Brownian Agents and Active Particles

1. Front Matter

   Pages I-XVI

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2. Complex Systems and Agent Models

   Pages 1-49

3. Active Particles

   Pages 51-131

4. Aggregation and Physicochemical Structure Formation

   Pages 133-173

5. Self-Organization of Networks

   Pages 175-201

6. Tracks and Trail Formation in Biological Systems

   Pages 203-245

7. Movement and Trail Formation by Pedestrians

   Pages 247-266

8. Evolutionary Optimization Using Brownian Searchers

   Pages 267-293

9. Analysis and Simulation of Urban Aggregation

   Pages 295-333

10. Economic Agglomeration

    Pages 335-355

11. Spatial Opinion Structures in Social Systems

    Pages 357-385

12. Erratum

    • Publisher

    Pages e1-e1

13. Back Matter

    Pages 387-420

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When we contemplate phenomena as diverse as electrochemical deposition or the spatial patterns of urban development, it is natural to assume that they havenothing incommon. Afterall,therearemanylevelsinthehierarchythat builds up from atoms to human society, and the rules that govern atoms are quite di?erent from those that govern the geographical emergence of a city. The common view among many, if not most, biologists and social scientists is that the devil is entirely in the details. This school of thought asserts that social science and biology have little or nothing in common, and indeed many biologists claim that even di?erent ?elds of biology have little in common. If they are right, then science can only proceed by recording vast lists of details that no common principles will ever link together. Physics, in contrast, has achieved a parsimonious description for a broad range of phenomena based on only a few general principles. The phenomena that physics addresses are unquestionably much simpler than those of biology or social science, and on the surface appear entirely dissimilar. A cell is far more complicated than a pendulum or an atom, and human society, being builtoutofagreatmanycells,isfarmorecomplicatedstill. Cellsandsocieties have many layers of hierarchical organization, with complex functional and computational properties; they have identities, idiosyncracies stemming from an accumulation of historical contingency that makes them impossible to characterize in simple mathematical terms. Their complexity is far beyond that of the simple systems usually studied in physics.

• agent based simulations
• agents
• brownian agents
• calculus
• complex networks
• complex system
• complex systems
• computer simulation
• evolution
• multiagent models
• optimization
• simulation

From the reviews:

"Schweitzer's approach is gradual. The first four chapters are devoted to introducing more and more complexities and subtleties in the Brownian agent models, and the focus is on the models themselves rather than on the systems… Reading and understanding these chapters may be a difficult time-consuming task, but the reward is high. Starting from chapter five (on tracks and trail formation in biological systems) and ending with chapter ten (on opinion formation), the reader can amuse him/herself in dealing with models of real systems and devote his/her attention to the more relevant issues for his/her research.

"This book contains some gems. My favorite one is in chapter nine: the discussion of a spatial dynamic model for the labor market introduced by the well-known US economist Paul Krugman where "workers are assumed to move toward locations that offer them higher real wages". Schweitzer shows not only that Krugman's model is nothing else that an instance of a selection equation of the Fisher-Eigen type, but also, using the formalism developed previously, he can easily generalize it and question the economic meaning of the assumptions leading to Krugman's equations.

"I can recommend this book to all those working in the field of complex systems. They will find a detailed survey of the Brownian agent method and they might get good hints for further research in some of the fascinating fields herein discussed."

- Enrico Scalas (econophysics.org)

"[…] the author explores such diverse topics as pattern formation in reaction diffusion systems, self organisations of networks, tracks and trail formations in biological systems, movement and trail formation by pedestrians, urban aggregation, economic aggregations and spatial opinion structures in social systems. The topics are selected thoughtfully and the presentation is lucid. It is an extremely useful text for graduate students who arethinking of working on some problem in non equilibrium statistical physics." (Jayanta K. Bhattacharjee, Indian Journal of Physics 2004, vol. 78, page 1011)

"This book is organized around two ideas. First, the link between the micro- and the macro-behaviour of systems and secondly, the idea of a Brownian agent. … Many of these models and ideas have been circulating for some time and will be found in specialist publications. It is helpful to have them brought together and systematically expounded in this book which both unifies what exists and paves the way for new developments." (Professor D. J. Bartholomew, Contemporary Physics, Vol. 45 (4), 2004)

"The aim of the book is to show that a large set of phenomena in natural and social sciences can be studied by writing down equations of motion for the pertinent Brownian agents. … The topics are selected thoughtfully and the presentation is lucid. It is an extremely useful text for graduate students who are thinking of working on some problem in non equilibrium statistical physics." (Jayanta K Bhattacharjee, Indian Journal of Physics, Vol. 78 (9), 2004)

• ETH Zürich, Zürich, Switzerland

  Frank Schweitzer

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