# Short talks

**
Otto Pulkkinen** (Saarbruecken):

*State estimation of long-range correlated non-equilibrium systems: media estimation*

Non-equilibrium systems have long-ranged spatial correlations even far away from critical points. This implies that the likelihoods of spatial steady state profiles of physical observables are nonlocal functionals. In this letter, it is shown that these properties are essential to a successful analysis of a functional level inverse problem, in which a macroscopic non-equilibrium fluctuation field is estimated from limited but spatially scattered information. To exemplify this, we dilute an out-of-equilibrium fluid flowing through random media with a marker, which can be observed in an experiment. We see that the hidden variables describing the random environment result in spatial long-range correlations in the marker signal. Two types of statistical estimators for the structure of the underlying media are then constructed: a linear estimator provides unbiased and asymptotically precise information on the particle density profiles, but yields negative estimates for the effective resistances of the media in some cases. A nonlinear, maximum likelihood estimator, on the other hand, results in a faithful media structure, but has a small bias. These two approaches complement each other. Finally, estimation of non-equilibrium fluctuation fields evolving in time is discussed.

reference: O. Pulkkinen, arXiv:0912.0714

**Anastasia Lavrova** (Berlin): *Phase reversal in Selkov model with inhomogeneous influx
*

The dynamical reaction-diffusion Selkov system as a model describing the complex traveling wave behavior is presented. The approximate amplitude-phase solution allows us to extract the base properties of the biochemical distributed system, which determines such patterns. It is shown that this relatively simple model could describe qualitatively the main features of the glycolysis waves observed in the experiments.

reference: PHYS REV E 79, 057102 (2009)

**Gunnar Pruessner** (Imperial): *Coalescing random walkers *

Brownian motion being so well understood, one might think the analysis of the distribution of the area traced out by two coalescing random walkers is rather straight forward. Indeed, scaling arguments and a bit of physical insight go a long way, but geometry goes much further and produces a couple of surprises. I will discuss a few of those unexpected findings, such as the construction of the correlation function, the existence of anti-correlations and some scaling arguments, which at first seem at odds with common sense.

references: Gunnar Pruessner, J. Phys. A: Math. Gen. 37, 7455 (2004); Peter Welinder, Gunnar Pruessner and Kim Christensen, New J. Phys. 9, 149 (2007)

**Tobias Galla** (Manchester): *Algebraic coarsening in voter models with intermediate states*

The introduction of intermediate states in the dynamics of the voter model modifies the ordering process and restores an effective surface tension. The logarithmic coarsening of the conventional voter model in two dimensions is eliminated in favour of an algebraic decay of the density of interfaces with time, compatible with Model A dynamics at low temperatures. This phenomenon is addressed by deriving Langevin equations for the dynamics of appropriately defined continuous fields. These equations are analyzed using field theoretical arguments and by means of a recently proposed numerical technique for the integration of stochastic equations with multiplicative noise. We find good agreement with lattice simulations of the microscopic model.

reference: Luca Dall'Asta, Tobias Galla, J. Phys. A: Math. Theor. 41 (2008) 435003

**Hira Affan Siddiqui** (Muenster): *Effect of Mean flow on Spiral Turbulence *

Spiral turbulence in Rayleigh-Benard convection is studied numerically in the framework of generalized Swift Hohenberg equations. The model equation consist of an order parameter equation for the temperature field coupled to an equation for the mean flow field. In contrast to the previous work [1,2] nonlinearities in the dynamics of the mean flow are retained leading to a two dimensional Navier-Stokes equation coupled to a Swift-Hohenberg equation. We present the numerical investigations of nonlinear effects due to the interaction of nonlinear two dimensional flows and the pattern forming process.

references: [1] M. Bestehorn, M. Fantz, R. Friedrich and H. Haken, Physics Letters A 174, (1993); [2] M. C. Cross and P.C. Hohenberg Rev. of Mod. Phys. 65, 851, (1993).

**Hugo Touchette** (Queen Mary): *Fluctuations of a Brownian particle with dry friction*

I will briefly discuss the solution of a Langevin equation with dry friction, studied in part by the late Pierre-Gilles de Gennes. I will show that the excitation paths of this equation have patterns that are reminiscent of a dynamical phase transition.

This is joint work with Adrian Baule and Eddie G. D. Cohen (Rockefeller University), arxiv0910.4663.

**Rosemary Harris** (Queen Mary): *Current fluctuations in stochastic systems with long-range memory*

We propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history-dependent rates. Long-range temporal correlations are seen to alter the speed of the large deviation function in analogy with long-range spatial correlations in equilibrium systems. We give some illuminating examples and discuss the applicability of the Gallavotti-Cohen fluctuation theorem.

reference: R. J. Harris and H. Touchette, J. Phys. A: Math. Theor. 42, 342001 (2009)

**Luis Fernández** (Palma de Mallorca): *Non-equilibrium phase transition in a system of coupled active rotators near the excitable regime *

We consider a variant of the Kuramoto model where the elements are active rotators near the excitable regime (which is equivalent to the regular Kuramoto model with an external periodic driving). It is shown that, for some distributions of the natural frequencies, there is a non-equilibrium phase transition which leads to a regime where the system exhibits coherent oscillations. We investigate the influence of the type of distribution and we derive expressions for the phase space of the system for the case of uniform distribution.

reference: C. J. Tessone, A. Scirè, R. Toral and P.Colet, Phys. Rev. E 75, 016203 (2007)

**Jamie Wood** (The University of York, UK): *Stochastic gating of assymetric exclusion process *

The asymmetric exclusion process is a well established model in statistical physics that exhibits non-equilibrium phase transitions. It has received considerable attention of late as it is widely applicable to problems in molecular biology involving the transit of component parts along specified tracks or pathways. In this short talk I will demonstrate that use of a self consistent mean-field approach, backed up by Monte-Carlo simulations, to examine the case where the exit from such a track is “gated” by the presence of some external component that is capable of binding and unbinding from an additional site to the track; exit from the path is only possible by the bound presence of this component. The relevant phase diagrams are computed for in terms of the exit and entrance rates as well as the binding and unbinding rates of the “gate”. An improved mean-field approach is also demonstrated as well as the case when the tract is gated both at its entrance and exit.