Institute for Complex Systems - Sapienza - CNR

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ISC Sapienza Stochastic Processes

Stochastic Processes

Research on stochastic processes



Fractal analysis of planetary topographies

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There exists an overwhelming diversity of landscapes on Earth. A cornerstone of modern geomorphology came with the realization that all the different features of the terrestrial surface result from the accumulated effect of current geological agents [Lyell, 1830]. This principle established for the first time a qualitative relationship between pattern and process in geology.

More than one century later, fractal geometry gave a theoretical framework able to provide quantitative measures for the patterns of landscapes, which were identified in a first approximation as self-similar, and triggered the research on mechanistic and theoretical models to identify the underlying constructive rules responsible for their appearance.

Last Updated on Thursday, 03 March 2011 11:19

Spatially correlated random walks and turbulence

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The wide applicability of the random walks (RW) to natural phenomena relies just on the possibility to introduce appropriate generalizations on the probabilistic nature of displacements. A straightforward generalization is realized by assuming correlations in displacements to obtain the so called correlated random walks (CRW).

This possibility extends also to a set of particles distributed in space leading to the definition of spatially correlated random walks. In this case the issue concerns what particle distribution emerges from reiterated displacements of the particles and how its properties can be directly inferred from the knowledge of the statistical correlation of the displacements.

Last Updated on Wednesday, 27 July 2011 12:42

Systems with multiplicative noise

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Problems susceptible to be mathematically represented by stochastic Langevin equations including a multiplicative noise abound not only in physics, but also
in biology, ecology, economy, or social sciences. In a broad sense a Langevin equation is said to be multiplicative if the noise amplitude depends on the state variables themselves. In this sense, problems exhibiting absorbing states, i.e. fluctuation-less states in which the system can be trapped, are described by equations whose noise amplitude is proportional to the square-root of the (space and time dependent) activity density, vanishing at the absorbing state. Systems within this class are countless: propagating epidemics, autocatalytic reactions, reaction-diffusion problems, self-organized criticality, pinning of lux lines in superconductors, etc..

Last Updated on Thursday, 03 March 2011 11:19

Dynamical Processes on Networks

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During the last decade it has become clear that the topology in many systems, ranging from technological to social to biological, is not well described by regular lattices nor by random graphs. Complex networks, characterized by small-world effects, large connectivity fluctuations, clustering, correlations and other nontrivial features are often a better description of many natural and man-made systems. Since many of such networks describe the topological patterns that mediate various sorts of interactions among nodes, it is natural and interesting to wonder what is the effect of complex topologies on dynamical processes taking place on them.

Last Updated on Monday, 17 November 2008 10:28