15,383 research outputs found

    Translational Diffusion of Polymer Chains with Excluded Volume and Hydrodynamic Interactions by Brownian Dynamics Simulation

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    Within Kirkwood theory, we study the translational diffusion coefficient of a single polymer chain in dilute solution, and focus on the small difference between the short--time Kirkwood value D(K)D^{(K)} and the asymptotic long--time value DD. We calculate this correction term by highly accurate large--scale Brownian Dynamics simulations, and show that it is in perfect agreement with the rigorous variational result D<D(K)D < D^{(K)}, and with Fixman's Green--Kubo formula, which is re--derived. This resolves the puzzle posed by earlier numerical results (Rey {\em et al.}, Macromolecules 24, 4666 (1991)), which rather seemed to indicate D>D(K)D > D^{(K)}; the older data are shown to have insufficient statistical accuracy to resolve this question. We then discuss the Green--Kubo integrand in some detail. This function behaves very differently for pre--averaged vs. fluctuating hydrodynamics, as shown for the initial value by analytical considerations corroborated by numerical results. We also present further numerical data on the chain's statics and dynamics.Comment: submitted to Journal of Chemical Physic

    Free boson representation of DY(sl^(M+1N+1))DY_{\hbar}(\hat{sl} (M+1|N+1)) at level one

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    We construct a realization of the central extension of super-Yangian double DY(sl^(M+1N+1))DY_{\hbar}(\hat{sl}(M+1|N+1)) at level-one in terms of free boson fields with a continuous parameter.Comment: 9 pages, latex, reference revise

    Robust H∞ control of time-varying systems with stochastic non-linearities: the finite-horizon case

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    The official published version can be obtained from the link below.This paper is concerned with the robust H∞ control problem for the class of uncertain non-linear discrete time-varying stochastic systems with a covariance constraint. All the system parameters are time-varying and the uncertainties enter into the state matrix. The non-linearities under consideration are described by statistical means and they cover several classes of well-studied non-linearities. The purpose of the addressed problem is to design a dynamic output-feedback controller such that, the H∞ disturbance rejection attenuation level is achieved in the finite-horizon case while the state covariance is not more than an individual upper bound at each time point. An algorithm is developed to deal with the addressed problem by means of recursive linear matrix inequalities (RLMIs). It is shown that the robust H∞ control problem is solvable if the series of RLMIs is feasible. An illustrative simulation example is given to show the applicability and effectiveness of the proposed algorithm.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany