BLANC - Blanc

Dynamique et Optimisation des Processus de TRansport Intermittents – DYOPTRI

Submission summary

Many transport and search processes can be analyzed in term of a succession of two types of exploring steps. This intermittency is a general feature for numerous physical, chemical, biological and industrial systems. At the microscopic scale, we can mention the diffusive motion of species in confined geometry and disordered porous media. In these interfacial systems, the trajectory of a molecule or a colloid can be decomposed as an alternate series of bulk confined excursion and localization steps near the interface. A representative example concerns the search for a specific target site on DNA by a protein, which alternates adsorption phases where the protein diffuses on the DNA strand and 3D bulk excursions. At the macroscopic scale, animals searching for food also exhibit such intermittent search behavior. Experimental studies of foraging behaviors over a broad range of animal species reveal that an intermittent behavior, combining local scanning phases and mere relocating phases is commonly observed. In all these examples, the time of transport or reaction is the limiting factor. Optimization of intermittent transport is hence a prerequisite, for instance in industrial applications or in biological processes. Two strategies are then possible. One can design and formulate an optimal confined geometry amenable to enhance (case of industrial catalyst) or moderate (case of durable diffusion barrier) a specific intermittent transport. When the restricted geometry cannot be manipulated, one can try to change the statistical nature of each elementary step of the intermittent transport. To be able to control or to formulate one of these strategies, a better understanding of the intermittent transport is needed. This is the objective of our project. It will require two main steps: 1) First, we propose to closely analyze stationary intermittent dynamics in confined geometry where periods of relocation in the bulky phase or in the pore network (bridges) alternate with adsorption or trapping steps generally located nearby an interface This subject is a domain of active research. Several groups have made important progress in various fields such as adsorbed polymers near a rough surface, impedance characteristics of rough surfaces, thermodynamics of rough surfaces, screening and accessibility by Brownian motion. We have recently attempted to clarify the role of the irregular geometry on the bridge statistics and analyzed the influence of the harmonic measure. A close domain concerns the first passage statistics and is directly related to the intermittent dynamics at longer time. A comprehensive treatise was published by Redner in 2002. We have recently obtained some results concerning first passage statistics of stochastic processes in general confining geometries. Our concern will be focused on the cross-correlation between elementary transport steps, the non-trivial properties of the time spent on the boundary, the influence of the boundary geometry (through the harmonic measure for example) and the first passage time statistics in relation with a multiscale time and space analysis of exploration. 2) Second, adding the possibility of a terminal step of reaction with a target will allow us to analyze search strategies. Since the pioneering works of Shlesinger and Klafter in 1986, the question of determining optimal search strategies has appealed a growing attention. In absence of any information about the position of the target, Lévy flights strategies have been proved to play a crucial role in such optimization problems. However, a major limitation of these strategies have to be mentioned. Lévy flights trajectories have been shown to optimize the search efficiency, but only in the particular case where the targets are regenerated at the same location after a finite time, which cannot be taken as a general rule. Alternatively to these Lévy strategies, we have elaborated and quantitatively studied a new class of search strategies: the intermittent search strategies, which combine slow scanning phases (which corresponds to adsorption phases introduced in the previous part) with mere relocating phases during which the searcher is unable to detect the target. Intuitively, the advantage of the fast phases for the searcher is to relocate into unvisited regions; the drawback being to consume time without any chance of finding the target. The net efficiency of this strategy is therefore not trivial. In this part of the project, our goal will be to determine on various theoretical models (simple geometries, fractal) and experimental systems (clayed and rod colloids, ants) when a searcher should adopt an intermittent strategy. And if so, which duration of each phase optimizes the search time? We will assess the effect of realistic confining geometry (typically irregular) on the search time, in particular on the optimal search strategy.

Project coordination

Olivier BENICHOU (Organisme de recherche)

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.

Partner

Help of the ANR 200,000 euros
Beginning and duration of the scientific project: - 36 Months

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