the wave equation. In this study, an efficient and scalable numerical homogenization tool is developed, relying on the similarity between the equations describing the propagation of elastic waves and the homogenization process. By exploiting the optimized implementation of an elastic modelling kernel based on a spectral-element discretization and domain decomposition, a fully scalable homogenization process, working directly on the spectral-element mesh, is presented. Numerical experiments on the entire SEAM II foothill model and a 3-D version of the Marmousi II model illustrate the efficiency and flexibility of this approach. A reduction of two orders of magnitude in terms of absolute computational cost is observed on the elastic wave modelling of the entire SEAM II model at a controlled accuracy. [ABSTRACT FROM AUTHOR]

To investigate the effects of slope geometric parameters and soil stratigraphic properties on the topographic amplification of ground motions, a large number of 2-D horizontally layered slope models are constructed. First, the linear and nonlinear seismic responses of a slope model are compared, and the result shows that the nonlinear characteristics of soils should be considered when studying the amplifying effect of slope topography on ground motions. Then, the nonlinear seismic responses of these slope models are analysed from four aspects: the maximum shear strain in the slopes, the effects of geometry and stratigraphy on the seismic response, the distance between the maximum topographic amplification indicators and the slope crest, and the influence range of slope topography behind the slope crest. The results indicate that the amplifying effect of slope topography on ground motions increases with increasing slope height or decreasing average shear wave velocity of the overlying soil layers. Besides, the variation of the topographic amplification effect with slope gradient is significantly influenced by soil stratigraphic properties. The distance between the maximum topographic amplification indicators and the slope crest is mainly in the range of 0–60 m, and the influence range of slope topography behind the slope crest is mainly in the range of 0–150 m. Subsequently, approximate relations are derived based on regression analyses of simulation results, which can provide meaningful references for the seismic design and seismic retrofitting of engineering structures behind the slope crest. Finally, the effects of slope geometric parameters and soil stratigraphic properties on ground motion modifications are further evaluated according to the prediction curves provided by the approximate relations. [ABSTRACT FROM AUTHOR]

Seismic gradient measurements from distributed acoustic sensors and rotational sensors are becoming increasingly available for field surveys. These measurements provide a wealth of information and are currently being considered for many applications such as earthquake detection and subsurface characterizations. In this work, using a simple 2-D numerical approach, we tackle the implications of such wavefield gradient measurements on full waveform inversion (FWI) techniques using a simple 2-D numerical test. In particular, we study the impact of the wavefield gradient measurement sensitivity to heterogeneities that are much smaller than the minimum wavelength. Indeed, as shown through the homogenization theory, small-scale heterogeneities induce an unexpected coupling of the strain components to the wavefield gradient measurement. We further show that this coupling introduces a potential limitation to the FWI results if it is not taken into account. We demonstrate that a gradient measurement-based FWI can only reach the accuracy of a classical displacement field-based FWI if the coupling coefficients are also inverted. Furthermore, there appears to be no specific gain in using gradient measurements instead of conventional displacement (or velocity, acceleration) measurements to image structures. Nevertheless, the inverted correctors contain fine-scale heterogeneities information that could be exploited to reach an unprecedented resolution, particularly if an array of receivers is used. [ABSTRACT FROM AUTHOR]

Investigating subsurface shear wave velocity (v s) structures using surface wave dispersion data involves minimizing a misfit function that is commonly solved through gradient-based optimization. Sensitivity kernels for model updates are commonly estimated using numerical differentiation, variational methods or implicit functions which however, may involve numerical instability and computational challenges when dealing with complex velocity models and large data sets. In this study, we propose a novel surface wave inversion framework in which error-free gradients are calculated by automatic differentiation (AD) and forward modelling is implemented by convenient computational graphs in the state-of-the-art deep learning framework. The AD-based inversion approach is first validated using two synthetic data sets. Then, the subsurface structures at three distinct locations, namely the Great Plains and the Long Beach in the US and Tong Zhou in China, are also derived using this method with seismic ambient noise data, which show nice consistency with those obtained using traditional methods. With the significantly improved computational efficiency, a great number of initial models can be inverted simultaneously to mitigate the impact of local minima and to estimate the uncertainty in the invert models. We have developed a new surface wave inversion package named ADsurf based on automatic differentiation and computational graphs in the deep learning framework, and its computational efficiency is also compared with the traditional finite-difference-based gradient estimation approach. While a great number of intriguing studies on the geophysical inverse problems have been conducted recently using deep learning for end-to-end mapping, the use of AD provided in the in the deep learning frameworks to assist and expedite the gradient computations are still underexploited in geophysics. Thus, it is expected that various geophysical inverse problems in many different areas beyond the surface wave inversion can also be tackled with this new paradigm in the future. [ABSTRACT FROM AUTHOR]

This study estimated the gravity change expected on the sea surface due to magma accumulation beneath submarine volcanoes. For calculation, a semi-analytical model describing the deformation of an infinite elastic cone was considered, in which a point spherical source was embedded on the axis. The expected gravity change exceeds 0.2 mGal in certain scenarios when |$\delta V = 10^8\, \mathrm{m^3}$| of source volume change occurs 2 km below the summit, and the summit is shallower than 300 m below the sea surface. The steeper the slope of a submarine volcano, the greater the expected gravity change. 0.2 mGal of gravity variation can be detected with recent marine gravimeters such as cold atom interferometers. The computation method for the gravity change based on the integral transform (Mellin type) is elaborated in this paper. [ABSTRACT FROM AUTHOR]

We apply the adjoint method to efficiently calculate sensitivity kernels for long-period seismic spectra with respect to structural and source parameters. Our approach is built around the solution of the frequency-domain equations of motion using the direct solution method (DSM). The DSM is currently applied within large-scale mode coupling calculations and is also likely to be useful within finite-element type methods for modelling seismic spectra that are being actively developed. Using mode coupling theory as a framework for solving both the forward and adjoint equations, we present numerical examples that focus on the spectrum close to four eigenfrequencies (the low-frequency mode, 0 S 2, and higher frequency modes, namely 2 S 2, 0 S 7 and 0 S 10 for comparison). For each chosen observable, we plot sensitivity kernels with respect to 3-D perturbations in density and seismic wave speeds. We also use the adjoint method to calculate derivatives of observables with respect to the matrices occurring within mode coupling calculations. This latter approach points towards a generalization of the two-stage splitting function method for structural inversions that does not rely on inaccurate self-coupling or group-coupling approximations. Finally, we verify through direct calculation that our sensitivity kernels correctly predict the linear dependence of the chosen observables on model perturbations. In doing this, we highlight the importance of non-linearity within inversions of long-period spectra. [ABSTRACT FROM AUTHOR]

In this paper, we study the cosmic dynamics of varying vacuum models where the dark matter interacts with the vacuum energy. We consider the homogeneous and isotropic spacetime with spatial curvature and apply the dynamical system technique to the varying vacuum models by specifying the form of energy exchange rate (Q) between the dark energy and dark matter. Further, we utilize the cosmographic parameters and statefinder parameters in the terms of dynamical variables of the cosmological dynamical system to explore the cosmic dynamics of the universe. The Milne universe solution exists as a consequence of spatially curved geometry in the model. The models also yield radiation- matter- and dark energy-dominated phases in order and thus explain the late-time accelerated expansion of the universe. The strength of interaction terms will affect the existence of cosmological phases in the model but there will always be an attractor corresponding to the accelerating universe. We numerically solve the system to illustrate the evolution of cosmological quantities and dynamical variables in the models. The role of curvature is visible during the transition from the decelerated phase into the accelerating phase. The numerical solutions affirm that the cosmological parameters in the models are consistent with their corresponding observational values. [ABSTRACT FROM AUTHOR]

We describe a pressure projection scheme for the simulation of incompressible flow in cubic domains with open boundaries based on fast Fourier transforms. The scheme is implemented in flow_solve, a numerical code designed for process studies of rotating, density‐stratified flow. The main algorithmic features of the open‐boundary code are the near‐spectral accuracy of the discrete differentiation and a dynamic two‐dimensional domain decomposition that scales efficiently to large numbers of processors. The simulated flows are not required to be periodic or to satisfy symmetry conditions at the open boundaries owing to the use of mixed series expansions combining cosine and singular Bernoulli polynomial basis functions. These expansions facilitate the imposition of inhomogeneous boundary conditions and allow the code to be used for offline, one‐way nesting within an arbitrarily embedded subdomain of a larger scale simulation. The projection scheme is designed to exploit a simple and powerful numerical engine: inversion of Poisson's equation with homogeneous Neumann boundary conditions using fast cosine transforms. Here, we describe the mathematical transformations used to accommodate the imposition of space‐ and time‐varying boundary conditions. The utility of the approach for process studies and for nesting within submesoscale‐resolving ocean models is demonstrated with simulations of wind‐driven near‐inertial waves in the upper ocean. Plain Language Summary: Internal gravity waves in the upper ocean are affected by the presence of features such as fronts, eddies, and geographically constrained winds and currents. Ocean models that are able to accurately capture geographic realism often lack the capacity to resolve the intricacies of the internal waves that may be generated. This paper presents a mathematical framework that combines the realism of ocean models with high‐fidelity simulation of small‐scale dynamics. The framework is demonstrated through a series of examples of increasing complexity, including wave trapping in a wind‐perturbed anticyclonic vortex and simulation of near‐inertial waves near a density front in the Gulf of Lion. The proposed methodology has the potential to take advantage of the increasing horizontal resolution and fine‐scale realism of ocean models, while also relaxing the approximations that limit their ability to resolve the detailed dynamics of the internal wave field. Key Points: A computational framework based on fast spectral transforms is developed for computing nonhydrostatic flow in domains with open boundariesMixed basis function expansions are formulated to differentiate discrete data lacking symmetry or periodicity with near‐spectral accuracyNested simulations of wave trapping in a vortex and near‐inertial waves near a density front in the Gulf of Lion demonstrate the approach [ABSTRACT FROM AUTHOR]

The traditional cubic B-spline method offers limited local control over the curve solution. Adjusting the position of a control point affects the entire curve, making it challenging to make localized changes, e.g., smoothness. Moreover, the basis functions vanish on one side by the cubic B-spline method near the end conditions where the initial and boundary conditions are applied. To address these limitations, this research proposes a new basis by including a free parameter γ with the purpose of modifying the weights of nearby control points. This free parameter γ can influence the curve’s behavior in specific regions as well as the entire curve. This modification of the cubic B-spline method was used to approximate the second-order derivative at each collocation point. The convergence test showed that the proposed method was second-order convergent. Numerical examples of ordinary differential equations were used with different step values to evaluate the accuracy of the proposed method. The findings persistently indicated that the proposed technique provided better error estimates as compared to the other methods discussed in the literatures.

The objective of the present study was to improve our understanding of the complex biological process of bone mineralization by performing mathematical modeling with the Caputo-Fabrizio fractional operator. To obtain a better understanding of Komarova's bone mineralization process, we have thoroughly examined the boundedness, existence, and uniqueness of solutions and stability analysis within this framework. To determine how model parameters affect the behavior of the system, sensitivity analysis was carried out. Furthermore, the fractional Adams-Bashforth method has been used to carry out numerical and graphical simulations. Our work is significant owing to its comparison of fractional- and integer-order models, which provides novel insight into the effectiveness of fractional operators in representing the complex dynamics of bone mineralization.

In this study, we investigate the traveling wave solutions of the Gilson-Pickering equation using two different approaches: F-expansion and (1/G$ ^\prime $)-expansion. To carry out the analysis, we perform a numerical study using the implicit finite difference approach on a uniform mesh and the parabolic-Monge-Ampère (PMA) method on a moving mesh. We examine the truncation error, stability, and convergence of the difference scheme implemented on a fixed mesh. MATLAB software generates accurate representations of the solution based on specified parameter values by creating 3D and 2D graphs. Numerical simulations with the finite difference scheme demonstrate excellent agreement with the analytical solutions, further confirming the validity of our approaches. Convergence analysis confirms the stability and high accuracy of the implemented scheme. Notably, the PMA method performs better in capturing intricate wave interactions and dynamics that are not readily achievable with a fixed mesh.

This study presents a theoretical analysis of the thermophoretic and Brownian diffusion effects on the magnetized flow of Carreau nanofluid over a stretchable curved surface. The investigation includes the impact of heat generation and activation energy, which are incorporated into the energy and concentration equations, respectively. The mathematical model of the boundary layer flow is formulated as a set of nonlinear partial differential equations using curvilinear coordinates. These equations are transformed into ordinary differential equations through the application of appropriate similarity variables. The resulting system is solved numerically by using the shooting method along with the Runge-Kutta technique. The accuracy of the numerical results is further verified by the Keller-box method, a finite difference technique. The obtained results are also checked by giving a comparison table with the published data in the literature. Furthermore, the convergence of the solutions is also checked by a convergent series method known as the homotopy analysis method (HAM). The study examines the influence of several key parameters, including the radius of curvature, Weissenberg number, Prandtl number, Lewis number, Brownian and thermophoretic diffusions parameters, Hartmann number, heat generation parameter, activation energy parameter, temperature difference parameter, chemical reaction parameter, and power law index. The effects of these parameters on momentum, temperature, concentration distributions, mass and heat transfer rates, and as well as the skin friction coefficient are examined through graphs and tables. Graphical observations declare that the velocity field diminishes against the rising values of the Hartmann number and Weissenberg number. However, the velocity profile rises with improved values of the radius of curvature parameter and power law index parameter. It is also noticed that the magnitude of the concentration field rises with growing values of the Brownian parameter, activation energy parameter and Lewis number, whereas it shows a decreasing manner against the enhanced values of the thermophoresis parameter and temperature difference parameter.

The article exposes the use of the Runge-Kutta Fehlberg method of order five, a rarely studied methodology, to address the complexity involved in solving fuzzy hybrid differential equations. The study focuses on evaluating the reliability and accuracy of this method in contrast to recognized procedures, providing a thorough analysis of its performance. The article assesses the effectiveness of the RK-Fehlberg scheme by comparing its results with exact solutions, using thorough analysis and well-supported examples. This comparison analysis highlights the potential of the method to provide more accuracy compared to classic methods like Euler, improved, or modified schemes. The article demonstrates the strength and effectiveness of the method by using numerical examples. This not only helps improve computational techniques for solving fuzzy hybrid systems but also highlights the wide range of applications and reliability of the Runge–Kutta Fehlberg method in mathematical modeling and analysis.

AbstractTemperature-dependent viscosity finds application in various industries such as oil and gas, polymer processing, and food manufacturing. Understanding how viscosity changes with temperature is critical for optimizing processes like drilling operations, polymer molding, and food product consistency. Additionally, it plays a vital role in controlling flow behavior, ensuring efficient heat transfer, and maintaining product quality across different temperature conditions. The exploration of temperature-dependent viscosity in Powell-Eyring nanofluid models represents a novel and unexplored avenue in the field. The study’s novelty is underscored by its comprehensive investigation into a range of factors, such as surface suction, thermal radiation, slip velocity effects, and nanoparticle concentration slip, all integrated within the Powell-Eyring nanofluid model. Moreover, the adoption of bvp4c as a numerical tool further emphasizes the research’s unique contributions. The curves of temperature, concentration, and velocity as a consequence of changes in physical parameters are discussed. Increasing the value of the suction parameter promotes heat transfer but slows the velocity of the nanofluid. The injection of a magnetic field is responsible for compensating for the suction rate. An improvement in the concentration of nanoparticles and temperature is observed as a result of an increase in the slip rate. It is evident that both nanoparticle concentration and temperature rise significantly when Bi, the Biot number, is increased. In the boundary layer, a decrease in velocity is observed as a consequence of an increase in velocity slip, porosity, and magnetic field parameters. [ABSTRACT FROM AUTHOR]

Piecewise fractional-order differential operators have received more attention in recent years because they can be used to describe various evolutionary dynamical problems to investigate crossover behaviors. In this manuscript, we use the aforementioned operators to investigate a mathematical model of COVID-19. By utilizing fractional calculus, our approach aims to capture the crossover dynamics of disease spread, considering heterogeneity and transitions between epidemic phases. This research seeks to develop a framework using specialized mathematical techniques, such as the Caputo fractional derivative, with the potential to investigate the crossover dynamical behaviors of the considered epidemic model. The anticipated contribution lies in bridging fractional calculus and epidemiology, offering insights for both theoretical advancements and practical public health interventions. In order to improve our understanding of epidemic dynamics and support, we used MATLAB to simulate numerical results for a visual representation of our findings. For this interpretation, we used various fractional-order values. In addition, we also compare our simulated results with some reported results for infected and death classes to demonstrate the efficiency of our numerical method. [ABSTRACT FROM AUTHOR]

This study describes thermal transmission features across a gravity-driven bioconvection flow of the viscoplastic-type Casson nanofluid caused by a vertically rotating cylinder under gyrotactic microorganisms. The research further quantifies the impact of nonlinear thermal radiations, heat source/sink and convective interface on the temperature and heat transmission rate of a nanofluid rotating on a cylindrical surface. The Buongiorno two-phase model characterizing Brownian diffusion and thermophoretic properties is utilized to examine the nanoparticle's effect on the Casson nanofluid. A system of strongly nonlinear PDEs is converted into a system of ODEs by using the appropriate variables. The MATLAB technique is used to build a numerical solution for nonlinear flow equations. The influences of various parameters on the volumetric concentration of nanoparticles, velocities, thermal fields, and microorganism profiles are examined. The finding indicates that an upsurge in the bioconvection Lewis parameter causes declines in the microorganism profile. The thermal and solutal distribution of species increases with an increase in thermophoresis parameter estimations. Significant thermal transport is acquired with greater radiation impacts. The microorganism's distribution is improved with a larger Peclet number. [ABSTRACT FROM AUTHOR]

In this study, we investigate the traveling wave solutions of the Gilson-Pickering equation using two different approaches: F-expansion and (1/G')-expansion. To carry out the analysis, we perform a numerical study using the implicit finite difference approach on a uniform mesh and the parabolic-Monge-Ampère (PMA) method on a moving mesh. We examine the truncation error, stability, and convergence of the difference scheme implemented on a fixed mesh. MATLAB software generates accurate representations of the solution based on specified parameter values by creating 3D and 2D graphs. Numerical simulations with the finite difference scheme demonstrate excellent agreement with the analytical solutions, further confirming the validity of our approaches. Convergence analysis confirms the stability and high accuracy of the implemented scheme. Notably, the PMA method performs better in capturing intricate wave interactions and dynamics that are not readily achievable with a fixed mesh. [ABSTRACT FROM AUTHOR]

AbstractNanoparticles mixed with base liquids result in the formation of nanofluids, known for their exceptional thermal conductivity and their ability to enhance the performance of electrical and mechanical devices. Therefore, this study investigates the peristaltic activity of fourth-grade nanomaterial by taking the consideration of magnetic aspects. Analysis is carried out in the presence of motile gyrotactic microorganisms, Ohmic heating, and viscous dissipation. Thermal transport incorporated effects of nonlinear thermal radiation along with Brownian motion and thermophoresis. Thermal and mass convective conditions are imposed on elastic symmetric channels. The assumptions of low Reynolds number and long wavelength approximations have led to the simplification of the nonlinear partial differential equations system into ordinary differential equations. The governing system is solved numerically by NDSolve technique via Mathematica. Graphs are plotted and examined for velocity, thermal field, density of motile gyrotactic microorganisms, and heat transfer rate. [ABSTRACT FROM AUTHOR]

Viscoelastic fluids exhibit complex viscous and elastic behavior and are found in nature and industries like polymer solutions and biological fluids. This research is devoted to the examination of the heat and mass flow characteristics of viscoelastic fluids with heightened viscous effects relative to elasticity. Mathematical models are crucial for understanding and predicting their responses to mechanical stresses. The models are based on spring and dashpot elements and vary in arrangement to capture behavioral dominance. In this study, a spring in parallel with one dashpot and a second dashpot in series creates a viscoelastic three-element viscous model for the fluid. This model is employed in transport equations to analyze the heat and mass flow properties of a viscoelastic fluid across a variable thickness sheet. The numerical Runge-Kutta (RK) technique is used to find the solutions to these equations. The influence of viscosity on the outcomes is shown to be more significant than other parameters. Additionally, there is a 22% and 137% enhancement in the Nusselt number and entropy generation rate, respectively, at $\mu = 0.005.$μ=0.005. [ABSTRACT FROM AUTHOR]

This work aims to investigate the characteristics of a suction-driven flow of a curved fluid layer using the Navier-Stokes equations. The examined fluid flow characteristics include the azimuthal velocity, the normal velocity, pressure gradients, and streamlines under different values of the Reynolds number. The results show that the problem provides symmetric solutions when the fluid keeps its primary direction of motion near the two porous boundaries of the thin fluid layer. The asymmetric solutions found highlight flow reversal near each porous boundary. The change of the direction of motion due to flow reversal manifests itself as a curvature of the streamlines, and in this case the normal pressure gradient presents an oscillatory behavior. [ABSTRACT FROM AUTHOR]

Muography is a promising and rapidly developing physical prospecting technique based on the attenuation of muon flux. The feasibility and potential of applying muography to mining were presented in a small number of previous case studies. In this work, we aimed to address three challenges that limit the applicability and efficiency of muography in mineral exploration: (1) application to low-density-contrast ore body exploration, (2) analysis of altitudinal impacts on measurements and (3) precise and efficient reconstruction. We conducted the first case of applying muography to the exploration for low-density-contrast ore bodies. Six muon imaging systems were placed underground to collect surviving muons for roughly half a year. We analysed the altitudinal impact on the data measurements and proposed a simplified method to eliminate it. We also developed the seed algorithm, a novel 3-D reconstruction algorithm, that can reconstruct anomalies located far away from the detectors and avoid their elongation along the observed directions. Benefitting from the seed algorithm, a low-density-contrast ore body and a limonitic siliceous slate structure were reconstructed, demonstrating the sensitivity of this technique in density distinction; discoveries of several mined-out areas are important for accident avoidance; and reconstruction of the stope and scarps served as strong circumstantial evidence of the reliability of the result. The success of this experiment shows the great value of muography in the economic, research and safety aspects of mineral exploration and inspection. Moreover, the overcoming of challenges is helpful for the development of muography, making it an effective and competitive technique in this field. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology to assist geophysicists in determining the first-break event in a 3-D seismic data set using the well-known technique called dynamic time warping algorithm (DTW), which is usually used to find the optimal alignment between two time-series. We used the optimal path from the cost matrix to identify the first break in the seismogram using a few picks (seeds) made by an interpreter as a reference to perform this task. Furthermore, the data were pre-conditioned by the topographic and linear moveout to improve the method's accuracy. To demonstrate the technique's robustness, first, we applied the methodology in a synthetic seismic data. After demonstrating the efficiency of the algorithm, we applied the aforementioned methodology in the Polo-Miranga 3-D seismic cube located in the Recôncavo sedimentary basin, Bahia-Brazil, and in the seismic data acquired from the Blackfoot field in Alberta, Canada. The high-quality results showed consistency in determining the first break in all ranges of offsets, demonstrating an alternative way to accelerate this seismic processing step. Furthermore, we compared the results obtained by the proposed methodology with an algorithm based on comparing the short-time averages with long-time averages. Finally, we performed the static correction calculation to ensure that the time distortion resulting from the terrain and the low-velocity layer was mitigated in shoot gathers and in the stacked section. [ABSTRACT FROM AUTHOR]

We present a time-domain distributional finite-difference scheme based on the Lebedev staggered grid for the numerical simulation of wave propagation in acoustic and elastic media. The central aspect of the proposed method is the representation of the stresses and displacements with different sets of B-splines functions organized according to the staggered grid. The distributional finite-difference approach allows domain-decomposition, heterogeneity of the medium, curvilinear mesh, anisotropy, non-conformal interfaces, discontinuous grid and fluid–solid interfaces. Numerical examples show that the proposed scheme is suitable to model wave propagation through the Earth, where sharp interfaces separate large, relatively homogeneous layers. A few domains or elements are sufficient to represent the Earth's internal structure without relying on advanced meshing techniques. We compare seismograms obtained with the proposed scheme and the spectral element method, and we show that our approach offers superior accuracy, reduced memory usage, and comparable efficiency. [ABSTRACT FROM AUTHOR]

In this paper, a Euler wavelets method for solving the variational problems is presented. The operational matrices of integration and product of Euler wavelets are calculated. Then, by using Euler wavelets and the operational matrices, the variational problems are reduced into the system of algebraic equations. Furthermore, the convergence analysis and error bound of the Euler wavelets method are given. Some examples are included to demonstrate the applicability and validity of the schemes. [ABSTRACT FROM AUTHOR]

In this paper, physics-informed liquid networks (PILNs) are proposed based on liquid time-constant networks (LTC) for solving nonlinear partial differential equations (PDEs). In this approach, the network state is controlled via ordinary differential equations (ODEs). The significant advantage is that neurons controlled by ODEs are more expressive compared to simple activation functions. In addition, the PILNs use difference schemes instead of automatic differentiation to construct the residuals of PDEs, which avoid information loss in the neighborhood of sampling points. As this method draws on both the traveling wave method and physics-informed neural networks (PINNs), it has a better physical interpretation. Finally, the KdV equation and the nonlinear Schrödinger equation are solved to test the generalization ability of the PILNs. To the best of the authors' knowledge, this is the first deep learning method that uses ODEs to simulate the numerical solutions of PDEs. [ABSTRACT FROM AUTHOR]

A hydro-dynamic thermal fully developed forced convective heat transfer analysis of magneto-hydrodynamics fluid flow through an annular sector duct is presented in this paper. Two types of thermal boundary conditions i.e., axially uniform heat flux along with peripherally uniform temperature (known as H1-condition) and, axially and peripherally uniform temperature (known as T condition), have been considered to carry out the thermal analysis of fluid. The velocity components along r and θ direction are transformed into algebraic form by using power law discretized scheme, whereas cross-sectional pressure P (r , θ) is estimated with the help of well know technique S I M P L E R. The governing partial differential equations are solved by numerically with the help of M A T L A B code. Furthermore, simulated results have been compared with the existing results of literature to validate the results. From the results, it is noted that hydro-dynamically and thermally impacts relate directly by increasing the Hartman number, (M). It is further reported that the effect of magnetic field becomes insignificant for the higher number of fins, N. The findings of the present analysis will be applicable in various types of thermal systems. [ABSTRACT FROM AUTHOR]

In this article, we employ the Mikhailov–Novikov–Wang integrable equation (MNWIE) appearing by means of the perturbatives symmetry approach to the rating of integrable non‐evolutionary PDEs. The new exact soliton solutions of this equation which were not achieved before have been realized for the first time in the framework of the (G′/G)‐expansion method. In the same vein and parallel, the corresponding numerical solutions of this equation have been established using the variational iteration method (VIM). [ABSTRACT FROM AUTHOR]

Studying fractures in rocks is crucial for understanding the driving mechanism, stress distribution, and strength of the materials. In this present study, we aim to understand the fracturing susceptibility of long linear veins and dykes, which are often replete with fractures within them. These fractures are found to be restricted within these veins and dykes that act as rigid bodies. We consider this rigid body an inclusion embedded in an infinitely homogeneous matrix. A 2D FEM model has been used to conduct the present study, where the model results are obtained for different boundary conditions. To understand the response of the model with respect to various physical and mechanical properties, the stresses are computed and plotted against the applied conditions, which in turn represent the fracturing susceptibility. When the inclusion is placed perpendicular to the applied maximum compressive stress, the intra-inclusion stress becomes tensile, producing restricted tensile fractures. As the inclusion is rotated from this position beyond a critical angle of 28°, the intra-inclusion state of stress becomes compressive. Since the applied minimum compressive stress increases in magnitude, both tensile and shear fracture susceptibility within the inclusion decreases. Consequently, these model results are integrated to comment on the restricted fracturing in veins and dykes (competent layers) bounded by incompetent host rock (matrix). [ABSTRACT FROM AUTHOR]

Abstract We describe a pressure projection scheme for the simulation of incompressible flow in cubic domains with open boundaries based on fast Fourier transforms. The scheme is implemented in flow_solve, a numerical code designed for process studies of rotating, density‐stratified flow. The main algorithmic features of the open‐boundary code are the near‐spectral accuracy of the discrete differentiation and a dynamic two‐dimensional domain decomposition that scales efficiently to large numbers of processors. The simulated flows are not required to be periodic or to satisfy symmetry conditions at the open boundaries owing to the use of mixed series expansions combining cosine and singular Bernoulli polynomial basis functions. These expansions facilitate the imposition of inhomogeneous boundary conditions and allow the code to be used for offline, one‐way nesting within an arbitrarily embedded subdomain of a larger scale simulation. The projection scheme is designed to exploit a simple and powerful numerical engine: inversion of Poisson's equation with homogeneous Neumann boundary conditions using fast cosine transforms. Here, we describe the mathematical transformations used to accommodate the imposition of space‐ and time‐varying boundary conditions. The utility of the approach for process studies and for nesting within submesoscale‐resolving ocean models is demonstrated with simulations of wind‐driven near‐inertial waves in the upper ocean.

The calendering process is pivotal in enhancing various materials’ surface properties and characteristics, making them indispensable for achieving desired product quality and performance. Also, this process holds significant relevance in various industrial applications, such as polymer processing, food production, and the manufacturing of composite materials. So, the aim of this study is to theoretically examine the calendering process applied to third-grade materials. It specifically explores how temperature variations impact material behavior during passage through two counter-rotating heated rolls. Particular consideration is given to the influence of temperature-dependent viscosity via Reynold’s model. The complexities of mass, momentum, and energy balance equations are reduced through the application of the Lubrication approximation theory. Solutions to these equations for variables such as velocity, flow rate, and temperature fields are accomplished by combining perturbation and numerical techniques. In relation to the calendering process, the thickness of the exiting sheet is specifically explored. Furthermore, this study quantifies substantial engineering parameters such as roll-separating force, pressure distribution, and power transferal from the rolls to the fluid. The governing equations belong to three key dimensionless parameters, namely, the Brinkman number, which is a product of Eckert number and Prandtl number, the temperature-dependent consistency index μ\mu , and a parameter η\eta correlating to non-Newtonian behavior. The outcomes of this study are presented both graphically and in tabular form. It has been observed that a rise in the third-grade parameter decreases detachment point and sheet thickness due to increased material rigidity. Furthermore, established results in the literature regarding the calendering of Newtonian fluids are validated.