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2. Brownian Motion 1.Historical Background 2.Characteristic Scales Of Brownian Motion 3.Random Walk 4.Brownian Motion, Random Force And Friction: The Langevin.

Published byElwin Wilkinson Modified over 9 years ago

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Presentation on theme: "2. Brownian Motion 1.Historical Background 2.Characteristic Scales Of Brownian Motion 3.Random Walk 4.Brownian Motion, Random Force And Friction: The Langevin."— Presentation transcript:

1 2. Brownian Motion 1.Historical Background 2.Characteristic Scales Of Brownian Motion 3.Random Walk 4.Brownian Motion, Random Force And Friction: The Langevin Equation 5.Solving The Langevin Equation: Approximations And Orders Of Magnitude 6.Applications And Implications

2 2.1. Historical Background Continuum vs Atomism –Mach vs Boltzmann Einstein’s kinetic theory on Brownian Motion –atomism Fluctuation-dissipation theorem –Transport, Noises, …

3 2.2. Characteristic Scales Of Brownian Motion Brownian motion: Random motion of particles (size ~  m) hovering in gas or on surface of fluid.

4 Thermal energy of a gas particle at room temperature: Density of gas: Mass density of each hovering particle: Mass of hovering particle: In equilibrium: Speed: Mass of the gas molecule: Speed:

5 L = mean free path of hovering particle S = l 2 = its cross section n = number density of gas  = mean free time

6 2.3. Random Walk Brownian motion: Major achievement of Einstein’s theory : Evaluate  using kinetic theory.

7 Random walk of a drunk

8 Average over behavior of many drunks = Average over different starting points of one drunk ( Average over Ensemble ) ( Average over Initial Conditions ) See Ex.2.2

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