Excluded Volume Effects and Anisotropic Interactions in a System of Hard Needles

Markus Schmidtchen (TU Dresden)

Jan 29. 2026, 11:00 — 11:30

In this talk, we will present recent work on the macroscopic dynamics of a system of hard Brownian needles in two dimensions, focusing on the role of anisotropic steric interactions. Although the needles themselves have zero volume, their mutual exclusion creates a non-trivial effective volume in configuration space, significantly influencing the system’s collective behaviour. Starting from the underlying stochastic hard needle dynamics, we apply the method of matched asymptotic expansions to rigorously derive a nonlinear, non-local partial differential equation governing the evolution of the needle density in position and orientation. In the regime of strong rotational diffusion, we obtain a reduced equation for the spatial density alone and use it to compare the effective excluded volume of needle systems with that of hard spheres. Finally, we investigate spatially homogeneous solutions and demonstrate an isotropic-to-nematic transition at increasing densities, in agreement with Onsager’s theory. Our work highlights the interplay between geometry, hardcore interactions, and the emergence of order in anisotropic systems.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Modelling Diffusive Systems: Theory & Biological Applications (MoDiS) (Workshop)
Organizer(s):
Valeria Giunta (Swansea U)
Annalisa Iuorio (Parthenope U of Naples)
Angelika Manhart (U of Vienna)
Cinzia Soresina (U of Trento)