Christian von Ferber

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.

Attack Vulnerability of Public Transport Networks

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.

Transportation Network Stability: A Case Study Of City Transit

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 ∈ [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.

Fractal transit networks: Self-avoiding walks and Lévy flights

Using the 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 Lévy-flights. The latter property may result from the fact that the routes are planned to be adapted to the fluctuating demand densities throughout the served area. We also relate this to optimization properties of Lévy flights.

The shapes of simple three and four junction comb polymers

A scheme originally proposed by G. Wei [Physica A 222, 152 (1995); Physica A 222, 155 (1995)] is redesigned to produce numerical shape parameters of arbitrary tree-branched polymers based on the Kirchhoff matrix eigenvalue spectrum. This method and two different Monte Carlo techniques (pivot and growth) are employed to investigate the asphericity of three and four junction comb polymers in both the ideal and excluded volume regimes. It is found that the extrapolated g-ratio and asphericity values obtained by all of these methods are in excellent agreement with each other and the available theory in the ideal regime and that polymers with a complete set of interior branches display a more sphere-like shape.

Interactions and phase transitions of colloidal dispersions in bulk and at interfaces

Recent progress in the theory and computer simulation of effective interactions and phase transitions of colloidal dispersions is reviewed. Particular emphasis is put on the role of the discrete solvent in determining the effective interaction between charged colloids, bulk fluid–fluid phase separation of star–polymer–colloid mixtures, and on interfacial freezing transitions of sterically stabilized colloids on patterned substrates.

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.

Public transportation in Great Britain viewed as a complex network

ABSTRACT In this paper, we investigate the topological and spatial features of public transport networks (PTN) within Great Britain. 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 PTN with respect to their stability, which is the first of this kind for national networks. Taking advantage of various fractal properties we gain useful insights into the serviceable area of stations. Moreover, we investigate universal load dynamics of these systems. These features can be employed as key performance indicators in aid of further developing efficient and stable PTN.