We consider the one-dimensional motion of a particle randomly accelerated by Gaussian white noise on the line segment 00 of the velocity just after reflection from the boundary vanish.
The motion of polymers with inhomogeneous structure through nanopores is discussed theoretically. Specifically, we consider the translocation dynamics of polymers consisting of double-stranded and single-stranded blocks. Since only the single-stranded chain can go through the nanopore the double-stranded segment has to unzip before the translocation. Utilizing a simple analytical model, translocation times are calculated explicitly for different polymer orientations, i.e., when the single-stranded block enters the pore first and when the double-stranded segment is a leading one. The dependence of the translocation dynamics on external fields, energy of interaction in the double-stranded segment, size of the polymer, and the fraction of double-stranded monomers is analyzed. It is found that the order of entrance into the pore has a significant effect on the translocation dynamics. The theoretical results are discussed using free-energy landscape arguments.
The transport of polymers with folded configurations across membrane pores is investigated theoretically by analyzing simple discrete stochastic models. The translocation dynamics is viewed as a sequence of two events: motion of the folded segment through the channel followed by the linear part of the polymer. The transition rates vary for the folded and linear segments because of different interactions between the polymer molecule and the pore. It is shown that the translocation time depends nonmonotonously on the length of the folded segment for short polymers and weak external fields, while it becomes monotonous for long molecules and large fields. Also, there is a critical interaction between the polymers and the pore that separates two dynamic regimes. For stronger interactions, the folded polymer moves slower, while for weaker interactions, the linear chain translocation is the fastest. In addition, our calculations show that the folding does not change the translocation scaling properties of the polymer. These phenomena can be explained by the interplay between translocation distances and transition rates for the folded and linear segments of the polymer. Our theoretical results are applied for analysis of experimental translocations through solid-state nanopores.
We consider a particle moving on the half line x > 0 and subject to a constant force in the -x direction plus a delta-correlated random force. At x = 0 the particle is reflected inelastically. The velocities just after and before the reflection satisfy v(f) = -r v(i), where r is the coefficient of restitution. This simple model is of interest in connection with studies of driven granular matter in a gravitational field. With an exact analytical approach and simulations we study the steady-state distribution function P(x,v).
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