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We analyse the effects of the environment (solvent quality, presence of extended structures - crowded environment) that may have impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. We find that the effects studied significantly influence the strength of the first order transition. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory to calculate entropic exponents associated with the denaturated loop distribution. For the $d = 3$ case, the corresponding diverging $\epsilon = 4-d$ expansions are evaluated by restoring their convergence via the resummation technique. For the space dimension $d = 2$, the exponents are deduced from mapping the polymer model onto a two-dimensional random lattice, i.e., in the presence of quantum gravity. We also show that the first order transition is further strengthened by the presence of extended impenetrable regions in a solvent that restrict the number of the macromolecule configurations., Comment: Submitted to Condensed Matter Physics Journal

In this paper we study the shape characteristics of star-like polymers in various solvent quality using a mesoscopic level of modeling. The dissipative particle dynamics simulations are performed for the homogeneous and four different heterogeneous star polymers with the same molecular weight. We analyse the gyration radius and asphericity at the bad, good and $\theta$-solvent regimes. Detailed explanation based on interplay between enthalpic and entropic contributions to the free energy and analyses on of the asphericity of individual branches are provided to explain the increase of the apsphericity in $\theta$-solvent regime.

The galaxy data provided by COSMOS survey for 1 by 1 degree field of sky are analysed by methods of complex networks. Three galaxy samples (slices) with redshifts ranging within intervals 0.88-0.91, 0.91-0.94 and 0.94-0.97 are studied as two-dimensional projections for the spatial distributions of galaxies. We construct networks and calculate network measures for each sample, in order to analyse the network similarity of different samples, distinguish various topological environments, and find associations between galaxy properties (colour index and stellar mass) and their topological environments. Results indicate a high level of similarity between geometry and topology for different galaxy samples and no clear evidence of evolutionary trends in network measures. The distribution of local clustering coefficient C manifests three modes which allow for discrimination between stand-alone singlets and dumbbells (0 <= C <= 0.1), intermediately (0 < C < 0.9) and clique (0.9 <= C <= 1) like galaxies. Analysing astrophysical properties of galaxies (colour index and stellar masses), we show that distributions are similar in all slices, however weak evolutionary trends can also be seen across redshift slices. To specify different topological environments we have extracted selections of galaxies from each sample according to different modes of C distribution. We have found statistically significant associations between evolutionary parameters of galaxies and selections of C: the distribution of stellar mass for galaxies with interim C differ from the corresponding distributions for stand-alone and clique galaxies, and this difference holds for all redshift slices. The colour index realises somewhat different behaviour., Comment: 12 pages, 8 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

In this paper we investigate the topological and spatial features of public transport networks (PTN) within the UK. Networks investigated include London, Manchester, West Midlands, Bristol, national rail and coach networks during 2011. Using methods in complex network theory and statistical physics we are able to discriminate PTNs with respect to their stability; which is the first of this kind for national networks. Moreover, taking advantage of various fractal properties we gain useful insights into the serviceable area of stations. These features can be employed as key performance indicators in aid of further developing efficient and stable PTNs., Comment: 23 pages, 9 figures

We study the effect of the molecular architecture of amphiphilic star polymers on the shape of aggregates they form in water. Both solute and solvent are considered at a coarse-grained level by means of dissipative particle dynamics simulations. Four different molecular architectures are considered: the miktoarm star, two different diblock stars and a group of linear diblock copolymers, all of the same composition and molecular weight. Aggregation is started from a closely packed bunch of $N_{\text a}$ molecules immersed into water. In most cases, a single aggregate is observed as a result of equilibration, and its shape characteristics are studied depending on the aggregation number $N_{\text a}$. Four types of aggregate shape are observed: spherical, rod-like and disc-like micelle and a spherical vesicle. We estimate "phase boundaries" between these shapes depending on the molecular architecture. Sharp transitions between aspherical micelle and a vesicle are found in most cases. The pretransition region shows large amplitude oscillations of the shape characteristics with the oscillation frequency strongly dependent on the molecular architecture., Comment: 10 pages, 7 figures

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., Comment: 6 pages

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 law behaviour. This indicates that the routes may in part also be described as L\'evy-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 L\'evy flights., Comment: 7 pages, 3 figures, style files included. Submitted to the topical issue 'From Brownian motion to self-avoiding walks and L\'evy flights' of the journal 'EPJ - Special Topics'

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, \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., Comment: 17 pages, 7 figures

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 the 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., Comment: 16 pages, 6 figures, style files included

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., Comment: 18 pages, 7 figures. Submitted to the topical issue of the journal 'Advances in Complex Systems'

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 \epsilon=4-d, \delta=4-a expansion., Comment: 20 pages, 5 figures

We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions which are of fundamental interest in the theory of critical phenomena and have previously been theoretically and experimentally explored in the context of various magnetic, fluid, and superconducting systems in two and three dimensions. Here, we obtain general scaling functions for the entropy, the constant-field heat capacity, and the isothermal magnetocaloric coefficient near the critical point in scale-free networks, where the node-degree distribution exponent $\lambda$ appears to be a global variable and plays a crucial role, similar to the dimensionality $d$ for systems on lattices. This extends the principle of universality to systems on scale-free networks and allows quantification of the impact of fluctuations in the network structure on critical behavior., Comment: 8 pages, 4 figures

In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices, such corrections appear at some marginal values of the order parameter or space dimension. We present new scaling relations for these exponents. We also consider a spin system on a scale-free network which exhibits logarithmic corrections due to the specific network properties. To this end, we analyze the phase behavior of a model with coupled order parameters on a scale-free network and extract leading and logarithmic correction-to-scaling exponents that determine its field- and temperature behavior. Although both non-trivial sets of exponents emerge from the correlations in the network structure rather than from the spin fluctuations they fulfil the respective thermodynamic scaling relations. For the scale-free networks the logarithmic corrections appear at marginal values of the node degree distribution exponent. In addition we calculate scaling functions, which also exhibit nontrivial dependence on intrinsic network properties., Comment: 15 pages, 4 figures

Public transport routes sharing the same grid of streets and tracks are often found to proceed in parallel along shorter or longer sequences of stations. Similar phenomena are observed in other networks built with space consuming links such as cables, vessels, pipes, neurons, etc. In the case of public transport networks (PTNs) this behavior may be easily worked out on the basis of sequences of stations serviced by each route. To quantify this behavior we use the recently introduced notion of network harness. It is described by the harness distribution P(r,s): the number of sequences of s consecutive stations that are serviced by r parallel routes. For certain PTNs that we have analyzed we observe that the harness distribution may be described by power laws. These power laws observed indicate a certain level of organization and planning which may be driven by the need to minimize the costs of infrastructure and secondly by the fact that points of interest tend to be clustered in certain locations of a city. This effect may be seen as a result of the strong interdependence of the evolutions of both the city and its PTN. To further investigate the significance of the empirical results we have studied one- and two-dimensional models of randomly placed routes modeled by different types of walks. While in one dimension an analytic treatment was successful, the two dimensional case was studied by simulations showing that the empirical results for real PTNs deviate significantly from those expected for randomly placed routes., Comment: 12 pages, 24 figures, paper presented at the Conference ``Statistical Physics: Modern Trends and Applications'' (23-25 June 2009, Lviv, Ukaine) dedicated to the 100th anniversary of Mykola Bogolyubov (1909-1992)

The behavior of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable to targeted attacks. In recent studies of public transport networks of fourteen major cities of the world it was shown that these systems when represented by appropriate graphs may exhibit scale-free behavior [C. von Ferber et al., Physica A 380, 585 (2007), Eur. Phys. J. B 68, 261 (2009)]. Our present analysis, focuses on the effects that defunct or removed nodes have on the properties of public transport networks. Simulating different directed attack strategies, we derive vulnerability criteria that result in minimal strategies with high impact on these systems., Comment: 13 pages, 11 figures

The system of two scalar order parameters on a complex scale-free network is analyzed in the spirit of Landau theory. To add a microscopic background to the phenomenological approach we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean field approximation. Our results show that the system is characterized by either of two types of ordering: either one of the two order parameters is zero or both are non-zero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale free network there are notable differences for the amplitude ratios and susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all T

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., Comment: 6 pages; sent to Proceedings of "XI International Workshop on Complex Systems", Trento (Italy)

We use complex network concepts to analyze statistical properties of urban public transport networks (PTN). To this end, we present a comprehensive survey of the statistical properties of PTNs based on the data of fourteen cities of so far unexplored network size. Especially helpful in our analysis are different network representations. Within a comprehensive approach we calculate PTN characteristics in all of these representations and perform a comparative analysis. The standard network characteristics obtained in this way often correspond to features that are of practical importance to a passenger using public traffic in a given city. Specific features are addressed that are unique to PTNs and networks with similar transport functions (such as networks of neurons, cables, pipes, vessels embedded in 2D or 3D space). Based on the empirical survey, we propose a model that albeit being simple enough is capable of reproducing many of the identified PTN properties. A central ingredient of this model is a growth dynamics in terms of routes represented by self-avoiding walks., Comment: 19 pages, 23 figures

We analyze the impact of a porous medium (structural disorder) on the scaling of the partition function of a star polymer immersed in a good solvent. We show that corresponding scaling exponents change if the disorder is long-range-correlated and calculate the exponents in the new universality class. A notable finding is that star and chain polymers react in qualitatively different manner on the presence of disorder: the corresponding scaling exponents increase for chains and decrease for stars. We discuss the physical consequences of this difference., Comment: Submitted to the Proceedings of the International Conference "Path Integrals - New Trends and Perspectives", September 23-28, 2007, Dresden, Germany

We present results of a survey of public transport networks (PTNs) of selected 14 major cities of the world with PTN sizes ranging between 2000 and 46000 stations and develop an evolutionary model of these networks. The structure of these PTNs is revealed in terms of a set of neighbourhood relations both for the routes and the stations. The networks defined in this way display distinguishing properties due to the constraints of the embedding 2D geographical space and the structure of the cities. In addition to the standard characteristics of complex networks like the number of nearest neighbours, mean path length, and clustering we observe features specific to PTNs. While other networks with real-world links like cables or neurons embedded in two or three dimensions often show similar behavior, these can be studied in detail in our present case. Geographical data for the routes reveal surprising self-avoiding walk properties that we relate to the optimization of surface coverage. We propose and simulate an evolutionary growth model based on effectively interacting self-avoiding walks that reproduces the key features of PTN., Comment: 10 pages, 7 figures

The behavior of complex networks under attack depends strongly on the specific attack scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure or attack but appear to be especially vulnerable to targeted attacks. In a recent study of public transport networks of 14 major cities of the world we have shown that these networks may exhibit scale-free behaviour [Physica A 380, 585 (2007)]. Our further analysis, subject of this report, focuses on the effects that defunct or removed nodes have on the properties of public transport networks. Simulating different attack strategies we elaborate vulnerability criteria that allow to find minimal strategies with high impact on these systems., Comment: 10 pages, 6 figures

We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of $f$-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the pair correlation function $g(r) \sim r^{-a}$. Applying the field-theoretical renormalization group approach we show in a double expansion in $\epsilon=4-d$ and $\delta=4-a$ that there is a range of correlation strengths $\delta$ for which the disorder changes the scaling behavior of star polymers. In a second approach we calculate for fixed space dimension $d=3$ and different values of the correlation parameter $a$ the corresponding scaling exponents $\gamma_f$ that govern entropic effects. We find that $\gamma_f-1$, the deviation of $\gamma_f$ from its mean field value is amplified by the disorder once we increase $\delta$ beyond a threshold. The consequences for a solution of diluted chain and star polymers of equal molecular weight inside a porous medium are: star polymers exert a higher osmotic pressure than chain polymers and in general higher branched star polymers are expelled more strongly from the correlated porous medium. Surprisingly, polymer chains will prefer a stronger correlated medium to a less or uncorrelated medium of the same density while the opposite is the case for star polymers., Comment: 14 pages, 7 figures

We analyse the statistical properties of public transport networks. These networks are defined by a set of public transport routes (bus lines) and the stations serviced by these. For larger networks these appear to possess a scale-free structure, as it is demonstrated e.g. by the Zipf law distribution of the number of routes servicing a given station or for the distribution of the number of stations which can be visited from the chosen one without changing the means of transport. Moreover, a rather particular feature of the public transport network is that many routes service common subsets of stations. We discuss the possibility of new scaling laws that govern intrinsic features of such subsets., Comment: 9 pages, 4 figures

We study the structure of complexes formed between ionic surfactants (SF) and a single oppositely charged polyelectrolyte (PE) chain. For our computer simulation we use the ``primitive'' electrolyte model: while the polyelectrolyte is modeled by a tethered chain of charged hard sphere beads, the surfactant molecules consist of a single charged head bead tethered to a tail of tethered hard spheres. A hydrophobic attraction between the tail beads is introduced by assuming a Lennard-Jones potential outside the hard-sphere diameter. As a function of the strengths of both the electrostatic and the hydrophobic interactions, we find the following scenario: switching on and increasing the electrostatic forces first leads to a stretching of the PE and then by condensation of SF to the formation of a complex. For vanishing hydrophobic forces this complex has the architecture of a molecular bottle-brush cylindrically centered around the stretched PE molecule. Upon increasing the hydrophobic attraction between the SF tails, a transition occurs inverting this structure to a spherical micelle with a neutral core of SF tails and a charged corona of SF heads with the PE molecule wrapped around. At intermediate hydrophobicity there is a competition between the two structures indicated by a non-monotonic dependence of the shape as function of the Coulomb strength, favoring the cylindrical shape for weak and the spherical micellar complex for strong interaction., Comment: 11 pages, 12 figures

In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum for a general type of tree-like networks. Close to the percolation threshold we find characteristic scaling functions for the density of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for small lambda, where alpha_1 holds below and alpha_2 at the percolation threshold. In the range where the spectra are accessible from a numerical diagonalization procedure the two methods lead to very similar results., Comment: 9 pages, 6 figures

The scaling properties of self-avoiding walks on a d-dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Y. Meir and A. B. Harris (Phys. Rev. Lett. 63:2819 (1989)) and argue that via renormalization its multifractal properties are directly accessible. While the former first order perturbation did not agree with the results of other methods, we find that the asymptotic behavior of a self-avoiding walk on the percolation cluster is governed by the exponent nu_p=1/2 + epsilon/42 + 110epsilon^2/21^3, epsilon=6-d. This analytic result gives an accurate numeric description of the available MC and exact enumeration data in a wide range of dimensions 2<=d<=6., Comment: 4 pages, 2 figures

We extend existing renormalization group calculations for the exponents describing scaling of star polymers and polymer networks constituted by chains of different species (the so-called copolymer star exponents). Our four loop results find application in the description of various phenomena involving self-avoiding and random walks that interact., Comment: 9 pages, 1 figure, style file included

We investigate the critical properties of d-dimensional magnetic systems with quenched extended defects, correlated in $\epsilon_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-\epsilon_d$ 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 $d, \epsilon_d$. 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., Comment: 8 figures. To appear in Phys. Rev. B

In these lectures, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range-correlated random-site disorder, and (iii) random anisotropy. Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of these lectures is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models., Comment: Lectures given at the Second International Pamporovo Workshop on Cooperative Phenomena in Condensed Matter (28th July - 7th August 2001, Pamporovo, Bulgaria). 51 pages, 12 figures, 1 style files included

Using monomer-resolved Molecular Dynamics simulations and theoretical arguments based on the radial dependence of the osmotic pressure in the interior of a star, we systematically investigate the effective interactions between hard, colloidal particles and star polymers in a good solvent. The relevant parameters are the size ratio q between the stars and the colloids, as well as the number of polymeric arms f (functionality) attached to the common center of the star. By covering a wide range of q's ranging from zero (star against a flat wall) up to about 0.75, we establish analytical forms for the star-colloid interaction which are in excellent agreement with simulation results. A modified expression for the star-star interaction for low functionalities, f < 10 is also introduced., Comment: 37 pages, 14 figures, preprint-version

We examine the demixing transition in star polymer-colloid mixtures for star arm numbers f=2,6,16,32 and different star-colloid size ratios. Theoretically, we solve the thermodynamically self-consistent Rogers-Young integral equations for binary mixtures using three effective pair potentials obtained from direct molecular computer simulations. The numerical results show a spinodal instability. The demixing binodals are approximately calculated, and found to be consistent with experimental observations., Comment: 4 pages, 4 figures, submitted to PRL