Statistical Physics and Interdisciplinary Applications

When we try to study the organization and the properties of ecological systems, non-equilibrium statistical physics is a natural candidate to develop a unified framework for understanding the emergent properties of these kind of systems. Simple interacting particle systems, such as the Voter Model (VM), have found a surprisingly good agreement with empirical data and proved to be a useful null-model that can be treated analytically. Despite the recent progress in this field, still a major issue in ecology and conservation ecology is to understand the effects of habitat fragmentation and heterogeneities on the biodiversity of an ecosystem. Motivated by this open problem, we study the effects of quenched spatial disorder on the long-time behavior of the VM and its nonlinear generalizations.

In my report I will show that the secondary structures of random
heteropolymers undergo a topological transition. Namely, for c less than the critical value the fraction of "active'' nucleotides (which form the base pairs) tends to 1 as the length of the chain goes to infinity, signaling the formation of a virtually "perfect'' secondary structure without gaps. In turn,
for c > c_{cr} always a non-perfect structure with gaps is formed. It was proved mathematically that 2 < c_{cr} < 3; our current research deals with determination a value of transition point; it directly connects with developing new methods to generate random sequences with "effectively" non integer alphabet.
Our previous results have shown that transition point is very close to alphabet used by Nature in real RNAs. Such a critical behavior can point to some statistical exclusivity of natural alphabet.