Drift-dominated motion

Case b) Drift Dominated Motion. The Fokker-Planck equation in a domain of x, where K(x) 4= 0, and for < 1 will now be considered. The solution (2.75) indicates that in this drift dominated domain the variance o(t) remains of the order of magnitude O (e) if the motion is started with an initial variance Og of the... 

Case c) Fluctuation Initiated Motion. If motion is started from a distribution concentrated around an unstable stationary point Xq where K(xo) = 0 and K (xq) = y > 0, the expansion of (2.82, 84,85) fails since the initial fluctuations are enhanced exponentially, see (2.92) before the drift dominated motion sets in. The appropriate approximation here, developed by Haake [2.2, 3] and by Suzuki [2.4] essentially consists of two steps 1) Solve the Fokker-Planck equation for the first fluctuation dominated stage and 2) Find a smoothly fitting solution for the second drift dominated stage. 

Case d) Fluctuation Dominated Motion. An initial distribution P x 0) concentrated at the potential minima x and x+ neighbouring the unstable point Xq will now be considered. In this case a slow equilibration process will take place by means of a probability flux between the modes until the stationary distribution Pst ( ) is established. Since the drift force K (jc) is directed towards the minima X- and x+, it cannot be primarily responsible for this process. In fact the motion... 

The inward motion of anions is assumed to be the dominant ionic transport across the oxide. The ionic movement is field-assisted drifting and is the rate-limiting process. The diffusion of ions at room temperature is considered to be too slow to account for the oxide growth rates. The current density is written as... 

All experiments dealing with large-scale dynamics of suspended particles in solutions are bounded by the above two limits. The Einsteinian law is manifest when collisions by the solvent molecules due to their thermal motion dominate the dynamics of the particle. On the other hand, if the externally imposed forces on the particle dominate, then the Newtonian limit is approached. In general, the behavior is diffusion-drift. ... 

Diffusion-limited regime When the diffusion of the macromolecule due to thermal motion dominates over the drift arising from any externally imposed flow fields and the barrier contributions, the steady-state flux is given by the law,... 

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