This book contains selected papers of NSC08, the 2nd Conference on Nonlinear Science and Complexity, held 28-31 July, 2008, Porto, Portugal. It focuses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physics and mathematics. Topics treated include - Chaotic Dynamics and Transport in Classic and Quantum Systems - Complexity and Nonlinearity in Molecular Dynamics and Nano-Science - Complexity and Fractals in Nonlinear Biological Physics and Social Systems - Lie Group Analysis and Applications in Nonlinear Science - Nonlinear Hydrodynamics and Turbulence - Bifurcation and Stability in Nonlinear Dynamic Systems - Nonlinear Oscillations and Control with Applications - Celestial Physics and Deep Space Exploration - Nonlinear Mechanics and Nonlinear Structural Dynamics - Non-smooth Systems and Hybrid Systems - Fractional dynamical systems

Engineering practice often has to deal with complex systems of multiple variable and multiple parameter models almost always with strong non-linear coupling. The conventional analytical techniques-based approaches for describing and predicting the behaviour of such systems in many cases are doomed to failure from the outset, even in the phase of the construction of a more or less appropriate mathematical model. These approaches normally are too categorical in the sense that in the name of modelling accuracy they try to describe all the structural details of the real physical system to be modelled. This can significantly increase the intricacy of the model and may result in a enormous computational burden without achieving considerable improvement of the solution. The best paradigm exemplifying this situation may be the classic perturbation theory: the less significant the achievable correction, the more work has to be invested to obtain it.

A further important component of machine intelligence is a kind of structural uniformity giving room and possibility to model arbitrary particular details a priori not specified and unknown. This idea is similar to the ready-to-wear industry, which introduced products, which can be slightly modified later on in contrast to tailor-made creations aiming at maximum accuracy from the beginning. These subsequent corrections can be carried out by machines automatically. This learning ability is a key element of machine intelligence.

The past decade confirmed that the view of typical components of the present soft computing as fuzzy logic, neural computing, evolutionary computation and probabilistic reasoning are of complementary nature and that the best results can be applied by their combined application.

Today, the two complementary branches of Machine Intelligence, that is, Artificial Intelligence and Computational Intelligence serve as the basis of Intelligent Engineering Systems. The huge number of scientific results published in Journal and conference proceedings worldwide substantiates this statement. The present book contains several articles taking different viewpoints in the field of intelligent systems. "

This book contains some of the contributions, divided into five main sections, that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering, held in Cankaya University, Ankara, April 27-29, 2006.The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory.

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation.

As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Discontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed.

This book explores recent developments in theoretical research and mathematical modelling of real-world complex systems, organized in four parts. The first part of the book is devoted to the mathematical tools for the design and analysis in engineering and social science study cases. We discuss the periodic evolutions in nonlinear chemical processes, vibro-compact systems and their behaviour, different types of metal-semiconductor self-assembled samples, made of silver nanowires and zinc oxide nanorods. The second part of the book is devoted to mathematical description and modelling of the critical events, climate change and robust emergency scales. In three chapters, we consider a climate-economy model with endogenous carbon intensity and the behaviour of Tehran Stock Exchange market under international sanctions. The third part of the book is devoted to fractional dynamic and fractional control problems. We discuss the novel operational matrix technique for variable-order fractional optimal control problems, the nonlinear variable-order time fractional convection-diffusion equation with generalized polynomials The fourth part of the book concerns solvability and inverse problems in differential and integro-differential equations. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists and urban planners.

In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy.

This wide range of applications is of interest to engineers, physicists and mathematicians.

An Introduction to Bond Graph Modeling with Applications presents a collection of exercises on dynamical systems, modeling and control for university students in the areas of engineering, physics and applied mathematics. We can find several books on bond graphs, but most merely a small set of exercises and, in a few cases, some commands for computer packages like MATLAB or Mathematica. It is difficult to find books with a broad set of solved exercises and proposed exercises with solutions, guiding researchers starting their work with bond graphs, or students who are just beginning their study of the topic. This book aims to fill that gap, and provide a comprehensive, reader-friendly introduction to the Bond Graph modeling tool. Features Gives in-depth theoretical background coupled with practical, hands-on instructions. Provides a clear pedagogical framework, with numerous exercises and problems. Suitable for students and researchers who work with bond graphs: principally such as applied mathematicians, physicist and engineers.

In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy. This wide range of applications is of interest to engineers, physicists and mathematicians.

This book contains selected papers of NSC08, the 2nd Conference on Nonlinear Science and Complexity, held 28-31 July, 2008, Porto, Portugal. It focuses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physics and mathematics. Topics treated include * Chaotic Dynamics and Transport in Classic and Quantum Systems * Complexity and Nonlinearity in Molecular Dynamics and Nano-Science * Complexity and Fractals in Nonlinear Biological Physics and Social Systems * Lie Group Analysis and Applications in Nonlinear Science * Nonlinear Hydrodynamics and Turbulence * Bifurcation and Stability in Nonlinear Dynamic Systems * Nonlinear Oscillations and Control with Applications * Celestial Physics and Deep Space Exploration * Nonlinear Mechanics and Nonlinear Structural Dynamics * Non-smooth Systems and Hybrid Systems * Fractional dynamical systems

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation.

As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

This book contains some of the contributions that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering, held in Cankaya University, Ankara, April 2006. The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory.

Engineering practice often has to deal with complex systems of multiple variable and multiple parameter models almost always with strong non-linear coupling. The conventional analytical techniques-based approaches for describing and predicting the behaviour of such systems in many cases are doomed to failure from the outset, even in the phase of the construction of a more or less appropriate mathematical model. These approaches normally are too categorical in the sense that in the name of modelling accuracy they try to describe all the structural details of the real physical system to be modelled. This can significantly increase the intricacy of the model and may result in a enormous computational burden without achieving considerable improvement of the solution. The best paradigm exemplifying this situation may be the classic perturbation theory: the less significant the achievable correction, the more work has to be invested to obtain it.

A further important component of machine intelligence is a kind of structural uniformity giving room and possibility to model arbitrary particular details a priori not specified and unknown. This idea is similar to the ready-to-wear industry, which introduced products, which can be slightly modified later on in contrast to tailor-made creations aiming at maximum accuracy from the beginning. These subsequent corrections can be carried out by machines automatically. This learning ability is a key element of machine intelligence.

The past decade confirmed that the view of typical components of the present soft computing as fuzzy logic, neural computing, evolutionary computation and probabilistic reasoning are of complementary nature and that the best results can be applied by their combined application.

Today, the two complementary branches of Machine Intelligence, that is, Artificial Intelligence and Computational Intelligence serve as the basis of Intelligent Engineering Systems. The huge number of scientific results published in Journal and conference proceedings worldwide substantiates this statement. The present book contains several articles taking different viewpoints in the field of intelligent systems. "

This book presents recent developments in nonlinear and complex systems. It provides recent theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers information theory, relativistic chaotic dynamics, data analysis, relativistic chaotic dynamics, solvability issues in integro-differential equations, and inverse problems for parabolic differential equations, synchronization and chaotic transient. Presents new concepts for understanding and modeling complex systems   

This book presents recent developments in nonlinear and complex systems. It provides recent theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers information theory, relativistic chaotic dynamics, data analysis, relativistic chaotic dynamics, solvability issues in integro-differential equations, and inverse problems for parabolic differential equations, synchronization and chaotic transient. Presents new concepts for understanding and modeling complex systems