Ageing in disordered magnets and local scale-invariance

The ageing of the bond-disordered two-dimensional Ising model quenched to below its critical point is studied through the two-time autocorrelator and thermoremanent magnetization (TRM). The corresponding ageing exponents are determined. The form of the scaling function of the TRM is well described by the theory of local scale-invariance.Comment: Latex2e, with epl macros, 7 pages, final for

On the predictive power of Local Scale Invariance

Local Scale Invariance (LSI) is a theory for anisotropic critical phenomena designed in the spirit of conformal invariance. For a given representation of its generators it makes non-trivial predictions about the form of universal scaling functions. In the past decade several representations have been identified and the corresponding predictions were confirmed for various anisotropic critical systems. Such tests are usually based on a comparison of two-point quantities such as autocorrelation and response functions. The present work highlights a potential problem of the theory in the sense that it may predict any type of two-point function. More specifically, it is argued that for a given two-point correlator it is possible to construct a representation of the generators which exactly reproduces this particular correlator. This observation calls for a critical examination of the predictive content of the theory.Comment: 17 pages, 2 eps figure

Ageing without detailed balance: local scale invariance applied to two exactly solvable models

I consider ageing behaviour in two exactly solvable reaction-diffusion systems. Ageing exponents and scaling functions are determined. I discuss in particular a case in which the equality of two critical exponents, known from systems with detailed balance, does not hold any more. Secondly it is shown that the form of the scaling functions can be understood by symmetry considerations.Comment: 6 pages, contribution to the summer school "Ageing and the Glass Transition" held in Luxemburg in September 05. Published versio

Kinetics of the long-range spherical model

The kinetic spherical model with long-range interactions is studied after a quench to $T < T_c$ or to $T = T_c$. For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale-invariance.Comment: added "fluctuation-dissipation ratios"; fixed typo

Service-based survey of dystonia in Munich

We performed a service-based epidemiological study of dystonia in Munich, Germany. Due to favourable referral and treatment patterns in the Munich area, we could provide confident data from dystonia patients seeking botulinum toxin treatment. A total of 230 patients were ascertained, of whom 188 had primary dystonia. Point prevalence ratios were estimated to be 10.1 (95% confidence interval 8.4-11.9) per 100,000 for focal and 0.3 (0.0-0.6) for generalised primary dystonia. The most common focal primary dystonias were cervical dystonia with 5.4 (4.2-6.7) and essential blepharospasm with 3.1 (2.1-4.1) per 100,000 followed by laryngeal dystonia (spasmodic dysphonia) with 1.0 (0.4-1.5) per 100,000. Copyright (C) 2002 S. Karger AG, Base

Residual entropy in a model for the unfolding of single polymer chains

We study the unfolding of a single polymer chain due to an external force. We use a simplified model which allows to perform all calculations in closed form without assuming a Boltzmann-Gibbs form for the equilibrium distribution. Temperature is then defined by calculating the Legendre transform of the entropy under certain constraints. The application of the model is limited to flexible polymers. It exhibits a gradual transition from compact globule to rod. The boundary line between these two phases shows reentrant behavior. This behavior is explained by the presence of residual entropy.Comment: 5 pages, 4 figures, extended version of arXiv:cond-mat/061225

Ageing in bosonic particle-reaction models with long-range transport

Ageing in systems without detailed balance is studied in bosonic contact and pair-contact processes with Levy diffusion. In the ageing regime, the dynamical scaling of the two-time correlation function and two-time response function is found and analysed. Exact results for non-equilibrium exponents and scaling functions are derived. The behaviour of the fluctuation-dissipation ratio is analysed. A passage time from the quasi-stationary regime to the ageing regime is defined, in qualitative agreement with kinetic spherical models and p-spin spherical glasses.Comment: Latex2e, 24 pages, with 9 figures include

DNA Spools under Tension

DNA-spools, structures in which DNA is wrapped and helically coiled onto itself or onto a protein core are ubiquitous in nature. We develop a general theory describing the non-equilibrium behavior of DNA-spools under linear tension. Two puzzling and seemingly unrelated recent experimental findings, the sudden quantized unwrapping of nucleosomes and that of DNA toroidal condensates under tension are theoretically explained and shown to be of the same origin. The study provides new insights into nucleosome and chromatin fiber stability and dynamics

Optimal Pacing for Running 400 m and 800 m Track Races

Physicists seeking to understand complex biological systems often find it rewarding to create simple "toy models" that reproduce system behavior. Here a toy model is used to understand a puzzling phenomenon from the sport of track and field. Races are almost always won, and records set, in 400 m and 800 m running events by people who run the first half of the race faster than the second half, which is not true of shorter races, nor of longer. There is general agreement that performance in the 400 m and 800 m is limited somehow by the amount of anaerobic metabolism that can be tolerated in the working muscles in the legs. A toy model of anaerobic metabolism is presented, from which an optimal pacing strategy is analytically calculated via the Euler-Lagrange equation. This optimal strategy is then modified to account for the fact that the runner starts the race from rest; this modification is shown to result in the best possible outcome by use of an elementary variational technique that supplements what is found in undergraduate textbooks. The toy model reproduces the pacing strategies of elite 400 m and 800 m runners better than existing models do. The toy model also gives some insight into training strategies that improve performance.Comment: 14 pages, 4 figures, submitted to the American Journal of Physic