Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox

Parrondo's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker-Planck equation, that rigorously establish the connection between Parrondo's games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo's games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.Comment: 17 pages, 5 figure

Wave-unlocking transition in resonantly coupled complex Ginzburg-Landau equations

We study the effect of spatial frequency-forcing on standing-wave solutions of coupled complex Ginzburg-Landau equations. The model considered describes several situations of nonlinear counterpropagating waves and also of the dynamics of polarized light waves. We show that forcing introduces spatial modulations on standing waves which remain frequency locked with a forcing-independent frequency. For forcing above a threshold the modulated standing waves unlock, bifurcating into a temporally periodic state. Below the threshold the system presents a kind of excitability.Comment: 4 pages, including 4 postscript figures. To appear in Physical Review Letters (1996). This paper and related material can be found at http://formentor.uib.es/Nonlinear

The flashing ratchet and unidirectional transport of matter

We study the flashing ratchet model of a Brownian motor, which consists in cyclical switching between the Fokker-Planck equation with an asymmetric ratchet-like potential and the pure diffusion equation. We show that the motor really performs unidirectional transport of mass, for proper parameters of the model, by analyzing the attractor of the problem and the stationary vector of a related Markov chain.Comment: 11 page

Multiple Front Propagation Into Unstable States

The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable periodic pattern. It is found by a numerical solution of a model of the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of decay of such periodic unstable states is the propagation of a second front which replaces the unstable pattern by a another unstable periodic state with larger wavelength. The speed of this second front and the periodicity of the new state are analytically calculated with a generalization of the marginal stability formalism suited to the study of front propagation into periodic unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+rComment: 12 page

A comparison of ensemble strategies for flash flood forecasting: The 12 October 2007 case study in Valencia, Spain

On 12 October 2007, several flash floods affected the Valencia region, eastern Spain, with devastating impacts in terms of human, social, and economic losses. An enhanced modeling and forecasting of these extremes, which can provide a tangible basis for flood early warning procedures and mitigation measures over the Mediterranean, is one of the fundamental motivations of the international Hydrological Cycle in the Mediterranean Experiment (HyMeX) program. The predictability bounds set by multiple sources of hydrological and meteorological uncertainty require their explicit representation in hydrometeorological forecasting systems. By including local convective precipitation systems, short-range ensemble prediction systems (SREPSs) provide a state-of-the-art framework to generate quantitative discharge forecasts and to cope with different sources of external-scale (i.e., external to the hydrological system) uncertainties. The performance of three distinct hydrological ensemble prediction systems (HEPSs) for the small-sized Serpis River basin is examined as a support tool for early warning and mitigation strategies. To this end, the Flash-Flood Event-Based Spatially Distributed Rainfall-RunoffTransformation-Water Balance (FEST-WB) model is driven by ground stations to examine the hydrological response of this semiarid and karstic catchment to heavy rains. The use of a multisite and novel calibration approach for the FEST-WB parameters is necessary to cope with the high nonlinearities emerging from the rainfall-runofftransformation and heterogeneities in the basin response. After calibration, FEST-WB reproduces with remarkable accuracy the hydrological response to intense precipitation and, in particular, the 12 October 2007 flash flood. Next, the flood predictability challenge is focused on quantitative precipitation forecasts (QPFs). In this regard, three SREPS generation strategies using the WRF Model are analyzed. On the one side, two SREPSs accounting for 1) uncertainties in the initial conditions (ICs) and lateral boundary conditions (LBCs) and 2) physical parameterizations are evaluated. An ensemble Kalman filter (EnKF) is also designed to test the ability of ensemble data assimilation methods to represent key mesoscale uncertainties from both IC and subscale processes. Results indicate that accounting for diversity in the physical parameterization schemes provides the best probabilistic high-resolution QPFs for this particular flash flood event. For low to moderate precipitation rates, EnKF and pure multiple physics approaches render undistinguishable accuracy for the test situation at larger scales. However, only the multiple physics QPFs properly drive the HEPS to render the most accurate flood warning signals. That is, extreme precipitation values produced by these convective-scale precipitation systems anchored by complex orography are better forecast when accounting just for uncertainties in the physical parameterizations. These findings contribute to the identification of ensemble strategies better targeted to the most relevant sources of uncertainty before flash flood situations over small catchments

Wound-up phase turbulence in the Complex Ginzburg-Landau equation

We consider phase turbulent regimes with nonzero winding number in the one-dimensional Complex Ginzburg-Landau equation. We find that phase turbulent states with winding number larger than a critical one are only transients and decay to states within a range of allowed winding numbers. The analogy with the Eckhaus instability for non-turbulent waves is stressed. The transition from phase to defect turbulence is interpreted as an ergodicity breaking transition which occurs when the range of allowed winding numbers vanishes. We explain the states reached at long times in terms of three basic states, namely quasiperiodic states, frozen turbulence states, and riding turbulence states. Justification and some insight into them is obtained from an analysis of a phase equation for nonzero winding number: rigidly moving solutions of this equation, which correspond to quasiperiodic and frozen turbulence states, are understood in terms of periodic and chaotic solutions of an associated system of ordinary differential equations. A short report of some of our results has been published in [Montagne et al., Phys. Rev. Lett. 77, 267 (1996)].Comment: 22 pages, 15 figures included. Uses subfigure.sty (included) and epsf.tex (not included). Related research in http://www.imedea.uib.es/Nonlinea

Spatiotemporal communication with synchronized optical chaos

We propose a model system that allows communication of spatiotemporal information using an optical chaotic carrier waveform. The system is based on broad-area nonlinear optical ring cavities, which exhibit spatiotemporal chaos in a wide parameter range. Message recovery is possible through chaotic synchronization between transmitter and receiver. Numerical simulations demonstrate the feasibility of the proposed scheme, and the benefit of the parallelism of information transfer with optical wavefronts.Comment: 4 pages, 5 figure

Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations

We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.Comment: 12 pages plus 2 appended figures, plain TeX, CU-MSC-747

Acoustic Emission from crumpling paper

From magnetic systems to the crust of the earth, many physical systems that exibit a multiplicty of metastable states emit pulses with a broad power law distribution in energy. Digital audio recordings reveal that paper being crumpled, a system that can be easily held in hand, is such a system. Crumpling paper both using the traditional hand method and a novel cylindrical geometry uncovered a power law distribution of pulse energies spanning at least two decades: (exponent 1.3 - 1.6) Crumpling initally flat sheets into a compact ball (strong crumpling), we found little or no evidence that the energy distribution varied systematically over time or the size of the sheet. When we applied repetitive small deformations (weak crumpling) to sheets which had been previously folded along a regular grid, we found no systematic dependence on the grid spacing. Our results suggest that the pulse energy depends only weakly on the size of the paper regions responsible for sound production.Comment: 12 pages of text, 9 figures, submitted to Phys. Rev. E, additional information availible at http://www.msc.cornell.edu/~houle/crumpling