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OSP 2016

The 2016 Open Statistical Physics meeting took place on Wednesday, 13 April 2016. This year, we had two parallel session of talks.


Time Session A Session B
10:25Welcome address
12:45Lunch break
15:10Tea break


Aleksandra Aloric (Kings)
Benjamin Aymard (Imperial)
Costanza Benassi (Warwick)
Claudia Clarke (UCL)
Carl Dettmann (Bristol)
Ollie Dyer (Warwick)
Ian Ford (UCL)
Gabriele Gradoni (Nottingham)
Uwe Grimm (Open)
Arturo Narros Gonzalez (Queen Mary)
Nina Haug (Queen Mary)
Arnold Mathijssen (Oxford)
Ben Mestel (Open)
Alexander Mozeika (Kings)
Tom Oakes (Nottingham)
Marc Pradas (Open)
Thomas Prellberg (Queen Mary)
Dominic Rose (Nottingham)
Grzegorz Siudem (Queen Mary)
Paul Upton (Open)
Paul Verschueren (Open)
Michael Wilkinson (Open)
Anthony Wood (Edinburgh)

Talks and Abstracts

Aleksandra Aloric (Kings)
Emergence of cooperative long-term market loyalty in double auction markets

Benjamin Aymard (Imperial)
Multiphase flows in confinement with complex geometry
Microengineered devices (MED) have recently seen an explosive growth in a wide spectrum of areas, from microchemical and biological engineering to materials processing and the rapidly growing field of microfluidics, especially lab-on-a-chip systems. Integrated MED offer numerous advantages over traditional technologies, such as small operating volume, ease of use point-of-care diagnostics, fast reaction of samples and excellent control of the fluids involved.
The numerical treatment of fluid flow problems with a sharp interface is in general a difficult task and the corresponding numerical methodologies are rather elaborate and cumbersome often requiring the simultaneous solution for the flow field and the location of the interface. Even when certain simplifications are possible, i.e. for the problem of droplet spreading on a horizontal substrate which is governed by a single partial-differential equation for the film thickness, numerical solutions are highly-nontrivial due to the imposed boundary conditions. The complexity of these solutions increases substantially with the dimensionality of the problem.
Cahn-Hilliard (CH) phase-field models on the other hand provide an alternative description in the face of these difficulties. These models are based on the introduction of an ''order parameter" or ''phase field" which assumes distinct constant values in each bulk phase and undergoes rapid but smooth variation in the interfacial region. The interface is now ''diffuse" i.e. it has a finite thickness (characterized by the length scale over which the order parameter changes), which in turn removes the singularities associated with topological transitions such as moving contact lines and interface pinch off.
Our first aim here is the development of a rigorous, systematic and efficient numerical methodology for the solution of the CH equations for the phase field coupled to the full Navier-Stokes equations. These equations are coupled to the Cahn boundary condition which enables to include the wetting properties of the substrate in the formulation. The methodology is exemplified with two model systems in order of increasing complexity: (a) a droplet on a spatially (chemically and/or topographically) heterogeneous substrate; and (b) a typical MED which can be found in microscale fluid separators where two phases, liquid and gas, are put in contact with each other through a microcontactor aiming to maintain a stable liquid-gas interface for continuous heat and mass transport.

Constanza Benassi (Warwick)
Correlation inequalities for the quantum XY model

Claudia Clarke (UCL)
Obversibility: a measure of dynamical irreversibility in a closed quantum system
We investigate the mean time-integrated dissipation function as a measure of macroscopic irreversibility in a quantum system. This is an alternative to the more usual focus on the production of von Neumann entropy. It is a measure of irreversibility in the form of a test of 'obversibility' [1], a feature that resembles, but differs from, dynamical reversibility.
In a closed system, the dynamics could be reversible but there might still be a preference for a directionality in the statistical behaviour arising from the given pdf over initial coordinates. An obversibility test in a classical system compares the likelihood that a trajectory and its reversed counterpart might follow from a random sampling of these coordinates, the latter requiring an inversion of velocities and reverse Hamiltonian driving. We extend these ideas to a framework of quantum dynamics and consider the case of a two level system, or qubit, specified by a pdf of initial states on the Bloch sphere.
[1] I.J. Ford, Measures of thermodynamic irreversibility in deterministic and stochastic dynamics, New J. Physics 17, 075017 (2015).

Carl Dettmann (Bristol)
Spatial networks with random connections
Many networks of current interest have a spatial structure, in that the nodes and/or links are located in physical space. Examples include climate, communications, conduction, infrastructure, neural and transport networks. An early and still popular model of spatial networks is the random geometric graph, where nodes are located randomly and links formed between sufficiently close nodes. Recent studies have considered random connection models, in which there is a link probability depending on distance. It turns out that the overall connection probability can be estimated from just a few moments of the link probability function for a wide variety of domain geometries. Furthermore, there are qualitative differences as a result of the random connections. In particular, the more realistic model allows a more accurate estimation of connectivity and resilience than the original.

Ollie Dyer (Warwick)
Simulating soft-matter with stochastic wavelet hydrodynamics
This talk is about developing a Monte Carlo based simulation technique for semi-dilute soft-matter systems, which uses wavelets to make simulation faster and simpler than competing methods (e.g. Brownian Dynamics).

Ian Ford (UCL)
A MaxEnt procedure for selecting a nonequilibrium stationary state
The selection of an equilibrium state by maximizing the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, where conclusions are reached on the basis of incomplete information. Such a framework can be more compelling if it is underpinned by dynamical arguments, and we show how this can be provided by stochastic thermodynamics. We select a stationary state by maximizing the change, averaged over all realizations of the motion, in the principal relaxational or nonadiabatic component of stochastic entropy production. We show that this recovers the stationary nonequilibrium pdf for a particle confined to a potential under nonisothermal conditions.
[1] I.J. Ford, Maximum entropy principle for stationary states underpinned by stochastic thermodynamics, Phys. Rev. E 92, 052142 (2015).

Arturo Narros Gonzalez (Queen Mary)
Winding angle distributions for two-dimensional collapsing polymers
We provide numerical support for a long-standing prediction of universal scaling of winding angle distributions. Simulations of interacting self-avoiding walks show that the winding angle distribution for N -step walks is compatible with the theoretical prediction of a Gaussian with a variance growing asymptotically as C log N , with C = 2 in the swollen phase (previously verified), and C = 24/7 at the θ-point. At low temperatures weaker evidence demonstrates compatibility with the same scaling and a value of C = 4 in the collapsed phase, also as theoretically predicted [1].
We will also show simulation results for the winding angle distribution of self- avoiding trails (ISAT) in the swollen and collapsed phases, and at the critical point. Such results in the collapsed phase and at the critical point are seen for the first time in this model, and there are not any theoretical predictions.
Simulations were performed with a modified version of flatPERM algorithm [2], allowing to obtain the microcanonical partition function as a function of chain size, energy and winding. The quality of the data shows the expected corrections due to finite size, never seen so clearly before in both models [3].
[1] B. Duplantier and H. Saleur, Phys. Rev. Lett. 60, 2343 (1988).
[2] T. Prellberg and J. Krawczyk, Phys. Rev. Lett. 92, 120602 (2004).
[3] A. Narros, A. L. Owczarek, and T. Prellberg, arXiv:1510.08287v1, (2015).

Chris Lynch (Open)
Modelling financial bubbles and anti-bubbles with log periodic power laws
Since the mid-1990s, the theory of renormalization and discrete scale invariance from statistical mechanics and complex systems has been used to model bubbles and anti-bubbles in financial time series. In this talk we review log-periodic power law models and compare the now established hierarchy of models with a model derived from a logistic perturbation of linear scaling around the critical point.

Arnold Mathijssen (Oxford)
Hydrodynamics of micro-swimmers in films

Alexander Mozeika (Kings)
Statistical mechanics of clonal expansion in lymphocyte networks modelled with slow and fast variables
We study the Langevin dynamics of the adaptive immune system, modelled by a lymphocyte network in which the B cells are interacting with the T cells and antigen. We assume that B clones and T clones are evolving in different thermal noise environments and on different timescales. We derive stationary distributions and use statistical mechanics to study clonal expansion of B clones in this model when the B and T clone sizes are assumed to be the slow and fast variables respectively and vice versa. We derive distributions of B clone sizes and use general properties of ferromagnetic systems to predict characteristics of these distributions, such as the average B cell concentration, in some regimes where T cells can be modelled as binary variables. This analysis is independent of network topologies and its results are qualitatively consistent with experimental observations. In order to obtain full distributions we assume that the network topologies are random and locally equivalent to trees. The latter allows us to employ the Bethe-Peierls approach and to develop a theoretical framework which can be used to predict the distributions of B clone sizes. As an example we use this theory to compute distributions for the models of immune system defined on random regular networks.

Tom Oakes (Nottingham)
Emergence of cooperative dynamics in fully packed classical dimers
We study the behaviour of classical dimer coverings of the square lattice - a paradigmatic model for systems subject to constraints - evolving under local stochastic dynamics, by means of Monte Carlo simulations and theoretical arguments. We observe clear signatures of correlated dynamics in both global and local observables and over a broad range of time scales, indicating a breakdown of the simple continuum description that approximates well the statics. We show that this collective dynamics can be understood in terms of one-dimensional "strings" of high mobility, which govern both local and long-wavelength dynamical properties. We introduce a coarse-grained description of the strings, based on the Edwards-Wilkinson model, which leads to exact results in the limit of low string density and provides a detailed qualitative understanding of the dynamics in all flux sectors. We discuss the implications of our results for the dynamics of constrained systems more generally.

Thomas Prellberg (Queen Mary)
The pressure of surface-attached polymers and vesicles
A polymer grafted to a surface exerts pressure on the substrate. Similarly, a surface-attached vesicle exerts pressure on the substrate. By using directed walk models, we compute the pressure exerted on the surface for grafted polymers and vesicles, and the effect of surface binding strength and osmotic pressure on this pressure.

Dominic Rose (Nottingham)
Metastability in the open quantum Ising model
We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. This system is known to have a non-equilibrium phase transition where the stationary state changes from paramagntic to ferromagnetic. We show that for a range of parameters close to this transition point the dynamics displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states, before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we are able to characterise the low-dimensional manifold of metastable states. We also show that for long times the dynamics can be approximated by classical dynamics on this manifold. We discuss how metastability is related to the intermittent dynamics of quantum trajectories.

Grzegorz Siudem (Queen Mary)
Bell polynomials and combinatorics of the Ising model
In this talk we consider Bell polynomials-based formalism which describes canonical systems. This approach provides combinatorial insights into basis of statistical mechanics and allows one to obtain exact formulas for the density of states i.e. coefficients of the series expansion of the partition function into the low-temperature series. We will focus on the lattice models, particularly on the Ising model on a square and triangular lattices. We will show that the ferromagnetic--to--paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model. What was surprising, this interpretation fails for the triangular lattice case.

Paul Verschueren (Open)
The quasiperiodic product of sines
Quasiperiodic sums and products arise in many areas of mathematics, and particularly in the study of critical phenomena. The product of sines has been found in work on the birth of Strange Non-Chaotic Attractors, Critical KAM Theory, and q-series (much used in String Theory) as well as a number of pure topics such as Power Series analysis, Partition Theory, and Diophantine Approximation.
We will review existing work and report new results. In particular these allows us to settle an open question of Erdős & Szekeres from 1959, and to prove a number of experimental results in in critical KAM theory reported recently by Knill & Tangerman (2011).