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Fluctuations are inherent to biological systems, arising from the stochastic nature of molecular interactions, and influence various aspects of system behavior, stability, and robustness. These fluctuations can be categorized as intrinsic, stemming from the system's inherent structure and dynamics, and extrinsic, arising from external factors, such as temperature variations. Understanding the interplay between these fluctuations is crucial for obtaining a comprehensive understanding of biological phenomena. However, studying these effects poses significant computational challenges. In this study, we used an underexplored methodology to analyze the effect of extrinsic fluctuations in stochastic systems using ordinary differential equations instead of solving the master equation with stochastic parameters. By incorporating temperature fluctuations into reaction rates, we explored the impact of extrinsic factors on system dynamics. We constructed a master equation and calculated the equations for the dynamics of the first two moments, offering computational efficiency compared with directly solving the chemical master equation. We applied this approach to analyze a biological oscillator, focusing on the p53 model and its response to temperature-induced extrinsic fluctuations. Our findings underscore the impact of extrinsic fluctuations on the nature of oscillations in biological systems, with alterations in oscillatory behavior depending on the characteristics of extrinsic fluctuations. We observed an increased oscillation amplitude and frequency of the p53 concentration cycle. This study provides valuable insights into the effects of extrinsic fluctuations on biological oscillations and highlights the importance of considering them in more complex systems to prevent unwanted scenarios related to health issues. [ABSTRACT FROM AUTHOR]

The Boyle temperature, TB, for an n-segment polymer in solution is the temperature where the second osmotic virial coefficient, A2, is zero. This characteristic is of interest for its connection to the polymer condensation critical temperature, particularly for n → ∞. TB can be measured experimentally or computed for a given model macromolecule. For the latter, we present and examine two approaches, both based on the Mayer-sampling Monte Carlo (MSMC) method, to calculate Boyle temperatures as a function of model parameters. In one approach, we use MSMC calculations to search for TB, as guided by the evaluation of temperature derivatives of A2. The second approach involves numerical integration of an ordinary differential equation describing how TB varies with a model parameter, starting from a known TB. Unlike general MSMC calculations, these adaptations are appealing because they neither invoke a reference for the calculation nor use special averages needed to avoid bias when computing A2 directly. We demonstrate these methods by computing TB lines for off-lattice linear Lennard-Jones polymers as a function of chain stiffness, considering chains of length n ranging from 2 to 512 monomers. We additionally perform calculations of single-molecule radius of gyration Rg and determine the temperatures Tθ, where linear scaling of R g 2 with n is observed, as if the polymers were long random-walk chains. We find that Tθ and TB seem to differ by 6% in the n → ∞ limit, which is beyond the statistical uncertainties of our computational methodology. However, we cannot rule out systematic error relating to our extrapolation procedure as being the source of this discrepancy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a comparative analysis of spherically and cylindrically shaped nanoparticles immersed separately in a graphene oxide/water nanofluid mixture over a rotating disk influenced by Hall current. The disk's surface is permeable with suction/injection impact. In order to reveal the thermal integrity of the flow, the effect of nanoparticle diameter and the liquid–solid interfacial layer at the molecular level is also introduced. Estimates of thermal conductivity, interfacial layer thickness and the radius of both spherical and cylindrical particles are taken from experimental studies and utilized to investigate the thermal behavior of the flows. The Tiwari–Das model for nanofluid flow is considered that incorporates the thermal radiative impact in the energy equation. The equations obeying boundary layer theory are resolved to ordinary differential equations using a transformation, and further numerically computed with the bvp4c scheme. The velocities and the temperature profiles are graphically demonstrated versus the dimensionless parameters. Quantities of physical interest such as surface heat flux and surface drag coefficient are tabulated numerically. The results show that the surface drag is larger for nanofluids having cylindrical particles than for nanofluids containing spherical particles. Is also found that the heat transfer rate is greater for nanofluids containing cylindrical particles than spherical particles at higher interfacial layer thicknesses. [ABSTRACT FROM AUTHOR]

We intend to analyze the influences of heat dissipation and heat generation on steady nanofluid stagnated flow along an extending surface along with thermal boundary layers. Water-based Cu and Al2O3 nanoparticles are considered. Moreover, the mechanism of injection/suction has been analyzed for such flows. Fundamental governing equations for the flow of an isotropic in-compressible thermally radiative single-phase nanofluid are defined by the set of nonlinear Partial Differential Equations (PDEs) which are transmuted to Ordinary Differential Equation (ODEs) and dealt with numerically by using Runge–Kutta (RK) fourth-order adopting shooting technique that gives approximate simulations. The numerical findings are illustrated as graphical and tabular representations after a careful parametric examination of determined parameters is carried out. The current outcomes specify that the velocity profiles decrease under the influence of magnetic strength while heat distribution positively changes under the effect of magnetic strength, heat source, radiative term and Biot number quantity. The temperature profiles behave negatively with the thermal Grashof number and Prandtl number. Moreover, the comparative simulations of the ongoing study with existing the literature for ensuing the obtained simulations have been worked out. [ABSTRACT FROM AUTHOR]

This study intends to examine the consequences of the externally applied magnetic field and modified Hall effect on nanofluid flow across two symmetrically spinning and extending discs, where continuously the upper disc moves upward and downward. The lower disc is vertically fixed. The discs rotate and move vertically, generating a 3D flow. The mass density, heat transfer and flow motion have been evaluated and modeled in the form of the system of partial differential equations (PDEs) with an additional influence of activation energy, heat source and chemical reaction. The system of PDEs is modified to an ordinary set of differential equations by employing the resemblance substitution method. The obtained system of ODEs is further solved through the numerical approach (bvp4c). The results are compared to the bvp4c package and published work for validity purposes. In the case of downward displacement of the upper disc, magnetic and Hall characteristics have a significant impact on the velocity curve. The energy curve elevates with the upward movement of the disc, while it reduces with the downward fluctuation. Furthermore, the mass transmission rate enhances with the influence of hall current, while diminishing with the impact of chemical reaction rate. [ABSTRACT FROM AUTHOR]

Owing to the practical importance of nanofluids and their adjustable thermal capabilities, this study intends to develop a robust generalized differential quadrature local linearization (GDQLL) algorithm for examining realistically the heat and mass aspects of electrically conducting nanofluids during their non-Darcian laminar motion nearby a convectively heating vertical surface of an active electromagnetic actuator (i.e., Riga plate). By invoking Wakif–Buongiorno model and Oberbeck–Boussinesq approximations along with other generalized transport laws (i.e., Cattaneo–Christov and non-Fick's laws) and Grinberg's concept, a set of gigantic partial differential equations is stated appropriately in the sense of the boundary layer approximations for describing exhaustively the present EMHD mixed convective nonhomogeneous flow under the passive control strategy of nanoparticles within the nanofluidic medium. Operationally, the dimensionless differential forms of the governing boundary equations are derived properly by introducing reasonable mathematical adjustments into the preliminary formulation. In this case, the differential complexity of the leading differential structure is reduced to a nonlinear coupled system of ordinary differential equations, whose discrete numerical solutions are computed perfectly via a well-structured GDQLL algorithm. As foremost outcomes, it is demonstrated that the nanofluid motion and its surface thermal enhancement rate can be reinforced significantly through the thermal strengthening in the convective heating and mixed convective process as well as via the electromagnetic improvement in the driven aspect of Lorentz's forces. [ABSTRACT FROM AUTHOR]

Physics-informed spatial-temporal discrete sequence learning networks have great potential in solving partial differential equations and time series prediction compared to traditional fully connected PINN algorithms, and can serve as the foundation for data-driven sequence prediction modeling and inverse problem analysis. However, such existing models are unable to deal with inverse problem scenarios in which the parameters of the physical process are time-varying and unknown, while usually failing to make predictions in continuous time. In this paper, we propose a continuous time series prediction algorithm constructed by the physics-informed graph neural ordinary differential equation (PGNODE). Proposed parameterized GNODE-GRU and physics-informed loss constraints are used to explicitly characterize and solve unknown time-varying hyperparameters. The GNODE solver integrates this physical parameter to predict the sequence value at any time. This paper uses epidemic prediction tasks as a case study, and experimental results demonstrate that the proposed algorithm can effectively improve the prediction accuracy of the spread of epidemics in the future continuous time. [ABSTRACT FROM AUTHOR]

Stochastic collocation (SC) is a well‐known non‐intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full‐field uncertainty propagation that characterizes the distributions of the high‐dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter‐to‐solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. This work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data‐driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC‐over‐dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full‐field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the heat transfer mechanism while considering the attributes of viscous dissipation, Joule heating, and nonlinear thermal radiations in the three-dimensional steady incompressible flow of Carreau liquid on an extendable rotating disk. By using the similarity transformation, the governed equations were converted into the nonlinear coupled ordinary differential equations. The essential characteristics of various variables like Prandtl number, Lewis number, Carreau liquid parameter, Brownian motion, thermophoresis parameter, radiation parameter, Eckert number and Hartmann number on velocity, thermal, and concentration are discussed through graphs and tables. The presented investigation divulges that the thermal and mass transfer rates enhance when Brownian motion and thermophoresis processes extended and manifest as opposing features on the concentration field. [ABSTRACT FROM AUTHOR]

We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and show that the initial value problem is well posed with data given at the singularity. This is understood by considering conformally rescaled equations. The Einstein equations become a system of singular ordinary differential equations, for which we establish an existence theorem which requires several differentiability and eigenvalue conditions on the coefficient functions together with the Fuchsian conditions. The Boltzmann equation is regularized by a suitable choice of time coordinate, but still has singularities in momentum variables. This is resolved by considering singular weights, and the existence is obtained by exploiting singular moment estimates. [ABSTRACT FROM AUTHOR]

In this note, we study three differential problems with a dynamic, which are be represented by a self referred equation and a boundary condition, which are expressed as an integral constraint. We prove that under certain assumptions, there exists at least one solution of for all of these problems by using Schauder's fixed point theorem. In the end, we propose briefly some open problems. [ABSTRACT FROM AUTHOR]

Sparse identification of nonlinear dynamics is a popular approach to system identification. In this approach system identification is reformulated as a sparse regression problem, and the use of a good sparse regression method is crucial. Sparse Bayesian learning based on collaborative neurodynamic optimization is a recent method that consistently produces high-quality solutions. In this article, we extensively assess how this method performs for ordinary differential equation identification. We find that it works very well compared with sparse regression algorithms currently used for this task in terms of the tradeoff between the approximation accuracy and the complexity of the identified system. We also propose a way to substantially reduce the computational complexity of this algorithm compared with its original implementation, thus making it even more practical. [ABSTRACT FROM AUTHOR]

This work presents a novel approach for the optimization of dynamic systems on finite-dimensional Lie groups. We rephrase dynamic systems as so-called neural ordinary differential equations (neural ODEs), and formulate the optimization problem on Lie groups. A gradient descent optimization algorithm is presented to tackle the optimization numerically. Our algorithm is scalable, and applicable to any finite-dimensional Lie group, including matrix Lie groups. By representing the system at the Lie algebra level, we reduce the computational cost of the gradient computation. In an extensive example, optimal potential energy shaping for control of a rigid body is treated. The optimal control problem is phrased as an optimization of a neural ODE on the Lie group SE (3), and the controller is iteratively optimized. The final controller is validated on a state-regulation task. [ABSTRACT FROM AUTHOR]

By combining millimeter wave (mmWave) with abundant spectral resources and advanced directional beamforming technology, mmWave aerial base stations (mAeBSs) can provide high-speed services to users on the ground while reducing interference to existing terrestrial networks. Due to the mobility of users and the corresponding changes of other environmental factors, the beam misalignment between mAeBSs and users will pose a serious challenge to the stability and quality of communication link. Consequently, we propose schemes based on deep learning for beam prediction tracking in this paper. On the basis of received signals from both the present and previous beam training, we apply long short term memory (LSTM) module to realize the beam prediction. In order to enhance performance of LSTM scheme, cascaded LSTMs are designed in the model. Furthermore, we attain the derivative of implicit state function of the beam changes to formulate an ordinary differential equation (ODE) problem and construct the LSTM_ODE model for beam prediction. Simulations demonstrate that, in comparison to existing other schemes, our proposed approaches attain greater beamforming gain while incurring less overhead during beam training. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a class of conservative systems including asymmetric exclusion processes and zero-range processes as examples, where some particles are initially placed on N positions. A particle jumps from a position to another at a rate depending on the coordinates of these two positions and the number of particles on these two positions. We show that the hydrodynamic limit of our model is driven by a nonlinear function-valued ordinary differential equation which is consistent with a mean field analysis. Furthermore, in the case where the number of particles on all positions are bounded by K < + ∞ , we show that the fluctuation of our model is driven by a generalized Ornstein–Uhlenbeck process. A crucial step in the proofs of our main results is to show that the number of particles on different positions are approximately independent by utilizing a graphical method. [ABSTRACT FROM AUTHOR]

This article investigates the non-linear forced vibrations and primary resonance analysis of stiffened FGM conical panels (OCPs) resting on a viscoelastic foundation utilizing a semi-analytical method. The classical shells theory and von Kármán nonlinear strain–displacement relations are used to model of OCPs. The equations of motion are derived by applying Hamilton's principle. Then, the dimensionless equations of motion are established and converted into dimensionless nonlinear ordinary differential equations by applying Galerkin's method. The solution of the ordinary differential equations is carried out based on the multiple-scale method for analyzing the vibration behavior. In this regard, the necessary relations for the nonlinear primary resonance and internal resonance of stiffened FGM-OCPs are obtained. To validate the suggested methodology, first, the results are verified with various previous research. Second, a numerical method based on the fourth-order Runge-Kutta's approach is used for verifying the nonlinear vibration analysis. Finally, changes in various parameters such as viscoelastic foundation coefficients, stiffeners, temperature, semi-vertex angle and subtended angle are examined by helping the frequency response plots. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the combined influences of pore imperfection, initial geometric imperfection, elasticity of tangential constraints of ends, elastic foundations and elevated temperature on the nonlinear vibration of functionally graded material (FGM) beams. The pores are assumed to distribute into FGM according to even and uneven patterns and effective properties of porous FGM are estimated using a modified rule of mixture. Motion equations of geometrically imperfect beams are established within the framework of Timoshenko beam theory incorporating von Kármán nonlinearity and foundation interaction. Analytical solutions are assumed to satisfy simply supported and clamped conditions of beam ends and Galerkin method is applied to derive a nonlinear time ordinary differential equation. The frequencies of nonlinear free vibration are determined employing fourth-order Runge-Kutta numerical integration scheme. Parametric studies are carried out to assess numerous effects on both linear and nonlinear frequencies. The results reveal that frequency nonlinearity is more significant for beams with tangentially restrained ends, especially at elevated temperatures. It is also found that geometric imperfection increases the linear frequency and lowers ratio of nonlinear-to-linear frequencies. [ABSTRACT FROM AUTHOR]

This paper studies the global existence of bounded smooth solutions for the compressible ideal magnetohydrodynamic (MHD) system. We assume that the solutions have planar symmetry. Then, the MHD system can be reduced to a 7 × 7 first-order quasilinear hyperbolic system. We find a sufficient condition on the initial data to ensure the global existence of bounded smooth solutions. The main difficulty for the global existence is to establish a priori estimates for the derivatives of the solution. To this end, we derive a group of delicate characteristic decompositions for the MHD system. These characteristic decompositions can be seen as a system of "nonlinear ordinary differential equations" for C + and C - characteristic directional derivatives of the unknown functions. Owing to the good structures of the characteristic decompositions, we use "maximum principle" to obtain some uniform a priori estimates for the derivatives of the solution. [ABSTRACT FROM AUTHOR]

In the current study, we solve the nonlinear time fractional‐order enzyme kinematic system and the linear time fractional blood alcohol level using an effective method called the Adomian natural decomposition method (ANDM), which is a combination of the Adomian decomposition method (ADM) and the natural transform method (NTM). On the basis of the Banach fixed point theorem, we offer proofs for the existence and uniqueness theorems as they apply to nonlinear ordinary differential equations. Using the current method, approximate analytical solutions of nonlinear time fractional‐order enzyme kinematic system and exact solutions to the linear time fractional‐order blood alcohol level problem have been obtained. The outcomes indicate that the ANDM is highly efficient and useful. The method outlined in this paper is intended to be applied in subsequent work to handle comparable nonlinear problems connected to fractional calculus. [ABSTRACT FROM AUTHOR]

The global bifurcation diagrams for two different one-parametric perturbations ( + λ x and + λ x 2 ) of a dissipative scalar nonautonomous ordinary differential equation x ′ = f (t , x) are described assuming that 0 is a constant solution, that f is recurrent in t, and that its first derivative with respect to x is a strictly concave function. The use of the skewproduct formalism allows us to identify bifurcations with changes in the number of minimal sets and in the shape of the global attractor. In the case of perturbation + λ x , a so-called generalized pitchfork bifurcation may arise, with the particularity of lack of an analogue in autonomous dynamics. This new bifurcation pattern is extensively investigated in this work. [ABSTRACT FROM AUTHOR]

We present a computer-assisted approach to prove the existence of Hopf bubbles and degenerate Hopf bifurcations in ordinary and delay differential equations. We apply the method to rigorously investigate these nonlocal orbit structures in the FitzHugh–Nagumo equation, the extended Lorenz-84 model and a time-delay SI model. [ABSTRACT FROM AUTHOR]

In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allows us to revisit a recent result of admissibility, obtaining an alternative formulation with a particular simplicity. [ABSTRACT FROM AUTHOR]

We introduce the notion of conditional Lipschitz shadowing, which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain nonautonomous ordinary differential equations have such a property. The first criterion applies to a semilinear differential equation provided that its linear part is hyperbolic and the nonlinearity is small in a neighborhood of the prescribed set. The second criterion requires that the logarithmic norm of the derivative of the right-hand side with respect to the state variable is uniformly negative in a neighborhood of the prescribed set. The results are applicable to important classes of model equations including the logistic equation, whose conditional shadowing has recently been studied. Several examples are constructed showing that the obtained conditions are optimal. [ABSTRACT FROM AUTHOR]

We present a gradient-based calibration algorithm to identify the system matrices of a linear port-Hamiltonian system from given input–output time data. Aiming for a direct structure-preserving approach, we employ techniques from optimal control with ordinary differential equations and define a constrained optimization problem. The input-to-state stability is discussed which is the key step towards the existence of optimal controls. Further, we derive the first-order optimality system taking into account the port-Hamiltonian structure. Indeed, the proposed method preserves the skew symmetry and positive (semi)-definiteness of the system matrices throughout the optimization iterations. Numerical results with perturbed and unperturbed synthetic data, as well as an example from the PHS benchmark collection [17] demonstrate the feasibility of the approach. [ABSTRACT FROM AUTHOR]

The present article presents the technique for finding exact wave solutions of nonlinear fractional-order partial differential equations (NLFPDEs). The singular manifold method (SMM) is applied by starting with the fractional complex transformation (FCT) to reduce the equations to ordinary differential equations (ODEs). Then using the Bäcklund transformation (BT) and the resulting Schwarzian derivatives of the Eigen functions, a new variety of exact solutions is obtained. The method is applied to nonlinear (2 + 1) time-fractional Zoomeron equation, nonlinear (3 + 1) conformable time-fractional Zakharov–Kuznetsov equation, and nonlinear fractional Fokas equation. Some resulting solutions are graphically presented, revealing different solitary wave solutions. [ABSTRACT FROM AUTHOR]

In this article, an analysis is conducted on the flow over a circular cylinder enduring torsional motion immersed in a viscous fluid. The thermal energy distribution is examined for constant and variable surface temperatures. The problem is formulated for an axisymmetric flow in the Cattaneo–Christov double diffusion theory, wherein the energy equation is modified. Note that the rotation of the cylinder is axially dependent, and the phenomenon of wall jet arises due to the axially dependent velocity component, mainly because of the axial pressure gradient. Using the appropriate variables, the dimensionless ordinary differential equations are developed by governing partial differential equations. To solve them, we implemented a built-in function in MATLAB, namely, bvp5c. It is perceived that the peak of the wall jet rises by enhancing the values of Reynolds number Re; however, the azimuthal velocity distribution reduces. The impact of pertinent parameters on thermal and solutal transport in viscous fluid flow is also studied. In general, it is seen that they reduce the heat and mass transfer rates according to their physical influence on the flow. Moreover, the axial and swirl wall-shear stresses are plotted as a function of Re over the range of 0.01 ≤ Re ≤ 104. [ABSTRACT FROM AUTHOR]

This paper presents the impact of thermophoretic particle deposition in the flow of a hybrid nanofluid (Fe3O4-Go/H2O) over a moving thin needle in the presence of a convective boundary condition. The set of non-linear partial differential equations is transformed into ordinary differential equations with the implementation of suitable transformations. Further, the numerical evaluation is carried out by employing the RKF-45 method along with the shooting procedure via the aid of Maple 17 software. It should be noted that the approval of the results shows a good correlation with the existing results. The obtained graphs mainly explain the fundamental characteristics and impacts of different constraints on hybrid nanofluid and mano nanofluid. The main outcomes bring out that enhancement of thermophoretic parameter increases the concentration field and increase in Biot number increases thermal efficiency. Also, the velocity and concentration profiles of hybrid nanofluid reduce with the increment of the magnetic parameter. But the thermal profile of hybrid nanofluid exhibits contrasting behavior. [ABSTRACT FROM AUTHOR]

This thermal research communicates the thermal aspect of hybrid Casson nanofluid in the presence of entropy generation and double stratification. The contributions of Buoyancy force are studied through mixed convection. Darcy Forchheimer condition is also applied in momentum equation along with the effects of thermal radiation, viscous dissipation and convective condition. The flow is generated by stretching a thin needle. Double stratification effect is implemented in boundary conditions of the thermal and concentration equation. Transformations are implemented to form ordinary differential equations from partial differential equations. The shooting numerical method is used to find the solution of local similar expressions. The motion of the fluid slows down for higher Casson fluid parameter and Forchheimer number. The temperature shows the contrast behavior for Brinkman number and thermal relaxation parameter. Solutal relaxation parameter and thermophoresis parameter have opposite behavior for concentration parameter. The entropy generation enhances for Forchheimer number and Casson fluid. [ABSTRACT FROM AUTHOR]

The goal of this article is to examine the heat and mass transportation of a Maxwell fluid flow in the rotating frame with double stratification and porous medium through a linear stretching surface. The heat transfer scrutiny has been presented in the existence of Cattaneo-Christov theory and variable thermal conductivity. The suitable transformation is considered to modify the flow model into the nonlinear system of ordinary differential equations. The numerical computation for the nonlinear system of equations is built-in by the Bvp4c MATLAB approach. It is found that both rotation and stretching have a noteworthy impact on temperature and the velocity profile. Thermal stratification enhances the heat transfer rate as well as higher estimations of rotation parameter condense the heat flux. The novel idea of the present problem is to analyze the heat transfer and Maxwell fluid flow into the rotating frame along Cattaneo-Christov theory induced by the stretching sheet. A relative analysis of current computations with prevailing literature revealed an exceptional agreement. [ABSTRACT FROM AUTHOR]

This analysis evaluates the characteristics of conventional nanofluid heat transfer with those of emerging hybrid nanofluid. Hybrid nanofluid, a new type of conventional fluid, has been used toward the enhancement of heat transfer in the boundary layer flow. This research also prompts that 0.001 solid volume fraction of Gold (Au) is fixed, then consequently, various solid volume fractions of Molybdenum disulfide (Mo) are added into the mixture with water as the base fluid to form Au - Mo/water hybrid nanofluid. Using the necessary similarity variables, the governing non-linear partial differential equations are resolved into a system of coupled ordinary non-linear differential equations. The transformed equations are numerically solved by employing the Runge-Kutta Fehlberg method with shooting technique. The numerical parametric analysis, which has been conducted to explore the effects of different physical parameters involved in the problem, provides comparisons. The present problem is new, original, with many substantial findings in the current industry for practical problems. It is found that dual solutions exist up to a certain value of the decreases as nanoparticle volume fractions for Molybdenum disulfide increase. [ABSTRACT FROM AUTHOR]

The present work is devoted to discuss the transient wave propagation in an isotropic homogenous thermoelastic spherical body with voids due to harmonically varying heat sources in the context of nonlocal thermoelasticity. The constitutive relations and the governing equations are resolved by applying harmonic variations in time and transformed into coupled ordinary differential equations. The outer and the inner surfaces of the sphere are kept stress-free and free from void concentration. A harmonically varying heat source is supplied on the inner surface along the radial direction and the outer surface is assumed to be isothermal. Numerical simulations are implemented to the analytical results with the support of MATLAB software tool. Numerically, generated data are presented graphically for the field variables of interest (temperature, stresses, cubical dilation, displacement and void volume fraction field) and at the end analysis of these results are given. [ABSTRACT FROM AUTHOR]

Constrained mixture models have successfully simulated many cases of growth and remodeling in soft biological tissues. So far, extensions of these models have been proposed to include either intracellular signaling or chemo-mechanical coupling on the organ-scale. However, no version of constrained mixture models currently exists that includes both aspects. Here, we propose such a version that resolves cellular signal processing by a set of logic-gated ordinary differential equations and captures chemo-mechanical interactions between cells by coupling a reaction-diffusion equation with the equations of nonlinear continuum mechanics. To demonstrate the potential of the model, we present 2 case studies within vascular solid mechanics: (i) the influence of angiotensin II on aortic growth and remodeling and (ii) the effect of communication between endothelial and intramural arterial cells via nitric oxide and endothelin-1. [ABSTRACT FROM AUTHOR]

Enhancement of "heat transfer" using "nanofluid" has diverse potential applications in heat exchangers, thermal management of electric devices, cooling of tractors, solar thermal systems, manufacturing of paper, and many others. Hence, the aim of the current investigation is to explore the impacts of "mixed convection" on "nanofluid flow" over a permeable rotating disk, which is stretched radially in a porous medium. Variable wall "temperature" and "convective boundary conditions" are also considered here. This makes the present investigation different from others. The suitable "similarity transformations" are imposed to alter the governing partial differential equations into a set of coupled ordinary differential equations (ODEs). Then, these ODEs are solved numerically by the "4th order Runge‐Kutta method" using the "shooting technique" with the help of the bvp4c package in MATLAB software. The effects of fluid controlling "parameters" on "flow and thermal fields" as well as "skin friction coefficient" and "Nusselt number" are presented graphically and explained physically. Due to enhanced rotation of the disk, the radial and azimuthal velocity of the fluid increase and the temperature of the fluid decreases. Most importantly, it is observed that when the disk rotates faster than the stretching rate, the temperature of the nanofluid decreases rapidly, which has wider applications for cooling purposes. It is also noted that when the suction parameter increases its value from −1 to 1, for Ag–water nanofluid, the "skin friction coefficient" decreases by 73.56%, and the Nusselt number also decreases by 24.11%, and for Fe3O4–water nanofluids, the "skin friction coefficient" decreases by 71.25% and the Nusselt number decreases by 24.47%. [ABSTRACT FROM AUTHOR]

This study investigates the heat and mass transfer dynamics in exothermic, chemically reactive fluids over variable‐thickness surfaces using advanced numerical methods and artificial neural networks (ANN). The importance of understanding these processes lies in their significant industrial applications, such as in chemical reactors and heat exchangers. We transformed nonlinear partial differential equations into ordinary differential equations and used the bvp4c numerical method to generate a comprehensive data set. The ANN model, trained with the Levenberg–Marquardt algorithm, was evaluated for its accuracy in simulating complex fluid dynamics and thermosolutal transport phenomena. Our results revealed that increasing the second‐grade fluid parameter α1 enhanced skin friction by 20.38%, heat transfer rate by 1.16%, and mass transfer rate by 4.06%. The ANN model demonstrated high predictive precision with a validation mean squared error of 1.145×10−9. These findings highlight the effectiveness of the ANN methodology in providing precise simulations of fluid dynamics, which is crucial for optimizing industrial processes. [ABSTRACT FROM AUTHOR]

This study investigates the various uses of density of motile microorganisms in the context of the flow of a binary base fluid with double diffusion past a vertical surface. The research aims to comprehend the interactions between motile microorganisms and the fluid dynamics, as well as the heat and mass transport mechanisms in this system. The analysis involves mathematically constructing the governing equations, transforming them into dimensionless nonlinear ordinary differential equations using similarity transformations, and numerically solving them using the MATLAB bvp4c solver. An analysis of the influence of several parameters on the profiles of velocity, temperature, concentration, nanoparticle concentration, and density of motile microorganisms is conducted using graphical representation. The findings demonstrate that boosting the thermophoresis parameter intensifies the temperature profile. In addition, an increase in the nanofluid Schmidt number results in a larger concentration of nanoparticles, whereas a higher bioconvection Lewis number reduces the density of the motile microorganism profile. These findings may find use in biomedical engineering as well as industrial processes that include enhancing the efficiency of mass transfer and bioconvection. Numeric simulation prophesies 99.9% for both shear stress and heat transfer rate intensification for Prandtl values are noticed. [ABSTRACT FROM AUTHOR]

This article uses a finite-element approximation approach for solving a three-dimensional flow problem of a nanofluid influenced by heat transfer due to nanoparticles over a non-linearly stretching sheet within an unbounded domain. Utilising similarity transformations, a well-posed coupled system of nonlinear ordinary differential equations is derived from the governing partial differential equations describing the flow and heat transfer processes. The resulting system is then solved by using quadratic Lagrange polynomials as basic functions over a mesh of different finite elements through the Galerkin finite element (GFE) technique. This implementation is based on a regular grid utilising Lagrange polynomials for solving the converted equations. The effects of various parameters of interest are efficiently discussed with the help of graphs and numeric tables. Both numerical and exact solutions are compared favourably, demonstrating a high level of accuracy. It is noteworthy that the GFE method emerges as a much more stable numerical technique than the other existing analytic and semi-analytical methods. Furthermore, the adopted finite-element method reduces the dimensionality of Sobolev's space's finite-dimensional subspace and also improves the solution's convergence rate. Moreover, the velocity is negative, and its magnitude increases as the stretching rates ratio increases due to the downward flow in the vertical direction. The temperature and heat transmission from the sheet are barely impacted by Brownian motion due to the dominance of other forces and length scales involved in the heat transfer process. [ABSTRACT FROM AUTHOR]

The heat transfer characterisation of the three-phase local thermal non-equilibrium analysis due to the nanofluid (solid particle phase and the base fluid phase) and the absorbing phase (due to the porous surface) is performed for a third-grade nanofluid impinging over a receding surface. The mathematical formulation of the physical model includes the Rivlin–Ericksen tensor for fluids of grade three with appropriate restriction to viscous flows and also incorporates the Buongiorno nanofluid model for studying the impact of thermophoresis and Brownian motion. The resultant governing time-dependent partial differential equations has been converted to ordinary differential equations by applying similarity transformation. The computational results are obtained using the finite-difference approach in the Matlab software. The non-Newtonian and the time-dependent flow phenomena demands an additional boundary condition to ensure the uniqueness of the solution. With a general third-grade assumption with the wall shrinking and unsteadiness, the resultant equations govern the occurrence of dual solution in the obtained numerical results. The stability investigation reports the existence of multiple (dual) solutions due to the unsteadiness imparted in the flow and the flow behaviour of both the stable and unstable solutions are revealed. The boundary layer characteristics are explored for various vital physical parameters, such as material parameter, porous permeability parameter, Brownian motion parameter, thermophoresis parameter, inter-phase heat transfer coefficient, modified thermal capacity ratio, modified thermal diffusivity ratio and buoyancy ratio parameter. The temperature distribution across different phases is analysed for the stable solutions. [ABSTRACT FROM AUTHOR]

In the evaluation of cervical spine disorders, precise positioning of anatomo-physiological hallmarks is fundamental for calculating diverse measurement metrics. Despite the fact that deep learning has achieved impressive results in the field of keypoint localization, there are still many limitations when facing medical image. First, these methods often encounter limitations when faced with the inherent variability in cervical spine datasets, arising from imaging factors. Second, predicting keypoints for only 4% of the entire X-ray image surface area poses a significant challenge. To tackle these issues, we propose a deep neural network architecture, NF-DEKR, specifically tailored for predicting keypoints in cervical spine physiological anatomy. Leveraging neural memory ordinary differential equation with its distinctive memory learning separation and convergence to a singular global attractor characteristic, our design effectively mitigates inherent data variability. Simultaneously, we introduce a Multi-Resolution Focus module to preprocess feature maps before entering the disentangled regression branch and the heatmap branch. Employing a differentiated strategy for feature maps of varying scales, this approach yields more accurate predictions of densely localized keypoints. We construct a medical dataset, SCUSpineXray, comprising X-ray images annotated by orthopedic specialists and conduct similar experiments on the publicly available UWSpineCT dataset. Experimental results demonstrate that compared to the baseline DEKR network, our proposed method enhances average precision by 2% to 3%, accompanied by a marginal increase in model parameters and the floating-point operations (FLOPs). The code (https://github.com/Zhxyi/NF-DEKR) is available. [ABSTRACT FROM AUTHOR]

In current work, the unsteady stagnation point's flow on a special third-grade fuzzy hybrid (Al2O3 + Cu/SA) nanofluid (HNF) through a permeable convective shrinking/stretching sheet has been scrutinized. In addition, the adverse consequences of heat source, viscous dissipation, nonlinear thermal radiation, and fuzzy nanoparticle volume fraction are likewise taken into consideration. Non-linear coupled partial differential equations (PDEs) get transformed into ordinary differential equations (ODEs) using an effective similarity transformation. After that, the ODEs are numerically solved using the bvp4c algorithm. Regarding validation, the present results align with earlier published research. The effects of heat distribution, flow rate, Nusselt number, and skin friction coefficient on hybrid nanofluid dynamics are explored using graphical and tabular forms. The nanoparticle volume fraction is considered a triangular fuzzy number (TFN) [0, 5%, 10%]. With the use of TFNs, ODEs are transformed into fuzzy differential equations (FDEs). The TFNs are controlled using a widely used ζ - cut technique and ζ - cut ∈ [0, 1], which requires minimal computational effort to examine their dynamical performance. Also, the comparison of Al2O3/SA, Cu/SA and Al2O3 + Cu/SA through the fuzzy membership functions (MFs). The fuzzy MFs show that the hybrid nanofluid (Al2O3 + Cu/SA) in terms of rate of heat transfer is better than both Cu/SA and Al2O3/SA nanofluids. [ABSTRACT FROM AUTHOR]

In this work, computational intelligence methodologies are used to investigate the trihybrid nanofluid, a new theoretical model with remarkable thermal transmission properties to enhance liquid thermal performance. The nanostructure Cu, Al2O3, and TiO2 were immersed in the base liquid (C2H6O2) to produce (Cu + Al2O3 + TiO2/C2H6O2) trihybrid nanofluid. In a Darcy-Forchheimer porous medium over a stretching Riga sheet, this study examines the electromagnetic ternary hybrid nanofluid flow under various slip situations. The study takes into account the complex interactions between a number of variables, including as viscous dissipation, radiation, heat sources, and chemical reactions. Similarity transformations are used to convert complex partial differential equations for flow, energy, and concentration into nonlinear ordinary differential equations. The highly nonlinear equations of the problem are solved numerically with the use of techniques from the bvp4c approach. The results of the bvp4c method produce the reference dataset required for the Levenberg-Marquardt backpropagation of neural networks (LMBNN). The neural network performance is validated using regression analysis, mean square errors, and error histogram data. The model problem's consistency and precision are evaluated using the absolute error, which is given for each model instance at around 10-06 - 10-08, 10-05 - 10-10 and 10-06 05-10-09. In order to reduce mean square error, the nonlinear fluid dynamics system's numerical solutions have been taken into consideration. Using the comparative configurations of MSE, error histograms, state transitions, correlation, and regression, the reliability and competence of the stochastic technique are verified. [ABSTRACT FROM AUTHOR]

The space–time perturbed fractional Gerdjikov–Ivanov equation is the main topic of this work, together with quintic nonlinearity and self-steepening, as it involves several intricate physical phenomena including nonlinearity, self-steepening and fractional calculus, where the fractional derivative is described by employing a conformable derivative. In addition, the governing equation is transformed into an integer-order ordinary differential equation by using an appropriate fractional complex transformation. Under certain restrictions, a direct algebraic method is employed to investigate the structures of chirp soliton solutions enfolding hyperbolic functional terms. The dynamic behaviour and bifurcation of equilibria of the system are thoroughly examined; chirp soliton solutions under specified constraints are investigated and the evolving profiles of the obtained solutions are visualized. Moreover, this research offers valuable perspectives on the behaviour of chirp solitons under specific conditions, which have practical applications in nonlinear physical systems and optical communication systems. The significant contribution of this work is the investigation and obtaining of novel chirp soliton solutions with hyperbolicfunctional terms under particular limitations using a novel approach. It further extends the prior approaches by treating difficult fractional differential equations from a fresh angle, offering new tools, and closely examining soliton solutions. [ABSTRACT FROM AUTHOR]

In this paper, a compartmental model on the co-infection of pneumonia and HIV/AIDS with optimal control strategies was formulated using the system of ordinary differential equations. Using qualitative methods, we have analysed the mono-infection and HIV/AIDS and pneumonia co-infection models. We have computed effective reproduction numbers by applying the next-generation matrix method, applying Castillo Chavez criteria the models disease-free equilibrium points global stabilities were shown, while we have used the Centre manifold criteria to determine that the pneumonia infection and pneumonia and HIV/AIDS co-infection exhibit the phenomenon of backward bifurcation whenever the corresponding effective reproduction number is less than unity. We carried out the numerical simulations to investigate the behaviour of the co-infection model solutions. Furthermore,wehave investigated various optimal control strategies to predict the best control strategy to minimize and possibly to eradicate the HIV/AIDS and pneumonia co-infection from the community. [ABSTRACT FROM AUTHOR]

The Levin method is a well-known technique for evaluating oscillatory integrals, which operates by solving a certain ordinary differential equation in order to construct an antiderivative of the integrand. It was long believed that this approach suffers from "low-frequency breakdown," meaning that the accuracy of the calculated value of the integral deteriorates when the integrand is only slowly oscillating. Recently presented experimental evidence, however, suggests that if a Chebyshev spectral method is used to discretize the differential equation and the resulting linear system is solved via a truncated singular value decomposition, then no low-frequency breakdown occurs. Here, we provide a proof that this is the case, and our proof applies not only when the integrand is slowly oscillating, but even in the case of stationary points. Our result puts adaptive schemes based on the Levin method on a firm theoretical foundation and accounts for their behavior in the presence of stationary points. We go on to point out that by combining an adaptive Levin scheme with phase function methods for ordinary differential equations, a large class of oscillatory integrals involving special functions, including products of such functions and the compositions of such functions with slowly-varying functions, can be easily evaluated without the need for symbolic computations. Finally, we present the results of numerical experiments which illustrate the consequences of our analysis and demonstrate the properties of the adaptive Levin method. [ABSTRACT FROM AUTHOR]

We present a novel approach to generate developable strips along a space curve. The key idea of the new method is to use the rotation angle between the Frenet frame of the input space curve, and its Darboux frame of the curve on the resulting developable strip as a free design parameter, thereby revolving the strip around the tangential axis of the input space curve. This angle is not restricted to be constant but it can be any differentiable function defined on the curve, thereby creating a large design space of developable strips that share a common directrix curve. The range of possibilities for choosing the rotation angle is diverse, encompassing constant angles, linearly varying angles, sinusoidal patterns, and even solutions derived from initial value problems involving ordinary differential equations. This enables the potential of the proposed method to be used for a wide range of practical applications, spanning fields such as architectural design, industrial design, and papercraft modeling. In our computational and physical examples, we demonstrate the flexibility of the method by constructing, among others, toroidal and helical windmill blades for papercraft models, curved foldings, triply orthogonal structures, and developable strips featuring a log-aesthetic directrix curve. [ABSTRACT FROM AUTHOR]

We propose a method to reproduce dynamic appearance textures with space-stationary but time-varying visual statistics. While most previous work decomposes dynamic textures into static appearance and motion, we focus on dynamic appearance that results not from motion but variations of fundamental properties, such as rusting, decaying, melting, and weathering. To this end, we adopt the neural ordinary differential equation (ODE) to learn the underlying dynamics of appearance from a target exemplar. We simulate the ODE in two phases. At the "warm-up" phase, the ODE diffuses a random noise to an initial state. We then constrain the further evolution of this ODE to replicate the evolution of visual feature statistics in the exemplar during the generation phase. The particular innovation of this work is the neural ODE achieving both denoising and evolution for dynamics synthesis, with a proposed temporal training scheme. We study both relightable (BRDF) and non-relightable (RGB) appearance models. For both we introduce new pilot datasets, allowing, for the first time, to study such phenomena: For RGB we provide 22 dynamic textures acquired from free online sources; For BRDFs, we further acquire a dataset of 21 flash-lit videos of time-varying materials, enabled by a simple-to-construct setup. Our experiments show that our method consistently yields realistic and coherent results, whereas prior works falter under pronounced temporal appearance variations. A user study confirms our approach is preferred to previous work for such exemplars. [ABSTRACT FROM AUTHOR]

We investigate a variable-coefficient wave equation with interior local frictional damping and memory-type dynamic boundary conditions. The innovation of the paper lies in the presence of dynamic boundary conditions, thus we need some special techniques to deal with the high-order terms on the boundary. By the Riemannian geometry method and the multiplier technique, we establish the stable results, and the energy decay result of system is described by employing the solution of a stable first-order ordinary differential equation. The stability depends on the frictional damping function and kernel function, thereby improving and generalizing the results of prior references. [ABSTRACT FROM AUTHOR]