Narrow Results

A previously introduced model (B. Cleuren and C. Van den Broeck, Europhys. Lett.54, 1 (2001)) is studied numerically. Pure negative mobility is found for the minimum number of three interacting walkers.

We study the noise induced transport of an overdamped Brownian particle in frictional ratchet systems in the presence of a special class of external multiplicative Gaussian white noise fluctuations. The analytical expressions for current and diffusion coefficient are derived and the reliability or coherence of transport are discussed by means of their ratio. We show that these frictional ratchets exhibit larger coherence as compared to the flashing and rocking ratchets.

We investigated the motion of two-head Brownian motors by introducing a model in which the two heads coupled through an elastic spring is subjected to a stochastic flashing potential. The ratchet potential felt by the individual head is anti-correlated. The mean velocity was calculated based on Langevin equations. It turns out that we can obtain a unidirectional current. The current is sensitive to the transition rates and neck length and other parameters. The coupling of transition rate and neck length leads to variations both in the values and directions of currency. With a larger neck length, the bi-particle system has a larger velocity in one direction, while with a smaller neck length, it has a smaller velocity in the other direction. This is very likely the case of myosins with a larger neck length and larger velocity in the positive direction of filaments and kinesins with a smaller neck length and smaller velocity in the negative direction of microtubules. We also further investigated how current reversal depended on the neck length and the transition rates.

In a previous work, we described transport in a classical, externally driven, overdamped ratchet. A transport current arises under two possible conditions: either by increasing the external driving or by adding an optimal amount of noise when the system operates below threshold. In this work, we study the underdamped case. In order to obtain transport it is necessary for the presence of both — a damping mechanism and the lack of symmetries in the potential. Some interesting properties were found: under particular conditions the system could be considered as a mass separation device, and for a specific range of the control parameter, the maximum Lyapunov exponent is reduced when noise is added to the system. We also study analytically and numerically the quantum analog of the same system and explore the conditions to find transport.

We introduce a new family of Parrondo's games of alternating losing strategies in order to get a winning result. In our version of the games we consider an ensemble of players and use "social" rules in which the probabilities of the games are defined in terms of the actual state of the neighbors of a given player.

We present new versions of the Parrondo's paradox by which a losing game can be turned into winning by including a mechanism that allows redistribution of the capital amongst an ensemble of players. This shows that, for this particular class of games, redistribution of the capital is beneficial for everybody. The same conclusion arises when the redistribution goes from the richer players to the poorer.

We address the problem of the chaotic transport of particles in an asymmetric periodic ratchet potential. We consider the case of deterministic rocking ratchets and analyze different regimes for the amplitude of rocking. When the inertial term is taken into account, the dynamics can be chaotic and modify the transport properties. We compare the dynamics of point particles and extended objects under the action of the ratchet potential and show that we can segregate particles according to its size.

A discrete-time Markov chain solution with exact rules for general computation of transition probabilities of the one-dimensional cooperative Parrondo's games is presented. We show that winning and the occurrence of the paradox depends on the number of players. Analytical results are compared to the results of the computer simulation and to the results based on the mean-field approach.

Inspired by asynchronous cooperative Parrondo's games we introduce two new types of games in which all players simultaneously play game A or game B or a combination of these two games. These two types of games differ in the way a combination of games A and B is played. In the first type of synchronous games, all players simultaneously play the same game (either A or B), while in the second type players simultaneously play the game of their choice, i.e. A or B. We show that for these games, as in the case of asynchronous games, occurrence of the paradox depends on the number of players. An analytical result and an algorithm are derived for the probability distribution of these games.

We analyze a model for a walker moving on an asymmetric periodic ratchet potential. This model is motivated by the properties of transport of the motor protein kinesin. The walker consists of two feet represented as two particles coupled nonlinearly through a double-well bistable potential. In contrast to linear coupling, the bistable potential admits a richer dynamics where the ordering of the particles can alternate during the walking. The transitions between the two stable points on the bistable potential, correspond to a walking with alternating particles. In our model, each particle is acted upon by independent white noises, modeling thermal noise, and additionally we have an external time-dependent force that drives the system out of equilibrium, allowing directed transport. In the equilibrium case, where only white noise is present, we perform a bifurcation analysis which reveals different walking patterns. In particular, we distinguish between two main walking styles: alternating and no alternating. These two ways of walking resemble the hand-over-hand and the inchworm walking in kinesin, respectively. Numerical simulations showed the existence of current reversals and significant changes in the effective diffusion constant. We obtained an optimal coherent transport, characterized by a maximum dimensionless ratio of the current and the effective diffusion (Péclet number), when the periodicity of the ratchet potential coincides with the equilibrium distance between the two particles.

I give a simple analysis of the game that I previously published in Scientific American which shows the paradoxical behavior whereby two losing games randomly combine to form a winning game. The game, modeled on a random walk, requires only two states and is described by a first-order Markov process.