The work shows, by means of examples coming from different corners of physics, how physical and mathematical questions can be answered using a computer. Starting with maps and neural networks, applications from Newton's mechanics described by ordinary differential equations come into the focus, like the computation of planetary orbits or classical molecular dynamics. A large part of the textbook is dedicated to deterministic chaos normally encountered in systems with sufficiently many degrees of freedom.
Partial differential equations are studied considering (nonlinear) field theories like quantum mechanics, thermodynamics or fluid mechanics. In the second edition, a new chapter gives a detailed survey on delay or memory systems with a direct application to epidemic and road traffic models.
Most of the algorithms are realized in FORTRAN, a language most suitable for effectively solving the discussed problems. On the other hand, the codes given and presented on the book's homepage can be easily translated into other languages. Moreover, several MATLAB examples are presented, mainly for didactic reasons. The book is addressed to advanced Bachelor or Master students of physics, applied mathematics and mechanical engineering.
About the Author: After completing his PhD in 1988 Michael Bestehorn worked as a scientific assistant at the Institute for Theoretical Physics and Synergetics, University of Stuttgart. In 1991 he spent one year working at the University of Navarra (Pamplona, Spain) on an EC (EU) -funded research grant. In 1995 he completed his Habilitation and he obtained the Venia Legendi in Theoretical Physics at the University of Stuttgart. Between 1995 and 1999 he was a Privat Dozent at the University of Stuttgart before becoming a full Professor at Brandenburg University of Technology Cottbus in 1999. In 2007/08 he was a visiting professor at Norwegian University of Life Sciences, Aas, Norway. In 2011 he was a visiting professor at Reservoir Engineering Research Inst. Palo Alto, USA. In 2015 he was a visiting researcher at Swinburne University of Technology, Melbourne, Australia.
Michael Bestehorn's expertice is in theoretical fluid dynamics and macroscopic pattern formation in non-equilibrium complex systems, including interfacial hydrodynamic instabilities, oscillatory instabilities in binary mixtures, thin liquid films, chemical non-equilibrium reactions, and light-matter interaction at interfaces. Recent work is devoted to epidemic models including stochastic and delay effects. He published more than 150 journal articles and three monographs that attracted over 3600 citations, his h-index is 35. In 2016 he chaired the 8th Conference of the International Marangoni Association in Bad Honnef, Germany. He was a lead researcher in several international projects, including the EU-funded project on the Application of the Phase-Field model to study boundary layers at liquid-liquid and liquid-gas interfaces (2000-2004) and the Convection and Interfacial Mass Exchange program (CIMEX), funded by the European Space Agency (2000-2008). He is currently leading the DFG (Deutsche Forschungsgemeinschaft) funded project on the Transport and mixing in parametrically excited fluid layers. He is a referee in numerous high-ranked journals: Physical Review A, E, Fluids, Physical Review Letters, Physics of Fluids, Journal of Fluid Mechanics, European Physical Journal, Fluid Dynamics Research, Langmuir, Advances in Water Resources. Throughout his career, Bestehorn has initiated and was a part of numerous international collaborations. The list of his co-authors contains 50 reputable names, including Hermann Haken of Stuttgart University, the founder of modern Synergetics, an interdisciplinary science that explains self-organization and pattern formation in open systems far from equilibrium.
Michael Bestehorn has made substantial contributions in the fields of fluid dynamics and nonlinear complex systems, covering such topics as Rayleigh-Bénard and Bénard-Marangoni convection, Rayleigh-Taylor, Kelvin-Helmholz and Faraday instabilities, liquid film dewetting and evaporation, interfacial mass and energy transfer, tidal waves and laser ablation patterns.
