Indrani A. Vasudeva Murthy


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References for SOC, Statistical Mechanics and related topics

Here is a list of books, websites and papers related to complextity and SOC:


  1. How Nature Works
    Per Bak, Copernicus, Springer Verlag, New York (1996).
    This is a popular-level book on SOC and the ideas behind it.

  2. Self Organized Criticality
    Henrik Jeldtoft Jensen, Cambridge Lecture Notes in Physics:10, Cambridge University Press (1998).
    This is a more technical book than Bak's, with mathematical details.

  3. The Computational Beauty of Nature
    Gary William Flake, The MIT Press, Cambridge, Massachusetts (1998).
    This is a popular-level book, highlights the computer science point of view on complexity.

  4. Statistical Mechanics
    Kerson Huang, 2nd Edition, Wiley (1987).
    A classic text book on Statistical Mechanics.

  5. Principles of condensed matter physics
    P.M.Chaikin & T.C.Lubensky , Cambridge University Press (1995). An advanced graduate-level book on condensed matter physics.


  1. Self-organization of Complex Systems [ PDF ].
    Maya Paczuski and Per Bak, Proceedings of the 12thChris Engelbrecht Summer School, e-print (1999).
    Here is a brief overview of the SOC ideas that appear in Bak's book.

  2. Punctuated Equilibrium and Criticality in a Simple Model of Evolution [ PDF ].
    Per Bak and Kim Sneppen, Phys. Rev. Letters, 71, (24), 4083 (1993).
    This is the original paper presenting the simple Bak-Sneppen model of evolution.

  3. Punctuated equilibrium in software evolution [ PDF ].
    A.A. Gorshenev and Yu. M. Pismak, Phys. Rev. E, 70, 067103-1 (1993).
    This paper treats software evolution as an SOC process. The model is based on the Bak-Sneppen model.

  4. Flocks, herds, and schools: A quantitative theory of flocking [ PDF ].
    John Toner and Yuhai Tu, Phys. Rev. E, 58, 4, 4828 (1998).
    This paper treats flocking as a phase transition in a fluid of self-propelled objects.

  5. Turing model for the patterns of lady beetles [ PDF ].
    S.S. Liaw, C.C. Yang, R.T. Liu and J.T. Hong, Phys. Rev. E, 64, 041909-1 (2001).
    Here is a nice illustration of simulating pattern formation (on the wings of beetles) using (coupled) reaction-diffusion equations.

  6. Critical and oscillatory behavior of a system of smart preys and predators [ PDF ].
    Alejandro F. Rozenfeld and Ezwquiel V. Albano, Phys. Rev. E, 63, 061907-1 (2001).
    This paper presents a lattice-gas model of a predator-prey system, leading to phase transitions between different regimes of species densities.

  7. Self-Segregation versus Clustering in the Evolutionary Minority Game [ PDF ].
    Shahar Hod and Ehud Nakar, Phys. Rev. Letters, 88, (23), 238702-1 (2002).
    This paper presents a theory for the evolution of populations of interacting agents which can adapt themselves, using probability distributions.

  8. Evolution kinetics and phase transitions of complex adaptive systems [ PDF ].
    Bing-zhen Xu, Guojun Jin and Yuqiang Ma, Phys. Rev. E, 71, 026107-1 (2005).
    This paper is similar to the one above; it uses the diffusion equation explicitly

Websites - People and Places

Here are some websites of people and places interested in Complexity, SOC, etc.
  1. Rajesh R.Parwani. This is a nice website with interesting topics. Check out the course notes on complexity, which I found very useful. Has a lot of references too: Complexity: A course by Rajesh R.Parwani.

  2. Henrik Jeldtoft Jensen. Prof.Jensen's homepage has a lot of interesting information on complexity, SOC, and other topics.

  3. Kim Christensen. Also works on SOC and complexity.

  4. Ole Peters. Nice discussions on SOC, including rainfall models.

  5. Cosma Shalizi. A website containing an amazing number of links, references, and much more.

  6. The Santa Fe Institute. The Santa Fe Institute is dedicated to the study of all forms of complexity.

  7. Center for the Study of Complex Systems.

  8. New England Complex Systems Institute.

  9. NANIA (Novel Approach to Networks of Interacting Autonomes).This is the website of a project bringing together many-body techniques and the agent approach to study the dynamics of complex systems via computation.

  10. Complex Systems. A journal devoted to complex systems.

Simulation and other websites

  1. The Computational Beauty of Nature. This is the website of the book by Gary William Flake.

  2. Sergei Maslov's Sandpile Applet. This is an interactive Java applet of the Bak, Tang and Wiesenfeld sandpile model.

  3. A bibliography on 1/f noise. This is just to show you that 1/f noise occurs in a large number of systems.

  4. Sodaplay. This website has interesting examples of `emergent' life-like behaviour constructed out of masses and springs.

  5. Artificial Termites. Here is an artificial termite simulation. You can play with the wood-chip and termite percentage, and the size of the wood-chips. The termites move the chips into piles.

  6. Boids. This is Craig Reynolds' website on boids. It explains boids and has a large list of links to other websites on boids and similar objects, as well as a whole host of interesting topics.

  7. Physics simulation with Java. This site has nice Java simulations of several physical systems, including the double pendulum, along with the mathematical explanation.

Statistical Mechanics and Agents

  1. Statistical Mechanics Course (M.Tuckerman). Here are lecture notes providing an introduction to Statistical Mechanics, as well as some advanced stuff.

  2. The Mathematical Theory of Minority Games
    Statistical mechanics of interacting agents.

    A.C.C. Coolen, Oxford University Press (2005).
    The book's website has a link to the first few pages, giving an introduction to minority games. The book is on order right now at the Schulich Library.

  3. Agent based models. Dynamics of social systems. This is the website of one of the groups at the Cross Disciplinary Physics Department of IMEDEA, the Mediterranean Institute for Advanced Studies. There are links to presentations and publications which may be interesting.

  4. Here is a small write-up about the application of statistical mechanics and SOC ideas to epidemiology.