Statistical Mechanics and Soft Condensed Matter

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Presentation transcript:

Statistical Mechanics and Soft Condensed Matter Brownian motion by Pietro Cicuta

Slide 1: The movement of particles in a fluid can be described in terms of the average behaviour of a large number of particles in random motion. Reprinted with permission from MIT (Figure is credited to Ziad Ganim).

Fick’s first law of diffusion: Fick’s second law: if D is independent of concentration Slide 2: Diffusion.

For a walk in one dimension: In 3 dimensions: In d dimensions: Slide 3: Random walk. (Ziad Ganim, reprinted with permission from MIT.)

Slide 4: General equation of motion for a particle in a fluid.

an example of the fluctuation dissipation theorem Slide 5: Solutions when the force is “random noise”.

Einstein relation: Stokes–Einstein relation: Slide 6: Mean square displacement.