Smoluchowski with interactions

Seminar
Speaker
Prof. Baruch Meerson, Racah Institute of Physics, Hebrew University
Date
03/11/2014 - 12:30Add to Calendar 2014-11-03 12:30:00 2014-11-03 12:30:00 Smoluchowski with interactions In 1917 von Smoluchowski suggested a simple-minded model of diffusion-controlled binary    reactions. It consists of an immobile spherical trap of radius R surrounded by a gas of Brownian particles. The particle flux into the trap mimics the rate of diffusion-controlled reactions. Since its inception, the Smoluchowski model and its extensions inspired multitudes of studies. The vast majority of them continued to assume that the particles do not interact with other. Here we extend this model to a whole class of diffusive gases of interacting particles. Employing the Macroscopic Fluctuation Theory, we evaluate the probability P(T) that no gas particle hits the trap until a long but finite time T. We also find the most likely density history of the gas conditional on the non-hitting. The results crucially depend on the dimension of space d and on the rescaled parameter   l = R/√D0T where D0 is the gas diffusivity. Room 301, Physics Bld. 202 המחלקה לפיזיקה physics.dept@mail.biu.ac.il Asia/Jerusalem public
Place
Room 301, Physics Bld. 202
Abstract

In 1917 von Smoluchowski suggested a simple-minded model of diffusion-controlled binary   
reactions. It consists of an immobile spherical trap of radius R surrounded by a gas of Brownian

particles. The particle flux into the trap mimics the rate of diffusion-controlled reactions. Since

its inception, the Smoluchowski model and its extensions inspired multitudes of studies. The vast

majority of them continued to assume that the particles do not interact with other. Here we extend

this model to a whole class of diffusive gases of interacting particles. Employing the Macroscopic

Fluctuation Theory, we evaluate the probability P(T) that no gas particle hits the trap until a

long but finite time T. We also find the most likely density history of the gas conditional on the

non-hitting. The results crucially depend on the dimension of space d and on the rescaled parameter

  l = R/√D0T where D0 is the gas diffusivity.

תאריך עדכון אחרון : 26/10/2014