Mathematical Modelling and Computing in Physics, Chemistry and Biology

This book  keeps an eye in the direction of applications of advanced and high performance scientific computing in  describing the behavior of natural and constructed systems, e.g. chaos, bifurcation, fractal, Lyapunov exponent, period doubling, Poincaré map, strange attractor etc. With the aid of powerful computers the modem theory of chaos and its geometry, the fractals, and attractors are developed. The concepts of object oriented computing are introduced early in the text and steadily expanded as one progresses through the chapters. The beginning of each chapter is of an introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on nonlinear stability and convergence.

This is the first complete introduction to process modelling and computing that fully integrates software tools — enabling professionals and students to master critical techniques hands on through computer simulations based on the popular MATLAB environment. The book offers a simple tool for all those oscillations that are travelling through the world, helping them discover its hidden beauty.

Many applications as well as results of computer simulations are presented. The center of concern is set on existing as well as emerging continuous methods of investigations useful for researchers, engineers and practitioners active in many and often interdisciplinary fields, where physics, electrochemistry, biology and medicine play a key role. Coverage includes:

• Dynamic behavior of nonlinear systems,

• Fundamental descriptions of processes exhibiting nonlinear oscillations,

• Mechanism and function of structures of nonlinear oscillations’ patterns,

• Analysis of dynamical oscillations in electric circuits and systems,

• Artificial intelligence models of natural systems,

• Nonlinear oscillations in chemistry, biologyand medicine,

• Oscillations in mechanics and transport systems,

• Oscillations in fractional-order systems,

• Energy harvesting systems from the surrounding environment.

With an insatiable appetite for exploring the surrounding world and doing research, this book can help readers quickly find ways to use new computers and facilitate the quest for greater knowledge and understanding of reality. The reach of novelty of the book ranges from new mathematical ideas to motivating questions and science issues in many subject areas.

Zdzislaw Trzaska received the Ph.D.  and D.Sc. degrees in electrical engineering both from the  Warsaw University of Technology, Warsaw, Poland, in 1970 and 1989, respectively.             

In 1975, he was a Visiting Professor with the Direction des Etudes et Recherches, EDF, Paris, France. In 1994, he was a Full Professor. He has published numerous papers on electric power systems and grids, stability of   power systems, distributed parameter systems and partial differential-algebraic models, analysis and design of electric circuits, and assessment via power functional. He is the author of seven books published by Polish Scientific Publisher, Publishing Office of the Warsaw University of Technology and the publishing Office of the HSE&M. His current research interests include analysis and synthesis of dynamical systems, electromagnetic and thermal fields, nanotechnology, electrochemical spectroscopy. Chaotic oscillations, DAE systems and mixed mode oscillations focus his special attention. He developed the foundations of the hitherto unsolved energy determination of components operating in the periodic non-sinusoidal state. Recently he has published in Springer-Verlag a book “Mixed Mode Oscillations (MMOs)”.