Accumulation and absorption of active particles at surfaces
Project Description
Active matter provides a powerful quantitative framework for understanding complex biological processes by examining the interplay between self-organizing, energy-consuming particles and their surrounding environment. Systems such as motile bacteria, self-propelled colloids, or cytoskeletal filaments exemplify this paradigm. Canonical models include run-and-tumble particles (RTPs), which change direction through discrete reorientations, and active Brownian particles (ABPs), whose motion combines constant propulsion speed with rotational diffusion. While the local energy consumption puts these systems inherently out-of-equilibrium, in isolation, active particles seen at long enough time and large enough distances remain diffusive; true nonequilibrium features stem from the interactions of active particles with their environment.
For instance, when confined within a channel, active particles tend to accumulate at the channel walls, even in the absence of inter-particle interactions. This is in clear contradiction with equilibrium Boltzmann distributions. Each particle pushes against the wall until a tumbling event or rotational diffusion redirects its motion enough that they can scatter off; this makes the wall behave like a sticky boundary. At the multi-particle level this results in a pressure being exerted on the confining walls. This behavior can also be described in terms of so-called sticky boundary condition: upon colliding with the wall, a particle remains attached for a random time governed by its tumbling dynamics. The degree of stickiness is characterized by the escape time back into the bulk; it spans from totally reflecting boundaries (instantaneous escape) to totally absorbing ones (permanent adhesion), with intermediate cases characterized by partial retention. Sticky boundary conditions are also relevant in understanding biological phenomena such as the dynamics of growing and shrinking polymer filaments.
Extending this concept, partially permeable walls introduce another layer of complexity. Particles interacting with sticky boundaries may either re-enter the bulk or escape permanently, leading to a distinct set of behaviors compared to impermeable walls. In this scenario, the system lacks a steady-state density for particle position and orientation, and attention shifts to dynamic quantities like the mean first passage time (MFPT) for permanent absorption and its higher-order moments. These features underscore how the interactions between active particles and their environments drive nonequilibrium phenomena central to active matter systems.
Main objectives of the project
The main goal of this project is to combine nonequilibrium statistical physics, mean field theory, and multi-scale computation to investigate the accumulationof particles. Recent studies have started to extend the equilibrium theory of wetting to systems of active particles showing that the stiffness of the wall controls a transition to wetting. We will here similarly study the condition of emergence of a wetting transition as a function of the absorption behaviour of the wall.
• First-passage statistics – At the particle level, our study will also focus on determining important first-passage statistics including the mean first-passage time for single-particle absorption at a permeable wall as well as the extremal statistics of absorption in the case of multiple particles, quantifying for instance, first absorption times.
• Theory of particle-surface interactions – We will develop a microscopic theory of particle-surface interactions and how this affects the accumulation and absorption of particles, including for flexible and active interfaces (modelling for instance a biological membrane).
• Breakdown of mean-field – Throughout the project, we will compare large-scale particle-based simulations and mean-field analytical arguments. We will then investigate the breakdown of mean field theory due to the absorption and removal of particles from the population.
Details of Software/Data Deliverables
The success of this project will rely on the development of a number of advanced numerical simulations:
numerical algorithms for a large-scale computational exploration of a variety of minimal systems in statistical mechanics including efficient sampling techniques to explore rare events, extremal statistics and first-passage time statistics;
development of efficient numerical algorithms for systems of coupled SDEs;
purpose-built, scalable and adaptable software implementing advanced numerical solutions to highly nonlinear systems of PDEs and SPDEs to solve our mean-field models.
