In this project we plan to use ideas and techniques from the
Statistical Mechanics of Disorder Systems to clarify the behavior of
a number of systems of high complexity, both developing useful and new
techniques and by focusing on systems of biological interest,
and connecting to active matter agent based models and to interesting
descriptions of systems in Neuroscience. We will on one side study
paradigms of disordered statistical mechanics, the so called spin
glasses, also in connection with recent. modern experiments on spin
glass films. We will work to improve methods to integrate the
equations of motion of system of high complexity, and work on
the Renormalization Group approach to systems of active matter.
We believe that all of the activities we are planning can potentially
lead to very interesting results.
We have a large experience in the analysis of spin glass systems. Our
numerical simulations, also thanks to Janus, the programmable
dedicated super computer we have built, are very large scale and are
able to give us a large amount of information.
As far as neurosciences are concerned we are testing new ideas,
concerning patterns with ultrametric correlations, and we believe that
our approach could really give very useful contributions.
Our study on active systems, both theoretical and experimental, have
had a large impact, and created, we believe, a new state of the
art. We believe that the developments that we propose here, that go in
the direction of a precise rigorous analysis of the system, will
probably also lead to results of large impact and resonance.
We also feel that the integration algorithms we have and we will
developed will be useful in many contexts.