Li Jheng-Wei
le 20 février 2025
Publié le 11 décembre 2025– Mis à jour le 11 décembre 2025
Arthur Alexandre
Effective models for complex systems: From transportin channels to evolution in populations
Jeudi 20 Février 2025, 14h00, salle E4.13b
EPFL Lausanne
Effective models for complex systems:
From transportin channels to evolution in populations
Recent research challenges the traditional view that the brain is composed of densely In this seminar, I propose two problems: one from hydrodynamics and another from population genetics where an effective description enables to capture the essential mechanisms and phenomena at stake.
1)Effective description of Taylor dispersion in strongly corrugated channels [1]
Taylor dispersion is a fundamental concept in hydrodynamics that describes the enhanced spreading of tracer particles in a fluid due to the combined effects of molecular diffusion and shear flow. We investigate this problem in the context of periodic yet highly corrugated channels. Exact analytical expressions for the long-time diffusion constant and drift along the channel are derived to next-to-leading order in the limit of small channel period. Using these results we show how an effective model for Taylor dispersion in tortuous porous media can be framed in terms of dispersion in a uniform channel with absorption/desorption at its surface, an effective slip length for the flow at the surface and an effective, universal, diffusion constant on the surface. This work thus extends the concept of an effective slip-length for hydrodynamics flows to Taylor dispersion by those flows. The analytical results are confirmed by numerical calculations, and present a robust method to understand and upscale the transport properties of flows in porous media.
2.Bridging Wright–Fisher and Moran models[2]
The Wright–Fisher and Moran models are both commonly used in the field of population genetics to describe the evolution of a population of fixed size. We propose a simple and tractable model which bridges the Wright–Fisher and the Moran descriptions. We consider that the population is composed of two types (wild-type and mutant) and we assume that a fixed fraction of the population is updated at each discrete time step, thus modeling birth and death processes. In this model, we determine the fixation probability of a mutant (that is to say the probability that the mutant spreads through the population and fully replaces the wild type) and its average fixation and extinction times, under the diffusion approximation. We further study the associated coalescent process, which converges to Kingman’s coalescent. These findings highlight the concept of effective population size, which we compute within our framework. Then, we generalize our model, first by taking into account fluctuating updated fractions or individual lifetimes, and then by incorporating selection on the lifetime as well as on the reproductive fitness.