Relaxation, overdamped

In the frame of the present review, we discussed different approaches for description of an overdamped Brownian motion based on the notion of integral relaxation time. As we have demonstrated, these approaches allow one to analytically derive exact time characteristics of one-dimensional Brownian diffusion for the case of time constant drift and diffusion coefficients in arbitrary potentials and for arbitrary noise intensity. The advantage of the use of integral relaxation times is that on one hand they may be calculated for a wide variety of desirable characteristics, such as transition probabilities, correlation functions, and different averages, and, on the other hand, they are naturally accessible from experiments. 

It is conceivable that diffusion of kinks, or overdamped solitons, along the DNA could act to relax the FPA with a time dependence similar to that predicted for torsional deformation/31 32) High levels of intercalated dyes would be expected to alter both the equilibrium population of kinks and their mobility along the DNA. Hence, this question is addressed by examining the effect of intercalating dyes on the torsional dynamics. 

If the PEP-PEE triblock chains are arranged in microdomains separated by well-defined interfaces, then the additional fast relaxation process observed by NSE would result from the undulation motions of the interface. The thermal motions of the interface are driven by the surface tension and overdamped. With an effective viscosity r eff in the interfacial region, the relaxation rate if Q) ... 

We next consider the effective force balance for all >N variables, while treating the system as an unconstrained system. For simplicity, we consider the case in which the crossover from ballistic motion to diffusion occurs at a timescale much less than any characteristic relaxation time for vibrations of the hard coordinates, so that the vibrations are overdamped, but in which the vibrational relaxation times are much less than any timescale for the diffusion of the soft coordinates. In this case, we may assume local equilibration of all 3N momenta at timescales of order the vibration time. Repeating the analysis of the Section V.A, while now treating all 3N coordinates as unconstrained, yields an effective force balance... 

Expecially when AGf is very small, such overdamped solvent relaxation due to dielectric friction may contribute significantly to v, so that in some cases... 

S ps mentioned above. This relaxation component has been suggested that it is associated with a relaxation of overdamped local collective modes. 7... 

The friction coefficient y defines the timescale, y of thermal relaxation in the system described by (8.13). A simpler stochastic description can be obtained for a system in which this time is shorter than any other characteristic timescale of our system. This high friction situation is often referred to as the overdamped limit. In this limit of large y, the velocity relaxation is fast and it may be assumed to quickly reaches a steady state for any value of the applied force, that is, v = x = 0. This statement is not obvious, and a supporting (though not rigorous) argument is provided below. If true then Eqs (8.13) and (8.20) yield... 

When the relaxation is not overdamped we need to consider the full Kramers equation (14.41) or, using Eqs (14.42) and (14.43), Eq. (14.44) forf. In contrast to Eq. (14.45) that describes the overdamped limit in terms of the stochastic position variable x, we now need to consider two stochastic variables, x and v, and their probability distribution. The solution of this more difficult problem is facilitated by invoking another simplification procedure, based on the observation that if the... 

Using fe = 5 X 10 ergcm , estimated from Eq. (88), results in To 5 x 10 ° s. In the normal fluid Tq cluster center on the time scale of Tq, which is short relative to the electron tunneling time from the normal fluid cluster. Accordingly, electron tunneling from bubbles in normal liquid clusters of helium will occur from a thermally equilibrated position of the bubble. 

For Eq. (3.25) to be valid additionally (i) the particle must be strongly overdamped and (ii) as shown in the Appendix Section F.9, its motion on timescales short compared to the relaxation time x.4 for particle accelerations must be observationally irrelevant. 

A similar equation was found by deGennes. For V" > 0, t is positive, giving rise to an overdamped relaxation. For K" <0 and K<(—2V /yy, r becomes negative, and the squeezing mode will grow in accordance with (4.34), potentially producing film rupture. The maximum value of t is found at K =(- with t- =tJ = -(h y/24v)Kl... 

The overdamped limit gives the golden rule rate, with k proportional to the square of the coupling, J, and inversely proportional to the damping strength, /. Note that the population relaxation rate in the eigenstate representation is simply f M in both regimes. Thus,... 

Bier M, Derenyi I, Kostnr M, Astumian RD (1999) Intrawell relaxation of overdamped Brownian particles. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 59 6422-6432... 

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