Dietrich Stauffer’s research while affiliated with University of Cologne and other places

The nonlinear Barabási–Albert network (NLBA) of Krapivsky, Redner and Leyvraz (2000) is reinvestigated and modified here. We check the distribution of k(i) versus i for strong peaks and sharp gaps, where node number i has k(i) neighbors. No gaps as seen in our earlier studies of directed networks are found now, but strong peaks occur in our modified version nonlinear Barabási–Albert networks (NLBA2) while they show up only if the nonlinearity exponent is larger than one in the traditional version (NLBA1).

Cooperation is fundamental for the long-term survival of biological, social, and technological networks. Previously, mechanisms for the enhancement of cooperation, such as network reciprocity, have largely been studied in isolation and with often inconclusive findings. Here, we present an evolutionary, multiagent-based, and spatially explicit computer model to specifically address the interactive interplay between such mechanisms. We systematically investigate the effects of phenotypic diversity, network structure, and rewards on cooperative behavior emerging in a population of reproducing artificial decision makers playing tag-mediated evolutionary games. Cooperative interactions are rewarded such that both the benefits of recipients and costs of donators are affected by the reward size. The reward size is determined by the number of cooperative acts occurring within a given reward time frame. Our computational experiments reveal that small reward frames promote unconditional cooperation in populations with both low and high diversity, whereas large reward frames lead to cycles of conditional and unconditional strategies at high but not at low diversity. Moreover, an interaction between rewards and spatial structure shows that relative to small reward frames, there is a strong difference between the frequency of conditional cooperators populating rewired versus non-rewired networks when the reward frame is large. Notably, in a less diverse population, the total number of defections is comparable across different network topologies, whereas in more diverse environments defections become more frequent in a regularly structured than in a rewired, small-world network of contacts. Acknowledging the importance of such interaction effects in social dilemmas will have inevitable consequences for the future design of cooperation-enhancing protocols in large-scale, distributed, and decentralized systems such as peer-to-peer networks.

The energy balance $E=h\nu$ of the quantum-mechanical photo effect looks so simple but we have to go to the unsteady perturbation theory at the end in order to understand it.

Taking Boltzmann’s probability $\sim \exp (-E/kT)$ as the basic axion, we derive both classical thermodynamics of the 19th century as well as quantum statistics and critical phenomena from the 20th century.

From Kepler’s laws to hydrodynamics via Lagrange and Hamilton functions this first chapter covers classical mechanics, i.e. without relativistic or quantum effects.

Dynamical systems theory offers a different, geometrical view for describing the evolution of a system. It leads to the puzzling notions of deterministic chaos and universal routes to chaos.

Random walks and Sierpinski gaskets are used to introduce fractal dimensions, and diffusion limited aggregates finish this “dessert”, which is closely related to the critical exponents at the end of the previous chapter .

From Coulomb’s law $\text {force = charge}_1\times$ charge$_2/$distance$^2$ to Einstein’s relativistic electrodynamics of moving bodies, via Maxwell equations with and without matter, we need to get to this chapter’s end to understand why the above equality is not merely a proportionality, in our CGS units: Magnetic fields are the relativistic corrections to the electric fields.

This textbook takes the reader on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, as well as the most modern and exciting of all: elementary particles and the physics of fractals. The second edition has been supplemented with a new chapter devoted to concise though complete presentation of dynamical systems, bifurcations and chaos theory. The treatment is confined to the essentials of each area, presenting all the central concepts and equations at an accessible level. Chapters 1 to 4 contain the standard material of courses in theoretical physics and are supposed to accompany lectures at the university; thus they are rather condensed. They are supposed to fill one year of teaching. Chapters 5 and 6, in contrast, are written less condensed since this material may not be part of standard lectures and thus could be studied without the help of a university teacher. An appendix on elementary particles lies somewhere in between: It could be a summary of a much more detailed course, or studied without such a course. Illustrations and numerous problems round off this unusual textbook. It will ideally accompany the students all along their course in theoretical physics and prove indispensable in preparing and revising the exams. It is also suited as a reference for teachers or scientists from other disciplines who are interested in the topic.