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V. Blavatska

Publications and source records attributed to V. Blavatska.

34 records · Page 2Linked to original sources
arXiv2017

One-Dimensional Random Walk in Multi-Zone Environment

We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are considered to be differently fixed. We derive analytically the probability to find a walker at the given position and time. The probability distribution function is found and has no Gaussian form because of properties of adsorption in the bulk of zones and partial reflection at the separation points. Time dependence of the mean squared displacement of a walker is studied as well and revealed the transient anomalous behavior as compared with ordinary RW.

cond-mat.stat-mech↗
arXiv2015

Loop formation in polymers in crowded environment

We analyze the probability of a single loop formation in a long flexible polymer chain in disordered environment in $d$ dimensions. The structural defects are considered to be correlated on large distances $r$ according to a power law $\sim r^{-a}$. Working within the frames of continuous chain model and applying the direct polymer renormalization scheme, we obtain the values of critical exponents governing the scaling of probabilities of loop formation with various positions along the chain as function of loops length. Our results quantitatively reveal that the presence of structural defects in environment decreases the probability of loop formation in polymer macromolecules.

cond-mat.soft↗
arXiv2015

Lattice models of directed and semiflexible polymers in anisotropic environment

We study the conformational properties of polymers in presence of extended columnar defects of parallel orientation. Two classes of macromolecules are considered: the so-called partially directed polymers with preferred orientation along direction of the external stretching field and semiflexible polymers. We are working within the frames of lattice models: partially directed self-avoiding walks (PDSAWs) and biased self-avoiding walks (BSAWs). Our numerical analysis of PDSAWs reveals, that competition between the stretching field and anisotropy caused by presence of extended defects leads to existing of three characteristic length scales in the system. At each fixed concentration of disorder we found a transition point, where the influence of extended defects is exactly counterbalanced by the stretching field. Numerical simulations of BSAWs in anisotropic environment reveal an increase of polymer stiffness. In particular, the persistence length of semiflexible polymers increases in presence of disorder.

cond-mat.soft↗
arXiv2014

Polymers in disordered environments

A brief review of our recent studies aiming at a better understanding of the scaling behaviour of polymers in disordered environments is given. The main emphasis is on a simple generic model where the polymers are represented by (interacting) self-avoiding walks and the disordered environment by critical percolation clusters. The scaling behaviour of the number of conformations and their average spatial extent as a function of the number of monomers and the associated critical exponents $γ$ and $ν$ are examined with two complementary approaches: numerical chain-growth computer simulations using the PERM algorithm and complete enumerations of all possible polymer conformations employing a recently developed very efficient exact counting method.

cond-mat.soft↗
arXiv2014

Ring polymers in crowded environment: conformational properties

We analyze the universal size characteristics of flexible ring polymers in solutions in presence of structural obstacles (impurities) in d dimensions. One encounters such situations when considering polymers in gels, colloidal solutions, intra- and extracellular environments. A special case of extended impurities correlated on large distances r according to a power law \sim r^{-a} is considered. Applying the direct polymer renormalization scheme, we evaluate the estimates for averaged gyration radius $\langle R_{g\,{\rm ring}} \rangle$ and spanning radius $\langle R_{1/2\,{\rm ring}} \rangle$ of typical ring polymer conformation up to the first order of double \varepsilon=4-d, δ=4-a expansion. Our results quantitatively reveal an extent of the effective size and anisotropy of closed ring macromolecules in disordered environment. In particular, the size ratio of ring and open (linear) polymers of the same molecular weight grows when increasing the strength of disorder according to $\langle R^2_{g\,{\rm ring}} \rangle / \langle R^2_{g\,{\rm chain}} \rangle =\frac{1}{2} \left(1+\frac{13}{48}δ\right)$.

cond-mat.soft↗
arXiv2014

Conformational properties of polymers in anisotropic environments

We analyze the conformational properties of polymer macromolecules in solutions in presence of extended structural obstacles of (fractal) dimension $\varepsilon_d$ causing the anisotropy of environment. Applying the pruned-enriched Rosenbluth method (PERM), we obtain numerical estimates for scaling exponents and universal shape parameters of polymers in such environments for a wide range $0<\varepsilon_d<2$ in space dimension $d=3$. An analytical description of the model is developed within the des Cloizeaux direct polymer renormalization scheme. Both numerical and analytical studies qualitatively confirm the existence of two characteristic length scales of polymer chain in directions parallel and perpendicular to the extended defects.

cond-mat.soft↗
arXiv2013

Randomly charged polymers in porous environment

We study the conformational properties of charged polymers in a solvent in the presence of structural obstacles correlated according to a power law $\sim x^{-a}$. We work within the continuous representation of a model of linear chain considered as a random sequence of charges $q_i=\pm q_0$. Such a model captures the properties of polyampholytes -- heteropolymers comprising both positively and negatively charged monomers. We apply the direct polymer renormalization scheme and analyze the scaling behavior of charged polymers up to the first order of an $ε=6-d$, $δ=4-a$-expansion.

cond-mat.soft↗
arXiv2012

Polymers in anisotropic environment with extended defects

The conformational properties of flexible polymers in d dimensions in environments with extended defects are analyzed both analytically and numerically. We consider the case, when structural defects are correlated in \varepsilon_d dimensions and randomly distributed in the remaining d-\varepsilon_d. Within the lattice model of self-avoiding random walks (SAW), we apply the pruned enriched Rosenbluth method (PERM) and find the estimates for scaling exponents and universal shape parameters of polymers in environment with parallel rod-like defects (\varepsilon_d=1). An analytical description of the model is developed within the des Cloizeaux direct polymer renormalization scheme.

cond-mat.dis-nn↗
arXiv2012

Disorder effects on the static scattering function of star branched polymers

We present an analysis of the impact of structural disorder on the static scattering function of f-armed star branched polymers in d dimensions. To this end, we consider the model of a star polymer immersed in a good solvent in the presence of structural defects, correlated at large distances r according to a power law \sim r^{-a}. In particular, we are interested in the ratio g(f) of the radii of gyration of star and linear polymers of the same molecular weight, which is a universal experimentally measurable quantity. We apply a direct polymer renormalization approach and evaluate the results within the double \varepsilon=4-d, δ=4-a-expansion. We find an increase of g(f) with an increasing δ. Therefore, an increase of disorder correlations leads to an increase of the size measure of a star relative to linear polymers of the same molecular weight.

cond-mat.soft↗
arXiv2012

Shapes of macromolecules in good solvents: field theoretical renormalization group approach

In this paper, we show how the method of field theoretical renormalization group may be used to analyze universal shape properties of long polymer chains in porous environment. So far such analytical calculations were primarily focussed on the scaling exponents that govern conformational properties of polymer macromolecules. However, there are other observables that along with the scaling exponents are universal (i.e. independent of the chemical structure of macromolecules and of the solvent) and may be analyzed within the renormalization group approach. Here, we address the question of shape which is acquired by the long flexible polymer macromolecule when it is immersed in a solvent in the presence of a porous environment. This question is of relevance for understanding of the behavior of macromolecules in colloidal solutions, near microporous membranes, and in cellular environment. To this end, we consider a previously suggested model of polymers in d-dimensions [V. Blavats'ka, C. von Ferber, Yu. Holovatch, Phys. Rev. E, 2001, 64, 041102] in an environment with structural obstacles, characterized by a pair correlation function h(r), that decays with distance r according to a power law: h(r) \sim r-a. We apply the field-theoretical renormalization group approach and estimate the size ratio / and the asphericity ratio \hat{A}_d up to the first order of a double ε=4-d, δ=4-a expansion.

cond-mat.soft↗
arXiv2010

Fractals Meet Fractals: Self-Avoiding Random Walks on Percolation Clusters

The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by numerical simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our numerical results yield estimates of critical exponents, governing the scaling laws of disorder averages of the configurational properties of SAWs, and clearly indicate a multifractal spectrum which emerges when two fractals meet each other.

cond-mat.dis-nn↗
arXiv2009

Polymers in crowded environment under stretching force: globule-coil transitions

We study flexible polymer macromolecules in a crowded (porous) environment, modelling them as self-attracting self-avoiding walks (SASAW) on site-diluted percolative lattices in space dimensions d=2, 3. The influence of stretching force on the polymer folding and properties of globule-coil transitions are analyzed. Applying the pruned-enriched Rosenbluth chain-growth method (PERM), we estimate the transition temperature T_Θ 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.

cond-mat.soft↗
arXiv2008

Scaling of complex polymers: new universality classes and beyond

We analyse scaling laws that govern macromolecules of different topology: polymer chains, homogeneous and miktoarm star polymers in a good solvent possibly constrained by a porous medium. The latter is modelled by long-range-correlated disorder with a pair correlation function g(r) that decays with a power law g(r) r^{-a} at large distances r. We show that this type of disorder changes the universality class of the system. Within the frames of the field-theoretical renormalization group approach we obtain the corresponding new universal critical exponents for systems of homogeneous and star copolymers and discuss different consequences of the architecture dependent change of the scaling behaviour.

cond-mat.soft↗
arXiv2005

Enhancement of the critical slowing down influenced by extended defects

We study an influence of the quenched extended defects on the critical dynamics of the d=3-dimensional systems with m-component non-conserved order parameter (model A dynamics). Considering defects to be correlated in ε_d dimensions and randomly distributed in d-ε_d dimensions we obtain reliable numerical values for the critical exponents governing divergence of the relaxation time as function of m and ε_d.

cond-mat.dis-nn↗
arXiv2003

Critical behavior of magnetic systems with extended impurities in general dimensions

We investigate the critical properties of d-dimensional magnetic systems with quenched extended defects, correlated in $ε_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-ε_d$ dimensions; both in the case of fixed dimension d=3 and when the space dimension continuously changes from the lower critical dimension to the upper one. The renormalization group calculations are performed in the minimal subtraction scheme. We analyze the two-loop renormalization group functions for different fixed values of the parameters $d, ε_d$. To this end, we apply the Chisholm-Borel resummation technique and report the numerical values of the critical exponents for the universality class of this system.

cond-mat.dis-nn↗