Bøger af Michael Bestehorn

Transport and diffusion processes are central in numerous scientific and technical applications. Prominent examples are the temperature distribution in continuous media, the flow of liquids or gases, the dynamics of reaction-diffusion systems, or the concentration distributions in mixtures. The theoretical and numerical description of these systems is based on partial differential equations. The theory of non-equilibrium thermodynamics provides a frame to derive these equations from basic conservation laws and first principles. The first part of the textbook discusses the concept of equilibrium thermodynamics and its generalization to systems in local equilibrium. Thermodynamic fluxes are defined and caused by generalized forces. Finally, linear relations, the Onsager relations, between fluxes and forces allow for a closed description. In this way, conservation equations for mass (continuity), momentum (Euler or Navier-Stokes), and energy (temperature) are derived and solved analytically or numerically for several examples. The second part is based on the kinetic gas theory describing a classical many particle system. At the example of a perfect gas the conservation equations derived phenomenologically in the first part are thereby put on statistical grounds. The textbook addresses advanced Bachelor or Master students of physics, mechanical engineering and applied mathematics.

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.

Drawing on examples from various areas of physics, this textbook introduces the reader to computer-based physics using Fortran(R) and Matlab(R). It elucidates a broad palette of topics, including fundamental phenomena in classical and quantum mechanics, hydrodynamics and dynamical systems, as well as effects in field theories and macroscopic pattern formation described by (nonlinear) partial differential equations. A chapter on Monte Carlo methods is devoted to problems typically occurring in statistical physics. ContentsIntroduction Nonlinear maps Dynamical systems Ordinary differential equations I Ordinary differential equations II Partial differential equations I, basics Partial differential equations II, applications Monte Carlo methods (MC) Matrices and systems of linear equations Program library Solutions of the problems README and a short guide to FE-tools

Auf Basis von Beispielen aus den verschiedensten Gebieten der Physik fuhrt dieses Lehrbuch in die Computerphysik mit Fortran und Matlab ein. Ausgehend von grundlegenden Problemstellungen aus der klassischen Mechanik werden (chaotische) dynamische Systeme untersucht. Feldtheorien wie Quantenmechanik, irreversible Thermodynamik und Hydrodynamik bis hin zur selbstorganisierten makroskopischen Strukturbildung bilden den zweiten Schwerpunkt des Buches. Ein Kapitel uber Monte-Carlo-Methoden und deren Anwendung in der statistischen Physik schliet die bunte Palette physikalischer Themen ab. Inhalt:EinfuhrungAbbildungenDynamische SystemeGewohnliche Differentialgleichungen IGewohnliche Differentialgleichungen IIPartielle Differentialgleichungen I, GrundlagenPartielle Differentialgleichungen II, AnwendungenMonte Carlo-Verfahren (MC)Matrizen und lineare GleichungssystemeProgramm-LibraryLosungen der AufgabenREADME und Kurzanleitung FE-ProgrammeStichwortverzeichnis

Komplett, umfassend erlautert, mit zahlreichen Aufgaben inkl. Loesungen. Diese umfassende Darstellung der Hydrodynamik vermittelt alle notwendigen Kenntnisse. Studierende profitieren vom breiten, didaktisch sehr gut aufbereiteten Spektrum dieses Lehrbuchs...