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Abstract |
In this talk, I will recall some results I got during my PhD and show new results obtained since then. In a
second part, I will present part of the results I got during my postdoc in Geneva.
The question of first-passage time, typically the time needed for two particles to encounter, is of
importance to quantify the rate of reaction of any diffusion-limited process. If the problem is essentially
solved for markovian (that is memoryless) random walks such as brownian motion, only sparse results do
exist for non-markovian random walks. I will present a formalism we have developed to quantify the mean
first passage time to a target for a confined non-markovian random walker, whose position statistics is
gaussian and with stationary increments. Then, I will present some features of confined ageing processes
(that is : if the stationary increments hypotheses is relaxed), and decipher the links with the associated
unconfined processes. In particular, the importance of the so-called persistance exponent will be
emphasised. I will finally show how our gaussian formalism can be extended to ageing unconfined
processes in order to get the value of the persistance exponent.
In a second part, I will present a physical description of the actin cytoskeleton, which is a layer of fibers in
interaction with molecular motors. This layer is polymerizing along the plasma membrane. Usual model
typically see it as a thin layer, that is neglecting the dynamics in the direction orthogonal to the membrane.
I will show that a more precise description that account for this direction leads to a new instability
mechanism that cannot be observed within the thin-layer approach. Finally, I will briefly mention
experimental works in agreement with this predicted instability. |
