Laplace Adomian Decomposition Method to study Chemical ion transport through soil

The paper deals with a theoretical study of chemical ion transport in soil under a uniform external force in the transverse direction, where the soil is taken as porous medium. The problem is formulated in terms of boundary value problem that consists of a set of partial differential equations, which is subsequently converted to a system of ordinary differential equations by applying similarity transformation along with boundary layer approximation. The equations hence obtained are solved by utilizing Laplace Adomian Decomposition Method (LADM). The merit of this method lies in the fact that much of simplifying assumptions need not be made to solve the non-linear problem. The decomposition parameter is used only for grouping the terms, therefore, the nonlinearities is handled easily in the operator equation and accurate approximate solution are obtained for the said physical problem. The computational outcomes are introduced graphically. By utilizing parametric variety, it has been demonstrated that the intensity of the external pressure extensively influences the flow behavior

MHD Natural Convection of grade three of non-Newtonian fluid flow between two Vertical Flat Plates through Porous Medium with heat source effect

Analytical and numerical solutions are investigated to study solution of the Magneto hydrodynamics (MHD) natural convection flow of grade three of a non- Newtonian fluid flow between two vertical flat plates through embedded in a porous medium and considering the effect heat source using Multi−step differential transform method and finite difference method. The system of coupled nonlinear ordinary differential equations are solved analytically using Multi−step differential transform method (MDTM) and numerically using finite difference method (FDM). The results of (MDTM), (FDM), and another analytical method are all in good agreement, demonstrating that these methods are capable of solving similar problems. Graphs and tables show the effect of various parameters on velocity and temperature. The current studies, as well as comparisons to previous findings, are presented in figures and tables. The study results showed that the analytical solution using Multi−step differential transform method and numerical solution using finite difference method agrees well with recent analytical and numerical solutions

Topological and dynamical complexity in epidemiological and ecological systems

In this work, we address a contribution for the rigorous analysis of the dynamical complexity arising in epidemiological and ecological models under different types of interactions. Firstly, we study the dynamics of a tumor growth model, governing tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we characterize the topological entropy from one-dimensional iterated maps identified in the dynamics. This analysis is complemented with the computation of the Lyapunov exponents, the fractal dimension and the predictability of the chaotic dynamics. Secondly, we provide the analytical solutions of the mentioned tumor growth model. We apply a method for solving strongly nonlinear systems - the Homotopy Analysis Method (HAM) - which allows us to obtain a one-parameter family of explicit series solutions. Due to the importance of chaos generating mechanisms, we analyze a mathematical ecological model mainly focusing on the impact of species rates of evolution in the dynamics. We analytically proof the boundedness of the trajectories of the attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. The topological entropy of existing one-dimensional iterated maps is characterized using symbolic dynamics. To extend the previous analysis, we study the predictability and the likeliness of finding chaos in a given region of the parameter space. We conclude our research work with the analysis of a HIV-1 cancer epidemiological model. We construct the explicit series solution of the model. An optimal homotopy analysis approach is used to improve the computational efficiency of HAM by means of appropriate values for the convergence control parameter. We end up this dissertation presenting some final considerations; RESUMO: Este trabalho constitui um contributo para a análise rigorosa da complexidade dinâmica de modelos epidemiológicos e ecológicos submetidos a diferentes tipos de interações Primeiramente, estudamos a dinâmica de um modelo de crescimento tumoral, representando a interacção de células tumorais com tecidos saudáveis e células efectoras do sistema imunitário. Usando a teoria da dinâmica simbólica, caracterizamos a entropia topológica de aplicações unidimensionais identificadas na dinâmica. Esta análise ´e complementada com o cálculo dos expoentes de Lyapunov, dimensão fractal e o cálculo da previsibilidade dos atractores caóticos. Seguidamente, apresentamos soluções analíticas do modelo de crescimento tumoral mencionado. Aplicamos um método para resolver sistemas fortemente não lineares - o Método de Análise Homotópica (HAM) - o qual nos permite obter uma família a um parâmetro de soluções explícitas em forma de série. Devido à importância dos mecanismos geradores de caos, analisamos um modelo matemático em ecologia, centrando-nos no impacto das taxas de evolução das espécies na dinâmica. Provamos analiticamente a compacticidade das trajectórias do atractor. A complexidade do acoplamento entre as variáveis dinâmicas é quantificada utilizando índices de observabilidade. A entropia topológica de aplicações unidimensionais é caracterizada usando a dinâmica simbólica. Para estender a análise anterior, estudamos a previsibilidade e a probabilidade de encontrar comportamento caótico numa determinada região do espaço de parâmetros. Concluímos o nosso trabalho de investigação com a análise de um modelo epidemiológico tumoral HIV-1. Construímos uma solução explícita do modelo. Usamos uma análise homotópica optimal para melhorar a eficiência computacional do HAM através de valores apropriados para o parâmetro de controlo da convergência. Terminamos esta dissertação com a apresentação de algumas considerações finais

Numerical Simulation

Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students

Response statistics and failure probability determination of nonlinear stochastic structural dynamical systems

Novel approximation techniques are proposed for the analysis and evaluation of nonlinear dynamical systems in the field of stochastic dynamics. Efficient determination of response statistics and reliability estimates for nonlinear systems remains challenging, especially those with singular matrices or endowed with fractional derivative elements. This thesis addresses the challenges of three main topics. The first topic relates to the determination of response statistics of multi-degree-of-freedom nonlinear systems with singular matrices subject to combined deterministic and stochastic excitations. Notably, singular matrices can appear in the governing equations of motion of engineering systems for various reasons, such as due to a redundant coordinates modeling or due to modeling with additional constraint equations. Moreover, it is common for nonlinear systems to experience both stochastic and deterministic excitations simultaneously. In this context, first, a novel solution framework is developed for determining the response of such systems subject to combined deterministic and stochastic excitation of the stationary kind. This is achieved by using the harmonic balance method and the generalized statistical linearization method. An over-determined system of equations is generated and solved by resorting to generalized matrix inverse theory. Subsequently, the developed framework is appropriately extended to systems subject to a mixture of deterministic and stochastic excitations of the non-stationary kind. The generalized statistical linearization method is used to handle the nonlinear subsystem subject to non-stationary stochastic excitation, which, in conjunction with a state space formulation, forms a matrix differential equation governing the stochastic response. Then, the developed equations are solved by numerical methods. The accuracy for the proposed techniques has been demonstrated by considering nonlinear structural systems with redundant coordinates modeling, as well as a piezoelectric vibration energy harvesting device have been employed in the relevant application part. The second topic relates to code-compliant stochastic dynamic analysis of nonlinear structural systems with fractional derivative elements. First, a novel approximation method is proposed to efficiently determine the peak response of nonlinear structural systems with fractional derivative elements subject to excitation compatible with a given seismic design spectrum. The proposed methods involve deriving an excitation evolutionary power spectrum that matches the design spectrum in a stochastic sense. The peak response is approximated by utilizing equivalent linear elements, in conjunction with code-compliant design spectra, hopefully rendering it favorable to engineers of practice. Nonlinear structural systems endowed with fractional derivative terms in the governing equations of motion have been considered. A particular attribute pertains to utilizing localized time-dependent equivalent linear elements, which is superior to classical approaches utilizing standard time-invariant statistical linearization method. Then, the approximation method is extended to perform stochastic incremental dynamical analysis for nonlinear structural systems with fractional derivative elements exposed to stochastic excitations aligned with contemporary aseismic codes. The proposed method is achieved by resorting to the combination of stochastic averaging and statistical linearization methods, resulting in an efficient and comprehensive way to obtain the response displacement probability density function. A stochastic incremental dynamical analysis surface is generated instead of the traditional curves, leading to a reliable higher order statistics of the system response. Lastly, the problem of the first excursion probability of nonlinear dynamic systems subject to imprecisely defined stochastic Gaussian loads is considered. This involves solving a nested double-loop problem, generally intractable without resorting to surrogate modeling schemes. To overcome these challenges, this thesis first proposes a generalized operator norm framework based on statistical linearization method. Its efficiency is achieved by breaking the double loop and determining the values of the epistemic uncertain parameters that produce bounds on the probability of failure a priori. The proposed framework can significantly reduce the computational burden and provide a reliable estimate of the probability of failure

The structure and reactivity of heterogeneous surfaces and study of the geometry of surface complexes

Issued as Progress report, Project no. G-41-68

Planification de trajectoire et contrôle d'un système collaboratif : Application à un drone trirotor

This thesis is dedicated to the creation of a complete framework, from high-level to low-level, of trajectory generation for a group of independent dynamical systems. This framework, based for the trajectory generation, on the resolution of Burgers equation, is applied to a novel model of trirotor UAV and uses the flatness of the two levels of dynamical systems.The first part of this thesis is dedicated to the generation of trajectories. Formal solutions to the heat equation are created using the differential flatness of this equation. These solutions are transformed into solutions to Burgers' equation through Hopf-Cole transformation to match the desired formations. They are optimized to match specific requirements. Several examples of trajectories are given.The second part is dedicated to the autonomous trajectory tracking by a trirotor UAV. This UAV is totally actuated and a nonlinear closed-loop controller is suggested. This controller is tested on the ground and in flight by tracking, rolling or flying, a trajectory. A model is presented and a control approach is suggested to transport a pendulum load.L'objet de cette thèse est de proposer un cadre complet, du haut niveau au bas niveau, de génération de trajectoires pour un groupe de systèmes dynamiques indépendants. Ce cadre, basé sur la résolution de l'équation de Burgers pour la génération de trajectoires, est appliqué à un modèle original de drone trirotor et utilise la platitude des deux systèmes différentiels considérés. La première partie du manuscrit est consacrée à la génération de trajectoires. Celle-ci est effectuée en créant formellement, par le biais de la platitude du système considéré, des solutions à l'équation de la chaleur. Ces solutions sont transformées en solution de l'équation de Burgers par la transformation de Hopf-Cole pour correspondre aux formations voulues. Elles sont optimisées pour répondre à des contraintes spécifiques. Plusieurs exemples de trajectoires sont donnés.La deuxième partie est consacrée au suivi autonome de trajectoire par un drone trirotor. Ce drone est totalement actionné et un contrôleur en boucle fermée non-linéaire est proposé. Celui-ci est testé en suivant, en roulant, des trajectoires au sol et en vol. Un modèle est présenté et une démarche pour le contrôle est proposée pour transporter une charge pendulaire

Advanced Topics in Mass Transfer

This book introduces a number of selected advanced topics in mass transfer phenomenon and covers its theoretical, numerical, modeling and experimental aspects. The 26 chapters of this book are divided into five parts. The first is devoted to the study of some problems of mass transfer in microchannels, turbulence, waves and plasma, while chapters regarding mass transfer with hydro-, magnetohydro- and electro- dynamics are collected in the second part. The third part deals with mass transfer in food, such as rice, cheese, fruits and vegetables, and the fourth focuses on mass transfer in some large-scale applications such as geomorphologic studies. The last part introduces several issues of combined heat and mass transfer phenomena. The book can be considered as a rich reference for researchers and engineers working in the field of mass transfer and its related topics