Marco Baiesi (Padova), Giambattista Giacomin (Paris), Yariv Kafri (Haifa), Hervé Kunz (Lausanne), David Mukamel (Rehovot), Julien Poisat (Lyon).

A conformation with two long polymers in a double-helical form is unstable at high temperature. In this condition, the dynamics leading to separated chains is characterized primarily by the unwinding of the chains. With simulations on a three-dimensional lattice we show that the unwinding time scales as a power of the polymer length. The exponent of this power-law is close to 2.6. Other simulations, with a Poland-Scheraga model taking into account the local helical state, suggest the existence of a second characteristic time that scales roughly as the cube of the polymer length. A time scale like this can be derived from theoretical arguments in which one considers a dynamics passing through equilibrium-like configurations.

Giambattista Giacomin (Paris): Disorder and critical phenomena in pinning models. pdf

The thermodynamics of disordered pinning models has attracted much attention both for this model naturally emerges in a variety of contexts (notably, DNA denaturation) and because it represents an ideal framework in which to tackle the important issue of understanding if and how disorder modifies the critical behavior of a system. The aim of this talk is to review and discuss the mathematically rigorous results available for this model, with particular attention to the effect of noise on the critical behavior.

Yariv Kafri (Haifa): Dynamics of DNA melting.

The talk will considers the dynamics of loops at the DNA denaturation transition. A scaling argument is used to evaluate the asymptotic behavior of the autocorrelation function of the state of complementary bases (either open or closed). The long-time asymptotic behavior of the autocorrelation function is expressed in terms of the entropy exponent, c, of a loop. The validity of the scaling argument is tested using a microscopic model of an isolated loop and a toy model of interacting loops. This suggests a method for measuring the entropy exponent using single-molecule experiments such as florescence correlation spectroscopy.

Hervé Kunz (Lausanne): Critical behaviour of a model of DNA melting and wetting in the absence or presence of disorder.

Presentation of the model introduced by Lifson-Poland-Sheraga for DNA melting. Some wetting problems are equivalent to it. Summary of the original model (no disorder). In the case of weak disorder an extension of the model is reduced to a matrix field theory. A mean field treatment of it shows how disorder affects the critical behaviour.

David Mukamel (Rehovot): Denaturation of circular DNA. pdf

The denaturation transition of circular DNA is analyzed by extending the Poland-Scheraga model to include the winding degrees of freedom [1]. In this topology the winding number of the helix is conserved. The resulting denaturation transition is found to be rather different from that of linear DNA. Assuming that the winding number which is released by loops formation is absorbed by supercoiles, it is shown that the model exhibits no transition for loop exponent c<2. However for c>2 a continuous transition with arbitrary high order as c approaches 2 is found. The transition becomes second order for c>3.
[1] Amir Bar, Alkan Kabakcioglu, David Mukamel, Phys. Rev. E 84, 041935 (2011).

Julien Poisat (Lyon): Disordered pinning model with weak correlations.

The pinning model is a statistical mechanics model based, in its general form, on a renewal process in a disordered potential, and models a variety of situations such as DNA denaturation. Recently a lot of work has been done on the influence of i.i.d. disorder on the phase transition features of the model, in accordance with Harris criterion. In this talk we study the case of disorder with finite range correlations, via Markov renewal theory, and discuss a possible extension of the method to the case of infinite - but decaying fast enough - correlations.