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 $epsilon=6-d$, $delta=4-a$-expansion.
Using data on the Berlin public transport network, the present study extends previous observations of fractality within public transport routes by showing that also the distribution of inter-station distances along routes displays non-trivial power l
aw behaviour. This indicates that the routes may in part also be described as Levy-flights. The latter property may result from the fact that the routes are planned to adapt to fluctuating demand densities throughout the served area. We also relate this to optimization properties of Levy flights.
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 struct
ural 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, delta=4-a-expansion. We find an increase of g(f) with an increasing delta. 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.
This paper analyses the impact of random failure or attack on the public transit networks of London and Paris in a comparative study. In particular we analyze how the dysfunction or removal of sets of stations or links (rails, roads, etc.) affects th
e connectivity properties within these networks. We show how accumulating dysfunction leads to emergent phenomena that cause the transportation system to break down as a whole. Simulating different directed attack strategies, we find minimal strategies with high impact and identify a-priory criteria that correlate with the resilience of these networks. To demonstrate our approach, we choose the London and Paris public transit networks. Our quantitative analysis is performed in the frames of the complex network theory - a methodological tool that has emerged recently as an interdisciplinary approach joining methods and concepts of the theory of random graphs, percolation, and statistical physics. In conclusion we demonstrate that taking into account cascading effects the network integrity is controlled for both networks by less than 0.5 % of the stations i.e. 19 for Paris and 34 for London.
The goals of this paper are to present criteria, that allow to a priori quantify the attack stability of real world correlated networks of finite size and to check how these criteria correspond to analytic results available for infinite uncorrelated
networks. As a case study, we consider public transportation networks (PTN) of several major cities of the world. To analyze their resilience against attacks either the network nodes or edges are removed in specific sequences (attack scenarios). During each scenario the size S(c) of the largest remaining network component is observed as function of the removed share c of nodes or edges. To quantify the PTN stability with respect to different attack scenarios we use the area below the curve described by S(c) for c in [0,1] recently introduced (Schneider, C. M, et al., PNAS 108 (2011) 3838) as a numerical measure of network robustness. This measure captures the network reaction over the whole attack sequence. We present results of the analysis of PTN stability against node and link-targeted attacks.
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 scalin
g 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. Blavatska, 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 <R_e^2>/<R_G^2 > and the asphericity ratio hat{A}_d up to the first order of a double epsilon=4-d, delta=4-a expansion.
