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This research paper attempts to describe the transmission dynamic of zoonotic visceral leishmaniasis with the aid of a mathematical model by considering the asymptomatic stages in humans and animals. The disease is endemic in several countries. Data used in the research are obtained from the literature while some are assumed based on the disease dynamic. The consideration of both asymptomatic and the symptomatic infected individuals is incorporated in both humans and animals (reservoir), as well as lines of treatment for the human population. It is found that the model has two fixed points; the VL-free fixed point and the VL-endemic fixed point. Stability analysis of the fixed points shows that the VL-free fixed point is globally asymptotically stable whenever the basic reproduction number is less than one and the VL-endemic fixed point is globally asymptotically stable whenever the basic reproduction number is greater than one. Sensitivity analysis is conducted for the parameters in the basic reproduction number, and the profile of each state variable is also depicted using the data obtained from the literature and those assumed. The transmission probability from infected sandflies to animals, transmission probability from infected animals to sandflies, per capita biting rate of sandflies of animals, and rate of transfer from symptomatic infected animals to the recovered class are among the most sensitive parameters that have the greatest influence on the basic reproduction number. Moreover, the value of the basic reproduction number is obtained to be 0.98951, which may require further study, as the margin between potential disease control and outbreak is thin. [ABSTRACT FROM AUTHOR]

In this study, we applied the Riccati-Bernoulli sub-ODE method and Bäcklund transformation to analyze the time-space fractional Oskolkov equation for kink solutions by matching the coefficients and optimal series parameters. The time-space fractional Oskolkov equation is used to analyze the behavior of solitons for different applications such as fluid dynamics and viscoelastic flow. The kink solutions derived have important consequences for stability analysis and interaction dynamic in these systems, and these are useful in controlling the physical behaviour of systems described by this equation. Such effects are illustrated by 2D and 3D plots, showing that the proposed model can handle both fractional and integer-order solitons with different but equally efficient outcomes. This research contributes to a valuable analytical method that can determine and manage processes in diversified systems based on fractional differential equations. This work provides a basis for subsequent analysis in other branches of science and technology in which the fractional Oskolkov model is used. [ABSTRACT FROM AUTHOR]

In this study, we applied the Riccati-Bernoulli sub-ODE method and Bäcklund transformation to analyze the time-space fractional Oskolkov equation for kink solutions by matching the coefficients and optimal series parameters. The time-space fractional Oskolkov equation is used to analyze the behavior of solitons for different applications such as fluid dynamics and viscoelastic flow. The kink solutions derived have important consequences for stability analysis and interaction dynamic in these systems, and these are useful in controlling the physical behaviour of systems described by this equation. Such effects are illustrated by 2D and 3D plots, showing that the proposed model can handle both fractional and integer-order solitons with different but equally efficient outcomes. This research contributes to a valuable analytical method that can determine and manage processes in diversified systems based on fractional differential equations. This work provides a basis for subsequent analysis in other branches of science and technology in which the fractional Oskolkov model is used.

The goal of this paper is to use general perturbation theory that is, singular perturbation theory and regular perturbation theory to solve both linear and nonlinear differential equations. We initially demonstrate the regular perturbation method's application to the classification of nonlinear differential equations in order to demonstrate its efficacy. Next, in the event that normal perturbation approaches prove fruitless, we employ and demonstrate Lindstedt-Poincaré and singular perturbation methods to approximate periodic solutions to nonlinear ordinary differential equations. Upon computing the approximate solutions by Lindstedt-Poincaré, or by singular perturbation methods, we compare it with the exact solution found using MATHEMATICA software, we determine the absolute error and demonstrate the accuracy of our approach. [ABSTRACT FROM AUTHOR]

In this paper, the mathematical model of the biofiltration of a mixture of n-propanol and toluene is developed based on the gasbiofilm phases. The homotopy perturbation technique is applied to get the approximate analytical expression for the concentration of toluene and n-propanol in non-steady-state conditions for both gasbiofilm interfaces. Our analytical results were validated by direct comparison with numerical simulations generated using the "bvp4c" function in the MATLAB platform. For various parameter values, the comparison was found to be in good agreement. The saturated and unsaturated kinetics also have been investigated analytically. [ABSTRACT FROM AUTHOR]

This research paper attempts to describe the transmission dynamic of zoonotic visceral leishmaniasis with the aid of a mathematical model by considering the asymptomatic stages in humans and animals. The disease is endemic in several countries. Data used in the research are obtained from the literature while some are assumed based on the disease dynamic. The consideration of both asymptomatic and the symptomatic infected individuals is incorporated in both humans and animals (reservoir), as well as lines of treatment for the human population. It is found that the model has two fixed points; the VL-free fixed point and the VL-endemic fixed point. Stability analysis of the fixed points shows that the VL-free fixed point is globally asymptotically stable whenever the basic reproduction number is less than one and the VL-endemic fixed point is globally asymptotically stable whenever the basic reproduction number is greater than one. Sensitivity analysis is conducted for the parameters in the basic reproduction number, and the profile of each state variable is also depicted using the data obtained from the literature and those assumed. The transmission probability from infected sandflies to animals, transmission probability from infected animals to sandflies, per capita biting rate of sandflies of animals, and rate of transfer from symptomatic infected animals to the recovered class are among the most sensitive parameters that have the greatest influence on the basic reproduction number. Moreover, the value of the basic reproduction number is obtained to be 0.98951, which may require further study, as the margin between potential disease control and outbreak is thin.

The analysis of non-linear differential equations is discussed in this study using a new, straight-forward method that is also incredibly precise. The new method is illustrated with certain examples, which makes it easier to understand. The accuracy of the approximate analytical solutions obtained is checked by comparison with numerical solutions, exact solutions and other approximate analytical methods with significant agreement. The results demonstrate that this method is most effective, simple and convenient. The results obtained are explained graphically and analytically. It is simple to adapt this approach to address more non-linear boundary value issues in the physical, chemical, and biological sciences. [ABSTRACT FROM AUTHOR]

Despite the fact that our physical observations can often be described by derived physical laws, such as the wave equation, in many cases, we observe data that do not match the laws or have not been described physically yet. Therefore recently, a branch of machine learning has been devoted to the discovery of physical laws from data. We test this approach for discovering the wave equation from the observed spatial-temporal wavefields. The algorithm first pre-trains a neural network (NN) in a supervised fashion to establish the mapping between the spatial-temporal locations (x, y, z, t) and the observation displacement wavefield function u (x, y, z, t). The trained NN serves to generate metadata and provide the time and spatial derivatives of the wavefield (e.g. utt and uxx) by automatic differentiation. Then, a preliminary library of potential terms for the wave equation is optimized from an overcomplete library by using a genetic algorithm. We, then, use a physics-informed information criterion to evaluate the precision and parsimony of potential equations in the preliminary library and determine the best structure of the wave equation. Finally, we train the 'physics-informed' neural network to identify the corresponding coefficients of each functional term. Examples in discovering the 2-D acoustic wave equation validate the feasibility and effectiveness of our implementation. We also verify the robustness of this method by testing it on noisy and sparsely acquired wavefield data. [ABSTRACT FROM AUTHOR]

High-precision prediction of polar motion (PM) plays an important role in fields such as astronomy, geodesy, navigation and aerospace. Incorporating information on the effective angular momentum (EAM) of the geophysical fluid is an effective way to improve the precision of PM prediction. Based on the EOP_20_C04 data set and the EAM function, this study applies complex segmented least-squares (CSLS) + the long short term memory (LSTM) neural network and CSLS + autoregression (AR) models to predict PM. For the 6-d PM prediction, the mean absolute errors (MAEs) achieved by CSLS+AR are 1.03 and 0.8 mas in the X- and Y -directions, respectively, corresponding to reductions of 45.80 and 31.97 per cent when compared to predictions reported routinely in Bulletin A of the International Earth Rotation and Reference Systems Service (IERS). For the 365-d PM prediction, the MAEs gained by CSLS+LSTM model are 14.58 and 10.59 mas in the X- and Y -directions, respectively, corresponding to reductions of 28.17 and 51.09 per cent compared to predictions of the Bulletin A, and the prediction accuracy attained by CSLS+LSTM is higher than other prediction schemes. The experimental results show that, when considering EAM information, the CSLS+AR model can achieve better prediction accuracy for short-term PM prediction, however, the CSLS+LSTM model is more effective for medium- and long-term PM prediction owning to the excellent nonlinear fitting capability of the LSTM deep learning algorithm. [ABSTRACT FROM AUTHOR]

Various linear and non-linear first-order differential equations with different arguments are considered. Exact solutions to these equations are provided. Systems of two coupled linear first-order differential equations are also solved explicitly and exactly. [ABSTRACT FROM AUTHOR]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this work, we find the results for the folded part projection of the butterfly catastrophe model onto the control space, using methods from catastrophe theory to obtain stability and the catastrophic behavior of finite periodic solutions for some non-linear differential equations. Finally, we have shown that a saddle-node bifurcation, which can be classified as a butterfly mutation, accompanies butterfly surface folding.

Tong has proposed an adjoint-state traveltime tomography method to determine velocity heterogeneity and azimuthal anisotropy. This method, however, ignores the Earth's curvature when deriving the eikonal equation for azimuthally anisotropic media. Thus, further coordinate transformation or approximation is required to ensure the accuracy of traveltime prediction in large-scale tomography. To address this problem, we derive the eikonal equation for azimuthally anisotropic media in spherical coordinates, which naturally considers the Earth's curvature. Another key ingredient is the forward modelling algorithm, whose accuracy and efficiency dominate the numerical error and computational cost of the inversion. In this study, we apply a modified fast sweeping method to solve the eikonal equation in spherical coordinates. Two approaches, including the third-order weighted essentially non-oscillatory approximation and multiplicative factorization technique, are applied to improve the accuracy. According to the numerical experiments, this new eikonal solver achieves a second-order accuracy and is about two orders of magnitude more accurate than the commonly used first-order fast sweeping method with similar runtime. Taking advantage of the two improvements, we develop a novel eikonal equation-based adjoint-state traveltime tomography method for azimuthally anisotropic media in spherical coordinates. This method is applicable for large-scale tomography, and its performance is verified by a synthetic checkerboard test and a practical seismic tomographic inversion in central California near Parkfield. [ABSTRACT FROM AUTHOR]

The viscoelasticity of subsurface media is succinctly represented in the generalized wave equation by a fractional time derivative. This generalized viscoelastic wave equation is characterized by the viscoelastic parameter and the viscoelastic velocity, but these parameters are not well formulated and therefore unfavourable for seismic implementation. Here, we prove that the generalized wave equation is causal and stable by deriving the rate-of-relaxation function. Causality and stability are two necessary conditions for the applicability of the wave equation in seismic simulations. On this basis, we determine the physical parameters for the application of the generalized wave equation. First, we formulate the relationship between the viscoelastic parameter and the constant Q model. The proposed frequency-independent relation agrees with the theoretical solution and fits the field data. Then, we formulate the viscoelastic velocity in terms of the reference velocity and the viscoelastic parameter. These two formulations adequately represent the viscoelastic effect in seismic wave propagation and lead to an improvement in the accuracy of the numerical simulation of the generalized viscoelastic wave equation. [ABSTRACT FROM AUTHOR]

The study of Von Kármán swirling flow is a subject of active interest due to its applications in a wide range of fields, including biofuel manufacturing, rotating heat exchangers, rotating disc reactors, liquid metal pumping engines, food processing, electric power generating systems, designs of multi-pore distributors, and many others. This paper focusses on investigating Von Kármán swirling flows of viscous incompressible fluid due to a rotating disk electrode. The model is based on a system of four coupled second-order non-linear differential equations. The purpose of the present communication is to derive analytical expressions of velocity components by solving the non-linear equations using the homotopy analysis method. Combined effects of the slip λ and porosity γ parameters are studied in detail. If either parameter is increased, all velocity components are reduced, as both have the same effect on the mean velocity profiles. The porosity parameter γ increases the moment coefficient at the disk surface, which monotonically decreases with the slip parameter λ. The analytical results are also compared with numerical solutions, which are in satisfactory agreement. Furthermore, the effects of porosity and slip parameters on velocity profiles are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with the asymptotic and oscillatory behaviour of third-order non-linear differential equations with mixed non-linear neutral terms and a canonical operator. The results are obtained via utilising integral conditions as well as comparison theorems with the oscillatory properties of first-order advanced and/or delay differential equations. The proposed theorems improve, extend, and simplify existing ones in the literature. The results are illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper develops the combined effects of free convection magnetohydrodynamic (MHD) flow past a vertical plate embedded in a porous medium. The dimensionless coupled non-linear equations are solved to get the approximate analytical expression for the concentration by using the homotopy perturbation method. For all possible values of parameters, skin lubrication, Nusselt number and Sherwood number are derived.

In this study, a stochastic differential equation capable of describing (using the motion function) the automatic manufacturing process of a lithium battery with a sleeve shell is introduced. The boundary-condition modeling method for this type of motion is an ordinary differential equation. The nonlinear equation is found using a dynamic method. The equations of the motions for the assembly process are derived by reducing the order of terms and separating the variables. Both the derivatives and integrals of the motion functions are derived and applied to describe the assembly process for a lithium battery. By using a characteristic constitutive assembly model, a new method to calculate the nonlinear terms is proposed. The main advantage of this method is that it can simplify the problem, which is done by finding the algebraic error in the region space of the motion function. The reliability and the applicability of the method were confirmed using a real-life example. Finally, by solving and improving the Euler model, the fourth-order Kutta method and Taylor series are applied to verify the correctness of the algorithm, and the convergence order of the function and the optimization of the assembly model are discussed. Through a one-dimensional search of the convergence domain, a method is found to make the analytical solution approximate the exact solution and reduce the calculation cost. This method in dynamics and mathematical engineering.

This study presents comparison approximate analytical solutions of immobilized enzyme in porous planar, cylindrical, and spherical particle using two approach of Homotopy analysis method. The diffusion reaction model for immobilized enzyme systems in porous, obeying reversible Michaelis - Menten kinetics with product inhibition effects, is the mathematical model that we took into consideration in this research. NHAM and q-HAM were used to establish analytical equations for the dimensionless concentration profile and effectiveness factor for planar, cylindrical, and spherical particles in this model. At the same order of approximation, q-HAM can offer greater accuracy than HAM. Additionally. q-HAM has two auxiliary parameters, and this method makes it simple to control and alter the convergence region. It can be seen through a comparison of solutions obtained by q-HAM. NHAM, and numerical solutions (MATLAB) that q-HAM is a reliable and accurate method for resolving nonlinear differential equations. Our analytical findings, which are given graphically with tabular data and great consistency with prior work, demonstrate the realization of our investigation. [ABSTRACT FROM AUTHOR]

Copyright of Kirkuk University Journal for Scientific Studies is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the present study, we consider Casson fluid flow between two porous plates with permeability criteria in the presence of heat transfer and magnetic effect. A proper set of similarity transformations simplify the Navier-Stokes equations to non-linear ODEs with boundary conditions. The homotopy perturbation method is an efficient and stable method which is used to get solutions. Further, the results obtained are compared with the solution computed through an effective and efficient finite difference approach. The purpose of this analysis is to study the four different cases arise viz: suction, injection, mixed suction and mixed injection in this problem, along with magnetic effect and heat transfer characteristics. The results obtained are used to analyse the fluid velocity and temperature profiles, and the skin friction at the upper and lower plate by using both methods are displayed in the form of figures and tables. The semi-analytical solution obtained is in good agreement with the numerical solution. [ABSTRACT FROM AUTHOR]

A previously developed SIR model with three mutually exclusive compartments is solved using new' approach to Homotopy perturbation method. The mathematical model is discussed for a situation without demography and a situation with demography separately. The numerical simulation of the problem is also presented. Comparison between the numerical simulation and the analytical solution gives a satisfactory agreement. The effect of various parameters on the susceptible, infected and recovered population is also discussed. [ABSTRACT FROM AUTHOR]

SUMMARY: A suggested model to explain the episodic nature of slow earthquakes involves shear zones exhibiting rate- and temperature-dependent frictional behaviour hosting fluid-release chemical reactions. In this work we extend the considerations of that approach, coupling the effects of the mechanics at different faulting regimes to the chemically induced fluid pressurization inside the fault. By introducing a pressure and temperature dependence of the mechanical response in an elasto-viscoplastic model we are able to correlate the inclination angles of those specific faults with their dynamical response and enrich their faulting regimes with kinematic characterization. We retrieve that steeply dipping (normal) faults exhibit a simple response of either being locked or slip at fast seismic velocities; shallow dipping (reverse) faults on the other hand exhibit a much richer behaviour where episodic stick-slip instabilities can be encountered. When present, their magnitude depends on the (reverse) fault's angle with faults dipping at around 45° exhibiting a maximum, whereas sub-horizontal thrusts exhibit episodic stick-slip events as low velocities and magnitude. These findings position slow earthquakes and episodic tremor and slip sequences as a natural response of shallow dipping (thrust) faults, in a regime that according to rate-and-state friction considerations is intrinsically stable. [ABSTRACT FROM AUTHOR]

The viruses has spread globally and have been impacted lives of people socially and economically, which causes immense suffering throughout the world. Thousands of people died and millions of illnesses were brought, by the outbreak worldwide. In order to control the coronavirus pandemic, mathematical modeling proved to be an invaluable tool for analyzing and determining the potential and severity of the illness. This work proposed and assessed a deterministic six-compartment model with a novel stochastic neural network. The significance of the proposed model was demonstrated by numerical simulation in which the results are agreed with sensitivity analysis. Furthermore, the efficacy of stochastic neural network has been proven with the help of numerical simulations. Some investigations have been conducted through graphs and tables that how the vaccination process is helpful to minimize stress in society. The numerical simulations also focused on preventing the community-wide spread of the disease. The lowest residual errors have been achieved by our proposed stochastic neural network and compared with numerical solvers to assess the accuracy and robustness of the proposed approach., Competing Interests: Declaration of competing interest The authors declare that they have no competing or financial interests., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

A transverse harmonic seismic wave, which propagates through the upper fractured layer of the Earth towards the Earth's surface, is considered. It is shown that the attenuation of a seismic wave in the Earth's upper crust is due to internal friction, i.e., friction between the sides of micro-fractures. Such a damping mechanism does not work in the deeper layers of the Earth where high lithostatic pressure prevents the movement along fractures. The governing equation for a brittle fractured medium is nonlinear. In the study of wave propagation, an approximate method of harmonic linearization is used. It is shown that internal friction in the upper crust leads to the transformation of a transverse harmonic wave into a shock wave.

The purpose of this study is to describe the outbreak of a novel coronavirus (COVID-19) and review the computational model, which was based on non-linear ordinary differential equations. The main idea developed was to describe the formulation, integration, and application of mathematical models by using data from China, Austria, Poland, and France. The Logistic Model and its solution Sigmoid Curve, and the SIR Model were used for the determination. After taking the measured data, the total number of cases was predicted, and it was found that the results were obtained in good approximation to the measured results. To predict the number of deaths over time, generalized models were developed in response to COVID-19.

This paper develops the combined effects of free convection magnetohydrodynamic (MHD) flow past a vertical plate embedded in a porous medium. The dimensionless coupled non-linear equations are solved to get the approximate analytical expression for the concentration by using the homotopy perturbation method. For all possible values of parameters, skin lubrication, Nusselt number and Sherwood number are derived. [ABSTRACT FROM AUTHOR]

Two approaches for the data-driven modeling of aggregation kinetics, described by Smoluchowski equations, are analyzed for binary and ternary coagulation. The first approach uses the dynamic mode decomposition (DMD) and the second one is based on the artificial neural networks (ANN). We obtain the numerical solution of the Smoluchowski equations and compare it with the predictions yielding by DMD and ANN methods. To construct the forecast for the solution, the initial stage of the system evolution was used. We demonstrate that the DMD approach can accurately predict the size distribution of the aggregates up to the time, five times larger than the training time. In contrast, the straightforward application of the ANN approach fails to provide an accurate forecast. Hence we conclude that the DMD approach is an effective tool for modeling aggregation kinetics, even for complex aggregation events. At the same time the application of the ANN approach requires its further adaptation for the studied system, perhaps by implementation of physically-informed ANN and specially tailored loss functions. [ABSTRACT FROM AUTHOR]

We study rotational hypersurfaces with constant 2-mean curvature in ℝn+1. We derive the ODE for the generating curves of such hypersurfaces, and find an integral expression for the inverse function of the solution. [ABSTRACT FROM AUTHOR]

This paper is written with a purpose of obtaining an approximate analytical solution to a system of non-linear ordinary differential equation involving non-Michaelis-Menten parameters. Approximate analytical expressions have been derived for the substrate concentration, enzyme substrate concentration, enzyme concentration and product concentration using the new approach to Homotopy perturbation method. The effect of the various parameters on the concentrations is also discussed. [ABSTRACT FROM AUTHOR]

The existence of man is dependent on nature, and this existence can be disturbed by either man-made devastations or by natural disasters. As a universal phenomenon in nature, symmetry has attracted the attention of scholars. The study of symmetry provides insights into physics, chemistry, biology, and mathematics. One of the most important characteristics in the expressive assessment and development of computational design techniques is symmetry. Yet, mathematical models are an important method of studying real-world systems. The symmetry reflected by such a mathematical model reveals the inherent symmetry of real-world systems. This study focuses on the contagious model of pine wilt disease and symmetry, employing the q-HATM (q-Homotopy Analysis Transform Method) to the leading fractional operator Atangana–Baleanu (AB) to arrive at better understanding. The outgrowths are exhibited in the forms of figures and tables. Finally, the paper helps to analyze the practical theory, assisting the prediction of its manner that corresponds to the guidelines when contemplating the replica. [ABSTRACT FROM AUTHOR]

• We derived the differential equation for the assembly process of a lithium battery. • A new mathematical method to solve assembly dynamics is proposed. • The new method performs generally better than other algorithms. In this study, a stochastic differential equation capable of describing (using the motion function) the automatic manufacturing process of a lithium battery with a sleeve shell is introduced. The boundary-condition modeling method for this type of motion is an ordinary differential equation. The nonlinear equation is found using a dynamic method. The equations of the motions for the assembly process are derived by reducing the order of terms and separating the variables. Both the derivatives and integrals of the motion functions are derived and applied to describe the assembly process for a lithium battery. By using a characteristic constitutive assembly model, a new method to calculate the nonlinear terms is proposed. The main advantage of this method is that it can simplify the problem, which is done by finding the algebraic error in the region space of the motion function. The reliability and the applicability of the method were confirmed using a real-life example. Finally, by solving and improving the Euler model, the fourth-order Kutta method and Taylor series are applied to verify the correctness of the algorithm, and the convergence order of the function and the optimization of the assembly model are discussed. Through a one-dimensional search of the convergence domain, a method is found to make the analytical solution approximate the exact solution and reduce the calculation cost. This method in dynamics and mathematical engineering. [ABSTRACT FROM AUTHOR]

The study of Von Kármán swirling flow is a subject of active interest due to its applications in a wide range of fields, including biofuel manufacturing, rotating heat exchangers, rotating disc reactors, liquid metal pumping engines, food processing, electric power generating systems, designs of multi-pore distributors, and many others. This paper focusses on investigating Von Kármán swirling flows of viscous incompressible fluid due to a rotating disk electrode. The model is based on a system of four coupled second-order non-linear differential equations. The purpose of the present communication is to derive analytical expressions of velocity components by solving the non-linear equations using the homotopy analysis method. Combined effects of the slip λ and porosity γ parameters are studied in detail. If either parameter is increased, all velocity components are reduced, as both have the same effect on the mean velocity profiles. The porosity parameter γ increases the moment coefficient at the disk surface, which monotonically decreases with the slip parameter λ. The analytical results are also compared with numerical solutions, which are in satisfactory agreement. Furthermore, the effects of porosity and slip parameters on velocity profiles are discussed.

A general-purpose model combining concepts from rational continuum mechanics, fracture and damage mechanics, plasticity and poromechanics is devised in Eulerian coordinates, involving objective time derivatives. The model complies with mass, momentum and energy conservation as well as entropy inequality and objectivity. It is devised to cover many diverse phenomena, specifically rupture of existing lithospheric faults, tectonic earthquakes, generation and propagation of seismic waves, birth of new tectonic faults, or volcanic activity, aseismic creep, folding of rocks, aging of rocks, long-distance saturated water transport and flow in poroelastic rocks, melting of rocks and formation of magma chambers, or solidification of magma. [ABSTRACT FROM AUTHOR]

Magnetic surveys conducted in complex conditions, such as low magnetic latitudes, uneven observation surfaces, or above high-susceptibility sources, pose significant challenges for obtaining stable solutions for reduction-to-the-pole (RTP) and upward-continuation processing on arbitrary surfaces. To tackle these challenges, in this study, we propose constructing an equivalent-susceptibility model based on the partial differential equation (PDE) framework in the space domain. A multilayer equivalent-susceptibility method was used for RTP and upward-continuation operations, thus allowing for application on undulating observation surfaces and strong self-demagnetization effect in a non-uniform mesh. A novel positivity constraint is introduced to improve the accuracy and efficiency of the inversion. We analysed the effect of the depth-weighting function in the inversion of equivalent susceptibility for RTP and upward-continuation reproduction. Iterative and direct solvers were utilized and compared in solving the large, sparse, non-symmetric and ill-conditioned system of linear equations produced by PDE-based equivalent-source construction. Two synthetic models were used to illustrate the efficiency and accuracy of the proposed method in processing both ground and airborne magnetic data. Aeromagnetic and ground data collected in Brazil at a low magnetic latitude region were used to validate the proposed method for processing RTP and upward-continuation operations on magnetic data sets with strong self-demagnetization. [ABSTRACT FROM AUTHOR]

In this research, a soft computing approach based on a Nature-inspired technique, the Fractional-Order Darwinian Particle Swarm Optimization (FO-DPSO) algorithm, is hybridized with feed-forward artificial neural network (FF-ANN) to suggest and calculate better solutions for non-linear second-order ordinary differential equation (ODE) representing the corneal shape model (CSM). The unknown weights involved in approximate solutions obtained through ANN are tuned with the help of FO-DPSO. To test the robustness of our approach and conditionality of CSM, we have considered several cases of CSM with different aspects of the problem. Solutions obtained by Adam's method are used as a reference point for the sake of comparison. We establish it that FO-DPSO is a suitable technique for tuning the unknown weights involved in the solution designed with ANNs. Our results suggest that the proposed approach is a suitable candidate for solving real-world problems involving differential equations.

The existence of man is dependent on nature, and this existence can be disturbed by either man-made devastations or by natural disasters. As a universal phenomenon in nature, symmetry has attracted the attention of scholars. The study of symmetry provides insights into physics, chemistry, biology, and mathematics. One of the most important characteristics in the expressive assessment and development of computational design techniques is symmetry. Yet, mathematical models are an important method of studying real-world systems. The symmetry reflected by such a mathematical model reveals the inherent symmetry of real-world systems. This study focuses on the contagious model of pine wilt disease and symmetry, employing the q-HATM (q-Homotopy Analysis Transform Method) to the leading fractional operator Atangana–Baleanu (AB) to arrive at better understanding. The outgrowths are exhibited in the forms of figures and tables. Finally, the paper helps to analyze the practical theory, assisting the prediction of its manner that corresponds to the guidelines when contemplating the replica.

The Shinmoe-dake volcano started with three sub-Plinian eruptions from 26 to 27 January 2011, followed by a magma effusive stage from 28 to 31 January 2011, and Vulcanian eruptions occurred frequently during 1 to 10 February 2011. During the magma effusive and Vulcanian stages, multiple episodes of harmonic tremors were observed at stations near the summit crater. Although harmonic tremors have been observed at various volcanoes worldwide, the source mechanism remains poorly understood. This paper proposes a source model for harmonic tremors, which is composed of a non-linear viscous fluid flow in a flexible channel. A simple lumped parameter model is used to consider the process. The dynamics are described by a third-order system of ordinary differential equations using model variables for a cross-sectional area of the constricted segment and the fluid velocities in the upstream and downstream tubes. This model produces various kinds of trajectories for self-sustained oscillations that change the reservoir pressure connected on the upstream channel of the model. Linearization analysis around the stationary point and global analysis using nullcline planes reveal the mechanism of self-sustained oscillations of the system qualitatively. To consider both the frequency peaks of the harmonic tremor and the characteristics of observed phase spectra, the qualitative characteristics of an observed phase portrait are compared to those of a simulated one. This tremor model simulates the frequency peaks and the phase portraits of typical harmonic tremors observed during the 2011 Shinmoe-dake eruption. Because this model involves several geometrical configuration parameters, it has the potential to reveal the source mechanism of various kinds of harmonic tremors. [ABSTRACT FROM AUTHOR]

The nonlinear differential equations governing the inherent irreversibility in a steady hydromagnetic permeable channel flow of a conducting fluid with variable electrical conductivity and asymmetric Navier slip at the channel walls in the presence of induced electrical field is solved. An approximate analytical solution for dimensionless velocity and dimensionless temperature are derived using Homotopy Analysis Method. The current density, the entropy generation number and the Bejan number are also derived analytically. The results obtained are discussed graphically and analytically. [ABSTRACT FROM AUTHOR]

We consider solutions, with infinity of zeros, of real second-order linear differential equations. The graph of a solution locates the zeros with a certain precision, which means that zeros are between some successive numerical values of the solution. Once the first zero is calculated, the given equation is converted into a new first-order equation. The zeros of this new equation form a subset of numerical values of the solution of the first order equation.

In this paper, stability results of central concern for control theory are given for finite-dimensional linear and nonlinear local fractional or fractal differential systems. The main purpose of this paper is to provide some results on stability and asymptotic stability of conformable order systems, together with some illustrating examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of motion of an axisymmetric solid around a fixed point in a resistive medium, described by nonlinear dynamic Euler equations. An analytical solution to the problem when the moments of external resistance forces are proportional to the corresponding projections of the angular velocity of the body is obtained by partial discretization of nonlinear differential equations based on the theory of generalized functions. Curves of angular velocity change are constructed and graphs of comparison of these curves with previously known exact solutions are given. [ABSTRACT FROM AUTHOR]

We discuss the application of the Simple Equations Method (SEsM) for obtaining exact solutions of non-linear differential equations to several cases of equations containing non-polynomial non-linearity. The main idea of the study is to use an appropriate transformation at Step (1.) of SEsM. This transformation has to convert the non-polynomial non- linearity to polynomial non-linearity. Then, an appropriate solution is constructed. This solution is a composite function of solutions of more simple equations. The application of the solution reduces the differential equation to a system of non-linear algebraic equations. We list 10 possible appropriate transformations. Two examples for the application of the methodology are presented. In the first example, we obtain kink and anti- kink solutions of the solved equation. The second example illustrates another point of the study. The point is as follows. In some cases, the simple equations used in SEsM do not have solutions expressed by elementary functions or by the frequently used special functions. In such cases, we can use a special function, which is the solution of an appropriate ordinary differential equation, containing polynomial non-linearity. Specific cases of the use of this function are presented in the second example.

Consider an origin which is fixed at the Earth’s surface, and a rectangular celestial coordinates axes with this origin. The gravity acceleration is the approximate sum of the centrifugal acceleration of the origin relatively to the Earth’s center and the Newton’s gravitational acceleration due to the Earth’s attraction. Thus the selected reference frame is formally an inertial frame. The origin is also a point of a rigid heavy body. The dynamical differential system of absolute motion of the three degrees-of- freedom body is given. Some notable solutions of this system are calculated relatively to a moving laboratory frame with the angular velocity of the Earth.

The lattice Boltzmann method (LBM) is a method to simulate fluid dynamics based on modelling distributions of particles moving and colliding on a lattice. The Python scripting language provides a clean programming paradigm to develop codes based on the LBM, however in order to reach performance comparable to compiled languages, it needs to be carefully implemented, maximizing its vectorized tools, mostly integrated in the NumPy module. We present here the details of a Python implementation of a concise LBM code, with the purpose of offering a pedagogical tool for students and professionals in the geosciences who are approaching this technique for the first time. The first half of the paper focuses on how to vectorize a 2-D LBM code and show how if carefully done, this allows performance close to a compiled code. In the second part of the paper, we use the vectorization described earlier to naturally write a parallel implementation using MPI and test both weak and hard scaling up to 1280 cores. One benchmark, Poiseuille flow and two applications, one on sound wave propagation and another on fluid-flow through a simplified model of a rock matrix are finally shown. [ABSTRACT FROM AUTHOR]