arXiv subjects

Christian von Ferber

Publications and source records attributed to Christian von Ferber.

At least 19 recordsLinked to original sources

arXiv2021

Variety of Scaling Laws for DNA Thermal Denaturation

We discuss possible mechanisms that may impact the order of the transition between denaturated and bound DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory approach to calculate entropic exponents associated with the denaturated loop distribution. We discuss in particular variants of this transition that may occur due to the properties of the solution and may affect the self- and mutual interaction of both single and double strands. We find that the effects studied significantly influence the strength of the first order transition. This is manifest in particular by the changes in the scaling laws that govern DNA loop and strand distribution. As a quantitative measure of these changes we present the values of corresponding scaling exponents. For the $d=4-\varepsilon$ case we get corresponding $\varepsilon^4$ expansions and evaluate the perturbation theory expansions at space dimension $d=3$ by means of resummation technique.

cond-mat.soft↗

arXiv2016

Universal shape characteristics for the mesoscopic polymer chain via dissipative particle dynamics

In this paper we study the shape characteristics of a polymer chain in a good solvent using a mesoscopic level of modelling. The dissipative particle dynamics simulations are performed in the $3D$ space at a range of chain lengths $N$. The scaling laws for the end-to-end distance and gyration radius are examined first and found to hold for $N\geq 10$ yielding reasonably accurate value for the Flory exponent $ν$. Within the same interval of chain lengths, the asphericity, prolateness, size ratio and other shape characteristics of the chain are found to become independent of $N$. Their mean values are found to agree reasonably well with the respective theoretical results and lattice Monte Carlo simulations. Broad probability distributions for the shape characteristics are found resembling in form the results of lattice Monte Carlo simulations. By means of analytic fitting of these distributions the most probable values for the shape characteristics are found to supplement their mean values.

cond-mat.soft↗

arXiv2015

How does a flexible chain of active particles swell?

We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain dragged at one end. First we consider an ideal chain with harmonic springs and no excluded volume between the monomers. The Rouse model of polymers is generalized to the case of self-propelled monomers and solved analytically. The swelling, as characterized by the spatial extension of the chain, scales with the monomer number defining a Flory exponent $ν$ which is $ν=1/2, 0, 1$ in the three different situations. As a result, we find that activity does not change the Flory exponent but affects the prefactor of the scaling law. This can be quantitatively understood by mapping the system onto an equilibrium chain with a higher effective temperature such that the chain swells under an increase of the self-propulsion strength. We then use computer simulations to study the effect of self-avoidance on active polymer swelling. In the three different situations, the Flory exponent is now $ν= 3/4, 1/4, 1$ and again unchanged under self-propulsion. However, the chain extension behaves non-monotonic in the self-propulsion strength.

cond-mat.soft↗

arXiv2011

Scaling behaviour of lattice animals at the upper critical dimension

We perform numerical simulations of the lattice-animal problem at the upper critical dimension d=8 on hypercubic lattices in order to investigate logarithmic corrections to scaling there. Our stochastic sampling method is based on the pruned-enriched Rosenbluth method (PERM), appropriate to linear polymers, and yields high statistics with animals comprised of up to 8000 sites. We estimate both the partition sums (number of different animals) and the radii of gyration. We re-verify the Parisi-Sourlas prediction for the leading exponents and compare the logarithmic-correction exponents to two partially differing sets of predictions from the literature. Finally, we propose, and test, a new Parisi-Sourlas-type scaling relation appropriate for the logarithmic-correction exponents.

cond-mat.stat-mech↗

arXiv2010

Star copolymers in porous environments: scaling and its manifestations

We consider star polymers, consisting of two different polymer species, in a solvent subject to quenched correlated structural obstacles. We assume that the disorder is correlated with a power-law decay of the pair correlation function g(x)\sim x^{-a}. Applying the field-theoretical renormalization group approach in d dimensions, we analyze different scenarios of scaling behavior working to first order of a double ε=4-d, δ=4-a expansion. We discuss the influence of the correlated disorder on the resulting scaling laws and possible manifestations such as diffusion controlled reactions in the vicinity of absorbing traps placed on polymers as well as the effective short-distance interaction between star copolymers.

cond-mat.soft↗

arXiv2010

Universal features of polymer shapes in crowded environment

We study the universal characteristics of the shape of a polymer chain in an environment with correlated structural obstacles, applying the field-theoretical renormalization group approach. Our results qualitatively indicate an increase of the asymmetry of the polymer shape in crowded environment comparing with the pure solution case.

cond-mat.soft↗

arXiv2010

Public Transport Networks under Random Failure and Directed Attack

The behaviour 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 a recent study of public transport networks of 14 major cities of the world we have shown that these systems when represented by appropriate graphs may exhibit scale-free behaviour. In this paper we briefly review some of the recent results about 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.

physics.soc-ph↗

arXiv2008

Fisher Renormalization for Logarithmic Corrections

For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.

cond-mat.stat-mech↗

arXiv2006

Network Harness: Metropolis Public Transport

We analyze the public transport networks (PTNs) of a number of major cities of the world. While the primary network topology is defined by a set of routes each servicing an ordered series of given stations, a number of different neighborhood relations may be defined both for the routes and the stations. The networks defined in this way display distinguishing properties, the most striking being that often several routes proceed in parallel for a sequence of stations. Other networks with real-world links like cables or neurons embedded in two or three dimensions often show the same feature - we use the car engineering term "harness" for such networks. Geographical data for the routes reveal surprising self-avoiding walk (SAW) properties. We propose and simulate an evolutionary model of PTNs based on effectively interacting SAWs that reproduces the key features.

physics.soc-ph↗

arXiv2005

Dynamics of end-linked star polymer structures

In this work we focus on the dynamics of macromolecular networks formed by end-linking identical polymer stars. The resulting macromolecular network can then be viewed as consisting of spacers which connect branching points (the cores of the stars). We succeed in analyzing exactly, in the framework of the generalized Gaussian model, the eigenvalue spectrum of such networks. As applications we focus on several topologies, such as regular networks and dendrimers; furthermore, we compare the results to those found for regular hyperbranched structures. In so doing, we also consider situations in which the beads of the cores differ from the beads of the spacers. The analytical procedure which we use involves an exact real-space renormalization, which allows to relate the star-network to a (much simpler) network, in which each star is reduced to its core. It turns out that the eigenvalue spectrum of the star-polymer structure consists of two parts: One follows in terms of polynomial equations from the relaxation spectrum of the corresponding renormalized structure, while the second part involves the motion of the spacer chains themselves. Finally, we show exemplarily the situation for copolymeric dendrimers, calculate their spectra, and from them their storage and the loss moduli.

cond-mat.soft↗

arXiv2002

Scaling exponents of star polymers

We review recent results of the field theoretical renormalization group analysis on the scaling properties of star polymers. We give a brief account of how the numerical values of the exponents governing the scaling of star polymers were obtained as well as provide some examples of the phenomena governed by these exponents. In particular we treat the interaction between star polymers in a good solvent, the Brownian motion near absorbing polymers, and diffusion-controlled reactions involving polymers.

cond-mat.soft↗

arXiv2002

Two-dimensional Copolymers and Multifractality: Comparing Perturbative Expansions, MC Simulations, and Exact Results

We analyze the scaling laws for a set of two different species of long flexible polymer chains joined together at one of their extremities (copolymer stars) in space dimension D=2. We use a formerly constructed field-theoretic description and compare our perturbative results for the scaling exponents with recent conjectures for exact conformal scaling dimensions derived by a conformal invariance technique in the context of D=2 quantum gravity. A simple MC simulation brings about reasonable agreement with both approaches. We analyse the remarkable multifractal properties of the spectrum of scaling exponents.

cond-mat.soft↗

arXiv2001

Polymers in long-range-correlated disorder

We study the scaling properties of polymers in a d-dimensional medium with quenched defects that have power law correlations ~r^{-a} for large separations r. This type of disorder is known to be relevant for magnetic phase transitions. We find strong evidence that this is true also for the polymer case. Applying the field-theoretical renormalization group approach we perform calculations both in a double expansion in epsilon=4-d and delta=4-a up to the 1-loop order and secondly in a fixed dimension (d=3) approach up to the 2-loop approximation for different fixed values of the correlation parameter, 2=<a=<3. In the latter case the numerical results need appropriate resummation. We find that the asymptotic behavior of self-avoiding walks in three dimensions and long-range-correlated disorder is governed by a set of separate exponents. In particular, we give estimates for the 'nu' and 'gamma' exponents as well as for the correction-to-scaling exponent 'omega'. The latter exponent is also calculated for the general m-vector model with m=1,2,3.

cond-mat.soft↗

arXiv2000

Cluster update and recognition

We present a fast and robust cluster update algorithm that is especially efficient in implementing the task of image segmentation using the method of superparamagnetic clustering. We apply it to a Potts model with spin interactions that are are defined by gray-scale differences within the image. Motivated by biological systems, we introduce the concept of neural inhibition to the Potts model realization of the segmentation problem. Including the inhibition term in the Hamiltonian results in enhanced contrast and thereby significantly improves segmentation quality. As a second benefit we can - after equilibration - directly identify the image segments as the clusters formed by the clustering algorithm. To construct a new spin configuration the algorithm performs the standard steps of (1) forming clusters and of (2) updating the spins in a cluster simultaneously. As opposed to standard algorithms, however, we share the interaction energy between the two steps. Thus the update probabilities are not independent of the interaction energies. As a consequence, we observe an acceleration of the relaxation by a factor of 10 compared to the Swendson and Wang procedure.

cond-mat.stat-mech↗

arXiv2000

Polydisperse star polymer solutions

We analyze the effect of polydispersity in the arm number on the effective interactions, structural correlations and the phase behavior of star polymers in a good solvent. The effective interaction potential between two star polymers with different arm numbers is derived using scaling theory. The resulting expression is tested against monomer-resolved molecular dynamics simulations. We find that the theoretical pair potential is in agreement with the simulation data in a much wider polydispersity range than other proposed potentials. We then use this pair potential as an input in a many-body theory to investigate polydispersity effects on the structural correlations and the phase diagram of dense star polymer solutions. In particular we find that a polydispersity of 10%, which is typical in experimental samples, does not significantly alter previous findings for the phase diagram of monodisperse solutions.

cond-mat.soft↗

arXiv2000

Triplet forces between star polymers

We analyze the effective triplet interactions between the centers of star polymers in a good solvent. Using an analytical short distance expansion inspired by scaling theory, we deduce that the triplet part of the three-star force is attractive but only 11% of the pairwise part even for a close approach of three star polymers. We have also performed extensive computer simulations for different arm numbers to extract the effective triplet force. The simulation data show good correspondence with the theoretical predictions. Our results justify the effective pair potential picture even beyond the star polymer overlap concentration.

cond-mat.soft↗

arXiv1999

Diffusion-controlled reactions in presence of polymers

We study the properties of diffusion controlled reactions with traps or reaction sites attached to polymer chains or to a star polymer. Using a field theoretical renormalization group approach we obtain the scaling of the moments of concentration of diffusing particles near the core of a star polymer and calculate numerical values of the exponents governing the scaling of the reaction rate.

cond-mat.soft↗

arXiv1999

Colloids with polymer stars: The interaction

We derive the short distance interaction of star polymers in a colloidal solution. We calculate the corresponding force between two stars with arbitrary numbers of legs f_1 and f_2. We show that a simple scaling theory originally derived for high f_1, f_2 nicely matches with the results of elaborated renormalization group analysis for f_1 + f_2 =< 6 generalizing and confirming a previous conjecture based only on scaling results for f_1=f_2=1,2.

cond-mat.soft↗