Biomedical subjects

T Prellberg

Publications and source records attributed to T Prellberg.

9 recordsLinked to original sources

PubMed2006

Self-avoiding random walk with multiple site weightings and restrictions.

We introduce a new class of models for polymer collapse, given by random walks on regular lattices which are weighted according to multiple site visits. A Boltzmann weight omegal is assigned to each (l+1)-fold visited lattice site, and self-avoidance is incorporated by restricting to a maximal number K of visits to any site via setting omegal=0 for l>or=K. In this Letter we study this model on the square and simple cubic lattices for the case K=3. Moreover, we consider a variant of this model, in which we forbid immediate self-reversal of the random walk. We perform simulations for random walks up to n=1024 steps using FlatPERM, a flat histogram stochastic growth algorithm. We find evidence that the existence of a collapse transition depends sensitively on the details of the model and has an unexpected dependence on dimension.

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PubMed2003

Scaling near the theta point for isolated polymers in solution.

Recently questions have been raised as to the conclusions that can be drawn from currently proposed scaling theory for a single polymer in various types of solution in two and three dimensions. Here we summarize the crossover theory predicted for low dimensions and clarify the scaling arguments that relate thermal exponents for quantities on approaching the theta point from low temperatures to those associated with the asymptotics in polymer length at the theta point itself.

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PubMed2000

Viscoelastic depinning of driven systems: mean-field plastic scallops

We have investigated the mean-field dynamics of an overdamped viscoelastic medium driven through quenched disorder. The model allows for the coexistence of pinned and sliding regions and can exhibit continuous elastic depinning or first-order hysteretic depinning. Numerical simulations indicate mean-field instabilities that correspond to macroscopic stick-slip events and lead to premature switching. The model describes the elastic and plastic dynamics of driven vortex arrays in superconductors and other extended disordered systems.

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PubMed2000

Four-dimensional polymer collapse: pseudo-first-order transition in interacting self-avoiding walks

In an earlier work we provided the first evidence that the collapse, or coil-globule transition of an isolated polymer in solution can be seen in a four-dimensional model. Here we investigate, via Monte Carlo simulations, the canonical lattice model of polymer collapse, namely, interacting self-avoiding walks, to show that it not only has a distinct collapse transition at finite temperature but that for any finite polymer length this collapse has many characteristics of a rounded first-order phase transition. However, we also show that there exists a "straight theta point" where the polymer behaves in a simple Gaussian manner (which is a critical state), to which these finite-size transition temperatures approach as the polymer length is increased. The resolution of these seemingly incompatible conclusions involves the argument that the first-order-like rounded transition is scaled away in the thermodynamic limit to leave a mean-field second-order transition. Essentially this happens because the finite-size shift of the transition is asymptotically much larger than the width of the pseudotransition and the latent heat decays to zero (algebraically) with polymer length. This scenario can be inferred from the application of the theory of Lifshitz, Grosberg, and Khokhlov (based upon the framework of Lifshitz) to four dimensions: the conclusions of which were written down some time ago by Khokhlov. In fact it is precisely above the upper critical dimension, which is 3 for this problem, that the theory of Lifshitz may be quantitatively applicable to polymer collapse.

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PubMed1995