Nov 27, 2005


Avalanches are physical phenomena of great interest, mainly because they represent a big risk for those who live or visit areas where this kind of natural disaster can occur. But avalanches are very complex. They arise from an instability in a pile of granular material like sand or snow. Granular materials can be piled but just until the slope of the sides of this pile is below a critical angle. When the slope is above this angle, any extra grain added to the pile can cause a chain reaction and start an avalanche. The point is that you never know exactly when the avalanche will start.

Avalanches are an example of what is called an emergent behavior. Complex systems, which are composed by a great number of interacting unities, can show exceptional characteristics that are not expected: strange organization phenomena and surprising effects.

Although the problem of modelling granular materials seems to be something easy at first sight, it is a difficult matter and to this date we haven´t a unified theory yet. There are different approaches to attack this problem. One is to try to model granular materials a kind of fluid with special properties. It is a hydrodynamical approach. The other is to build discrete toy models and analyze them mathematically.

The second approach is related to the famous Bak-Tang-Wisenfeld model of a sandpile, where they use a bidimensional cellular automaton to model a pile where at each time step a grain is added at random in some site. When a site has a slope above a critical slope relative to its neighbours, one or more grains is transferred to this neighbour. This model turn out to have a very special behavior called Self-Organized Criticality (SOC). This behavior is rrelated to the distribution of the sizes of the avalanches in the pile and to the fact that the pile has a set of quiescent states, named metastable states, where the pile is momentarily stable.

These models can be complicated or simplified as much as we want and their study is not an easy matter once they are models that should be studied out of equilibrium, and out-of-equilibrium phenomena and, once more, we don´t have a unified theory for them too. An interesting example of a simplified model where you can see "avalanches" was sent to me last week by a friend named Marlo who found it in the internet. It is a game where you have a bidimensional cellular automaton where each site can be in one of four different states. You can change the state of one site and the interaction between states can trigger an avalanche effect. The aim is to trigger the biggest possible avalanche, although it is funny just to look at the dynamics and the metastable states to see how they look like.

My friend becomes excited with the game and said to me that this could have a lot of consequences even in sociology... well, physicists already though of this and he is right. I´ll edit this post another day and will try to put some links to show this.

Picture taken from: Milford Road.

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