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SUMMARY:Intrinsic Langevin dynamics of rigid inclusions on curved surfaces
  - Ronojoy Adhikari (University of Cambridge)
DTSTART:20241004T140000Z
DTEND:20241004T143000Z
UID:TALK220963@talks.cam.ac.uk
DESCRIPTION:The stochastic dynamics of a rigid inclusion constrained to mo
 ve on a curved surface has many applications in biological and soft matter
  physics\, ranging from the diffusion of passive or active membrane protei
 ns to the motion of phoretic particles on liquid-liquid interfaces. Here w
 e construct intrinsic Langevin equations for an oriented rigid inclusion o
 n a curved surface using Cartan's method of moving frames. We first derive
  the Hamiltonian equations of motion for the translational and rotational 
 momenta in the body frame. Surprisingly\, surface curvature couples the li
 near and angular momenta of the inclusion. We then add to the Hamiltonian 
 equations linear friction\, white noise and arbitrary configuration-depend
 ent forces and torques to obtain intrinsic Langevin equations of motion in
  phase space. We provide the integrability conditions\, made non-trivial b
 y surface curvature\, for the forces and torques to admit a potential\, th
 us distinguishing between passive and active stochastic motion. We derive 
 the corresponding Fokker-Planck equation in geometric form and obtain fluc
 tuation-dissipation relations that ensure Gibbsian equilibrium. We extract
  the overdamped equations of motion by adiabatically eliminating the momen
 ta from the Fokker-Planck equation\, showing how a peculiar cancellation l
 eads to the naively expected Smoluchowski limit. The overdamped equations 
 can be used for accurate and efficient intrinsic Brownian dynamics simulat
 ions of passive\, driven and active diffusion processes on curved surfaces
 . Our work generalises to the collective dynamics of many inclusions on cu
 rved surfaces.
LOCATION:Seminar Room 1\, Newton Institute
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