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DY: Fachverband Dynamik und Statistische Physik

DY 59: Brownian Motion and Anomalous Diffusion

DY 59.11: Vortrag

Freitag, 22. März 2024, 12:15–12:30, BH-N 334

Langevin Dynamics of Oriented Active Particles on Curved Surfaces — •Balázs Németh and Ronojoy Adhikari — Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

The motion of active particles constrained to curved surfaces is an intriguing problem with wide range of applications in biological physics and soft matter, from rotating motors on membranes to Janus particles on interfaces. In this talk, we construct Langevin equations for oriented active particles on fixed surfaces using differential geometric principles. We derive the deterministic equations of motion for the translational and rotational velocities in the body frame of the particle in Hamiltonian form. We find that surface curvature couples the linear and angular momenta of the particle. To these Hamiltonian equations, we add linear friction and white noise to obtain a generalized Ornstein-Uhlenbeck process in phase space. We obtain the corresponding Fokker-Planck equation and the fluctuation-dissipation relation. The equations of Brownian dynamics are derived by adiabatically eliminating the momenta. These can be used to simulate biophysical diffusion processes on surfaces.

Keywords: Active particles; Langevin equations; Fokker-Planck equations; Curvature; Membrane proteins