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*OSP 2010*

The 2010 Open Statistical Physics meeting took place on Wednesday 10th March 2010. It was well attended with over 35 participants, and 28 talks scheduled in three parallel sessions.

**Schedule**

**Participants**

Douglas Abraham (Oxford)

Matthew Blow (Oxford)

Richard Blythe (Edinburgh)

John Cardy (Oxford)

Claudio Castelnovo (Oxford)

Paul Chleboun (Warwick)

Matteo Colangeli (Queen Mary)

Robert Concannon (Edinburgh)

Ernesto Estrada (Strathclyde)

Ian Ford (UCL)

Yan Fyodorov (Nottingham)

Juan P. Garrahan (Nottingham)

Uwe Grimm (Open)

Stefan Grosskinsky (Warwick)

Jim Hague (Open)

Rosemary Harris (Queen Mary)

Jo Hutchinson (Bristol)

Rainer Klages (Queen Mary)

Georgie Knight (Queen Mary)

Rodrigo Ledesma-Aguilar (Oxford)

Friedrich Lenz (Queen Mary)

Tim Lowe (Open)

Richard Matthews (Oxford)

Bernhard Mehlig (Gothenburg)

Ben Mestel (Open)

Bortolo Mognetti (Oxford)

Michael Morgan (Bristol)

Oliver Penrose (Heriot-Watt)

Thomas Prellberg (Queen Mary)

Victor Putz (Oxford)

Mike Reeks (Newcastle)

Takahiro Sakaue (Kyushu)

Richard Spinney (UCL)

Hemant Tailor (UCL)

Hugo Touchette (Queen Mary)

Daniel Ueltschi (Warwick)

Daniel Wacks (Newcastle)

Michael Wilkinson (Open)

Paul Upton (Open)

**Talks and Abstracts**

(please follow links to view the presentations)

**Douglas Abraham**(Oxford)

*Casimir interactions in Ising strips with boundary fields: exact results*An exact statistical mechanical derivation is given of the critical Casimir forces for Ising strips with arbitrary surface fields applied to edges. Our results show that the strength as well as the sign of the force can be controled by varying the temperature or the fields. An interpretation of the results is given in terms of a linked cluster expansion. This suggests a systematic approach for deriving the critical Casimir force which can be used in more general models.

**Matthew Blow**(Oxford)

*Wetting on hairy surfaces***Richard Blythe**(Edinburgh)

*Consensus-formation as a many-body nonequilibrium dynamical process and an application to language change*Consensus formation is a socially-inspired ordering process through which a shared convention is established in a coomunity by means of agents imitating the behaviour of others. One example is the use of a signal to convey a meaning: the first use of a new signal is agreed face-to-face between two agents, and may over time replace an existing convention within a wider community. Within any given model, the key questions are: how likely is this replacement to occur? and how long does it take? To answer these questions, we must solve the nonequilibrium dynamics of competing variants in a heterogeneous, spatially-extended system.

In this talk, I will examine a wide class of models that can be regarded as "neutral", in that there is no intrinsic preference for one signal over another. Only the usage frequency of a signal matters. I will relate these models to theories for language change, show how analytical results for replacement probabilities and times may be obtained, and apply these results to empirical data for New Dialect formation.

**John Cardy**(Oxford)

*Quantum and classical localisation in two and three dimensions*Consider a closed directed graph G in which each node has exactly two incoming and two outgoing edges. In the classical problem, the two ways of decomposing each node into two disjoint directed pieces are assigned probabilities p and 1-p. This decomposes G into a union of closed loops. A particle moving on G therefore performs a deterministic walk in a random medium. The quantum problem is similar, except that transition probabilities at the nodes are replaced by amplitudes, and the particle's wave-function can rotate as it propagates along each edge. It turns out that there is an exact mapping between a particular class of quantum problems with quenched edge disorder and the classical problem.

An interesting question when G is a regular lattice embedded in R

^{d}is whether, in the limit of an infinite lattice, almost all loops have finite length (corresponding to all states being localized), or whether there is a finite probability of escape (corresponding to extended states.) We consider this on some lattices in d=2 and 3 where the classical problem can be related to percolation, and argue that for d=2 almost all states tend to be localized while for d=3 there is a transition between localized and extended states as a function of p.

**Claudio Castelnovo**(Oxford)

*Quantum mechanical perspective on dynamical glass transitions*Using the mapping from the Fokker-Planck description of classical stochastic dynamics into a quantum Hamiltonian, we argue that a dynamical glass transition an be given a precise definition in terms of a static (equilibrium) quantum phase transition. This transition is characterised by a massive collapse of the excited states, leading to a divergent static quantum susceptibility throughout the glassy phase, which directly relates to a non-vanishing Edwards-Anderson order parameter. The quantum mechanical language allows to search for off-diagonal order parameters to detect the classical ‘dynamic order’ using transverse bases – an approach that corresponds to non-static observables in the original classical language. Even in the absence of local order parameters, the transition can be detected via quantum fidelity measures on the ground state wavefunction, which we show translates directly into a singularity in the heat capacity of the classical system.

**Matteo Colangeli**(Queen Mary)

**(with Martin Kröger and Hans Christian Öttinger)**

*Derivation of exact linear hydrodynamics from the Boltzmann equation*See M Colangeli, M Kröger and H C Öttinger, Boltzmann equation and hydrodynamic fluctuations, Phys. Rev. E 80 (2009) 051202.

**Ernesto Estrada**(Strathclyde)

*The connection between algebraic network theory and statistical mechanics***Ian Ford**(UCL)

*Rate equations for coagulation beyond the mean field approximation***Yan Fyodorov**(Nottingham)

*Extreme value statistics of 1/f noises: Statistical Mechanics approach*

**Juan P Garrahan**(Nottingham)

*Thermodynamics of quantum jump trajectories*We apply the large-deviation method to study trajectories in dissipative quantum systems. We show that in the long time limit the statistics of quantum jumps can be understood through an analogy to equilibrium thermodynamics. We consider three simple examples, which illustrate how this approach reveals novel dynamical properties even in well-studied systems: (i) a driven 2-level system where we find a particular scale invariance point in the ensemble of trajectories of emitted photons; (ii) a blinking 3-level system, where we argue that intermittency in photon count is related to a crossover between distinct dynamical phases; and (iii) a micromaser, where we find an actual first-order phase transition in the ensemble of trajectories. We also prove, via an explicit quantum mapping, that rare trajectories of one system can be realized as typical trajectories of an alternative system.

**Stefan Grosskinsky**(Warwick)

*Condensation and metastability in stochastic particle systems*The zero-range process is a recently well studied driven diffusive system that exhibits a condensation transition. When the total density exceeds a critical value, a finite fraction of all particles condenses on a single lattice site, which can be characterized mathematically by the equivalence of ensembles via convergence in specific relative entropy. Although the transition is continuous, finite systems exhibit interesting metastable behaviour and phase coexistence. We establish a law of large numbers for the excess mass fraction in the maximum, which turns out to jump from 0 to a positive value at the critical point. The metastable states can be characterized heuristically as fixed points of a simple effective dynamical system.

**Jim Hague**(Open)

*Statistical physics of cerebral embolization leading to stroke*We discuss the physics of embolic stroke using a minimal model of emboli moving through the cerebral arteries. We will introduce our model of the blood flow network, which consists of a bifurcating tree into which we introduce particles (emboli) that halt flow on reaching a node of similar size. Flow is weighted away from blocked arteries inducing an effective interaction between emboli. We justify the form of the flow weighting using a steady flow (Poiseuille) analysis and a more complicated nonlinear analysis. We discuss free flowing and heavily congested limits and examine the transition from free flow to congestion using numerics. The correlation time is found to increase significantly at a critical value and a finite-size scaling is carried out. An order parameter for nonequilibrium critical behavior is identified as the overlap of blockages’ flow shadows. Our work shows embolic stroke to be a feature of the cerebral blood flow network on the verge of a phase transition.

**Rosemary Harris**(Queen Mary

**)**

*Current fluctuations in stochastic systems with long-range memory***Georgie Knight**(Queen Mary)

*Linear and fractal diffusion coefficients, for a family of shifted, one dimensional maps (with Rainer Klages)*We analyse deterministic diffusion in a simple, one-dimensional setting. The setting consists of a family of four parameter dependent, chaotic maps defined over the real line. When iterated under these maps, a probability density function (p.d.f) spreads out and one can define a diffusion coefficient. We look at how the diffusion coefficient varies across the family of maps and under parameter variation. We do this by deriving analytic expressions for the diffusion coefficients via

Taylor-Green-Kubo formulae in terms of generalised Takagi functions. Typically, diffusion coefficients are fractal functions of a control parameter. However, our family of four maps exhibit both fractal and linear behavior. We explain this structure by looking at the Markov partitions of the maps.

**Rodrigo Ledesma-Aguilar**(Oxford)

*Thin film dynamics on chemically varying substrates***Friedrich Lenz**(Queen Mary)

*Velocity distributions of foraging bumblebees in the presence of predators (with Thomas C Ings, Lars Chittka, Holger Kantz and Rainer Klages)*

We analyse changes in the flight behaviour of foraging bumblebees under varying environmental conditions, measured in a laboratory experiment by Ings and Chittka [1]. We estimate parameters for different plausible velocity distributions by maximising their likelihood and compare their goodness of fit by applying the Akaike Information Criterion. Using Quantile-Quantile-plots we check for deviations between the estimated probability distributions and the data. We also discuss differences in these distributions for different individual bumblebees. On this basis, we look for systematic changes of the distributions due to the presence of different kinds of artificial spiders.

[1] Thomas C Ings and Lars Chittka. Current Biology 18(19): 1520-1524 (2008).

**Richard Matthews**(Oxford)

*Knotted filaments in shear flow***Bernhard Mehlig**(Gothenburg)

*Sample genealogies and genetic variation in populations of variable size***Bortolo Mognetti**(Oxford)

*Capillary filling in microchannels patterned by posts***Oliver Penrose**(Heriot-Watt)

*Statistical mechanics of nonlinear elasticity***Thomas Prellberg**(Queen Mary)

*Forcing adsorption of a tethered polymer by pulling*We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams.

We observe adsorbed and desorbed phases with a thermodynamic phase transition inbetween. In the absence of a pulling force this model has a second-order thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a non-zero vertical component this transition becomes first-order.

Strikingly, we find that if the angle between the pulling force and the surface is beneath a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system.

Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a reentrance transition at constant pulling force for small temperature, which has been observed previously for this model in the presence of vertical pulling.

**Victor Putz**(Oxford)

*Microscopic vs stroke-averaged dynamics in active suspensions at low Reynolds number***Mike Reeks**(Newcastle)

*A kinetic theory for the transport of particles in turbulent flows*This presentation is about the statistical motion of a suspension of small particles in a turbulent flow, how the particles are transported and deposited to surfaces exposed to the flow, and how they collide with one another and agglomerate. It's about the way they interact with the large and small scales of the turbulence and how that depends upon the structure and lifetime of those scales. Such behaviour is an important and controlling feature of many environmental and industrial processes from the transport and coalescence of water droplets in clouds to the release of radioactive aerosol from a nuclear reactor during a severe accident. An elegant and computationally efficient way of modelling such suspensions is to treat the dispersed phase of particles as a fluid in much the same way as the carrier phase is treated as a fluid in terms of a set continuum equations and constitutive relations. The focus of this presentation is on the development of a statistical approach for the treatment of the dispersed phase as a fluids. As such it is analogous to the Kinetic Theory since the quest is to find a suitable Mater equation (analogous to the Maxwell-Boltzmann equation), which acts as a source of the continuum equations and constitutive relations of the dispersed phase as well as properly accounting for particle-wall interactions that constitute the natural boundary conditions of the flow. Over the last 15 years, there has been a considerable interest in the way particles interact with the small scale structures in a turbulent flow and how this leads to segregation and demixing of the particles and enhanced particle collision rates [2, 5, 4, 1]. Whilst a number of theoretical and DNS studies have identified some very interesting and highly relevant features associated with this demixing process e.g. the existence of caustics and singularities in the particle concentration field [6] and the occurrence of random uncorrelated motion [3], these features are not an intrinsic part of a traditional two-fluid model. I will show how these features form part of a generalised kinetic formulation by extending the kinetic approach from one particle to two particle transport leading eventually to the calculation of enhanced collision rates in a similar way to deposition of inertial particles in turbulent boundary layers.

__References__

[1] J. Chun, D. L. Koch, S. L. Rani, A. Ahluwalia, and L. R. Collins. Clustering of aerosol particles in isotropic turbulence. J. Fluid Mech., 536:219-251, 2005.

[2] C. T. Crowe, J. N. Chung, and T. R. Troutt. Chapter 18. In M. C. Roco, editor, Particulate Two-Phase Flow, volume 626, pages 1-1. Heinemann, Oxford, 1993.

[3] P. Février, O. Simonin, and K. D. Squires. Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution; theoretical formalism and numerical study. J. Fluid Mech., 553:1-46, 2005.

[4] C. Marchioli and A. Soldati. Mechanisms for particle transfer and segregation in turbulent boundary layers. J. Fluid Mech., 468:283-315, 2002.

[5] L. P. Wang and M. R. Maxey. Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech., 256:27-68, 1993.

[6] M. Wilkinson, B. Mehlig, S. Östlund, and K. P. Duncan. Unmixing in random flows. Physics of Fluids, 19:113303, 2007.

**Takahiro Sakaue**(Kyushu)

*Asymmetric response and fluctuation in nonequilibrium steady state*Linear response analysis in the nonequilibrium steady state (Gaussian regime) provides two independent fluctuation-response relations. One, in the form of the symmetric matrix, manifests the departure from the equilibrium formula through the quantity so-called irreversible circulation. The other, in the anti-symmetric form, connects the asymmetries in the fluctuation and the response function.

These formulas represent characteristic features of fluctuations far from equilibrium, which have no counterparts in thermal equilibrium.

**Hemant Tailor**(UCL)

*Phase transitions in stretched multistranded biomolecules***Hugo Touchette**(Queen Mary)

*First-order phase transitions and poles in asymptotic representations of partition functions*Although partition functions of finite-size systems are always analytic, and hence have no poles, they can be expressed in many cases as series containing terms with poles. I will show that such poles are related to linear branches of the entropy, and can be used to determine whether the entropy is nonconcave or has linear parts, which is something that cannot be done with the sole knowledge of the thermodynamic free energy derived from the partition function. Applications for equilibrium systems having first-order phase transitions will be discussed.

**Daniel Ueltschi**(Warwick)

*The critical temperature of dilute Bose gases*Predicted by Einstein in 1924, the Bose-Einstein condensation is a striking phase transition that takes place in certain systems of quantum bosonic particles. The dependence of the critical temperature on the interparticle interactions has been a controversial issue in the physics community. I will review the mathematical setting and the literature, and I will describe a non-rigorous but hopefully exact way to compute the lowest order correction to the change of the critical temperature of dilute systems. The approach is based on "spatial random permutations". (This is joint work with V. Betz.)

**Daniel Wacks**(Newcastle)

*Velocity statistics in quantized turbulence*