The directed 2-linkage problem with length constraints

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Characteristics of the polymer transport in ratchet systems

Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency and non-uniform charge distributions. We also use currents in the non-equilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The dominating transport mechanisms are found via graph optimization methods. The results show that small changes in the molecule structure and the environment variables can lead to large increases of the drift. The drift and the coherence can be amplified by using deterministic flashing potentials and customized polymer charge distributions. Identifying the dominating transport mechanism by graph analysis tools is found to give insight in how the molecule is transported by the ratchet effect.Comment: 35 pages, 17 figures, to appear in Phys. Rev.

Long range action in networks of chaotic elements

We show that under certain simple assumptions on the topology (structure) of networks of strongly interacting chaotic elements a phenomenon of long range action takes place, namely that the asymptotic (as time goes to infinity) dynamics of an arbitrary large network is completely determined by its boundary conditions. This phenomenon takes place under very mild and robust assumptions on local dynamics with short range interactions. However, we show that it is unstable with respect to arbitrarily weak local random perturbations.Comment: 15 page

A polynomial algorithm for the Hamiltonian cycle problem in semicomplete multipartite digraphs

We describe a polynomial algorithm for the Hamiltonian cycle problem for semicomplete multipartite digraphs. The existence of such an algorithm was conjectured in G. Gutin, Paths and cycles in digraphs. Ph. D. thesis, Tel Aviv Univ., 1993. (see also G. Gutin, J Graph Theory 19 (1995) 481-505)