Ch4_No_Random_walks,_friction,_and_diffusion

# Ch4_No_Random_walks, - Ch.4 Random Walks Friction and Diffusion Origin of friction conversion of organized motion to disordered motion by

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1 Ch.4 Random Walks, Friction, and Diffusion Origin of friction : conversion of organized motion to disordered motion by collisions with surrounding, disordered medium Once we understand the origin of friction, a wide variety of other dissipative processes will make sense, too. irreversibly turn order into disorder

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2 Dissipative processes: Friction erases order in the initial directed motion of an object (4.1.4). The diffusion of ink molecules in water erases order (e.g. any pattern initially present) (4.4.2). Electric resistance runs down the batteries, making heat (4.6.4). The conduction of heat erases the initial separation into hot and cold regions (4.4.2’). Degraded energy by collisions with a large, random environment Random Walk
3 In the nanoworld, Diffusion : dominant form of material transport (4.4.1) The mathematics of random walks is the appropriate language to understand the conformations of many biological macromolecules (4.3.1). Diffusion ideas will give us a quantitative account of the permeability of bilayer membranes(4.6.1) and membrane potential (4.6.3). -important in cell physiology

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4 ¾ Biological Question : If everything is so random in the nanoworld of cells, how can we say anything predictive about what’s going on there? ¾ Physical Ideas : The collective activity of many randomly moving actors can be effectively predictable , even if the individual motions are not.
5 Roadmap 4.1 Brownian Motion 4.2 Excursion: Einstein’s Role 4.3 Other Random Walks 4.4 More about Diffusion 4.5 Functions, Derivatives, and Snakes under the Rug 4.6 Biological Application of Diffusion

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6 4.1 BROWNIAN MOTION 4.1.1 Just a little more history - 원자가설 ? 1773, B. Franklin : olive oil (~5 cm 3 ) on water Covered about 2,000 m 2 d=? d~ 5 cm 3 / 2,000 m 2 ~ 2.5 nm !! invisible Ideal gas law : pV= Nk B T product Nk B , not N and k B 1828, R. Brown : pollen grain( 1 μ m ) in water Life process? No!
7 1 .매우 불규칙적이다. 2 .두 입자가 충분히 가까이 있게 되어도 서로 독립적으로 움직인다. 3 .작은 입자일수록 활발하다. 4 .입자의 종류나 밀도와 무관하다. 5 .점성이 적은 유체에서 6 .온도가 높을수록 7 .운동이 결코 멈추지 않는다. Brownian motion by molecular kinetic theory By constant collisions between the pollen grains and the water molecules agitated by their thermal motion Any Problems? YES !

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8 Brownian motion_problems with kinetic theory, 1905 1. How can a molecular collision with a enormous pollen grain make the grain move appreciably? molecule ~ nm , pollen grain ~ μ m or 1,000 nm 2. Human eyes can’t see events faster than 30/s. molecular speed ~ 1,000m/s distance between molecules ~ 1nm Æ # of collisions ~ 10 12 /s ! Albert Einstein, student : The two problems cancel each other.
9 4.1.2 Random walks lead to diffusive behavior Tossing a coin once per sec: head-E, tail-W (1D RW) 0 d E W when 100 heads in a row : rare but possible Observer : can notice the displacement d Einstein, We cannot see the small, rapid jerks of the pollen grain, still we can and will see the rare large displacements .

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## This note was uploaded on 07/08/2009 for the course KIM 0150-5 taught by Professor Dong during the Spring '09 term at Ewha Womans University.

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Ch4_No_Random_walks, - Ch.4 Random Walks Friction and Diffusion Origin of friction conversion of organized motion to disordered motion by

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