Mathematical Modelling and Computing in Physics, Chemistry and Biology: Fundamentals and Applications

ISBN-13: 9783031399848 / Angielski

Zdzislaw Trzaska

Spis treści

Contents

 

1. Introduction to dynamical systems ……………………………………………….1

1.1. Cornerstone …………………………………………………………………………….. . 1

1.2. Concise Characterization of Natural Systems. . . . . . . . . . . ………. . . . . .  …………… 4

1.3. Relevance and Emergence of Natural Systems……………………………....................7

1.4. Unusual Behavior of Complex Dynamical Systems …………………………………. 9

1.5. Entropy of Complex Processes in Dynamical Systems……. ……………………….. 10

1.6. Instantaneous States of Dynamical Systems …………….……… ………………......13

            References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . ………. . .. . ... ..   29

2. Basic ingredients of nonlinear systems dynamics

2.1. Background…………………………. . . . . . . . . . . . . . .….….. . ……... . ….. . . .. . . …xx

2.2. Nonlinear Phenomena and Nonlinear Equations ……………………………………..  xx

2.3. Mathematical Modeling of System Dynamics. . . . . . . .. . . . . . . . … ….. .. … . .. …..  xx

2.3.1. Elementary Nonlinearities …...................…………………………………….…….. xx

2.3.2. Nonlinear Oscillators Solvable in Elementary Functions . . . ……………………. ... xx

2.4. Models of Complex Nonlinear Dynamic Systems …………………………………….  xx

2.4.1. Basic forms of Systems Oscillations..………………………………………………... xx

2.4.2. Systems under Periodic Pulsed Excitation…………………………………………… xx
2.4.3. Regular Periodic Impulses  . . . . . . . . . . . . . . . . . . . . . . . . …………………………. . xx

2.4.4. Harmonic Oscillator under the Periodic Impulsive Loading ………………….…....... xx

2.4.5. Periodic Impulses with a Temporal ‘Dipole’ Shift  . . ……………………………… xx

2.4.6. Fractional Order Differential Models ………………………………………………..xx

2.4.7. Artificial intelligence models………………………………………………………… xx

2.5. Mixed-Mode Oscillations ……………………………………………………………… xx

2.6. Stability and Bifurcation of Dynamic States ……………….………………………….. xx

2.7. Chaotic oscillations ……………………………………………………………………. xx

      References …………………………………………………………………………….... xx

 

3. Oscillations in physical systems  ………………………………………………..  xx

3.1. Lorenz System and Its Properties ……………………………………………………  xx

3.2. Logistic Equation and Its Applications ……………………………………………… xx

3.3. Predator–Prey Systems ………………………………………………………………. xx

3.4. The Two-Body Problem ……………………………………………………………… xx

3.5. Systems with the Double Scroll Attractors …………………………………………… xx

3.6. Applications of van der Pol Equation ……………………………………………….. xx

3.7. The Rössler Attractor ………………………………………………………………… xx

3.8. Furuta’s Pendulum Dynamics ……………………………………………………….. xx

3.9. Dynamic Analysis of the Nonlinear Energy Harvesting System …………………… xx

3.10. Duffing’s Forced oscillator ………………………………………………………….. xx

3.11. Chain of oscillators ………………………………………………………………….. xx

3.12. Oscillator with Weak or Strong Dissipation ………………………………………… xx

3.13. VSI Fractional Dynamical System  …………………………………………………. xx

3.14. Characteristics of the Water Natural Hammer …………………………………….. xx

 

4. Oscillatory Chemical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . ……………………………xx

4.1. Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ………………  xx

4.2. Enzyme Kinetics ……………………………………………………………………… xx

4.3. Autocatalysis, Activation and Inhibition ……………………………………………… xx

4.4. Oscillations in Chemical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …………..   xx

4.5. BZ Oscillating Reactions …………………………………………………………….. xx

4.6. Limit Cycle Oscillations in the BZ Reaction ………………………………………… xx

4.7. Numerical Simulations …………………………………………………………………. xx

4.8. The Mathematical Model of Electrochemical Reactors . . . . . . . . .…………………….. xx

4.9. MMOs in Electrochemical Reactors . . . . . . . . . . . . . . . . . . . . . . . . . …………………   xx

      References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ………………………  .   xx

5. Oscillations in Biological Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ………..   xx

5.1. Motivation, Brief History and Background . . . . . . . . . . . . . . . . . . . . . . . . …………..   xx

5.2. Feedback Control Mechanisms ………………………………………………………  xx 5.3. Parameter Space for Oscillations ……………………………………………………..  xx

5.4. The Hodgkin–Huxley Neuron with MMOs . . . . . . . . . . . . . . . . . . …………………...   xx

5.4.1. Basic Mathematical Model ………………………………………………………… xx

5.4.2. Periodic Neuron Firing ………………………………………………………………  xx

5.5. Reduced Model of a Single Neuron Activity . . . . . . . . . . . . . ………………………… xx

5.6. Nonlinear Human Cardiovascular System . . . . . . . . . . ………… ………………....... xx

5.6.1. Concise Characterization of a Cardiovascular System . . . ………………………......  xx

5.6.2. Thermodynamic Model of the Cardiovascular System Dynamics . . . . . . ………......  xx

5.6.3. MMOs as an Indicator of Illness in the Cardiovascular System . . . . ………………... xx

5.7. Models of Non-Linear DNA Dynamics ……………………………………………… xx

        References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …………………………

6. Energy Flow Analysis of Nonlinear Dynamical Systems …………………  xx

6.1. Introduction and Short Historical References………………………………………… xx

6.2. New Standards for the Energy Avenue in Non-Sinusoidal States …………………… xx   

6.2.1. Preliminary………………………………………………………………………….. xx

6.2.2. Hysteresis Loops on Energy Phase Plane………………………………………….. xx

6.2.3. Quantitative Measures of The Energy Hysteresis Loop……………………………. xx

6.2.4. Estimates for One-Period Energy Loops …………………………………………… xx

6.2.5. Analysis for Energy Aspects in Dynamical Systems With Switches ………………. xx

6.3. The Energy Approach to Electrochemical Corrosion Studies of Nano-Copper Coatings xx

6.3.1. Introduction ………………………………………………………………………...  xx

6.3.2. The One-Period Energy Approach …………………………………………………  xx

6.3.3. Experiments ………………………………………………………………………… xx

6.3.4. Results and Discussion ……………………………………………………………. . xx

6.4. Effective Harvesting of Braking Energy in Electric Cars ………………. ……… xx

6.4.1. Introduction …………………………………………………………………………. xx

6.4.2. Energy Losses in Sub-Systems of Electric Cars …………………………………… xx

6.4.3. Energy Regeneration in Subsystems of Electric Cars ……………………………… xx

6.4.4. Modification of the Car Brake Sub-System ………………………………………… xx

6.4.7. Simulations …………………………………………………………………………. xx

6.4.8 Summary and Conclusions ………………………………………………………….. xx

6.5. Electromechanical System for Charging Batteries of Electric Cars ………………. xx

6.5.1. Introduction ………………………………………………………………………… xx

6.5.2. Principle of Batteries Charging with the Faraday Disk Generator ………………… xx

6.5.3. Battery Property And Modeling ……………………………………………………… xx

6.5.4. Electro-magnetic-mechanical Model of the Faraday Disk Generators……………… xx

6.5.5. Structure of the Charging System …………………………………………………… xx

6.5.6. State-space Equations ………………………………………………………………  xx

6.5.7. Computer Simulations ……………………………………………………………… xx

6.5.8. Discussion and Ssummary ……………………………………………………………xx

6.6. Modeling of Energy Processes in Wheel-Rail Contacts Operating under      

        Influence of Periodic Discontinuous Forces ……………………………………….. xx

6.6.1. Introduction …………………………………………………………………………xx

6.6.2. The Problem Description …………………………………………………………..   xx

6.6.3. Dynamic Model of Wheel-Rail Contacts ………………………………………….. xx

6.6.4. Exact Periodic Solutions …………………………………………………………… xx

6.6.5. Application of One-Period Energy Approach ……………………………………… xx

6.6.6. Sleeper Nonlinear Characteristics ………………………………………………….. xx

6.6.7. Discussion and Summary …………………………………………………………… xx

         References …………………………………………………………………………..   xx

 

7. Artificial Intelligence in the Service of Dynamical Systems …………… xx

7.1. Background of AI Modeling ………………………………………………………  . xx

7.2. Artificial Neural Network ……………………………………………………………. xx

7.3. Fuzzy Logic Models …………………………………………………………………. xx

7.4. Agent‐based Modeling ……………………………………………………………….. xx

7.5. AI ability to understand and communicate with people ………………………………xx

7.6. AI in improvement of health quality and security …………………………………… xx

7.7. Real-life Artificial Intelligence Applications ………………………………………..    xx

       References ……………………………………………………………………………   xx

 

 

Subject Index …………………………………………………………………………..… xx

O autorze

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)”.

Blurb

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 modeling 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, biology and 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