# Seminars (PDS)

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Event When Speaker Title Presentation Material
PDSW01 9th January 2006
08:50 to 09:00
Welcome
PDSW01 9th January 2006
09:00 to 09:50
Field theory and exact stochastic equations for interacting particle systems
PDSW01 9th January 2006
09:50 to 10:40
P Sollich Activated aging dynamics and negative fluctuation-dissipation ratios

In glassy materials aging proceeds at large times via thermal activation. We show that this can lead to negative dynamic response functions and novel and well-defined violations of the fluctuation-dissipation theorem, in particular, negative fluctuation-dissipation ratios. Our analysis is based on detailed theoretical and numerical results for the activated aging regime of simple kinetically constrained models. Our results are relevant to a variety of physical situations such as aging in glass-formers, thermally activated domain growth and granular compaction.

PDSW01 9th January 2006
11:10 to 12:00
S Ruffo Slow dynamics in systems with long-range interactions
PDSW01 9th January 2006
14:00 to 14:50
Asymptotically exact scaling for nonequilibrium static and dynamic critical behaviour

We present a scaling approach which we have recently developed for nonequilibrium static and dynamic critical behaviour. It is based on majority rule blocking implemented using complete operator algebra descriptions. These latter descriptions are generally available for particle exclusion models, but have only been pushed to an exact solution for special cases such as the steady-state of the Asymmetric Exclusion Process (biassed hopping of hard core particles). For that particular process we first show how the static scaling can be obtained using the reduced algebra which describes the steady state. We then outline how the full static and dynamic scaling follows from the complete operator algebra. The method gives for any (odd) dilatation factor $b$ the exact critical condition and exponent relations. For $b \rightarrow \infty$, it gives exact values for each exponent, including the dynamic exponent. Generalisations, eg to the partially asymmetric case, and applications, eg to relaxational dynamics of profiles and correlation functions, will be indicated.

PDSW01 9th January 2006
15:20 to 16:10
Dynamical symmetries in phase-ordering kinetics

Dynamical scaling in phase-ordering kinetics is well-accepted. We consider the possibility of a larger dynamical symmetry (called local scale-invariance) for this non-equilibrium relaxation phenomenon. Indeed, in many systems with and without detailed balance the Langevin equation can be decomposed into a deterministic' and a stochastic' part in such a way that if the deterministic' part is Galilei-invariant, then the calculation of the full noisy response and correlation functions reduces exactly to the calculation of certain n-point functions calculable within the deterministic' part of the theory. Galilei- and Schroedinger-invariant equations will be constructed. This leads to explicit predictions for the two-time response and correlation functions, in good agreement with simulational results and with the results of several exactly solvable models.

PDSW01 9th January 2006
16:10 to 17:00
Pinning of random directed polymers: smoothening of the transition and some path properties

I will consider a class of models of directed polymers in interaction with a line of random defects. This includes (d+1)-dimensional pinning problems, the (1+1)--dimensional interface wetting model, random copolymers at selective interfaces and other examples. These models are known to present a (de)localization transition at some critical line in the phase diagram. In absence of disorder, the transition can be either of first or of higher order. I will show that, as soon as disorder is present, the transition is always at least of second order. I will then concentrate on the delocalized phase and discuss some typical properties of the paths. (in collaboration with G. Giacomin (Paris 7))

PDSW01 10th January 2006
09:00 to 09:50
J-P Bouchaud Dynamical heterogeneities and growing length scales in glassy systems: physical origin, models and experiments

After decades of research, a clear picture of the glass transition phenomenon, common to scores of different materials (molecular glasses, polymers, colloids) is still lacking. Recent theoretical works suggest the existence of dynamic criticality and growing dynamic lengthscales associated to the dynamic slowing down. Various experiments support this view but in a rather indirect manner. We will discuss the physical mechanisms leading to such a growing length scale and define multi-point dynamic susceptibilities quantifying the cooperative dynamics of glass-forming materials that are accessible to experiments, and present some recent experiments supporting these ideas.

PDSW01 10th January 2006
09:50 to 10:40
J-P Garrahan Dynamical facilitation view of glass formers

This talk deals with the dynamic facilitation approach to the glass transition problem. This perspective is based on the idea that the interesting structure in glass-forming systems is found in the space of trajectories of the dynamics, rather than that of configurations. In contrast to mean-field approaches, dynamic facilitation naturally accounts for the dynamic heterogeneity of glass-forming materials and related fluctuation phenomena such as transport decoupling. I will describe how in the d+1 dimensions of trajectory space one finds order-disorder phenomena that can be organized according to scaling and universality classes. Various predictions from this viewpoint, some yet to be verified experimentally, will be discussed.

PDSW01 10th January 2006
11:10 to 12:00
L Berthier Length scale for the onset of Fickian diffusion in supercooled liquids
PDSW01 10th January 2006
14:00 to 14:50
T Coolen Dynamics on finitely connected random graphs
PDSW01 10th January 2006
16:10 to 17:00
F Guerra Thermal stochastic dynamics in complex systems
PDSW01 11th January 2006
09:00 to 09:50
Low T scaling behavior of 2D disordered and frustrated models

The ground state and low T behavior of two-dimensional spin systems with discrete binary couplings are subtle. I present an analysis based on exact computations of finite volume partition functions. I first discuss the fully frustrated model without disorder, and then introduce disorder by changing random links (spin glass) or by unfrustrating random plaquettes (plaquette disorder). In both cases the introduction of disorder changes the properties of the T=0 critical point.

PDSW01 11th January 2006
09:50 to 10:40
Spectral approaches to ageing

We investigate spectral characteristics of Markov chains that exhibit ageing. We consider two rather systems with rather different properties, Bouchaud's trap model and Sinai's random walk, and show how in both cases it is possible to obtain enough information on eigennvalues and eigenfunctions to deduce in an easy way all relevant dynamical properties.

PDSW01 11th January 2006
11:10 to 12:00
Dynamics of gelling liquids

The dynamics of randomly crosslinked liquids is addressed via a Rouse- and Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium. It is shown that the cluster size distribution gives rise to an anomalous time decay (stretched exponential) in all of the sol phase. The critical behaviour near the sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by looking at stress relaxation in simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the exact results contradict long-standing scaling arguments.

PDSW01 12th January 2006
09:00 to 09:50
Anomalous heat transport in low dimensional systems

Statistical fluctuations are strongly dependent on the space dimension and may yield ill-defined transport coefficients in stationary out--of--equilibrium conditions. Numerical simulations reveal that the heat conductivity diverges in the thermodynamic limit as a power--law of the system size in several 1d models of coupled anharmonic oscillators and hard--sphere gases. Momentum conservation appears as a necessary ingredient for determining such anomalous behavior. Recent theoretical estimates based on the mode-coupling approach provide a possible interpretation of these results.

PDSW01 12th January 2006
09:50 to 10:40
A Montanari On the relation between length and time scales in glassy systems
PDSW01 12th January 2006
11:00 to 11:10
The Arcsine law and scaling limits for trap models
PDSW01 12th January 2006
14:00 to 14:50
Field theory for Brownian fluids, fluctuation-dissipation theorem and self-consistent resummations
PDSW01 12th January 2006
16:10 to 17:00
M Evans Disorder and non-conservation in a driven diffusive system

The asymmetric exclusion process is a prototypical driven diffusive system. I will discuss a disordered version of the model in which randomly chosen sites do not conserve particle number. The model is motivated by features of many interacting molecular motors such as RNA polymerases. I will discuss the appearance of Griffiths singularities in a nonequilibrium steady state despite the absence of any transition in the pure model. The disorder is also shown to induce a stretched exponential decay of system density with stretching exponent \phi= 2/5.

PDSW01 13th January 2006
09:00 to 09:50
Zero-range processes: prototypical stochastic models with slow dynamics and nonequilibrium phase transitions
PDSW01 13th January 2006
09:50 to 10:40
D Dean Statistics of a slave estimator

We analyze the statistics of an estimator, denoted by $\xi_t$ and referred to as the slave, for the equilibrium susceptibility of a one dimensional Langevin process $x_t$ in a potential $\phi(x)$~. The susceptibility can be measured by evolving the slave equation in conjunction with the original Langevin process. This procedure yields a direct estimate of the susceptibility and avoids the need, when performing numerical simulations, to include applied external fields explicitly. The success of the method however depends on the statistical properties of the slave estimator. The joint probability density function for $x_t$ and $\xi_t$ is analyzed. In the case where the potential of the system has a concave component the probability density function of the slave acquires a power law tail characterized by a temperature dependent exponent. Thus we show that while the average value of the slave, in the equilibrium state, is always finite and given by the fluctuation dissipation relation, higher moments and indeed the variance may show divergences. The behavior of the power law exponent is analyzed in a general context and it is calculated explicitly in some specific examples. Our results are confirmed by numerical simulations and we discuss possible measurement discrepancies in the fluctuation dissipation relation which could arise due to this behavior.

PDSW01 13th January 2006
11:10 to 12:00
M Moore Towards the theory of the structural glass transition

It will be shown that the behaviour described as the "structural glass transition" can be related to that of the Ising spin glass in a magnetic field.

PDSW01 13th January 2006
14:00 to 14:50
S Franz Metastable states, relaxation times and free-energy barriers in finite dimensional glassy systems
PDSW01 13th January 2006
15:20 to 16:10
Jamming percolation and glass transition in lattice models
PDSW01 13th January 2006
16:10 to 17:00
Recovering folding free energies of RNA molecules in an experimental test of Crooks fluctuation theorem
PDS 16th January 2006
14:00 to 18:00
Organisational Meeting
PDS 18th January 2006
14:00 to 18:00
PDS Discussion
PDS 19th January 2006
14:00 to 15:00
D Dean Diffusion in random media and the glass transition
PDS 24th January 2006
11:00 to 12:00
Dynamics and thermodynamics of systems with long range interactions
PDS 26th January 2006
14:00 to 15:00
The dynamics of weighted, directed networks and interacting particle systems

I will introduce a model for the rewiring dynamics of a directed, weighted network which undergoes two kinds of condensation: (i) a phase in which, for each node, a finite fraction of its out-strength condenses onto a single link; (ii) a phase in which a finite fraction of the total weight in the system is directed into a single node. I will describe how the model can be mapped onto an exactly solvable zero-range process with many species of interacting particles and illustrate how one can exploit the mapping in order to obtain theoretical predictions for the conditions under which the different types of condensation are observed.

PDS 31st January 2006
11:00 to 12:00
Unzipping flux lines from extended defects in type II superconductors
PDS 1st February 2006
11:00 to 18:00
L Berthier A (very) informal discussion on open problems in glasses
PDS 2nd February 2006
14:00 to 15:00
Metallic glasses - a glassy state from hard spheres?
PDS 7th February 2006
11:00 to 12:00
Fluctuation-dissipation relations out of equilibrium
PDS 8th February 2006
14:00 to 18:00
S Franz Informal discussion: Cohen-Gallavotti Theorem
PDS 9th February 2006
11:00 to 12:00
Evolutionary trajectories in rugged fitness landscapes
PDS 14th February 2006
11:00 to 12:00
The nonequilibrium dynamics of new dialect formation
PDS 16th February 2006
11:00 to 12:00
Wealth condensation as a zero range process

We discuss the wealth condensation mechanism in a simple toy economy in which individual agent's wealths are distributed according to a Pareto power law and the overall wealth is fixed. The observed behaviour is the manisfestation of a transition which occurs in Zero Range Processes (ZRPs) or balls in boxes'' models. An amusing feature of the transition in this context is that the condensation can be induced by {\it increasing} the exponent in the power law, which one might have naively assumed penalized greater wealths more.

PDS 21st February 2006
11:00 to 12:00
A Rakos Bethe Ansatz and current distributions for the TASEP with particle dependent hopping rate
PDS 22nd February 2006
11:00 to 12:00
Condensation and coarsening of step bunches
PDS 23rd February 2006
11:00 to 12:30
Overview of kinetically constrained models of glass-formers
PDS 28th February 2006
11:00 to 12:00
Phase transitions and scaling laws in step bunching on vicinal surfaces
PDS 1st March 2006
11:00 to 12:00
S Ciliberto Fluctuations in out of equilibrium systems
PDS 2nd March 2006
11:00 to 12:00
Stationary results on condensation in two-component zero-range processes
PDS 7th March 2006
11:00 to 12:00
Partially asymmetric exclusion process with strong disorder
PDS 9th March 2006
11:00 to 12:00
EGD Cohen Fluctuation relations in non-equilibrium stationary states of Langevin systems
PDS 10th March 2006
10:00 to 11:00
Informal Discussion
PDS 14th March 2006
14:30 to 15:30
What happens to detailed balance away from equilibrium

The principle of detailed balance puts a number of constraints on the stochastic dynamics of any system that is ergodic, microscopically reversible, and in an equilibrium state. If work is done to drive such a system out of equilibrium, it will, in many cases, remain ergodic, microscopically reversible, and in a statistically steady (albeit non-equilibrium) state. By studying how such conditions give rise to the constraints of detailed balance at equilibrium, we can apply the same principles to derive a non-equilibrium counterpart to detailed balance, applicable to a wide sub-class of driven steady states, and investigate the consequences for activated processes.

PDS 15th March 2006
14:15 to 15:15
Discussion: Overview of kinetically constrained models of glass-formers. Part II
PDS 16th March 2006
14:15 to 15:15
The Schrodinger-Virasoro algebra: a mathematical structure between conformal field theory and non-equilibrium dymanics

We explore the mathematical structure of the infinite-dimensional Schrodinger-Virasoro algebra, and discuss possible applications to the integrability of anisotropic or out-of-equilibrium statistical systems with a dynamic exponent z different from 1 by defining several correspondences with conformal field theory.

PDS 17th March 2006
11:00 to 13:00
Informal discussion: An overview of exclusion processes I

We aim to give an informal overview of the results achieved within the Physics community, and open questions remaining, concerning steady state and dynamical properties of exclusion processes

PDS 20th March 2006
14:15 to 16:00
Informal discussion: An overview of exclusion processes II

We aim to give an informal overview of the results achieved within the Physics community, and open questions remaining, concerning steady state and dynamical properties of exclusion processes

PDS 21st March 2006
14:15 to 15:15
Particle clustering in a traffic model
PDS 22nd March 2006
11:00 to 12:00
Spatial correlations of the 1D KPZ surface

We discuss the fluctuation properties of 1D growing surfaces in the KPZ universality class. The systems are defined on the infinite lattice. After a short review of the connection of the problems to random matrix theory and vicious walk problems, we discuss the joint distribution of the height fluctuation on a flat substrate.

PDSW02 27th March 2006
10:00 to 11:00
Fluctuations and large deviations in non-equilibrium systems: Lecture I

The exact solutions of simple models allow us to obtain the large deviation functions of density profiles and of the current through simple systems in contact with two reservoirs at different densities. These simple models show that non-equilibrium systems have a number of properties which contrast with equilibrium systems: phase transitions in one dimension, non local free energy functional, violation of the Einstein relation between the compressibility and the density fluctuation, non-Gaussian density fluctuations. They also lead to a general expression for the current fluctuations through a diffusive system in contact with two reservoirs.

B Derrida, J L Lebowitz, E R Speer Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case Phys. Rev. Lett. 87, 150601 (2001)

B Derrida, B Doucot, P-E Roche, Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries J. Stat. Phys. 115, 717-748 (2004)

T. Bodineau, B Derrida Current fluctuations in non-equilibrium diffusive systems: an additivity principle Phys. Rev. Lett. 92, 180601 (2004)

PDSW02 27th March 2006
11:30 to 12:30
The fluctuation and nonequilibrium free energy theorems, Theory and experiment: Lecture I

1. We give a brief summary of the derivations of the Evans-Searles Fluctuation Theorems (FTs) and the NonEquilibrium Free Energy Theorems (Crooks and Jarzynski). The discussion is given for time reversible Newtonian dynamics. We emphasize the role played by thermostatting. We also highlight the common themes inherent in the Fluctuation and Free Energy Theorems. We discuss a number of simple consequences of the Fluctuation Theorems including the Second Law Inequality, the Kawasaki Identity and the fact that the dissipation function which is the subject of the FT, is a nonlinear generalization of the spontaneous entropy production, that is so central to linear irreversible thermodyanamics. Lastly we give a brief update on the latest experimental tests of the FTs (both steady state and transient) and the NonEquilibrium Free Energy Theorem, using optical tweezer apparatus.

2 The Fluctutation Theorem: In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in small thermostatted nonequilibrium systems which are observed for a short period of time. This Theorem places quantitative restrictions on the operation of small (nano) machines and devices. These constraints cannot be circumvented. Quantitative predictions made by the Fluctuation Theorem regarding the probability of Second Law violations' have been confirmed experimentally, both using molecular dynamics computer simulation and very recently in two laboratory experiments[1] which employed optical tweezers. In this talk we give a brief summary of the theory [2] and a description of the experiments.

References

[1] Experimental demonstration of violations of the Second Law of Thermodynamics for small systems and short time scales, by Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J. and Evans, D.J., Phys. Rev. Lett., 89 (5), 050601/1?4 (2002).

[2] The Fluctuation Theorem by Denis J Evans and Debra J Searles, Advances in Physics, 51 , 1529-1585(2002).

PDSW02 27th March 2006
15:30 to 16:30
Hydrodynamic limit for driven diffusive systems: Lecture I

The large scale behaviour of microscopic stochastic particle systems can often be described in tems of nonlinear partial differential equations which can be predicted phenomenologically or sometimes derived rigorously using probabilistic tools. For one-component systems this allows not only for computing the (deterministic) space-time evolution of the coarse-grained local order parameter, but also for the derivation of the stationary phase diagram in bulk-driven finite systems with open boundaries. The Bethe ansatz provides the means to study fluctuations on finer scales. Systems with two or more components exhibit richer physics, but the theory is far less developed, both mathematically from a probabilistic and PDE point of view and from a statistical physics perspective. Focussing on paradigmatic one-dimensional lattice gas models for driven diffusive systems far from thermal equilibrium the lecture aims at giving a non-technical overview of some well-known rigorous and some more recent numerically established results for one-component systems with conserved particle dynamics or with slow reaction kinetics and at highlighting some aspects of the present incomplete state of art for two-component systems which deserve further investigation.

PDSW02 27th March 2006
16:30 to 17:30
H Hinrichsen Absorbing state phase transitions: Lecture I

The purpose of these lectures is to give a basic introduction to the physics of phase transitions far from equilibrium. Starting with a general introduction to non-equilibrium statistical mechanics four different topics will be addressed. At first the universality class of directed percolation will be discussed, which plays a fundamental role in non-equilibrium statistical physics. The second part concerns the properties of other universality classes which have been of interest in recent years. The third part deals with phase transitions in models with long-range interactions, including memory effects and so-called Levy-flights. Finally, deposition-evaporation phenomena leading to wetting transitions out of equilibrium will be reviewed.

PDSW02 28th March 2006
09:00 to 10:00
Fluctuations and large deviations in non equilibrium systems: Lecture II

The exact solutions of simple models allow us to obtain the large deviation functions of density profiles and of the current through simple systems in contact with two reservoirs at different densities. These simple models show that non-equilibrium systems have a number of properties which contrast with equilibrium systems: phase transitions in one dimension, non local free energy functional, violation of the Einstein relation between the compressibility and the density fluctuation, non-Gaussian density fluctuations. They also lead to a general expression for the current fluctuations through a diffusive system in contact with two reservoirs.

B Derrida, J L Lebowitz, E R Speer Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case Phys. Rev. Lett. 87, 150601 (2001)

B Derrida, B Doucot, P-E Roche, Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries J. Stat. Phys. 115, 717-748 (2004)

T. Bodineau, B Derrida Current fluctuations in non-equilibrium diffusive systems: an additivity principle Phys. Rev. Lett. 92, 180601 (2004)

PDSW02 28th March 2006
10:00 to 11:00
JL Cardy Stochastic Loewner Evolution and other growth processes in two dimensions: Lecture I

Random objects such as clusters in the plane can often be described in terms of the conformal mappings which take their boundaries into some standard shape. As the clusters grow, the mapping function changes in a well-defined manner, which is often easier to understand than the original problem. One of the simplest examples is Stochastic Loewner Evolution (SLE), which turns out to describe random curves in equilibrium statistical mechanics models. These lectures will give an introduction to the use of such conformal mappings, and to SLE in particular, from the physicist's point of view.

PDSW02 28th March 2006
11:30 to 12:30
SN Majumdar A class of mass transport models: Factorised steady states and condensation in real space: Lecture I

Lecture-I

The traditional Bose-Einstein condensation in an ideal quantum Bose gas occurs in momentum space, when a macroscopically large number of bosons condense onto the ground state. It is becoming increasingly clear over the last decade that condensation can also happen in real space (and even in one dimension) in the steady state of a broad class of physical systems. These are classical systems, generally lack a Hamiltonian and are defined by their microscopic kinetic processes. Examples include traffic jams on a highway, island formation on growing crystals and many other systems. In this lecture, I'll discuss in detail two simple models namely the Zero-range process and the Chipping model that exhbits condensation in real space. Lecture-II

I'll introduce a generalized mass transport model that includes in iteself, as specail cases, the Zero-range process, the Chipping model and the Random Average process. We will derive a necessary and sufficient condition, in one dimension, for the model to have a factorised steady state. Generalization to arbitrary graphs will be mentioned also.

Lecture-III

We will discuss, in the context of the mass transport model, the phenomenon of condensation. In particular we will address three basic isuues: (1) WHEN does such a condensation occur (the criterion) (2) HOW does the condensation happen (the mechanism) and (3) WHAT does the condensate look like (the nature of fluctuations and lifetime of the condensate etc.)? We will see how these issues can be resolved analytically in the mass transport model.

PDSW02 28th March 2006
15:30 to 16:30
The fluctuation and nonequilibrium free energy theorems: Theory and experiment: lecture II

1. We give a brief summary of the derivations of the Evans-Searles Fluctuation Theorems (FTs) and the NonEquilibrium Free Energy Theorems (Crooks and Jarzynski). The discussion is given for time reversible Newtonian dynamics. We emphasize the role played by thermostatting. We also highlight the common themes inherent in the Fluctuation and Free Energy Theorems. We discuss a number of simple consequences of the Fluctuation Theorems including the Second Law Inequality, the Kawasaki Identity and the fact that the dissipation function which is the subject of the FT, is a nonlinear generalization of the spontaneous entropy production, that is so central to linear irreversible thermodyanamics. Lastly we give a brief update on the latest experimental tests of the FTs (both steady state and transient) and the NonEquilibrium Free Energy Theorem, using optical tweezer apparatus.

2 The Fluctutation Theorem: In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in small thermostatted nonequilibrium systems which are observed for a short period of time. This Theorem places quantitative restrictions on the operation of small (nano) machines and devices. These constraints cannot be circumvented. Quantitative predictions made by the Fluctuation Theorem regarding the probability of Second Law violations' have been confirmed experimentally, both using molecular dynamics computer simulation and very recently in two laboratory experiments[1] which employed optical tweezers. In this talk we give a brief summary of the theory [2] and a description of the experiments.

References

[1] Experimental demonstration of violations of the Second Law of Thermodynamics for small systems and short time scales, by Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J. and Evans, D.J., Phys. Rev. Lett., 89 (5), 050601/1?4 (2002).

[2] The Fluctuation Theorem by Denis J Evans and Debra J Searles, Advances in Physics, 51 , 1529-1585(2002).

PDSW02 28th March 2006
16:30 to 17:30
Hydrodynamic limit for driven diffusive systems: Lecture II

The large scale behaviour of microscopic stochastic particle systems can often be described in tems of nonlinear partial differential equations which can be predicted phenomenologically or sometimes derived rigorously using probabilistic tools. For one-component systems this allows not only for computing the (deterministic) space-time evolution of the coarse-grained local order parameter, but also for the derivation of the stationary phase diagram in bulk-driven finite systems with open boundaries. The Bethe ansatz provides the means to study fluctuations on finer scales. Systems with two or more components exhibit richer physics, but the theory is far less developed, both mathematically from a probabilistic and PDE point of view and from a statistical physics perspective. Focussing on paradigmatic one-dimensional lattice gas models for driven diffusive systems far from thermal equilibrium the lecture aims at giving a non-technical overview of some well-known rigorous and some more recent numerically established results for one-component systems with conserved particle dynamics or with slow reaction kinetics and at highlighting some aspects of the present incomplete state of art for two-component systems which deserve further investigation.

PDSW02 29th March 2006
09:00 to 10:00
Some results in the dynamical large deviation approach to macroscopic fluctuations in stochastic lattice gases: Lecture I

1. Long range space correlations as a signature of violation of time reversal invariance (TRI)

We introduce the notions of strong and weak violation of time reversal invariance (TRI) according to whether the violation of TRI in the microscopic dynamics shows up or not at the hydrodynamical level. We then argue that long range space correlations seem to be a generic feature of dynamics strongly violating TRI. In particular, on the basis af a recently established Hamilton-Jacobi equation for the free energy, we show that equilibrium states of Glauber-Kawasaki type dynamics under strong violation of TRI have space correlations over a macroscopic scale. This result indicates that long range correlations are not specific to non equilibrium stationary states.

2. Dynamical phase transitions in large current fluctuations of stochastic lattice gases

In works in collaboration with L. Bertini, A. De Sole, D. Gabrielli and C. Landim we have shown that in large fluctuations of the current, averaged over long intervals of time, transitions to different dynamical regimes can take place. These are revealed by the time dependence of the thermodynamic variables associated to the fluctuations. In this case time shift invariance is spontaneously broken. So far two examples are known, the weakly asymmetric simple exclusion process with periodic boundary conditions discussed by Bodineau and Derrida and the Kipnis-Marchioro-Presutti model for which we have provided a rigorous proof of the transition.

PDSW02 29th March 2006
10:00 to 11:00
Dynamics of growing and equilibrium networks: Lecture I

The lectures will present an overview of the large-scale topological and dynamical properties of complex networks. First the methodology used to obtain large scale maps of several real networked systems in the social, biological and technology domains will be reviewed. Then the statistical features and regularities observed in the large scale structure of complex networks will be discussed along with the formulation of adequate dynamical models. Finally the effect of network complexity in spreading and percolation processes will be analyzed.

PDSW02 29th March 2006
11:30 to 12:30
SN Majumdar A class of mass transport models: Factorised steady states and condensation in real space: Lecture II

Lecture-I

The traditional Bose-Einstein condensation in an ideal quantum Bose gas occurs in momentum space, when a macroscopically large number of bosons condense onto the ground state. It is becoming increasingly clear over the last decade that condensation can also happen in real space (and even in one dimension) in the steady state of a broad class of physical systems. These are classical systems, generally lack a Hamiltonian and are defined by their microscopic kinetic processes. Examples include traffic jams on a highway, island formation on growing crystals and many other systems. In this lecture, I'll discuss in detail two simple models namely the Zero-range process and the Chipping model that exhbits condensation in real space. Lecture-II

I'll introduce a generalized mass transport model that includes in iteself, as specail cases, the Zero-range process, the Chipping model and the Random Average process. We will derive a necessary and sufficient condition, in one dimension, for the model to have a factorised steady state. Generalization to arbitrary graphs will be mentioned also.

Lecture-III

We will discuss, in the context of the mass transport model, the phenomenon of condensation. In particular we will address three basic isuues: (1) WHEN does such a condensation occur (the criterion) (2) HOW does the condensation happen (the mechanism) and (3) WHAT does the condensate look like (the nature of fluctuations and lifetime of the condensate etc.)? We will see how these issues can be resolved analytically in the mass transport model.

PDSW02 29th March 2006
14:00 to 15:00
Contributed Seminar: Stochastic thermodynamics: Energy Conservation and entropy production along a single trajectory

For stochastic dynamics of driven non-equilibrium systems, entropy production can be defined along a single trajectory [1]. It consists of two parts, entropy change of the system itself and entropy change of the surrounding medium. Total entropy production fulfills an integral fluctuation theorem for arbitrary initial state and arbitrary driving. For steady states, the total entropy production obeys the detailed fluctuation theorem even for finite times. These theorems can be derived without the notion of a surrounding heat bath of constant temperature. In the presence of such a bath as it is typical for many colloidal and biomolecular systems, however, a first law-like energy balance along the trajectory allows to identify dissipated heat and equate it with the entropy change of the medium.

I will sketch the derivation of these results both for a Langevin type dynamics of continuous degrees of freedom and for a master equation dynamics on a discrete set of states. Illustrative examples for the first type include our recent experiments on a colloidal particle in a time-dependent non-harmonic potential [2]. Examples for discrete dynamics include enzym models [3,4] and our experiments on an athermal optically driven two-level system [5].

[1] U. Seifert, Phys. Rev. Lett. 95: 040602/1-4, 2005. [2] V. Blickle et al, Phys. Rev. Lett. 96: 070603/1-4, 2006. [3] U. Seifert, Europhys. Lett. 70: 36-41, 2005. [4] T. Schmiedl, T. Speck and U. Seifert, cond-mat 0601636, 2006. [5] S. Schuler et al, Phys. Rev. Lett. 94: 180602/1-4, 2005.

PDSW02 30th March 2006
09:00 to 10:00
H Hinrichsen Absorbing state phase transitions: Lecture II

The purpose of these lectures is to give a basic introduction to the physics of phase transitions far from equilibrium. Starting with a general introduction to non-equilibrium statistical mechanics four different topics will be addressed. At first the universality class of directed percolation will be discussed, which plays a fundamental role in non-equilibrium statistical physics. The second part concerns the properties of other universality classes which have been of interest in recent years. The third part deals with phase transitions in models with long-range interactions, including memory effects and so-called Levy-flights. Finally, deposition-evaporation phenomena leading to wetting transitions out of equilibrium will be reviewed.

PDSW02 30th March 2006
10:00 to 11:00
Fluctuations and large deviations in non equilibrium systems: Lecture III

The exact solutions of simple models allow us to obtain the large deviation functions of density profiles and of the current through simple systems in contact with two reservoirs at different densities. These simple models show that non-equilibrium systems have a number of properties which contrast with equilibrium systems: phase transitions in one dimension, non local free energy functional, violation of the Einstein relation between the compressibility and the density fluctuation, non-Gaussian density fluctuations. They also lead to a general expression for the current fluctuations through a diffusive system in contact with two reservoirs.

B Derrida, J L Lebowitz, E R Speer Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case Phys. Rev. Lett. 87, 150601 (2001)

B Derrida, B Doucot, P-E Roche, Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries J. Stat. Phys. 115, 717-748 (2004)

T. Bodineau, B Derrida Current fluctuations in non-equilibrium diffusive systems: an additivity principle Phys. Rev. Lett. 92, 180601 (2004)

PDSW02 30th March 2006
11:30 to 12:30
SN Majumdar A class of mass transport models: Factorised steady states and condensation in real space: Lecture III

Lecture-I

The traditional Bose-Einstein condensation in an ideal quantum Bose gas occurs in momentum space, when a macroscopically large number of bosons condense onto the ground state. It is becoming increasingly clear over the last decade that condensation can also happen in real space (and even in one dimension) in the steady state of a broad class of physical systems. These are classical systems, generally lack a Hamiltonian and are defined by their microscopic kinetic processes. Examples include traffic jams on a highway, island formation on growing crystals and many other systems. In this lecture, I'll discuss in detail two simple models namely the Zero-range process and the Chipping model that exhbits condensation in real space. Lecture-II

I'll introduce a generalized mass transport model that includes in iteself, as specail cases, the Zero-range process, the Chipping model and the Random Average process. We will derive a necessary and sufficient condition, in one dimension, for the model to have a factorised steady state. Generalization to arbitrary graphs will be mentioned also.

Lecture-III

We will discuss, in the context of the mass transport model, the phenomenon of condensation. In particular we will address three basic isuues: (1) WHEN does such a condensation occur (the criterion) (2) HOW does the condensation happen (the mechanism) and (3) WHAT does the condensate look like (the nature of fluctuations and lifetime of the condensate etc.)? We will see how these issues can be resolved analytically in the mass transport model.

PDSW02 30th March 2006
15:30 to 16:30
Dynamics of growing and equilibrium networks: Lecture II

The lectures will present an overview of the large-scale topological and dynamical properties of complex networks. First the methodology used to obtain large scale maps of several real networked systems in the social, biological and technology domains will be reviewed. Then the statistical features and regularities observed in the large scale structure of complex networks will be discussed along with the formulation of adequate dynamical models. Finally the effect of network complexity in spreading and percolation processes will be analyzed.

PDSW02 30th March 2006
16:30 to 17:30
JL Cardy Stochastic Loewner Evolution and other growth processes in two dimensions: Lecture II

Random objects such as clusters in the plane can often be described in terms of the conformal mappings which take their boundaries into some standard shape. As the clusters grow, the mapping function changes in a well-defined manner, which is often easier to understand than the original problem. One of the simplest examples is Stochastic Loewner Evolution (SLE), which turns out to describe random curves in equilibrium statistical mechanics models. These lectures will give an introduction to the use of such conformal mappings, and to SLE in particular, from the physicist's point of view.

PDSW02 31st March 2006
09:00 to 10:00
JL Cardy Stochastic Loewner Evolution and other growth processes in two dimensions: Lecture III

Random objects such as clusters in the plane can often be described in terms of the conformal mappings which take their boundaries into some standard shape. As the clusters grow, the mapping function changes in a well-defined manner, which is often easier to understand than the original problem. One of the simplest examples is Stochastic Loewner Evolution (SLE), which turns out to describe random curves in equilibrium statistical mechanics models. These lectures will give an introduction to the use of such conformal mappings, and to SLE in particular, from the physicist's point of view.

PDSW02 31st March 2006
10:00 to 11:00
Some results in the dynamical large deviation approach to macroscopic fluctuations in stochastic lattice gases: Lecture II

1. Long range space correlations as a signature of violation of time reversal invariance (TRI)

We introduce the notions of strong and weak violation of time reversal invariance (TRI) according to whether the violation of TRI in the microscopic dynamics shows up or not at the hydrodynamical level. We then argue that long range space correlations seem to be a generic feature of dynamics strongly violating TRI. In particular, on the basis af a recently established Hamilton-Jacobi equation for the free energy, we show that equilibrium states of Glauber-Kawasaki type dynamics under strong violation of TRI have space correlations over a macroscopic scale. This result indicates that long range correlations are not specific to non equilibrium stationary states.

2. Dynamical phase transitions in large current fluctuations of stochastic lattice gases

In works in collaboration with L. Bertini, A. De Sole, D. Gabrielli and C. Landim we have shown that in large fluctuations of the current, averaged over long intervals of time, transitions to different dynamical regimes can take place. These are revealed by the time dependence of the thermodynamic variables associated to the fluctuations. In this case time shift invariance is spontaneously broken. So far two examples are known, the weakly asymmetric simple exclusion process with periodic boundary conditions discussed by Bodineau and Derrida and the Kipnis-Marchioro-Presutti model for which we have provided a rigorous proof of the transition.

PDSW02 31st March 2006
11:30 to 12:30
Hydrodynamic limit for driven diffusive systems: Lecture III

The large scale behaviour of microscopic stochastic particle systems can often be described in tems of nonlinear partial differential equations which can be predicted phenomenologically or sometimes derived rigorously using probabilistic tools. For one-component systems this allows not only for computing the (deterministic) space-time evolution of the coarse-grained local order parameter, but also for the derivation of the stationary phase diagram in bulk-driven finite systems with open boundaries. The Bethe ansatz provides the means to study fluctuations on finer scales. Systems with two or more components exhibit richer physics, but the theory is far less developed, both mathematically from a probabilistic and PDE point of view and from a statistical physics perspective. Focussing on paradigmatic one-dimensional lattice gas models for driven diffusive systems far from thermal equilibrium the lecture aims at giving a non-technical overview of some well-known rigorous and some more recent numerically established results for one-component systems with conserved particle dynamics or with slow reaction kinetics and at highlighting some aspects of the present incomplete state of art for two-component systems which deserve further investigation.

PDSW02 31st March 2006
14:00 to 15:00
J de Gier Contributed Seminar: Exact solution of the dynamics of the PASEP with open boundaries

The dynamics of the asymmetric exclusion process is governed by the spectrum of its transition matrix. In particular its lowest excited state describes the approach to stationarity at large times. I will discuss the exact diagonalisation of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. The resulting Bethe ansatz equations describe the {\em complete} spectrum of the transition matrix. For totally asymmetric diffusion I will present exact results for the spectral gap and derive the dynamical phase diagram. We observe boundary induced crossovers in and between massive, diffusive and KPZ scaling regimes.

PDSW02 31st March 2006
15:30 to 16:30
H Hinrichsen Absorbing state phase transitions: Lecture III

The purpose of these lectures is to give a basic introduction to the physics of phase transitions far from equilibrium. Starting with a general introduction to non-equilibrium statistical mechanics four different topics will be addressed. At first the universality class of directed percolation will be discussed, which plays a fundamental role in non-equilibrium statistical physics. The second part concerns the properties of other universality classes which have been of interest in recent years. The third part deals with phase transitions in models with long-range interactions, including memory effects and so-called Levy-flights. Finally, deposition-evaporation phenomena leading to wetting transitions out of equilibrium will be reviewed.

PDSW02 31st March 2006
16:30 to 17:30
Dynamics of growing and equilibrium networks: Lecture III

The lectures will present an overview of the large-scale topological and dynamical properties of complex networks. First the methodology used to obtain large scale maps of several real networked systems in the social, biological and technology domains will be reviewed. Then the statistical features and regularities observed in the large scale structure of complex networks will be discussed along with the formulation of adequate dynamical models. Finally the effect of network complexity in spreading and percolation processes will be analyzed.

PDSW02 3rd April 2006
09:00 to 10:00
Soluble models of self-organized criticality: Lecture I

In these lectures, I will discuss the abelian sandpile model of self-organized criticality, and its related models. The abelian group structure of the model, the burning test for recurrent states, equivalence to the spanning trees problem will be described. The exact solution of the directed version of the model in any dimension will be explained, and its relation to Scheidegger's model of river basins, Takayasu's aggregation model and the voter model will be discussed. I will summarize the known results about the undirected models. Generalization to the abelian distributed processors model, and time-dependent properties and the universality of critical behavior in sandpiles will be briefly discussed.

PDSW02 3rd April 2006
10:00 to 11:00
Introduction to nonequilibrium work theorems: Lecture I

When we drive a physical system away from a state of thermal equilibrium by forcing a change in one of its variables -- e.g. when we push a piston into a gas, or when we stretch a single molecule using optical tweezers -- then we perform a certain amount of work, W, on the system.

Over the past decade, a number of results -- collectively known as nonequilibrium work theorems (NWT's) -- have revealed that equilibrium information is subtly encoded in the statistics of W, even when the system is driven significantly far from equilibrium.

In my three lectures I will present an introduction to these theoretical results, as well as to their applications in the context of experiments and numerical simulations aimed at estimating thermodynamic properties of complex systems. The first lecture will present a general overview of these results. In the remaining two lectures I plan to cover a number of topics, including: useful mathematical tools for deriving and analyzing NWT's; practical issues regarding the applications of these results; generalizations of NWT's, and their relation to Fluctuation Theorems; and the connection of NWT's to deeper issues of macroscopic irreversibility.

PDSW02 3rd April 2006
11:30 to 12:30
Field-theoretic approaches to interacting particle systems: Lecture I

It is explained how field-theoretic methods and the dynamic renormalization group (RG) can be applied to study the universal scaling properties of interacting particle systems far from thermal equilibrium that either undergo a continuous phase transition or display generic scale invariance It is described how the master equation for stochastic particle reaction processes can be mapped onto a field theory action. The RG is then employed to analyze the ensuing power laws in simple diffusion-limited annihilation reactions as well as generic continuous transitions from active to inactive, absorbing states, which are characterized by the power laws of (critical) directed percolation. Certain other important universality classes including dynamic percolation and parity-conserving branching and annihilating random walks are discussed, and some open issues are mentioned.

PDSW02 3rd April 2006
14:00 to 15:00
Contributed Seminar: Membrane nanotubes pulled cooperatively by molecular motors

Long and very dynamic tubular structures growing along the cytoskeleton have been observed in vivo. Similar tubular nano-structures have been obtained in vitro with a minimal system composed of kinesins grafted on the membranes of giant vesicles, and moving along immobilized microtubule. When the kinesins are individually grafted to single lipids, dynamical clusters of motors pulling the tubes have been observed at the tip of the tubes, in agreement with theory. Different dynamical regimes have been observed : below a threshold depending on membrane tension and motor concentration, no tube is formed but above this threshold, we observe either stable tubes or oscillating tubes depending on the relative vesicle size and tube length

PDSW02 3rd April 2006
15:30 to 16:30
Modelling of traffic flow and related transport systems: Lecture I

In this series of lectures the basic empirical properties and theoretical modelling approaches for various traffic systems will be reviewed. The list of topics includes: 1) Empirical traffic data and their interpretation 2) Modelling approaches for highway traffic (hydrodynamic models, car-following models, etc.) 3) Cellular automata models of highway traffic (ASEP, Nagel-Schreckenberg model and their extensions) 4) Pedestrian dynamics 5) Transport in biological systems (ant trails, intracellular transport, etc)

PDSW02 3rd April 2006
16:30 to 17:30
Clustering, coarsening and directed transport in a granular gas: Lecture I

1. Clustering and Coarsening in a Granular Gas Granular gases are of great scientific and economic relevance. Scientific, because of their tendency to spontaneously separate into dense and dilute regions, which makes them fundamentally different from any textbook molecular gas. Economic, because no less than 5 per cent of the global energy budget is wasted due to problems with granular matter in conveyor belts, sorting machines, mixers, and other industrial machinery. Here we study - experimentally, numerically, and theoretically - the clustering of particles in a vertically vibrated array of N connected compartments. For strong shaking, the particles spread evenly over the compartments, but if the shaking strength is lowered beneath a critical level this uniform distribution gives way to a clustered state, consisting of a few well-filled compartments and a lot of diluted ones. In the course of time, this state coarsens: The smaller clusters are eaten by the larger ones, until finally only one big cluster remains. This coarsening process is exceptionally slow, with the mass of the surviving cluster growing only as the square root of log t.

2. Clustering and Directed Transport

In this second lecture we turn to the wonderful world of ratchets, which have become a hot topic in recent years. In order to extract mechanical work on a molecular scale (e.g., to make a muscle move), nature uses the concept of a Brownian ratchet: The stochastic forces from a noisy environment are converted into a directed motion. Here we create a "granular ratchet", exploiting the clustering phenomenon from the previous lecture in a slightly adapted array of N connected compartments: The stochastically colliding particles spontaneously generate a particle current perpendicular to the direction of energy input. This is the first practical realization of the theoretically predicted concept of a stochastic ratchet as a collective effect in a symmetric geometry.

A related problem of prime importance in modern society is the clustering of cars on the highway. We show how the formation of traffic jams on the Dutch highway A58 is well described - and predicted! - by a flux model similar to the one we use for the clustering of granular particles

3. Granular Impact Jets

A steel ball dropped onto loose, very fine sand ("dry quicksand") creates an upward jet exceeding the release height of the ball. There is a striking similarity with the impact of an object in a liquid: The jet is generated by the gravity-driven collapse of the void created by the ball, and the focused pressure pushes the sand straight up into the air. Using a 2-dimensional experimental setup and high-speed imaging, the collapse of the void is visualized. For high impact velocities the void collapse is seen to entrain air. The entrained air bubble slowly rises through the sand, and upon reaching the surface causes a granular eruption. The experimental observations are quantitatively explained by a Rayleigh-type model. Parallels are drawn with impacts on a planetary scale.

PDSW02 4th April 2006
09:00 to 10:00
Fourier Law in low-dimensional systems: Lecture I

The study of transport properties in low-dimensional models has attracted much attention in the scientific community. In fact, it has pointed out new basic for the theory of non-equilibrium stationary processes, while providing interesting perspectives of applications to new materials. These lectures will be mainly devoted to survey the achievements on the problem of heat transport in 1D and 2D systems. A pedagogically suitable approach will be proposed to the students, going through a historical pathway. Numerical results will be presented together with the main rigorous approaches and analytical results. These lectures aim at providing also an overview of the state of the art on this research topic, with reference to still open, challenging problems. Department of Physics, LE Fermi 2, 50125 Firenze

PDSW02 4th April 2006
10:00 to 11:00
Introduction to nonequilibrium work theorems: Lecture II

When we drive a physical system away from a state of thermal equilibrium by forcing a change in one of its variables -- e.g. when we push a piston into a gas, or when we stretch a single molecule using optical tweezers -- then we perform a certain amount of work, W, on the system.

Over the past decade, a number of results -- collectively known as nonequilibrium work theorems (NWT's) -- have revealed that equilibrium information is subtly encoded in the statistics of W, even when the system is driven significantly far from equilibrium.

In my three lectures I will present an introduction to these theoretical results, as well as to their applications in the context of experiments and numerical simulations aimed at estimating thermodynamic properties of complex systems. The first lecture will present a general overview of these results. In the remaining two lectures I plan to cover a number of topics, including: useful mathematical tools for deriving and analyzing NWT's; practical issues regarding the applications of these results; generalizations of NWT's, and their relation to Fluctuation Theorems; and the connection of NWT's to deeper issues of macroscopic irreversibility.

PDSW02 4th April 2006
11:30 to 12:30
Clustering, coarsening and directed transport in a Granular gas: Lecture II

1. Clustering and Coarsening in a Granular Gas Granular gases are of great scientific and economic relevance. Scientific, because of their tendency to spontaneously separate into dense and dilute regions, which makes them fundamentally different from any textbook molecular gas. Economic, because no less than 5 per cent of the global energy budget is wasted due to problems with granular matter in conveyor belts, sorting machines, mixers, and other industrial machinery. Here we study - experimentally, numerically, and theoretically - the clustering of particles in a vertically vibrated array of N connected compartments. For strong shaking, the particles spread evenly over the compartments, but if the shaking strength is lowered beneath a critical level this uniform distribution gives way to a clustered state, consisting of a few well-filled compartments and a lot of diluted ones. In the course of time, this state coarsens: The smaller clusters are eaten by the larger ones, until finally only one big cluster remains. This coarsening process is exceptionally slow, with the mass of the surviving cluster growing only as the square root of log t.

2. Clustering and Directed Transport

In this second lecture we turn to the wonderful world of ratchets, which have become a hot topic in recent years. In order to extract mechanical work on a molecular scale (e.g., to make a muscle move), nature uses the concept of a Brownian ratchet: The stochastic forces from a noisy environment are converted into a directed motion. Here we create a "granular ratchet", exploiting the clustering phenomenon from the previous lecture in a slightly adapted array of N connected compartments: The stochastically colliding particles spontaneously generate a particle current perpendicular to the direction of energy input. This is the first practical realization of the theoretically predicted concept of a stochastic ratchet as a collective effect in a symmetric geometry.

A related problem of prime importance in modern society is the clustering of cars on the highway. We show how the formation of traffic jams on the Dutch highway A58 is well described - and predicted! - by a flux model similar to the one we use for the clustering of granular particles

3. Granular Impact Jets

A steel ball dropped onto loose, very fine sand ("dry quicksand") creates an upward jet exceeding the release height of the ball. There is a striking similarity with the impact of an object in a liquid: The jet is generated by the gravity-driven collapse of the void created by the ball, and the focused pressure pushes the sand straight up into the air. Using a 2-dimensional experimental setup and high-speed imaging, the collapse of the void is visualized. For high impact velocities the void collapse is seen to entrain air. The entrained air bubble slowly rises through the sand, and upon reaching the surface causes a granular eruption. The experimental observations are quantitatively explained by a Rayleigh-type model. Parallels are drawn with impacts on a planetary scale.

PDSW02 4th April 2006
15:30 to 16:30
Soluble models of self-organized criticality: Lecture II

In these lectures, I will discuss the abelian sandpile model of self-organized criticality, and its related models. The abelian group structure of the model, the burning test for recurrent states, equivalence to the spanning trees problem will be described. The exact solution of the directed version of the model in any dimension will be explained, and its relation to Scheidegger's model of river basins, Takayasu's aggregation model and the voter model will be discussed. I will summarize the known results about the undirected models. Generalization to the abelian distributed processors model, and time-dependent properties and the universality of critical behavior in sandpiles will be briefly discussed.

PDSW02 4th April 2006
16:30 to 17:30
Field-theoretic approaches to interacting particle systems: Lecture II

It is explained how field-theoretic methods and the dynamic renormalization group (RG) can be applied to study the universal scaling properties of interacting particle systems far from thermal equilibrium that either undergo a continuous phase transition or display generic scale invariance It is described how the master equation for stochastic particle reaction processes can be mapped onto a field theory action. The RG is then employed to analyze the ensuing power laws in simple diffusion-limited annihilation reactions as well as generic continuous transitions from active to inactive, absorbing states, which are characterized by the power laws of (critical) directed percolation. Certain other important universality classes including dynamic percolation and parity-conserving branching and annihilating random walks are discussed, and some open issues are mentioned.

PDSW02 5th April 2006
09:00 to 10:00
Applications of nonequilibrium models in biological systems: Lecture I

There are many biological functions that involve movement of motors along a filament or polymeric molecule. The motors use chemical energy to propel themselves along the track. The description of these systems is in many cases done using models of driven systems. The lectures will give an introduction to molecular motors discussing their use in biological systems and the experiments which study them. Then several application of models of driven systems in the interpretation of experiments will be reviewed.

PDSW02 5th April 2006
10:00 to 11:00
Field-theoretic approaches to interacting particle systems: Lecture III

It is explained how field-theoretic methods and the dynamic renormalization group (RG) can be applied to study the universal scaling properties of interacting particle systems far from thermal equilibrium that either undergo a continuous phase transition or display generic scale invariance It is described how the master equation for stochastic particle reaction processes can be mapped onto a field theory action. The RG is then employed to analyze the ensuing power laws in simple diffusion-limited annihilation reactions as well as generic continuous transitions from active to inactive, absorbing states, which are characterized by the power laws of (critical) directed percolation. Certain other important universality classes including dynamic percolation and parity-conserving branching and annihilating random walks are discussed, and some open issues are mentioned.

PDSW02 5th April 2006
11:30 to 12:30
Growth models in one dimension and random matrices: Lecture I

The motion of an interface separating a stable from an unstable phase is a well-studied problem in nonequilibrium dynamics, in particular since the field-theoretic formulation by Kardar, Parisi, and Zhang. For a one-dimensional interface many universal quantities of physical interest can be computed exactly. Surprisingly enough, there are links to the soft edge scaling of Gaussian unitary matrices. We explain the type of growth models which can be handled, how the connection to random matrices arises, and some of the predictions for one-dimensional growth.

PDSW02 5th April 2006
14:00 to 15:00
Soluble models of self-organized criticality: Lecture III

In these lectures, I will discuss the abelian sandpile model of self-organized criticality, and its related models. The abelian group structure of the model, the burning test for recurrent states, equivalence to the spanning trees problem will be described. The exact solution of the directed version of the model in any dimension will be explained, and its relation to Scheidegger's model of river basins, Takayasu's aggregation model and the voter model will be discussed. I will summarize the known results about the undirected models. Generalization to the abelian distributed processors model, and time-dependent properties and the universality of critical behavior in sandpiles will be briefly discussed.

PDSW02 6th April 2006
09:00 to 10:00
Growth models in one dimension and random matrices: Lecture II

The motion of an interface separating a stable from an unstable phase is a well-studied problem in nonequilibrium dynamics, in particular since the field-theoretic formulation by Kardar, Parisi, and Zhang. For a one-dimensional interface many universal quantities of physical interest can be computed exactly. Surprisingly enough, there are links to the soft edge scaling of Gaussian unitary matrices. We explain the type of growth models which can be handled, how the connection to random matrices arises, and some of the predictions for one-dimensional growth.

PDSW02 6th April 2006
10:00 to 11:00
Fourier Law in low-dimensional systems: Lecture II

The study of transport properties in low-dimensional models has attracted much attention in the scientific community. In fact, it has pointed out new basic for the theory of non-equilibrium stationary processes, while providing interesting perspectives of applications to new materials. These lectures will be mainly devoted to survey the achievements on the problem of heat transport in 1D and 2D systems. A pedagogically suitable approach will be proposed to the students, going through a historical pathway. Numerical results will be presented together with the main rigorous approaches and analytical results. These lectures aim at providing also an overview of the state of the art on this research topic, with reference to still open, challenging problems. Department of Physics, LE Fermi 2, 50125 Firenze

PDSW02 6th April 2006
11:30 to 12:30
Applications of nonequilibrium models in biological systems: Lecture II

There are many biological functions that involve movement of motors along a filament or polymeric molecule. The motors use chemical energy to propel themselves along the track. The description of these systems is in many cases done using models of driven systems. The lectures will give an introduction to molecular motors discussing their use in biological systems and the experiments which study them. Then several application of models of driven systems in the interpretation of experiments will be reviewed.

PDSW02 6th April 2006
14:00 to 15:00
New critical phenomena in complex networks

Most of real-world networks are extremely compact, infinite-dimensional objects. Consequently, any cooperative model on any of these network substrates is surely in situation above the upper critical dimension. This is why critical phenomena in these models should be precisely described in the framework of a mean field approach. Nonetheless, due to specific architectures of complex networks, these mean field theories are surprisingly non-standard.

We discuss the unusual critical phenomena in complex networks by using representative examples: the Ising and Potts models, the percolation and its generalizations, etc. Remarkably, the critical behaviours are very different in equilibrium and growing networks. We explain that in a class of growing networks, the percolation and Ising models may even demonstrate a critical singularity of the Berezinskii-Kosterlitz-Thouless kind. We also touch upon the bootstrap (k-core) percolation problem and the k-core organization of complex networks.

S N Dorogovtsev, J F F Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003); Adv. Phys. 51, 1079 (2002).

S N Dorogovtsev, A V Goltsev, J F F Mendes, Ising model on networks with an arbitrary distribution of connections, Phys. Rev. E 66, 016104 (2002).

S N Dorogovtsev, J F F Mendes, A N Samukhin, Anomalous percolation properties of growing networks, Phys. Rev. E 64, 066110 (2001).

M Bauer, S Coulomb, S N Dorogovtsev, Phase transition with the Berezinskii-Kosterlitz-Thouless singularity in the Ising model on a growing network, Phys. Rev. Lett. 94, 200602 (2005).

S N Dorogovtsev, A V Goltsev, J F F Mendes, k-core organization of complex networks, Phys. Rev. Lett. 96, 17 February (2006).

PDSW02 6th April 2006
15:30 to 16:30
Modelling of traffic flow and related transport problems: Lecture II

In this series of lectures the basic empirical properties and theoretical modelling approaches for various traffic systems will be reviewed. The list of topics includes: 1) Empirical traffic data and their interpretation 2) Modelling approaches for highway traffic (hydrodynamic models, car-following models, etc.) 3) Cellular automata models of highway traffic (ASEP, Nagel-Schreckenberg model and their extensions) 4) Pedestrian dynamics 5) Transport in biological systems (ant trails, intracellular transport, etc)

PDSW02 7th April 2006
09:00 to 10:00
Applications of nonequilibrium models in biological systems: Lecture III

There are many biological functions that involve movement of motors along a filament or polymeric molecule. The motors use chemical energy to propel themselves along the track. The description of these systems is in many cases done using models of driven systems. The lectures will give an introduction to molecular motors discussing their use in biological systems and the experiments which study them. Then several application of models of driven systems in the interpretation of experiments will be reviewed.

PDSW02 7th April 2006
10:00 to 11:00
Modelling of traffic flow and related transport problems: Lecture III

In this series of lectures the basic empirical properties and theoretical modelling approaches for various traffic systems will be reviewed. The list of topics includes: 1) Empirical traffic data and their interpretation 2) Modelling approaches for highway traffic (hydrodynamic models, car-following models, etc.) 3) Cellular automata models of highway traffic (ASEP, Nagel-Schreckenberg model and their extensions) 4) Pedestrian dynamics 5) Transport in biological systems (ant trails, intracellular transport, etc)

PDSW02 7th April 2006
11:30 to 12:30
Growth models in one dimension and random matrices: Lecture III

The motion of an interface separating a stable from an unstable phase is a well-studied problem in nonequilibrium dynamics, in particular since the field-theoretic formulation by Kardar, Parisi, and Zhang. For a one-dimensional interface many universal quantities of physical interest can be computed exactly. Surprisingly enough, there are links to the soft edge scaling of Gaussian unitary matrices. We explain the type of growth models which can be handled, how the connection to random matrices arises, and some of the predictions for one-dimensional growth.

PDSW02 7th April 2006
15:30 to 16:30
Introduction to nonequilibrium work theorems: Lecture III

When we drive a physical system away from a state of thermal equilibrium by forcing a change in one of its variables -- e.g. when we push a piston into a gas, or when we stretch a single molecule using optical tweezers -- then we perform a certain amount of work, W, on the system.

Over the past decade, a number of results -- collectively known as nonequilibrium work theorems (NWT's) -- have revealed that equilibrium information is subtly encoded in the statistics of W, even when the system is driven significantly far from equilibrium.

In my three lectures I will present an introduction to these theoretical results, as well as to their applications in the context of experiments and numerical simulations aimed at estimating thermodynamic properties of complex systems. The first lecture will present a general overview of these results. In the remaining two lectures I plan to cover a number of topics, including: useful mathematical tools for deriving and analyzing NWT's; practical issues regarding the applications of these results; generalizations of NWT's, and their relation to Fluctuation Theorems; and the connection of NWT's to deeper issues of macroscopic irreversibility.

PDSW02 7th April 2006
16:30 to 17:30
Clustering, coarsening and directed transport in a granular gas: Lecture III

1. Clustering and Coarsening in a Granular Gas Granular gases are of great scientific and economic relevance. Scientific, because of their tendency to spontaneously separate into dense and dilute regions, which makes them fundamentally different from any textbook molecular gas. Economic, because no less than 5 per cent of the global energy budget is wasted due to problems with granular matter in conveyor belts, sorting machines, mixers, and other industrial machinery. Here we study - experimentally, numerically, and theoretically - the clustering of particles in a vertically vibrated array of N connected compartments. For strong shaking, the particles spread evenly over the compartments, but if the shaking strength is lowered beneath a critical level this uniform distribution gives way to a clustered state, consisting of a few well-filled compartments and a lot of diluted ones. In the course of time, this state coarsens: The smaller clusters are eaten by the larger ones, until finally only one big cluster remains. This coarsening process is exceptionally slow, with the mass of the surviving cluster growing only as the square root of log t.

2. Clustering and Directed Transport

In this second lecture we turn to the wonderful world of ratchets, which have become a hot topic in recent years. In order to extract mechanical work on a molecular scale (e.g., to make a muscle move), nature uses the concept of a Brownian ratchet: The stochastic forces from a noisy environment are converted into a directed motion. Here we create a "granular ratchet", exploiting the clustering phenomenon from the previous lecture in a slightly adapted array of N connected compartments: The stochastically colliding particles spontaneously generate a particle current perpendicular to the direction of energy input. This is the first practical realization of the theoretically predicted concept of a stochastic ratchet as a collective effect in a symmetric geometry.

A related problem of prime importance in modern society is the clustering of cars on the highway. We show how the formation of traffic jams on the Dutch highway A58 is well described - and predicted! - by a flux model similar to the one we use for the clustering of granular particles

3. Granular Impact Jets

A steel ball dropped onto loose, very fine sand ("dry quicksand") creates an upward jet exceeding the release height of the ball. There is a striking similarity with the impact of an object in a liquid: The jet is generated by the gravity-driven collapse of the void created by the ball, and the focused pressure pushes the sand straight up into the air. Using a 2-dimensional experimental setup and high-speed imaging, the collapse of the void is visualized. For high impact velocities the void collapse is seen to entrain air. The entrained air bubble slowly rises through the sand, and upon reaching the surface causes a granular eruption. The experimental observations are quantitatively explained by a Rayleigh-type model. Parallels are drawn with impacts on a planetary scale.

PDS 11th April 2006
14:15 to 15:15
Phase transitions or crossovers: Anomalous finite-size effects in low-dimensional driven systems

Asymmetric simple exclusion processes with two species of particles, driven in opposite directions, can be interpreted as simple traffic models describing fast and slow cars, or pedestrian encounters in narrow hallways. At first sight, these models appear to exhibit remarkably different behaviors, depending on the number of ''lanes'' in the model. Strictly one-dimensional (''one-lane'') models are clearly disordered, while simulations of ''two-lane'' models show a large, macroscopic jam.

In this talk, I will describe this puzzle and propose a resolution. Some other peculiar features, such as a region with negative response in a model with lane preference, will also be discussed.

PDS 18th April 2006
14:15 to 15:15
Chaos and the physics of non-equilibrium systems

After a brief introduction to chaos theory I will summarize some of the methods for relating it to non-equilibrium statistical mechanics.Then I will show how to use kinetic theory methods to calculate characteristic chaotic properties such as Lyapunov exponents and Kolmogorov-Sinai entropies for dilute interacting particle systems. For the Lorentz gas (a system of light point particles moving among fixed scatterers) these calculations are especially simple, but they can also be done for systems of moving hard spheres. Finally, I will consider the case of the Brownian motion of one large sphere in a very dilute gas of small spheres. Under these conditions the largest Lyapunov exponents are due to the Brownian particle. They can be calculated by solving a Fokker-Planck equation.

PDS 20th April 2006
14:15 to 15:15
A Bray Asymptotics of the Trapping Reaction
PDS 25th April 2006
14:15 to 15:15
Conformal invariance and its breaking in a stochastic model of a fluctuating interface
PDS 27th April 2006
14:15 to 15:15
Clustering in passive scalar systems
PDS 2nd May 2006
14:15 to 15:15
Stochastic models in biology and their deterministic analogues
PDS 4th May 2006
14:15 to 15:15
Bethe ansatz solution of the asymmetric exclusion process
PDS 9th May 2006
14:15 to 15:15
Fluctuation theorems and the zero-range process
PDS 11th May 2006
14:15 to 15:15
Moving interfaces in complex matter
PDS 16th May 2006
14:15 to 15:15
Shear-thickening and the glass transition

Some liquids become more viscous when sheared, even to the point of jamming completely. In some cases, this phenomenon can be interpreted as a shear-induced glass transition. A theory that explains shear-thickening in these systems must simultaneously provide an explanation for their glass transition, and, conversely, a theory of the glass transition must naturally incorporate shear-thickening in order to be credible. I will describe a schematic model that reproduces qualitatively the observations, and makes several predictions, some of which have been already tested.

PDS 18th May 2006
14:15 to 15:15
Quasi stationary distributions and Fleming Viot processes

We consider an irreducible pure jump Markov process with rates Q=(q(x,y)) on Lambda\cup\{0\} with \Lambda countable and 0 an absorbing state. A quasi-stationary distribution (qsd) is a probability measure \nu on \Lambda that satisfies: starting with \nu, the conditional distribution at time t, given that at time t the process has not been absorbed, is still \nu. That is, \nu = \nu P_t/(1-\nu P_t(0)), with P_t(x,y)= probability to go from x to y for the process with rates Q. A Fleming-Viot (fv) process is a system of N particles moving in \Lambda. Each particle moves independently with rates Q until it hits the absorbing state 0; but then instantaneously chooses one of the N-1 particles remaining in \Lambda and jumps to its position. Between absorptions each particle moves with rates Q independently. Under the condition \alpha:=\sum_x\inf Q(\cdot,x) > \sup Q(\cdot,0):=C we prove existence of qsd for Q; uniqueness has been proven by Jacka and Roberts. When \alpha>0 the fv process is ergodic for each N. Under alpha>C the mean normalized densities of the fv unique stationary state converge to the qsd of Q, as N \to \infty; in this limit the variances vanish.

PDS 23rd May 2006
14:15 to 15:15
Pattern formation in nonequilibrium systems: the Liesegang case
PDS 25th May 2006
14:15 to 15:15
Multiclass invariant measures for TASEP and multitype queuing systems
PDS 30th May 2006
14:15 to 15:15
A sigma model approach to glassy dynamics

I shall present a sigma-model approach to the out of equilibrium dynamics of glassy systems. First, I shall review some salient features of the relaxation of glassy systems. Next, I shall describe the main idea on which the theoretical approach is based: the development of an approximate asymptotic time-reparametrization invariance. I shall briefly describe numeric and analytic studies of several models (finite dimensional spin-glasses, kinetically constrained models, elastic lines in random environments and the O(N) model for coarsening in the large N limit) that put to the test our predictions. I shall end by discussing the general picture that emerges. This work is the result of a collaboration with Claudio Chamon (Boston University) et al.

PDS 31st May 2006
14:15 to 15:15
Phase transitions and mesoscopic structures in systems with long range interactions
PDS 1st June 2006
14:15 to 15:15
A possible classification for nonequilibrium steady states
PDS 2nd June 2006
11:00 to 12:00
Statistical mechanics: Historical overview and current issues
PDS 6th June 2006
14:15 to 15:15
Social balance on networks: The dynamics of friendship and hatred

PDS 8th June 2006
14:15 to 15:15
Dynamical and mosaic lengths in a model glass
PDS 9th June 2006
11:00 to 12:00
Informal discussions
PDS 13th June 2006
14:15 to 15:15
Point processes with specified correlation functions

Given a point process, in Euclidean space or on a lattice, the corresponding k-point correlation function, for k=1,2, . . ., expresses the probability of finding particles at k specified points. Here we ask a converse question: if we are given a finite number of candidate correlation functions, say those for k=1,2, . . . , n, does there exist a point process which realizes these correlations? We give some partial answers to this question and discuss some examples.

PDS 15th June 2006
14:15 to 15:15
M Bramson Exclusion processes in one and higher dimensions

Exclusion processes form one of the major classes of interacting particle systems. There, particles on a lattice execute independent random walks in continuous time, except when the target site is already occupied, in which case the particle remains at the original site.

Many results exist for the lattice Z. In particular, the equilibria of such exclusion processes are in many cases well understood. Little is presently known, however, for Z^d, d>1 . We will review the behavior of the exclusion process on Z and with the remaining time present the foundation of a theory for d>1 .

PDSW03 26th June 2006
10:00 to 11:00
Scaling functions for finite-size corrections in extreme statistics

Applications of extreme statistics are hindered by the notoriously slow convergence of the distributions to their limiting forms, thus studies of finite-size corrections are called for. Here we undertake a systematic investigation of the finite-size scaling functions and their universal aspects for the classical extreme statistics of i.i.d. variables, as well as for strongly correlated variables such as occuring in various surface growth problems.

PDSW03 26th June 2006
11:30 to 12:30
A nontrivial constant c=0.29795219028 in one and three dimensional random walks

Two different random walk problems, one in one dimension and the other in three dimensions, seem to share a nontrivial constant whose numerical value is c=0.29795219028.. In the first problem, this constant shows up in the finite size correction to the expected maximum of a discrete-time random walk on a continuous line with unform jump density. In the second problem, this constant appears as the Milne extrapolation length' in the expression for flux of discrete-time random walkers to a spherical trap in three dimensions. We prove why the same constant appears in the two problems and derive an exact analytical formula for this constant.

PDSW03 26th June 2006
14:00 to 14:10
First return time distribution for power law correlated Gaussian processes
It is known that numerical simulations of power law correlated Gaussian processes lead to 1st return time distributions strongly departing from the exponential regime characteristic of the uncorrelated case. An analytical description of the mechanism leading to the distribution profile is here proposed, taking into full account the long memory of the process. Excellent comparison with numerical data is observed.
PDSW03 26th June 2006
14:10 to 14:20
Random processes generated by random permutations.
In this talk, we overview recent results obtained for an exactly solvable model of a non-markovian random walk generated by random permutations of natural series [1,2,3,...,n]. In this model, a random walker moves on a lattice of integers and its moves to the right and to the left are prescribed the sequence of rises and descents characterizing each given permutation of [n]. We determine exactly the probability distribution function of the end-point of the trajectory, its moments, the probability measure of different excursions, as well as different characteristics showing how scrambled the trajectories are. In addition, we discuss properties of 1d and 2d surfaces associated with random permutations and calculate the distribution function of the number of local extrema. As a by-product, we obtain many novel results on intrinsic features of random permutations (statistics of rises, descents, peaks and throughs).
PDSW03 26th June 2006
15:30 to 16:30
Maximum of a brownian path, fluctuating interfaces and related problems

We present some functionals of the one dimensional Brownian motion which arise in various statistical physics problems: -maximal fluctuation of a growing interface -traversal time of a potential barrier -search algorithm of the maximum of a simple random walk. All these different cases involve certain functionals of the path and its maximum. We show how to compute these distributions by a path integral approach and discuss the link with probabilistic techniques based on meanders and excursions.

PDSW03 27th June 2006
09:00 to 10:00
First-Passage problems in systems with many degrees of freedom

Recent progress in the study of first-passage problems in systems with many degrees of freedom will be reviewed, and open questions discussed. The systems considered include coarsening systems, fluctuating interfaces, and reaction-diffusion systems.

PDSW03 27th June 2006
10:00 to 11:00
C Godreche The statistics of occupation times

I will present a mini-review of some results on the statistics of occupation times for coarsening systems (spin systems, diffusion equation), or for simpler stochastic models (e.g., renewal processes).

PDSW03 27th June 2006
11:30 to 12:30
The random acceleration process, with applications to granular matter and polymers

Some recent results for the equilibrium and non-equilibrium statistics of a particle which is randomly accelerated by Gaussian white noise are reviewed. The cases of motion on the half line x > 0 and motion on the finite line 0 < x < 1 with absorbing, partially absorbing, and inelastic boundary conditions are considered. The results for inelastic reflection at the boundary are of interest in connection with driven granular matter. The equilibrium properties of a semi-flexible polmer chain confined in a narrow cylindrical pore are also determined by the random acceleration process.

PDSW03 27th June 2006
14:00 to 15:00
Persistence and survival in equilibrium step fluctuations

The concepts of persistence and survival are used to characterize the first-passage properties of equilibrium fluctuations of steps on a vicinal surface. Analytic and numerical results are obtained for temporal and spatial persistence and survival probabilities and for the probability of persistent large deviations. These theoretical results are found to be in very good agreement with those obtained from experiments in which time-dependent scanning tunneling microscopy is used to study equilibrium step fluctuations.

PDSW03 27th June 2006
15:30 to 16:30
First passage and arrival time densities for Levy Flights

We discuss a few cases related to the first passage time problem when dominated by Lévy jump length distributions , namely, Lévy flights. These include crossing of a barrier, the semi- infinite interval and the nature of leap-overs. The latter is investigated for both symmetric and one-sided Lévy flights.

PDSW03 28th June 2006
09:00 to 10:00
The Unreasonable effectiveness of equilibrium-like theory for interpreting non-equilibrium experiments

There has been great interest in applying the results of statistical mechanics to single molecule experiements. Recent work has highlighted so-called non-equilibrium work-energy relations and Fluctuation Theorems that take on an equilibrium-like (time independent) form. Here I give a very simple heuristic example where an equilibrium result (the barometric law for colloidal particles) arises from theory describing the {\em thermodynamically} non- equilibrium phenomenon of a single colloidal particle falling through solution due to gravity. This simple description arises from the fact that the particle, even while falling, is in {\em mechanical} equilibrium (gravitational force equal the viscous drag force) at every instant. The results are generalized using Onsager's least dissipation approach for stochastic processes to derive time independent equations that hold for thermodynamically non-equilibrium (and even non-stationary) systems. These equations offer great possibilities for rapid determination of thermodynamic parameters from single molecule experiments.

PDSW03 28th June 2006
10:00 to 11:00
E Ben-Naim Nonequilibrium statistical physics of driven granular gases

Granular systems dissipate kinetic energy and thus, should be driven to maintain a steady-state. In particular, for granular gases, an energy source should balance the dissipation. This talk will review the different steady-states that characterize driven granular gases. When the system is supplied with energy at all scales, as is the case in most of the vigorous driving experiments, the energy input can be modeled using the standard thermal heat bath. The core of the velocity distribution is then close to a Maxwellian but the tail has a stretched exponential form and it is overpopulated with respect to a Maxwellian. When energy is injected at all energy scales, there is an energy cascade from large velocities to small velocities. In this case, the velocity distribution is characterized by a power-law tail.

PDSW03 28th June 2006
11:30 to 12:30
Extreme times in finance

We analyze the problem of extreme events for financial time series and models. The approach will be different according the nature of the data available. This means that for high-frequency data a micoscopic approach (for which the continuous tuime random walk is a good candidate) is needed; while for lower frequency data one can rely on the traditional approach based on diffusion equations.

PDSW03 28th June 2006
14:00 to 14:10
Weak ergodicity breaking in the continuous time random walk
The continuous-time random walk (CTRW) model exhibits a nonergodic phase when the average waiting time diverges. The first passage time probability density function for nonbiased and uniformly biased CTRWs is shown to yields the nonergodic properties of the random walk which show strong deviations from Boltzmann-Gibbs theory. Using numerical simulations we generalize the results for the CTRW in a potential field. We derive the distribution function of occupation times in a bounded region of space which in the ergodic phase recovers the Boltzmann-Gibbs theory, while in the nonergodic phase yields a generalized nonergodic statistical law.
PDSW03 28th June 2006
14:10 to 14:20
H Guclu Extreme fluctuations in small-world-coupled autonomous systems with relaxational dynamics
Synchronization is a fundamental problem in natural and artificial coupled multi-component systems. We investigate to what extent small-world couplings (extending the original local relaxational dynamics through the random links) lead to the suppression of extreme fluctuations in the synchronization landscape of such systems. In the absence of the random links, the steady-state landscape is "rough" (strongly de-synchronized state) and the average and the extreme height fluctuations diverge in the same power-law fashion with the system size (number of nodes). With small-world links present, the average size of the fluctuations becomes finite (synchronized state). For exponential-like noise the extreme heights diverge only logarithmically with the number of nodes, while for power-law noise they diverge in a power-law fashion. The statistics of the extreme heights are governed by the Fisher–Tippett–Gumbel and the Fréchet distribution, respectively. We also study the extreme-value scaling and distributions in scale-free networks. We illustrate our findings through an actual synchronization problem in parallel discrete-event simulations. * http://cnls.lanl.gov/External/people/Hasan_Guclu.php - Homepage * http://www.rpi.edu/~korniss - Homepage * http://cnls.lanl.gov/~guclu - Homepage * http://arxiv.org/abs/cond-mat/0311575 - Preprint
PDSW03 28th June 2006
14:20 to 14:30
Fluctuation-regularized front propagation up a reaction-rate gradient
We introduce and study a new class of fronts in finite particle number reaction-diffusion systems, corresponding to propagating up a reaction rate gradient. We show that these systems have no traditional mean-field limit, as the nature of the long-time front solution in the stochastic process differs essentially from that obtained by solving the mean-field deterministic reaction-diffusion equations. Instead, one can incorporate some aspects of the fluctuations via introducing a density cutoff. Using this method, we derive analytic expressions for the front velocity dependence on bulk particle density and show self-consistently why this cutoff approach can get the correct leading-order physics. * http://xxx.arxiv.org/abs/cond-mat/0406336 - Fluctuation-regularized Front Propagation Dynamics * http://xxx.arxiv.org/abs/q-bio.PE/0410015 - Recombination dramatically speeds up evolution of finite populations * http://xxx.arxiv.org/abs/cond-mat/0508128 - Front Propagation Dynamics with Exponentially-Distributed Hopping * http://xxx.arxiv.org/abs/cond-mat/0508663 - Front Propagation up a Reaction Rate Gradient
PDSW03 28th June 2006
14:30 to 14:40
Noisy kinks and diffusion-limited reaction
Kinks are examples of coherent structures'': clearly identifiable localized features in a noisy, spatially-extended system that can be followed as they move about under the influence of fluctuations. In the Phi4 stochastic partial differential equation, a steady-state mean density is dynamically maintained: kinks and antikinks are nucleated in pairs, follow Brownian paths and annihilate on meeting. Thus the kink-antikink reaction rate is controlled by collisions between diffusing particles. Classical treatment of such problems produces a hierarchy of particle correlation functions without an exact solution. However, it is possible to sidestep this hierarchy and find an exact solution for the mean number of particles per unit length as a function of time. We review an exact method for calculating the mean lifetime of a particles in a simplified model, and an exact rate equation in terms of the correlation function. In addition, the distribution of particle lifetimes is calculated under a constant-killing-rate'' approximation that compares favourably with the results of numerical experiments. Related Links * http://maths.leeds.ac.uk/~grant
PDSW03 28th June 2006
14:40 to 14:50
Interface roughening dynamics of spreading droplets
We review our recent experimental data of interface roughening dynamics of spreading mercury droplets on thin films (silver or gold), obtained using optical microscopy and other techniques (AFM, SEM). We discuss the various results obtained for the roughness and growth exponents associated with the interface dynamics, and their universality classes. We analyze the temporal width fluctuations, obtained for single interfaces, and show that these fluctuations contain information on the lateral correlation length of these interfaces. We show how to extract this length from experimental data, and demonstrate the validity of this method in a wide range of growing interfaces (droplet spreading experiments as well as water imbibition on paper). Finally, we discuss the persistence exponents of these systems. References: 1. A. Be'er, Y. Lereah and H. Taitelbaum, Physica A, 285, 156 (2000). 2. A. Be'er, Y. Lereah, I. Hecht and H. Taitelbaum, Physica A, 302, 297 (2001). 3. A. Be'er, Y. Lereah, A. Frydman and H. Taitelbaum, Physica A, 314, 325 (2002). 4. A. Be'er and Y. Lereah, J. of Microscopy, 208, 148 (2002). 5. I. Hecht and H. Taitelbaum, Phys. Rev. E, 70, 046307 (2004). 6. A. Be'er, I. Hecht and H. Taitelbaum, Phys. Rev. E, 72, 031606 (2005). 7. I. Hecht, A. Be'er and H. Taitelbaum, Fluctuation and Noise Letters, 5, L319 (2005).
PDSW03 29th June 2006
09:00 to 10:00
Tightness for the minimum displacement of branching random walk and some other old problems

Study of solutions of certain families of semilinear heat equations dates back to Kolmogorov-Petrovsky-Piscounov in 1937; since then this problem has been thoroughly analyzed. Substantially less is known about the behavior of their discrete time analogs; several basic questions have been unresolved since the 1970's. In the probabilistic context, the continuous time problem corresponds to the minimum displacement of branching Brownian motion, and the discrete time problem to the minimum displacement of branching random walk. Here, we summarize this background and present some new results for branching random walk.

PDSW03 29th June 2006
10:00 to 11:00
D Dean Phase transition in the Aldous-Shields Model of growing trees

We study analytically the late time statistics of the number of particles in a growing tree model introduced by Aldous and Shields. In this model, a cluster grows in continuous time on a binary Cayley tree, starting from the root, by absorbing new particles at the empty perimeter sites at a rate proportional to $c^{-l}$ where $c$ is a positive parameter and $l$ is the distance of the perimeter site from the root. For $c=1$, this model corresponds to random binary search trees and for $c=2$ it corresponds to digital search trees in computer science. By introducing a backward Fokker-Planck approach, we calculate the mean and the variance of the number of particles at large times and show that the variance undergoes a phase transition' at a critical value $c=\sqrt{2}$. While for $c>\sqrt{2}$ the variance is proportional to the mean and the distribution is normal, for $c<\sqrt{2}$ the variance is anomalously large and the distribution is non-Gaussian due to the appearance of extreme fluctuations. The model is generalized to one where growth occurs on a tree with $m$ branches and, in this more general case, we show that the critical point occurs at $c=\sqrt{m}$.

PDSW03 29th June 2006
11:30 to 12:30
Quantum random walks

A problem posed by Aldous is to estimate the complexity of finding a (1 - epsilon)-optimal particle in a branching random walk. This is computed in terms of the probability of existence of a trajectory staying forever above the critical drift minus epsilon. (it is known that no particle can stay above the critical drift forever). I will then discuss the computation of this probability, in a continous time (branching Brownian motion) setting, which involves estimating solutions to the KPP equation.

PDSW03 29th June 2006
14:00 to 15:00
Exact solutions for first-passage and related problems in certain classes of queueing system

This talk will examine discrete and continuous time queueing systems in the context of recognising the so-called busy period as the first-passage time of a random walk process. As well as identifying the queue duration (busy-period) distribution, consideration is also given to the distribution of the maximum (extreme) queue length during a busy period and, much harder, the distribution of the total waiting time (area under the curve) during a busy period. Physical examples of interest include traffic jams, Abelian sandpile (avalanche) models in the compact directed percolation universality class, and the statistics of lattice polygon models. Throughout, the emphasis is on providing exact solutions.

PDSW03 29th June 2006
15:30 to 16:30
One-species diffusion-limited reactions on the Bethe lattice
PDSW03 30th June 2006
09:00 to 10:00
J-P Bouchaud Extreme value problems in random matrix theory, spin glasses and directed polymers

We will review a few applications of extreme values in the theory of disordered systems and mention several open problems, in particular concerning the generalisation of Parisi's solution or of the Tracy-Widom distribution when the disorder has "fat tails".

PDSW03 30th June 2006
10:00 to 11:00
Optimal search strategies for hidden targets

Many physical, chemical or biological problems can be rephrased as search processes, involving a searcher and a target of unknown position. We show that intermittent search strategies, alternating active search phases and non reactive displacement phases, are universal for a wide class of problems involving search time optimization. More precisely, we address the general question of determining in which cases a searcher should, or should not, interrupt his search activity by "losing" time in non reactive phases of mere displacement, and which durations of each phase optimize the search time. Using a representative analytical model, we show that intermittent strategies do optimize the search time as soon as the target is "difficult" to detect, and we explicitly give the optimal search strategies, which depend on the memory skills of the searcher.

PDSW03 30th June 2006
11:30 to 11:40
Relation between global fluctuations in non-equilibrium systems and Gumbel statistics
We explain how the statistics of global observables in non-equilibrium or correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution G_a(x), with a real index a, in the study of global fluctuations. To illustrate these results, we introduce an exactly solvable nonequilibrium model describing an energy flux on a lattice, with local dissipation, in which the fluctuations of the global energy are precisely described by the generalized Gumbel distribution. Related Links * http://arxiv.org/abs/cond-mat/0506166 - Preprint version of the letter (to appear in PRL)
PDSW03 30th June 2006
11:40 to 11:50
Earthquake recurrence as a record breaking process
Extending the central concept of recurrence times for a point process to recurrent events in space-time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events. Linking record breaking events with edges between nodes in a graph generates a complex dynamical network isolated from any length, time or magnitude scales set by the observer. For Southern California, the network of recurrences reveals new statistical features of seismicity with robust scaling laws. The rupture length and its scaling with magnitude emerges as a generic measure for distance between recurrent events. Further, the relative separations for subsequent records in space (or time) form a hierarchy with unexpected scaling properties. Related Links * http://www.pks.mpg.de/~davidsen/ - homepage
PDSW03 30th June 2006
12:00 to 12:10
Effects of the low frequencies of noise on On--Off intermittency
A bifurcating system subject to multiplicative noise can exhibit on--off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the noise. Our study is based on the calculation of the Probability Density Function (PDF) of the unstable variable. We derive analytical results for some particular types of noises and interpret them in the framework of on-off intermittency. Besides, we perform a cumulant expansion \cite{VanKampen1} for a random noise with arbitrary power spectrum density and show that the intermittent regime is controlled by the ratio between the departure from the threshold and the value of the PSD of the noise at zero frequency. Our results are in agreement with numerical simulations performed with two types of random perturbations: colored Gaussian noise and deterministic fluctuations of a chaotic variable. Extensions of this study to another, more complex, system are presented and the underlying mechanisms are discussed.
PDSW03 30th June 2006
14:00 to 15:00
S Redner On the role of global warming on the statistics of record-breaking temperatures

We theoretically study long-term statistics of record-breaking daily temperatures and validate these predictions by simulations, and by comparing with 126 years of daily temperature data from the city of Philadelphia. Using extreme statistics, we derive the number and the magnitude of record temperature events, based on the observed Gaussian daily temperature distribution in Philadelphia. We then consider the effect of global warming on record temperature events. The current warming rate is insufficient to measurably influence the frequency of these events over the time range of the available observations.