Biomedical subjects

Thomas A Vilgis

Publications and source records attributed to Thomas A Vilgis.

5 recordsLinked to original sources

PubMed2005

Directed polymers with constrained winding angle.

In this paper we study from a nonperturbative point of view the entanglement of two directed polymers subjected to repulsive interactions given by a Dirac delta-function potential. An exact formula of the so-called second moment of the winding angle is derived. This result is used to provide a thorough analysis of entanglement phenomena in the classical system of two polymers subjected to repulsive interactions and related problems. No approximation is made in treating the constraint on the winding angle and the repulsive forces. In particular, we investigate how repulsive forces influence the entanglement degree of the two-polymer system. In the limit of ideal polymers, in which the interactions are switched off, we show that our results are in agreement with those of previous works.

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PubMed2005

Localization of a multiblock copolymer at a selective interface: scaling predictions and Monte Carlo verification.

We investigate the localization of a hydrophobic-polar regular copolymer at a selective solvent-solvent interface with emphasis on the impact of block length M on the copolymer behavior. The considerations are based on simple scaling arguments and use the mapping of the problem onto a homopolymer adsorption problem. The resulting scaling relations treat the gyration radius of the copolymer chain perpendicular and parallel to the interface in terms of chain length N and block size M, as well as the selectivity parameter chi. The scaling relations differ for the case of weak and strong localization. In the strong localization limit a scaling relation for the lateral diffusion coefficient D( parallel) is also derived. We implement a dynamic off-lattice Monte Carlo model to verify these scaling predictions. For chain lengths in a wide range (32</=N</=512) we find good agreement with the scaling predictions.

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PubMed2005

Constrained dynamics of a polymer ring enclosing a constant area.

The dynamics of an ideal polymer ring enclosing a constant algebraic area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the Lagrange multiplier function which is time dependent. The time dependence of the Lagrange multiplier is evaluated in a closed form both at short and long times. At long times, the time dependence is weak, and is mainly governed by the inverse of the first mode of the area. The presence of the constraint changes the nature of the relaxation of the internal modes. The time correlation of the position vectors of the ring is found to be dominated by the first Rouse mode which does not relax even at very long times. The mean square displacement of the radius vector is found to be diffusive, which is associated with the rotational diffusion of the ring.

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PubMed2004

Semiflexible polymers in a random environment.

We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of semiflexible polymers depends not only on the details of the disorder but also on the ease with which polymers can bend. The interplay of these two effects can lead to the delocalization of a localized polymer with an increase in either the disorder density or the stiffness. Our theory provides a general criterion for the delocalization of polymers with varying degrees of flexibility and allows us to propose a phase diagram for the highly folded (localized) states of semiflexible polymers as a function of the disorder strength and chain rigidity.

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PubMed2004

Localization and freezing of a Gaussian chain in a quenched random potential.

The Gaussian chain in a quenched random potential (which is characterized by the disorder strength Delta) is investigated in the d-dimensional space by the replicated variational method. The general expression for the free energy within so-called one-step-replica symmetry breaking (1-RSB) scenario has been systematically derived. We have shown that the replica symmetrical (RS) limit of this expression can describe the chain center-of-mass localization and collapse. The critical disorder when the chain becomes localized scales as Delta(c) approximately b(d)N(-2+d/2) (where b is the length of the Kuhn segment length and N is the chain length) whereas the chain gyration radius R(g) approximately b(b(d)/Delta)(1/(4-d)). The freezing of the internal degrees of freedom follows to the 1-RSB-scenario and is characterized by the beads localization length D(2). It was demonstrated that the solution for D(2) appears as a metastable state at Delta=Delta(A) and behaves similarly to the corresponding frozen states in heteropolymers or in p-spin random spherical model.

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