We investigate the riti al behaviour of a d = 3-dimensional weakly diluted quen hed Ising model, ... more We investigate the riti al behaviour of a d = 3-dimensional weakly diluted quen hed Ising model, analyzing the series for the renormalization group fun tions at d = 3 obtained in a minimal subtra tion s heme. Formerly it was established [R. Folk, Yu. Holovat h, T. Yavorskii, Phys. Rev. B 61, 15 114 (2000)℄ that the resummed renormalization group series possess an \optimal trun ation" behaviour, provided that a Chisholm{Borel resummation te hnique is applied. This resulted in a onje ture that a four-loop approximation is a nal one for the random Ising model renormalizationgroup fun tions in a d = 3 minimal subtra tion s heme. We apply the method of subsequent resummation, developed in the ontext of the d = 0-dimensional random Ising model, dis uss the onvergen e properties of the series and give the results of the riti al exponents in reasing the order of approximation to 5-loop level.
We study the impact of arm architecture of polymers with a single branch point on their structure... more We study the impact of arm architecture of polymers with a single branch point on their structure in solvents. Many physical properties of polymer liquids strongly dependent on the size and shape measures of individual macromolecules, which in turn are determined by their topology. Here, we use combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing $$f^c$$ f c linear branches and $$f^r$$ f r closed loops grafted to the central core. We determine size measures such as the gyration radius $$R_g$$ R g and the hydrodynamic radii $$R_H$$ R H , and obtain the estimates for the size ratio $$R_g /R_H$$ R g / R H with its dependence on the functionality $$f=f^c+f^r$$ f = f c + f r of grafted polymers. In particular, we obtain the quantitative estimate of the degree of compactification of these polymers with increasing number of closed loops $$f^r$$ f r as compared to linear ...
We analyze the properties of population spreading in environments with spatial anisotropy within ... more We analyze the properties of population spreading in environments with spatial anisotropy within the frames of a lattice model of asymmetric (biased) random walkers. The expressions for the universal shape characteristics of the instantaneous configuration of population, such as asphericity A and prolateness S are found analytically and proved to be dependent only on the asymmetric transition probabilities in different directions. The model under consideration is shown to capture, in particular, the peculiarities of invasion in presence of an array of oriented tubes (fibers) in the environment.
The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAW... more 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 bring about the estimates of critical exponents, governing the scaling laws of disorder averages of the configurational properties of SAWs.
We investigate the riti al behaviour of a d = 3-dimensional weakly diluted quen hed Ising model, ... more We investigate the riti al behaviour of a d = 3-dimensional weakly diluted quen hed Ising model, analyzing the series for the renormalization group fun tions at d = 3 obtained in a minimal subtra tion s heme. Formerly it was established [R. Folk, Yu. Holovat h, T. Yavorskii, Phys. Rev. B 61, 15 114 (2000)℄ that the resummed renormalization group series possess an \optimal trun ation" behaviour, provided that a Chisholm{Borel resummation te hnique is applied. This resulted in a onje ture that a four-loop approximation is a nal one for the random Ising model renormalizationgroup fun tions in a d = 3 minimal subtra tion s heme. We apply the method of subsequent resummation, developed in the ontext of the d = 0-dimensional random Ising model, dis uss the onvergen e properties of the series and give the results of the riti al exponents in reasing the order of approximation to 5-loop level.
We study the impact of arm architecture of polymers with a single branch point on their structure... more We study the impact of arm architecture of polymers with a single branch point on their structure in solvents. Many physical properties of polymer liquids strongly dependent on the size and shape measures of individual macromolecules, which in turn are determined by their topology. Here, we use combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing $$f^c$$ f c linear branches and $$f^r$$ f r closed loops grafted to the central core. We determine size measures such as the gyration radius $$R_g$$ R g and the hydrodynamic radii $$R_H$$ R H , and obtain the estimates for the size ratio $$R_g /R_H$$ R g / R H with its dependence on the functionality $$f=f^c+f^r$$ f = f c + f r of grafted polymers. In particular, we obtain the quantitative estimate of the degree of compactification of these polymers with increasing number of closed loops $$f^r$$ f r as compared to linear ...
We analyze the properties of population spreading in environments with spatial anisotropy within ... more We analyze the properties of population spreading in environments with spatial anisotropy within the frames of a lattice model of asymmetric (biased) random walkers. The expressions for the universal shape characteristics of the instantaneous configuration of population, such as asphericity A and prolateness S are found analytically and proved to be dependent only on the asymmetric transition probabilities in different directions. The model under consideration is shown to capture, in particular, the peculiarities of invasion in presence of an array of oriented tubes (fibers) in the environment.
The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAW... more 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 bring about the estimates of critical exponents, governing the scaling laws of disorder averages of the configurational properties of SAWs.
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Papers by Viktoria Blavatska