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On the chain length dependence of local correlations in polymer melts and a perturbation theory of symmetric polymer blends
The self-consistent field (SCF) theory of dense polymer liquids assumes that
short-range correlations are almost independent of how monomers are connected
into polymers. Some limits of this idea are explored in the context of a
perturbation theory for mixtures of structurally identical polymer species, A
and B, in which the AB pair interaction differs slightly from the AA and BB
interaction, and the difference is controlled by a parameter alpha Expanding
the free energy to O(\alpha) yields an excess free energy of the form alpha
, in both lattice and continuum models, where z(N) is a
measure of the number of inter-molecular near neighbors of each monomer in a
one-component liquid. This quantity decreases slightly with increasing N
because the self-concentration of monomers from the same chain is slightly
higher for longer chains, creating a deeper correlation hole for longer chains.
We analyze the resulting -dependence, and predict that , where is an invariant degree of
polymerization, and . This and other predictions are
confirmed by comparison to simulations. We also propose a way to estimate the
effective interaction parameter appropriate for comparisons of simulation data
to SCF theory and to coarse-grained theories of corrections to SCF theory,
which is based on an extrapolation of coefficients in this perturbation theory
to the limit . We show that a renormalized one-loop theory
contains a quantitatively correct description of the -dependence of local
structure studied here.Comment: submitted to J. Chem. Phy
Universality of subleading corrections for self-avoiding walks in presence of one dimensional defects
We study three-dimensional self-avoiding walks in presence of a
one-dimensional excluded region. We show the appearance of a universal
sub-leading exponent which is independent of the particular shape and
symmetries of the excluded region. A classical argument provides the estimate:
. The numerical simulation gives .Comment: 29 pages, latex2
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Dual state-parameter estimation of hydrological models using ensemble Kalman filter
Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state-parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model. © 2004 Elsevier Ltd. All rights reserved
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