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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]

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.)

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 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]

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]

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]

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]

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]

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]

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]

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]

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]

Sometimes, an increased reaction is caused by an immune system of the body to a non-toxic agent (e. g. eggs, dust, pollens or some drugs). This is called allergy or hypersensitivity. The regulatory T cells decrease these allergic reactions. Nowadays, it is noticed that immune system has a deep relationship with micro-organism present in the intestine, that can be explained by the example, that some bacteria of intestine increase production of Treg cells by producing butyric acid like fatty acids. This can also understand that sufficiently different types of T cell receptors of Treg cells are needed to stop the inflammatory response produced by intestinal bacteria. In this study, the dynamic relation of T helper cells, intestinal bacteria and Treg cells are illustrated by a conformable mathematical model. Memory effects are figured out and displayed through graphs. Different plots also show the effects of increasing/decreasing amount of Treg induction efficiency on the whole system. [ABSTRACT FROM AUTHOR]

In planetary fluid cores, the density depends on temperature and chemical composition, which diffuse at very different rates. This leads to various instabilities, bearing the name of double-diffusive convection (DDC). We investigate rotating DDC (RDDC) in fluid spheres. We use the Boussinesq approximation with homogeneous internal thermal and compositional source terms. We focus on the finger regime, in which the thermal gradient is stabilizing whereas the compositional one is destabilizing. First, we perform a global linear stability analysis in spheres. The critical Rayleigh numbers drastically drop for stably stratified fluids, yielding large-scale convective motions where local analyses predict stability. We evidence the inviscid nature of this large-scale double-diffusive instability, enabling the determination of the marginal stability curve at realistic planetary regimes. In particular, we show that in stably stratified spheres, the Rayleigh numbers Ra at the onset evolve like Ra ∼ Ek −1, where Ek is the Ekman number. This differs from rotating convection in unstably stratified spheres, for which Ra ∼ Ek −4/3. The domain of existence of inviscid convection thus increases as Ek −1/3. Secondly, we perform non-linear simulations. We find a transition between two regimes of RDDC, controlled by the strength of the stratification. Furthermore, far from the RDDC onset, we find a dominating equatorially antisymmetric, large-scale zonal flow slightly above the associated linear onset. Unexpectedly, a purely linear mechanism can explain this phenomenon, even far from the instability onset, yielding a symmetry breaking of the non-linear flow at saturation. For even stronger stable stratification, the flow becomes mainly equatorially symmetric and intense zonal jets develop. Finally, we apply our results to the early Earth core. Double diffusion can reduce the critical Rayleigh number by four decades for realistic core conditions. We suggest that the early Earth core was prone to turbulent RDDC, with large-scale zonal flows. [ABSTRACT FROM AUTHOR]

Fingering, veining, channelling and focussing of porous fluids are widely observed phenomena in the Earth's interior, driving a range of geo-processes across all scales. While observations suggest fairly localized flow patterns induced by fractures, the classical Darcian model predicts diffusive behaviour that leads to never-ending spreading and delocalization. We here investigate an alternative physical mechanism without the need to involve fractures. Decompaction weakening leads to the formation and propagation of localized flow-pathways in fluid-saturated porous media. We numerically solve the coupled equations using high-resolution 2-D and 3-D numerical modelling to predict non-linear porous flow in a non-linearly viscously deforming matrix. We show that high-porosity channels may be a dynamic and natural outcome of sufficiently resolved hydromechanical coupling and decompaction weakening. We propose an efficient solution strategy that involves an iterative pseudo-transient numerical method to solve the coupled system of equations in a matrix-free fashion. We discuss benefits and limitations of this approach that performs optimally on hardware accelerators such as graphical processing units and is well-suited for supercomputing. We benchmark the pseudo-transient routines against commonly used direct-iterative solving strategies and show convergence towards identical results. Furthermore, we use the fast solver to systematically study in 2-D the high-porosity channel propagation velocity as a function of bulk and shear viscosity ratios and report discrepancy between 2-D and 3-D configurations. We conclude that the fluid-flow rate in the channels is up to three orders of magnitude higher than expected by pure Darcian flow regimes and show that the high-porosity channels occurrence remains with strain rate dependant shear viscosity. We provide both the 2-D MATLAB-based direct-iterative and pseudo-transient routines for full reproducibility of the presented results and suggest our model configuration as a key benchmark case to validate the implementation of hydromechanical coupling in 2-D and 3-D numerical codes. The routines are available from Bitbucket and the Swiss Geocomputing Centre website, and are also supporting information to this paper. [ABSTRACT FROM AUTHOR]

Many problems in geodynamic modelling result in a non-linear Stokes problem in which the viscosity depends on the strain rate and pressure (in addition to other variables). After discretization, the resulting non-linear system is most commonly solved using a Picard fixed-point iteration. However, it is well understood that Newton's method – when augmented by globalization strategies to ensure convergence even from points far from the solution – can be substantially more efficient and accurate than a Picard solver. In this contribution, we evaluate how a straightforward Newton method must be modified to allow for the kinds of rheologies common in geodynamics. Specifically, we show that the Newton step is not actually well posed for strain rate-weakening models without modifications to the Newton matrix. We derive modifications that guarantee well posedness and that also allow for efficient solution strategies by ensuring that the top left block of the Newton matrix is symmetric and positive definite. We demonstrate the applicability and relevance of these modifications with a sequence of benchmarks and a test case of realistic complexity. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to study the effect of injection and suction on velocity profile, skin friction and pressure distribution of a Casson fluid flow between two parallel infinite rectangular plates approaching or receding from each other with suction or injection at the porous plates.Design/methodology/approach The governing Navier–Stokes equations are reduced to the fourth-order non-linear ordinary differential equation through the similarity transformations. The approximated analytic solution based on the Homotopy perturbation method is given and also compared with the classical finite difference method.Findings From this study, the authors observed that the skin friction is less in non-Newtonian fluids compared to Newtonian fluids. The use of non-Newtonian fluids reduces the pressure in all the cases compared to Newtonian and hence load-carrying capacity will be more. As γ value increases velocity, skin friction and pressure decreases. When γ is fixed, it is observed that skin friction and pressure is minimum for A=0.5 and maximum when A=−0.5. The result of this study also shows that the effect of suction on the velocity profiles, pressure and skin friction is opposite to the effect of injection.Originality/value The present work analyzes the characteristic of non-Newtonian fluid having practical and industrial applications. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a mathematical model of spreading any type of information. The model has the form of a system of nonlinear differential equations with non-stationary parameters. We have suggested the explicit solutions of the system differential non-linear equations describing the information spreading process. Special case of this model with jump discontinuity is considered. The numerical experiments demonstrated the practical meaning of the offered results. The results can be useful for algorithm development for estimation of dynamic of information spreading process. [ABSTRACT FROM AUTHOR]

In this paper, a matrix method is developed to solve quadratic non-linear differential equations. It is assumed that the approximate solutions of main problem which we handle primarily, is in terms of Bernoulli polynomials. Both the approximate solution and the main problem are written in matrix form to obtain the solution. The absolute errors are applied to numeric examples to demonstrate efficiency and accuracy of this technique. The obtained tables and figures in the numeric examples show that this method is very sufficient and reliable for solution of non-linear equations. Also, a formula is utilized based on residual functions and mean value theorem to seek error bounds. [ABSTRACT FROM AUTHOR]

Traveltime approximation plays an important role in seismic data processing, for example, anisotropic parameter estimation and seismic imaging. By exploiting seismic traveltimes, it is possible to improve the accuracy of anisotropic parameter estimation and the resolution of seismic imaging. Conventionally, the traveltime approximations in anisotropic media are obtained by expanding the anisotropic eikonal equation in terms of the anisotropic parameters and the elliptically anisotropic eikonal equation based on perturbation theory. Such an expansion assumes a small perturbation and weak anisotropy. In a realistic medium, however, the assumption of small perturbation likely breaks down. We present a retrieved zero-order deformation equation that creates a map from the anisotropic eikonal equation to a linearized partial differential equation system based on the homotopy analysis method. By choosing the linear and nonlinear operators in the retrieved zero-order deformation equation, we develop new traveltime approximations that allow us to compute the traveltimes for a medium of arbitrarily strength anisotropy. A comparison of the traveltimes and their errors from the homotopy analysis method and from the perturbation method suggests that the traveltime approximations provide a more reliable result in strongly anisotropic media. [ABSTRACT FROM AUTHOR]

Numerical modelling is a fundamental tool for scenario-based evaluation of hazardous phenomena such as tsunami. Nevertheless, the numerical prediction highly depends on the tool quality and therefore the design of efficient numerical schemes that provide robust and accurate solutions still receives considerable attention. In this paper, we implement two different second-order finite volume numerical schemes deriving from an a priori or an a posteriori limitation procedure and we compare their efficiency in solving the non-conservative shallow-water equations. The numerical schemes assessed here are two variants of the a priori Monotonic Upstream-Centred Scheme for Conservation Laws (MUSCL) and the recent a posteriori multidimensional optimal order detection (MOOD) technique. We benchmark the numerical code, equipped with MUSCL and MOOD techniques, against: (1) a 1-D stationary problem with non-constant bathymetry to assess the second-order convergence of the method when a smooth analytical solution is involved; (2) a 1-D dam-break test to show its capacity to deal with irregular and discontinuous bathymetry in wet zones; and (3) using a simple 1-D analytical tsunami benchmark, 'single wave on a sloping beach', we show that the classical 1-D shallow-water system can be accurately solved by the second-order finite volume methods. Furthermore, we test the performance of the numerical code for the real-case tsunami of Tohoku-Oki, 2011. Through a set of 2-D numerical simulations, the 2011 tsunami records from both DART and GPS buoys are checked against the simulated results using MUSCL and MOOD. We find that the use of the MOOD technique leads to a better approximation between the numerical solutions and the observations than the MUSCL one. MOOD allows sharper shock capture and generates less numerical diffusion, suggesting it as a promising technique for solving shallow-water problems. [ABSTRACT FROM AUTHOR]

Seismic waves travelling across fluid-saturated poroelastic materials with mesoscopic-scale heterogeneities induce fluid flow and Biot's slow waves generating energy loss and velocity dispersion. Using Biot's equations of motion to model these type of heterogeneities would require extremely fine meshes. We propose a numerical upscaling procedure to determine the complex and frequency-dependent P wave and shear moduli of an effective viscoelastic medium long-wave equivalent to a poroelastic solid saturated by a two-phase fluid. The two-phase fluid is defined in terms of capillary pressure and relative permeability flow functions. The P wave and shear effective moduli are determined using harmonic compressibility and shear experiments applied on representative samples of the bulk material. Each experiment is associated with a boundary value problem that is solved using the finite element method. Since a poroelastic solid saturated by a two-phase fluid supports the existence of two slow waves, this upscaling procedure allows to analyse their effect on the mesoscopic loss mechanism in hydrocarbon reservoir formations. Numerical results show that a two-phase Biot medium model predicts higher attenuation than classic Biot models. [ABSTRACT FROM AUTHOR]

The electrical potential at the interface between mineral and water is traditionally computed from the Poisson--Boltzmann (P-B) equation. Nevertheless, this partial differential equation is nonlinear and has no analytical solution for cylindrical geometries for instance. For that reason, the linearized P-B equation is mostly used in the literature. In our study, we present a short and easy-to-handle Matlab® code to solve the full (i.e. non-linearized) P-B equation inside a cylinder. Electrical potentials inside silica and montmorillonite nanotubes, containing NaCl or CaCl2 electrolytes, are computed. The zeta potential, which is an input parameter of our code, is first predicted from basic Stern and extended Stern models. We show that the linearized P-B equation overestimates the electrical potential from the full P-B equation when the zeta potential magnitude is above ~25.7 mV at 25° C, especially for Ca2+ ion in solution. This effect increases when salinity decreases from 0.1 to 0.001 mol L-1 because of increasing zeta potentials, and when the cylinder radius decreases to the nanometric range because of overlapping diffuse layers. Our results may have strong implications for simulating the electrical properties of sandstones and clays to interpret their self-potential and complex resistivity response. [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. [ABSTRACT FROM AUTHOR]

In order to derive local tsunami risks for a particular coast, hydro- and morphodynamic numerical models that are calibrated and compared with sedimentary field data of past tsunami impacts have proven very effective. While this approach has widely been used with regard to recent tsunami events, comparable investigations into pre-/historical tsunami impacts hardly exist, which is the objective of this study focusing on the Ambrakian Gulf in northwestern Greece. The Ambrakian Gulf is located in the most active seismotectonic and by this most tsunamigenic area of the Mediterranean. Accordingly, palaeotsunami field studies have revealed repeated tsunami impacts on the gulf during the past 8000 yr. The current study analyses 151 vibracores of the Ambrakian Gulf coast in order to evaluate tsunami signals in the sedimentary record. Based on a hydro- and morphodynamic numerical model of the study area, various tsunami waves are simulated with the aim of finding scenarios that compare favourably with tsunami deposits detected in the field. Both, field data and simulation results suggest a decreasing tsunami influence from the western to the eastern Ambrakian Gulf. Various scenarios are needed to explain tsunami deposits in different parts of the gulf. Whereas shorter period tsunami waves (T=30 min) from the south and west compare favourably with field data in the western gulf, longer period waves (T=80 min) from a western direction show the best agreement with tsunami sediments detected in southwestern Aktio Headland and in the more central parts of the Ambrakian Gulf including Lake Voulkaria. Tsunamis from the southwest generally do not accord with field traces. Besides the spatial sediment distribution, the numerical model accurately reflects the sedimentary composition of the detected event deposits and reproduces a number of essential features typical of tsunamites, which were also observed in the field. Such include fining- and thinning-landward and the marine character of the deposits. By contrast, the simulated thickness of tsunami sediments usually lags behind the observed thickness in the field and some event layers cannot be explained by any of the simulated scenarios. Regarding the frequency of past tsunami events and their spatial dimensions indicated by both field data and simulation results, a high tsunami risk has to be derived for the Ambrakian Gulf. [ABSTRACT FROM AUTHOR]

Accurate numerical computation of wave traveltimes in heterogeneous media is of major interest for a large range of applications in seismics, such as phase identification, data windowing, traveltime tomography and seismic imaging. A high level of precision is needed for traveltimes and their derivatives in applications which require quantities such as amplitude or take-off angle. Even more challenging is the anisotropic case, where the general Eikonal equation is a quartic in the derivatives of traveltimes. Despite their efficiency on Cartesian meshes, finite-difference solvers are inappropriate when dealing with unstructured meshes and irregular topographies. Moreover, reaching high orders of accuracy generally requires wide stencils and high additional computational load. To go beyond these limitations, we propose a discontinuous-finite-element-based strategy which has the following advantages: (1) the Hamiltonian formalism is general enough for handling the full anisotropic Eikonal equations; (2) the scheme is suitable for any desired high-order formulation or mixing of orders (p-adaptivity); (3) the solver is explicit whatever Hamiltonian is used (no need to find the roots of the quartic); (4) the use of unstructured meshes provides the flexibility for handling complex boundary geometries such as topographies (h-adaptivity) and radiation boundary conditions for mimicking an infinite medium. The point-source factorization principles are extended to this discontinuous Galerkin formulation. Extensive tests in smooth analytical media demonstrate the high accuracy of the method. Simulations in strongly heterogeneous media illustrate the solver robustness to realistic Earth-sciences-oriented applications. [ABSTRACT FROM AUTHOR]

This paper presents a numerical procedure for predicting subsurface temperatures and heatflow distribution in 3-D using inverse calibration methodology. The procedure is based on a modified version of the groundwater code MODFLOW by taking advantage of the mathematical similarity between confined groundwater flow (Darcy's law) and heat conduction (Fourier's law). Thermal conductivity, heat production and exponential porosity-depth relations are specified separately for the individual geological units of the model domain. The steady-state temperature model includes a model-based transient correction for the long-term palaeoclimatic thermal disturbance of the subsurface temperature regime. Variable model parameters are estimated by inversion of measured borehole temperatures with uncertainties reflecting their quality. The procedure facilitates uncertainty estimation for temperature predictions. The modelling procedure is applied to Danish onshore areas containing deep sedimentary basins. A 3-D voxel-based model, with 14 lithological units from surface to 5000 m depth, was built from digital geological maps derived from combined analyses of reflection seismic lines and borehole information. Matrix thermal conductivity of model lithologies was estimated by inversion of all available deep borehole temperature data and applied together with prescribed background heat flow to derive the 3-D subsurface temperature distribution. Modelled temperatures are found to agree very well with observations. The numerical model was utilized for predicting and contouring temperatures at 2000 and 3000 m depths and for two main geothermal reservoir units, the Gassum (Lower Jurassic-Upper Triassic) and Bunter/Skagerrak (Triassic) reservoirs, both currently utilized for geothermal energy production. Temperature gradients to depths of 2000-3000 m are generally around 25-30 °C km-1, locally up to about 35 °C km-1. Large regions have geothermal reservoirs with characteristic temperatures ranging from ca. 40-50 °C, at 1000-1500 m depth, to ca. 80-110 °C, at 2500- 3500 m, however, at the deeper parts, most likely, with too low permeability for non-stimulated production. [ABSTRACT FROM AUTHOR]

The gas transient pulse test (GTPT) is a reliable technique for efficiently measuring the permeability of low-porosity rocks, but requires an analytical model that well considers the compressibility of gas for data interpretation. In this study, an interpretive model was proposed for calculation of both permeability and porosity from the GTPT data based on the assumption of a constant gradient of pressure squared in the sample. The proposed model relies on the time-series of pressure data in both reservoirs, and is of high efficiency because the calculation could be readily obtained long before the final equilibrium state of the test is approached. The proposed model was analytically and numerically validated, and was applied for data interpretation of the GTPTs performed on a metamorphosed sandstone sample under deviatoric loading, showing that it corrects the limitation of the classic Brace et al.'s model for overestimating the permeability from the GTPT data. [ABSTRACT FROM AUTHOR]

We introduce a hybrid Galerkin modelling tool for the nonlinear acoustic and gravity wave propagation in planetary atmospheres coupled through topography to a solid medium. We rely on a 2-D spectral-element technique to model linear visco-elastic solid media and couple it to a discontinuous Galerkin method for the atmosphere modelled by the fully nonlinear Navier-Stokes equations. Significant benefits of such a method are, first, its versatility because it handles both acoustic and gravity waves in the same simulation, second, it enables one to observe nonlinear effects as convection or wave-breaking and, finally, it allows one to study the impact of ground-atmosphere coupling for waves propagating from seismic sources. Simulations are performed for 2-D isothermal atmosphere models with complex wind and viscosity profiles. We validate the computations by comparing them to finite-difference solutions, already validated in a previous paper. Specific benchmark validation cases are considered for both acoustic and gravity waves subject to viscosity variations, wind duct and nonlinear wave breaking. We apply this tool to study acoustic and gravity waves generated by a strong seismic source and its nonlinear breaking in the upper atmosphere. [ABSTRACT FROM AUTHOR]

We examine wave propagation in transversely homogeneous media characterized by variations of properties with respect to depth. Our intent is to provide analytic formulae that quantify scattering effects from fine scale inhomogeneities typically observed on seismic field data. We employ a Born scattering series approach that systematically includes higher order phenomena (transmission losses, mode conversions and multiples). Although, the Born series is inexact, it provides useful approximations. Analytic examples show how various terms of the Born series include higher order scattering effects. We also document the inexact nature of the approximation. Numerical examples illustrate the magnitude of scattering induced time delays and attenuation. A generalized (complex) reflection coefficient is introduced to describe backscattered energy from a discrete interval instead of an isolated interface. The main goal of this paper is to quantify thin-bed scattering in order to provide a more complete representation of seismic reflections in realistic geological settings. It is our hope that this insight will lead to useful applications. [ABSTRACT FROM AUTHOR]

Homotopy perturbation method is combined with Laplace transformation to obtain approximate analytical solutions of non-linear differential equations. An example is given to elucidate the solution process and confirm reliability of the method. The result indicates superiority of the method over the conventional homotopy perturbation method due its flexibility in choosing its initial approximation. [ABSTRACT FROM AUTHOR]

Numerical simulations of the thermal convection in a rotating spherical shell play an important role in dynamo simulations. In this paper, we present a highly scalable parallel solver for the Earth's outer core convection. The solver uses a second-order cell-centred finite volume spatial discretization based on the cubed-sphere grid instead of the traditional latitude-longitude grid to avoid grid singularity and enhance the parallel scalability. A second-order approximate factorization method combined with the Crank-Nicolson scheme is employed for splitting temporal integration. The two resultant sparse linear systems are solved by theKrylov subspace iterative method pre-conditioned with a restricted additive Schwarz pre-conditioner based on the domain decomposition of the cubed-sphere. The numerical results are in good agreement with the benchmark solutions and more accurate than the existing finite volume results. The solvers scale to over 10 000 processor cores with nearly linear scalability on the Sunway TaihuLight supercomputer. [ABSTRACT FROM AUTHOR]

We develop a layer-averaged, multiple-scale spectral ocean model and show how an oceanic double-gyre can communicate with the Earth's Chandler wobble. The overall transfers of energy and angular momentum from the double-gyre to the Chandler wobble are used to calibrate the turbulence parameters of the layer-averaged model. Our model is tested against a multilayer quasi-geostrophic ocean model in turbulent regime, and base states used in parameter identification are obtained from mesoscale eddy resolving numerical simulations. The Chandler wobble excitation function obtained from the model predicts a small role of North Atlantic ocean region on the wobble dynamics as compared to all oceans, in agreement with the existing observations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

An approach for approximate direct quadratic non-linear inversion in two-parameter (density and bulk modulus) heterogeneous acoustic media is being presented and discussed in this paper. The approach consists of two parts: the first is a linear generalized Radon transform (GRT) migration procedure based on the weighted true-amplitude summation of pre-stack seismic scattered data that is adapted to a virtually arbitrary observing system, and the second is a non-iterative quadratic inversion operation, produced from the explicit expression of amplitude radiation pattern that is acting on the migrated data. This ensures the asymptotic inversion can continue to simultaneously locate the discontinuities and reconstruct the size of the discontinuities in the perturbation parameters describing the acoustic media. We identify that the amplitude radiation pattern is the binary quadratic combination of the parameters in the process of formulating non-linear inverse scattering problems based on second-order Born approximation. The coefficients of the quadratic terms are computed by appropriately handling the double scattering effects. These added quadratic terms provide a better amplitude correction for the parameters inversion. Through numerical tests, we show that for strong perturbations, the errors of the linear inversion are significant and unacceptable. In contrast, the quadratic non-linear inversion can give fairly accurate inversion results and keep almost the same computational complexity as conventional GRT liner inversion. [ABSTRACT FROM AUTHOR]