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*Abstracts*

**OSP 2018 titles and abstracts**

**James Denholm **(Strathclyde)

*Scale behaviour of the kinetic Ising model*

Renormalization Group (RG) methods have been extensively used to explore the properties of the Ising model in thermodynamic equilibrium. The scale free behaviour at criticality being perhaps the most famous feature. Here we instead aim to use RG rescaling techniques to allow the same parameter space to simulate systems on a different scales through effective models. As a first area of application, we study the low temperature Glauber dynamics of the two dimensional model on a square lattice. This system is known for its long lived metastable features (diagonal stripes) but these eventually always settle into either homogeneity or stable stripes. Our initial investigations of the evolution of these structures are presented.

**Miguel Duran-Olivencia **(Imperial)

*General framework for nonequilibrium soft-matter systems*

We introduce a bottom-up derivation of a formal theoretical framework to describe soft-matter systems out of equilibrium subject to fluctuations. We provide a formal connection between the constituent-particle dynamics of real systems and the time evolution equation of their observables (coarse-grained quantities), such as local density and velocity. Through appropriate model-reduction techniques we obtain the fluctuating-hydrodynamic equations governing the time-evolution of the mesoscopic density and momentum fields. The equations have the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath [1]. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau et al. [1]. Our formalism is exemplified through one of themost frequent phase transitions, that of nucleation. Specifically, we offer a rigorous and systematic derivation of a mesoscopic nucleation theory (MeNT), reconciling the inherent randomness of the nucleation process with the deterministic nature of DDFT. For systems subject to strong dissipation due to the bath, as is the common case in colloidal fluids, we demonstrate that the most likely path (MLP) for nucleation to occur is determined precisely by the DDFT equations. We also present computations of MLPs for homogeneous and heterogeneous nucleation in colloidalsuspensions. For homogeneous nucleation, the MLP obtained is in excellent agreement with the reduced order-parameter description of MeNT, which predicts a multistage nucleation pathway. For heterogeneous nucleation, the presence of impurities in the fluid affects the MLP, but remarkably, the overall qualitative picture of homogeneous nucleation persists. Finally, we highlight the use of fluctuating DDFT as a simulation toolbox, which is especially appealing as there are no known applications of MeNT to heterogeneous nucleation.

[1] M. A. Duran-Olivencia, P. Yatsyshin, B. D. Goddard and S. Kalliadasis 2017 "General framework for fluctuating dynamic density functional theory", New J. Phys. 19, Art. No. 123022.

[2] L.D. Landau, E. Lifshitz and L. P. Pitaevskii 1980 "Statistical Physics" (Oxford: Pergamon Press).

**Oliver Dyer **(Warwick)

*Time-dependence of polymer diffusivity in low Reynolds number fluids*

The diffusivity of polymer chains in low Reynolds number fluids has well known scaling with chain length. Less well understood is how this depends on the time interval used to measure diffusion over, especially on the time scales of the overdamped Langevin equation where the phenomenology shows a slight decrease in diffusivity over time but a full physical understanding is lacking. The inherent difficulties in describing systems with fluctuating-hydrodynamics have been compounded by all work to date focussing on the magnitude, rather than the form, of this drop in diffusivity.

In this talk I will present data from recent Wavelet Monte Carlo dynamics (WMCD) simulations of a range of single-polymer systems that vary chain length, solvent quality and strength of monomer-monomer forces. With this breadth of data, common and differing features are used to identify likely underlying physics which simplified mathematical descriptions can be attempt to quantify.

**Benhamin Hourahine** (Strathclyde)

*Reaction diffusion patterning in crystal growth*

Turing pattern formation occurs in a wide variety of systems. This contribution will discuss the self assembled patterns produced on the hexagonal surface of nitride semiconductors [1]. These structures show a rich phase diagram of morphologies, and interestingly both fixed and variable scales depending on the controlling parameters.

[1] Nils. A.K. Kaufmann, L. Lahourcade, B. Hourahine, D. Martin, N. Grandjean, Journal of Crystal Growth 433, pp 36 (2016)

**Reimer Kühn**** **(Kings)

*Heterogeneous micro-structure of percolation in sparse networks*We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the probability of a particular node to remain part of the giant component, and in the expected size of small clusters containing that node. In the vicinity of the percolation threshold, weakly non-linear analysis reveals that node-to-node heterogeneity is captured by the recently introduced notion of non-backtracking centrality. We supplement these results for fixed finite networks by a population dynamics approach to analyse random graph models in the infinite system size limit, also providing closed-form approximations for the large mean degree limit of Erdös-Renyi random graphs. Interpreted in terms of the application of percolation to real-world processes, our results shed light on the heterogeneous exposure of different nodes to cascading failures, epidemic spread, and information flow.

**Alexander Mozeika**(Kings)

*Mean-field theory of Bayesian clustering*We map model-based Bayesian clustering, which is based on stochastic partitioning of data, into a statistical physics problem for a gas of particles. Using mean-field theory we show that, under natural assumptions, the lowest entropy state of this hypothetical `gas' corresponds to the optimal clustering of data. The byproduct of our analysis is a simple but effective clustering algorithm, which infers both the most plausible number of clusters and the corresponding partitions.

**Toru Ohira**(Nagoya)

*Collective behaviours of chases and escapes*"Chases and Escapes" is a traditional mathematical problem. Typically, problems of one escapee being chased by a single chaser have been considered in which the chasing trajectories and the position of the catches are obtained. In 2010, we have proposed a simple extended model where one group chasing another group, called a "Group Chase and Escape”[1]. This extension connects the traditional problem with current interests on collective motions of animals, insects, cars, etc. I will present our basic model and its rather complex behaviours. Each chaser approaches its nearest escapee while each escapee steps away from its nearest chaser. Although there are no communications within each group, aggregate formations are observed. How these behaviours appear as a function of parameters, such as densities will be discussed. Also, we consider the different expansions of this basic model. First, we introduced a fluctuation. Players now make errors in taking their step directions with some probability. It turns out that some level of fluctuations works better for more effective catching. Secondly, we introduce delay in the reaction of chasers in catching a target. Distance dependent reaction delay can cause quite complex behaviours. We also will discuss other extension and unsolved issues.

**Mayank Shreshtha**(Queen Mary)

*Bounds on current fluctuations in systems with memory: a toy model and open questions*Thermodynamic uncertainty relation and bounds on the time-integrated current fluctuations are the recent advances in non-equilibrium thermodynamics but have, so far, been derived only for Markovian processes. We explore the validity of one particular result (which states that the entropy production rate bounds statistical errors in current fluctuations) and discuss some open questions in a context of a simple non-Markovian toy model --- a discrete-time asymmetric random walk on a ring with one-step memory.

**Juraj Szavits-Nossan**(Edinburgh)

*Power series method for the inhomogeneous exclusion process with application to mRNA translation*We develop a power series method for the nonequilibrium steady state of the inhomogeneous totally asymmetric simple exclusion process (TASEP), which addresses a long outstanding problem in nonequilibrium statistical physics. The series expansion is performed in entrance and exit rates governing particle exchange with the reservoirs and the corresponding particle current is computed analytically up to the cubic order. We apply this method to the TASEP-based model of mRNA translation, which allow us to unveil, for the first time, simple design principles of nucleotide sequences determining protein production rates.

**Elsen Tjhung**(Cambridge)

*Reverse Ostwald process in active fluids: Cluster and bubble phases*It is known that repulsive self-propelled colloids can undergo liquid-vapor phase separation. In simulations and experiments, more complex steady-state are seen: a dynamic population of dense clusters in a sea of vapor, or dilute bubbles in a liquid. Here we show that this phenomenology emerges generically when we extend the φ

^{4}field theory of passive phase separation to locally break detailed balance. The required active terms, which we show to arise by coarse-graining of microscopic models, can reverse the classical Ostwald process that normally drives bulk phase separation.

**Peter Yatsyshin**(Imperial)

*Statistical mechanics of wetting*Wetting is a nucleation of a third phase (liquid) on the interface between two different phases (solid and gas). Practical applications of wetting at small scales are numerous and include the design of lab-on-a-chip devices and superhydrophobic surfaces. In many experimentally accessible cases of wetting, the interplay between the substrate structure, and the fluid-fluid and fluid-substrate intermolecular interactions leads to the appearance of a whole “zoo” of exciting interface phase transitions, associated with the formation of nano-droplets/bubbles, and thin films. These transitions are highly sensitive to the range of intermolecular forces and interface fluctuation effects. In this talk we will apply statistical mechanics in the density functional formulation to develop a robust and computationally friendly mean-field framework for investigation of adsorption and wetting. We will highlight the connections with Derjaguin-Frumkin picture, based on disjoining pressure and local interface binding potentials, and demonstrate how the latter can be obtained from statistical physics in a consistent way. We will discuss wetting on nano-patterned surfaces and show the highly non-trivial behaviour of the liquid-gas interface near decorated attractive substrates.