CE30 - Physique de la matière condensée et de la matière diluée

First Encounters in Complex Environments – ComplexEncounters

Submission summary

The goal of the project is to calculate analytically the statistics of encounter times between random walkers in complex environments. The first passage time (FPT), defined as the first time for two random walkers to meet « by chance », is a key property of random walk theory, notably in the context of reaction kinetics (since reactants have to meet before any reaction occurs). In general, keeping track of microscopic transport properties requires to take into account other variables than the random walker’s position, reflecting its interactions with its « complex » microscopic environment. In this case, the effective description of the reactant dynamics requires to include memory effects, which complicate the formulation of first-passage problems, and are overlooked in most FPT theories. However, microscopic complexity is clearly important for FPTs, because it determines the likelihood of a contact between two neighboring reactants. This project aims at quantifying the impact of the environment’s complex properties on first encounter times without assuming quasi-static evolution of non-reactive degrees of freedom. Here, the strategy consists in relying on a theoretical tool introduced by the PI and his collaborators to calculate mean FPTs for Gaussian random walks (Nature, 2016). This theory will be considerably developed to characterize analytically FPTs, and their fluctuations, in several classes of realistic complex media. We will calculate transport influenced encounter times between partially reactive particles moving in viscoelastic fluids (“temporal complexity”) or in locally heterogeneous media (« spatial complexity »). Characterizing encounter times in these two wide classes of complex media will indicate it they can be optimized by physical means (flows, forces, viscoelastic parameters…). Then, we will elucidate the effect of « complex structures » (when reactants are attached to complex macromolecules such as stiff DNA). Finally, we will characterize the consequences on rare transition dynamics of strong memory effects, i.e. in the joint limit of small noise and large number of degrees of freedom. These theoretical advances will reveal the key physical quantities that control encounter kinetics in complex environments.

Project coordination


The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.



Help of the ANR 220,124 euros
Beginning and duration of the scientific project: September 2021 - 48 Months

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