Excluded volume and order in systems of Brownian needles

Maria Bruna (U Cambridge)

Nov 22. 2022, 10:00 — 10:45

We study the role of anisotropic steric interactions in a system of hard Brownian needles in two dimensions. Despite having no volume, non-overlapping needles exclude a volume in configuration space that influences the macroscopic evolution of the system. Starting from the stochastic particle system, we use the method of matched asymptotic expansions and conformal mapping to systematically derive a nonlinear nonlocal partial differential equation for the evolution of the population density in position and orientation. We consider the regime of high rotational diffusion, resulting in an equation for the spatial density that allows us to compare the effective excluded volume of a hard-needles system with that of a hard-disks system. We further consider spatially homogeneous solutions, leading to a periodic  McKean-Vlasov equation, and find an isotropic to nematic transition as density increases, consistent with Onsager's theory.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Mathematical Methods for the Study of Self-organization in the Biological Sciences (Thematic Programme)
Pierre Degond (IMT)
Marie Doumic (Sorbonne U, Paris)
Anna Kicheva (ISTA, Klosterneuburg)
Sara Merino-Aceituno (U of Vienna)
Christian Schmeiser (U of Vienna)