Rigorous results on spontaneous symmetry breaking in a one-dimensional driven particle system

We study spontaneous symmetry breaking in a one-dimensional driven two-species stochastic cellular automaton with parallel sublattice update and open boundaries. The dynamics are symmetric with respect to interchange of particles. Starting from an empty initial lattice, the system enters a symmetry broken state after some time T_1 through an amplification loop of initial fluctuations. It remains in the symmetry broken state for a time T_2 through a traffic jam effect. Applying a simple martingale argument, we obtain rigorous asymptotic estimates for the expected times ~ L ln(L) and ln() ~ L, where L is the system size. The actual value of T_1 depends strongly on the initial fluctuation in the amplification loop. Numerical simulations suggest that T_2 is exponentially distributed with a mean that grows exponentially in system size. For the phase transition line we argue and confirm by simulations that the flipping time between sign changes of the difference of particle numbers approaches an algebraic distribution as the system size tends to infinity.Comment: 23 pages, 7 figure

Diffusion in a generalized Rubinstein-Duke model of electrophoresis with kinematic disorder

Using a generalized Rubinstein-Duke model we prove rigorously that kinematic disorder leaves the prediction of standard reptation theory for the scaling of the diffusion constant in the limit for long polymer chains $D \propto L^{-2}$ unaffected. Based on an analytical calculation as well as Monte Carlo simulations we predict kinematic disorder to affect the center of mass diffusion constant of an entangled polymer in the limit for long chains by the same factor as single particle diffusion in a random barrier model.Comment: 29 pages, 3 figures, submitted to PR

Studies of the limit order book around large price changes

We study the dynamics of the limit order book of liquid stocks after experiencing large intra-day price changes. In the data we find large variations in several microscopical measures, e.g., the volatility the bid-ask spread, the bid-ask imbalance, the number of queuing limit orders, the activity (number and volume) of limit orders placed and canceled, etc. The relaxation of the quantities is generally very slow that can be described by a power law of exponent $\approx0.4$. We introduce a numerical model in order to understand the empirical results better. We find that with a zero intelligence deposition model of the order flow the empirical results can be reproduced qualitatively. This suggests that the slow relaxations might not be results of agents' strategic behaviour. Studying the difference between the exponents found empirically and numerically helps us to better identify the role of strategic behaviour in the phenomena.Comment: 19 pages, 7 figure

Microtubule length dependence of motor traffic in cells

In living cells, motor proteins, such as kinesin and dynein can move processively along microtubule (MT), and also detach from or attach to MT stochastically. Experiments have found that, the traffic of motor might be jammed, and various theoretical models have been designed to understand this traffic jam phenomenon. But previous studies mainly focus on motor attachment/detachment rate dependent properties. Recent experiment of Leduc {\it et al.} found that the traffic jam formation of motor protein kinesin depends also on the length of MT [Proc. Natl. Acad. Sci. U.S.A. {\bf 109}, 6100-6105 (2012)]. In this study, the MT length dependent properties of motor traffic will be analyzed. We found that MT length has one {\it critical value} $N_c$, traffic jam occurs only when MT length $N>N_c$. The jammed length of MT increases with total MT length, while the non-jammed MT length might not change monotonically with the total MT length. The critical value $N_c$ increases with motor detachment rate from MT, but decreases with motor attachment rate to MT

Arm and hand skills: Training preferences after stroke

Item does not contain fulltextPurpose. An increasing demand for training after stroke has brought about the need to develop rehabilitation technology. This article reports an inquiry into skill preferences of persons after stroke regarding arm-hand training and examines the relationship between the use of the affected arm and the patient's training preference. Method. Data collection involved a semi-structured interview of 20 persons in the subacute and 20 persons in the chronic stage after stroke, based on an adaptation of the motor activity log. Results. Subacute and chronic patients after stroke agreed on seven out of 10 most preferred training skills. Patient preferences related mostly to 'manipulation in combination with positioning' and 'manipulation'. Eight motivation aspects for skill training were identified as being important. A positive correlation was found between skill preference scores and use of the impaired arm (r = 0.64) (p < 0.001). Conclusions. This study has resulted in an inventory of skills that persons after stroke prefer to train on. This list can be used for implementation of exercises in rehabilitation technology. Motivation for skill training pertains to optimising participation level, rather than function or activity level. This study suggests that client-centred assessment is advocated to set therapy goals that match patient training preferences