| 2. |
- Lizana, L., et al.
(author)
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Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics
- 2009
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In: Physical Review E (Statistical, Nonlinear, and Soft Matter Physics). - 1539-3755. ; 80:5
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Journal article (peer-reviewed)abstract
- We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Delta diffusing in a one-dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function rho T(yT,t vertical bar yT,0) that a tagged particle T (T=1,...,N) is at position yT at time t given that it at time t=0 was at position yT,0. Using a Bethe ansatz we obtain the N-particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle T, we arrive at an exact expression for rho T(yT,t vertical bar yT,0) in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large N, maintaining L finite, using a nonstandard asymptotic technique. We derive an exact expression for rho T(yT,t vertical bar yT,0) for a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) for times much smaller than the collision time t
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| 3. |
- Pedersen, Jonas, et al.
(author)
-
Bubble merging in breathing DNA as a vicious walker problem in opposite potentials.
- 2009
-
In: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 130:16
-
Journal article (peer-reviewed)abstract
- We investigate the coalescence of two DNA bubbles initially located at weak domains and separated by a more stable barrier region in a designed construct of double-stranded DNA. In a continuum Fokker-Planck approach, the characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behavior, while at high temperatures, the bubble corners perform drift diffusion toward coalescence. In the calculations, we map the bubble dynamics on the problem of two vicious walkers in opposite potentials. We also present a discrete master equation approach to the bubble coalescence problem. Numerical evaluation and stochastic simulation of the master equation show excellent agreement with the results from the continuum approach. Given that the coalesced state is thermodynamically stabilized against a state where only one or a few of the base pairs of the barrier region are re-established, it appears likely that this type of setup could be useful for the quantitative investigation of thermodynamic DNA stability data as well as the rate constants involved in the unzipping and zipping dynamics of DNA in single molecule fluorescence experiments.
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