Population and Dissipative Dynamical Systems

Airplane vortex. courses.gnowledge.org/lessonsview?ssid=3394

Dissipative systems are those that use the energy to maintain their form, as the atmospheric vortexes or alive organisms. If we consider for ex., a pendulum, under ideal conditions it would not stop, but under normal conditions, it would arrive to its point of minimum energy to continue moving and then it would stop. Now, if we take a multidirectional system of pendulums, small interferences could cause an avalanche in the system. These interferences can grow and spread through the system with very little resistance. As the energy vanishes in this process, this should be fed so that the avalanches continue.

Landslide induced by an earthquake over a neighborhood near Santal Tecla, El Salvador. 2001.http://carletong.files.wordpress.com/2009/04/landslide1.jpg

Another simple example would be that of the pile of sand. If we slowly add sand to a pile full with sand, a re-accommodation of particles will only take place. The individual grains of sand (or grades of freedom) will not interact in big distances. Continuing the process, we will end up increasing the pile achieving a critical value, with a slope that will produce an avalanche. The pile cannot already be described by means of local degrees of freedom. The distribution of avalanches follows a law of power.

The dissipative systems act opposing to the intent of displacing them of the state where they are. That is to say, they contain regulatory properties. In the dissipation, in the irreversibility, in the lost of equilibrium, is the key of evolution.

Mechanically speaking, dissipative systems are dynamical systems that are characterized by an “internal friction” that tends to contract phase space volume elements. Phase space is a mathematical space spanned by the dependent variables of the dynamical system. In our example of the pendulum, it has a one-dimension movement with a two-dimensional phase space spanned by the position and momentum variables.

These theoretical aspects are not exclusive of the physics, they are also applicable in urban morphology to population's limitless growth, to the ¨urban sprawl¨, and its search of organization levels; to cities and buildings’ overcrowding; to conventillos generation; to the multiple illegal constructions; “hot beds” (camas calientes) habits, usually the result of continuous arrival of immigrants. Severe analogical cases are the refugees coming massively to a country, local habitants being the original “pile of sand”. The system will reach a critical point where the internal regulatory properties will intend to look for the equilibrium. These properties may be reflected in the law, the “razzias”, the deportations, or the provision of dwellings and jobs opportunities, among other situations.

Refugees from Rwanda arrive in Tanzania. Photo by UNHCR/ P. Moumtzis. http://nocameranointervention.files.wordpress.com/2009/03/refugees9.jpg

The energy models provide us helpful analytic tools that explain the development of the societies, their collapse, the wars, the religions. It is considered that the human communities are dissipative systems, because they are in constant fluctuation, and life is in itself an expansible process.

Further readings (for glossary)
http://www.cna.org/isaac/Glossb.htm#Dissipative