Laboratoire de Physique Théorique
Toulouse - UMR 5152

In this talk, I will present part of the results I got during my PhD, and part of those obtained during my first postdoc.

I) The computation of the encounter time of particles is a key question in many contexts, as this time quantifies the reactivity rate for diffusion-limited processes. In the case of markovian random walks, such as brownian motion, some analytic results can be obtained. But in the case of non-markovian processes, much fewer results do exist, although "non-markov is the rule and markov is the exception" (Van Kampen). In this talk I will present a formalism we have developed to deal with non-markovian random walks and show its application to Fractional Brownian Motion, a paradigmatic example of highly-correlated process. If I have enough time, I will briefly present how aging of the dynamics can deeply modify the encounter time statistics.

II) In the second part of my talk, I will briefly present results I got during my first postdoc. I will show how chaotic motion can arise in an extended active gel layer, typically describing cortical cytoskeleton, where polymerization and contraction due to molecular motors are combined. This result questions the usual description of the cortex as a thin layer, as such a description cannot describe this instability. I will also briefly present recent experimental evidences of this predicted phenomenon.