Viktoria Blavatska

Shape anisotropy of polymers in disordered environment

We study the influence of structural obstacles in a disordered environment on the size and shape characteristics of long flexible polymer macromolecules. We use the model of self-avoiding random walks on diluted regular lattices at the percolation threshold in space dimensions d=2 and d=3. Applying the pruned-enriched Rosenbluth method, we numerically estimate rotationally invariant universal quantities such as the averaged asphericity and prolateness of polymer chain configurations. Our results quantitatively reveal the extent of anisotropy of macromolecules due to the presence of structural defects.

Walking on fractals: diffusion and self-avoiding walks on percolation clusters

We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in space dimensions d = 2, 3, 4. Our analysis yields estimates of universal exponents, governing the scaling laws for configurational properties of RWs and SAWs.

Multifractality of Self-Avoiding Walks on Percolation Clusters

We consider self-avoiding walks on the backbone of percolation clusters in space dimensions d=2,3,4. Applying numerical simulations, we show that the whole multifractal spectrum of singularities emerges in exploring the peculiarities of the model. We obtain estimates for the set of critical exponents that govern scaling laws of higher moments of the distribution of percolation cluster sites visited by self-avoiding walks, in a good correspondence with an appropriately summed field-theoretical epsilon=6-d expansion [H.-K. Janssen and O. Stenull, Phys. Rev. E 75, 020801(R) (2007)10.1103/PhysRevE.75.020801].

Polymer adsorption on a fractal substrate: Numerical study

We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration p(c) of attractive sites. The percolation cluster is characterized by a fractal dimension d(s) (p(c))=91/49. The conformational properties of polymer chains grafted to such a fractal substrate are studied by means of the pruned-enriched Rosenbluth method. We find estimates for the surface crossover exponent governing the scaling of the adsorption energy in the vicinity of transition point, φ(s)(p(c))=0.425±0.009, and for adsorption transition temperature, T(A)(p(c))=2.64±0.02. As expected, the adsorption is diminished when the fractal dimension of the substrate is smaller than that of a plain Euclidean surface. The universal size and shape characteristics of a typical spatial conformation which attains a polymer chain in the adsorbed state are analyzed as well.

Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects

We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to such system details. By contrast, we verify that the fractal dimension d_{f} is a universal quantity and unaffected by the choice of metric. We also show that for weak correlations, its value coincides with that for the uncorrelated system. In two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength, approaching d_{f}→2. The onset of this change does not seem to be determined by the extended Harris criterion.

Polymers in crowded environment under stretching force: Globule-coil transitions.

We study flexible polymer macromolecules in a crowded (porous) environment, modeling them as self-attracting self-avoiding walks on site-diluted percolative lattices in space dimensions d=2,3 . The influence of stretching force on the polymer folding and the properties of globule-coil transitions are analyzed. Applying the pruned-enriched Rosenbluth chain-growth method, we estimate the transition temperature TTheta between collapsed and extended polymer configurations and construct the phase diagrams of the globule-coil coexistence when varying temperature and stretching force. The transition to a completely stretched state, caused by applying force, is discussed as well.

Conformational properties of complex polymers: rosette versus star-like structures

Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyze the size and shape characteristics of complex polymer structures, containing in general

A one-dimensional random walk in a multi-zone environment

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Scaling laws for random walks in long-range correlated disordered media

loops (petals) and

Conformational transitions in random heteropolymer models

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