Workshop Program

10:00

Giorgio Volpe (UCL)

Sampling rare events in dissipative systems using unsupervised neural networks

Rare events are significant yet infrequent transitions between metastable states. Despite what their name suggests, their occurrence has a substantial impact on diverse phenomena such as protein folding, earthquakes, and market crashes. Classical computational methods for sampling such events are often inefficient, so that a plethora of enhanced sampling techniques has been proposed over the years. However, each of these techniques presents its own limitations and rarely extend to out-of-equilibrium systems. In this talk, I will present our novel physics-informed machine learning framework (named FlowRES), designed to address the inefficiencies of current techniques for sampling rare events. FlowRES utilizes unsupervised normalizing flow neural networks to enhance Monte Carlo sampling of rare events in both equilibrium and out-of-equilibrium systems. As our framework is efficient and largely free of the limitations presented by other enhanced sampling techniques, we envision its broad applicability to study, understand and control currently inaccessible phenomena impacted by rare events in statistical mechanics and beyond.

10:30

Gunnar Pruessner (Imperial)

Some open problems in Doi-Peliti field theories

Why is Doi-Peliti field theory not more popular? It seems like the perfect tool: Any stochastic process that can be cast in a Langevin or Fokker-Planck equation, even reaction-diffusion processes, is amenable to this procedure. It offers a systematic, perturbative treatment, a diagrammatic language to understand and calculate terms, supports the notion of relevance and, uniquely, gives access to the renormalisation group. There are no ad-hoc assumptions, no “coarse-graining” based on wishful thinking. What’s not to like? Concrete calculations for many constituent degrees of freedom quickly turn into an unwieldy mess. How does this happen? On the one hand, the framework is exact and therefore retains all microscopic details. Nothing gets lost. On the other hand, it is a perturbative procedure, building on the bilinear theory. To lowest order, a many-body problem thus is trivial, but to higher orders often contains intractably many terms, diagrammatics or not. In this presentation I discuss some possible solutions to these challenges and present some Mickey-Mouse models that capture the issues at stake.

11:00

Jaime Agudo Canalejo (UCL)

Mechanochemical coupling in active nanomachines

Enzymes, molecular motors, and microswimmers convert chemical energy into mechanical work. Using a minimal but thermodynamically consistent description of such nanoscale chemically-powered machines, which necessarily includes a two-way feedback between chemical and mechanical degrees of freedom, we consider both the dynamics of single machines as well as the interaction between multiple machines. Our study leads to several new results including mechanisms for the synchronization of stochastic dynamics [1-3], a simple model for an enzyme with mechanical catalytic action [4], a nonlinear response theory for the effect of external forces on the chemical dynamics of nanomachines [5], and novel protocols for the inference of nonequilibrium driving forces [6] and interparticle correlations [7] in active systems.

11:30

Eloise Lardet (Imperial)

Disordered Yet Directed: The Emergence of Polar Flocks with Disordered Interactions

Flocking is a prime example of how robust collective behaviour can emerge from simple interaction rules. The flocking transition has been studied extensively since the inception of the original Vicsek model. Here, we introduce a novel self-propelled particle model with quenched disorder in the pairwise alignment interaction couplings akin to a spin glass model. We show that the presence of quenched disorder can promote (rather than destroy) the emergence of global polar order. In particular, we show that our model can display a flocking phase even when the majority of the interaction couplings are anti-aligning. Activity is the key ingredient to reduce frustration in the system as it allows local particle clustering combined with self-organization of the particles to favour neighbourhoods with strong cooperative interactions. In this talk, I will present these numerical findings and describe the self-organisation mechanism by which this phenomenon occurs.

14:00

Flash Talks

15:30

Isabella Guido (Surrey)

Emergent behaviour of bioinspired living matter

In nature, the self-assembly of biopolymers and motor proteins within the complex intracellular environment leads to fascinating emergent behaviours that are crucial for cellular functions and motility. The dynamics of these self-organizing structures are driven by the continuous supply of energy at the molecular level, enabling the active components to generate internal stresses that produce spontaneous movements. In this study, we develop bioinspired active networks of intracellular cytoskeletal components that self-organize in vitro. By combining passive components that generate entropic forces with active stress exerted by motor proteins, the networks exhibit unique dynamic behaviour, which can also be influenced by external factors. Our goal is to use these minimal synthetic systems as new models for quantitatively understanding fundamental questions about living matter.

16:00

Marco Pensalfini (QMUL)

Bioinspired adaptive fibrillar materials with tunable mechanics

Animal cells and tissues adapt their mechanical properties by combining cytoskeletal networks with widely different characteristics. Short, crosslinked actin filaments can turn over rapidly and develop active tension, controlling cell mechanics at moderate strains, whereas long, physically entangled intermediate filaments (IFs), which lack motors or long-lived crosslinks, control the large strain behaviour [1]. Similarly, double-network microstructures have enabled the realization of hydrogel materials with remarkable mechanical properties. We have recently shown that entanglement-mediated self-organization provides corralled tangles inspired by IF organization in epithelial tissues with extremely non-affine and non-linear mechanics [2]. However, in actual cells, IF network reorganizations are hindered by interactions with the actin cytoskeleton or the nucleus. As a result, depending on the time-scale or inter-network interactions, cells can adapt their mechanics by switching between affinity – mediated by crosslinking – and extreme non-affinity/non-linearity – mediated by entanglement. Here, by understanding the mechanics of epithelial cells under stretch in terms of minimal models of corralled interacting networks, we identify the building principles of such living materials and anticipate their translation into artificial adaptive materials

Titles and Abstracts for Flash Talks

Matthew Butler (UCL)

Slender chemically-active artificial microswimmers.

Chemically active filaments are an exciting new category of artificial microswimmer. Surface chemical reactions locally generate or deplete the solute, and the resulting solute concentration gradients induce slip flows that can move the swimmer through the surrounding fluid. The consequent swimming motion depends on both the swimmer geometry and the chemical patterning across its surface. Previous work derived a Slender Phoretic Theory, which asymptotically simplifies the solute problem to calculating line integrals along the filament’s centreline. I will highlight recent work to extend this framework to expand the library of known solutions, including to looped filaments. These results are a key step forward in probing the interplay of chemical patterning and shape in these artificial microswimmers.

Norberto Lucero Azuara (QMUL)

Analyzing two dimensional stochastic processes in a comoving frame.

Have you ever imagined how a living organism moves in a plane? The most intuitive one is taking a step in a chosen direction, with a certain step length, and then repeat the process. However, this movement is fundamentally generated by you, solely in the comoving frame. Nevertheless, we don’t calculate our internal movements in a fixed Cartesian frame and then translate them into active steps as described. There’s no reason to assume that other living organisms operate this way either. To explore this, we investigate well-defined stochastic processes in two dimensions, first in a Cartesian frame and then transformed into the comoving frame. We provide a detailed characterization of these processes through their probability distributions, autocorrelations, and governing dynamical equations. Ultimately, we propose two simple equations in the comoving frame that reproduce the observed stochastic behaviour in the Cartesian frame.

Venkata Pamulaparthy (UCL)

Reinforcement Learning for Large Deviations in Non-Markov Processes

Machine learning methods have recently been developed for computationally intensive investigations of rare fluctuations in nonequilibrium systems. However, present methods have generally been designed for Markov processes, presenting a major limitation due to the important role of memory in many realistic models. Examples of memory dependence are routinely encountered while studying active-matter dynamics where models usually include hidden variables. Here we introduce a reinforcement learning method for non-Markov systems that extends the actor-critic framework given by Rose et al. [New.J.Phys.23, 013013(2021)] for obtaining scaled cumulant generating functions characterizing the fluctuations. The actor-critic is implemented using neural-networks; a particular innovation in our method is the use of an additional neural policy for processing memory variables, reminiscent of attention mechanisms used elsewhere in machine learning. We demonstrate results for current fluctuations in various memory-dependent models with special focus on semi-Markov systems where the dynamics is controlled by non-exponential inter-event waiting-time distributions.

Maks Pecnik Bambic (UCL)

Optimal face-to-face coupling for fast self-folding kirigami

Kirigami is a design method through which two-dimensional templates are transformed into complex three-dimensional structures by a series of cuts and folds. In practice, templates consist of flat and rigid panels connected through flexible hinges. Kirigami designs are easily scalable, providing a straightforward route to intricate structures at small scales. Unfortunately, at the meso-scale, folding around hinges is difficult to control directly. A possibility is to rely on indirect forces to drive actuation, such as collision with solvent molecules when suspending the template in a fluid. However, the lack of control over the folding process results in low yields and rates of folding, a problem made worse when target structures consist of several hierarchical levels. Here, I will discuss how Brownian motion is used to simulate the temperature driven folding of two-leveled kirigami structures consisting of coupled panels tethered on one side to a substate. The motion of panel pairs is coupled due to constraints of force and torque in an inertia-less system, which we parameterize using a hydrodynamic drag law. This coupling is tuned through simple modification of the panels and can significantly enhance the rate and yield of folding of our structures. The coupling resulting in the highest yield and rate can be predicted solely by the folding of the upper level, whose initial state depends on the folding time of the lower level. Exploiting hydrodynamic coupling in this way can improve the design of hierarchical multi-leveled meso-scale structures for many applications from soft robotics to drug encapsulation.

Alessia Gentili (UCL)

Tuning Anomalous Diffusion of Magnetic Walkers

Many natural transport phenomena exhibit deviations from Brownian motion, known as anomalous diffusion. Examples of these variations can be observed in a wide range of biological processes, including animal foraging, cellular signalling, and the spatial exploration by motile microorganisms. Besides the biological world, other processes described by anomalous diffusion include the spread of diseases, financial market trends, and climate records. Thus, investigating these phenomena enriches our understanding of transport processes in living matter systems as well as in many events in human life. Despite its interdisciplinary significance and the growing interest in its study, the experimental investigation of anomalous diffusion remains challenging. In my talk, I will present a novel experimental method based on the use of magnetic colloidal particles to reproduce anomalous diffusion dynamics under controllable conditions. This experimental technique can replicate the whole spectrum of anomalous diffusion, with varying degrees of correlation, by tuning a minimal set of parameters. I believe this approach will provide a valuable benchmark for testing and comparing theoretical models, data analysis techniques, and predictive tools, ultimately advancing the study of anomalous diffusion in real-life scenarios.

Callum Britton (Imperial)

Nested Resetting

Stochastic resetting is a minimal mechanism that breaks detailed balance and drives the formation of non-equilibrium steady states. Here, we consider a chain of diffusive processes $x_i(t)$ that interact unilaterally: $x_n$ stochastically resets to the instantaneous position of $x_{n-1}$ (and $x_0\in\mathbb{R}$ is fixed). We consider the steady-state statistics of these nested resetting processes such as the stationary distribution for each particle and the moments of its distribution. We also calculate exactly the steady-state correlations < x_n x_{n+j}> between processes by mapping the problem to one of ordering statistics of random counting processes. Our results provide a striking example of tractable correlations in non-equilibrium many-particle systems, building towards a model-independent framework for random processes with unilateral interactions.

Emir Sezik (Imperial)

Characterising collective excitations without a collective

Collective behaviour in the context of Active Matter has revealed many new phenomena previously thought to be impossible. One important tool to characterise these systems over large length scale are coarse-grained hydrodynamic equations which, in most cases, are posited rather than derived, based on the symmetries of the system. This procedure obscures the bridge between microscopic dynamics and macroscopic behaviour, potentially leading to a mischaracterisation of the system. In this talk, we will show an alternate way of analysing these systems. We will outline a novel procedure that captures the macroscopic behaviour while keeping the particle entity of its constituents. Finally, we will implement this to a minimal non-equilibrium model and characterise its steady state.

Adarsh Raghu (KCL)

Effective Affinity for Generic Currents in Markov Processes

In mesoscopic experiments it is common to observe a single fluctuating current, such as the position of a molecular motor, while the complete set of currents is inaccessible. For such scenarios with partial information we introduce an effective affinity for generic currents in Markov processes. The effective affinity quantifies dissipative and fluctuation properties of fluctuating currents. Notably, the effective affinity multiplied by the current lower bounds the rate of dissipation, and the effective affinity determines first-passage and extreme value statistics of fluctuating currents. In addition, we find that under certain conditions that ensure thermodynamic consistency, the effective affinity is approximately equal to a stalling force associated with the current. To derive these results we also introduce a family of martingales associated with generic currents.

Rainer Klages (QMUL)

Is there a Newtonian equation for modelling the movements of organisms?

I propose an approach based on generalised Langevin dynamics to model the active movements of organisms, which unifies generic models of active particles with models developed in movement ecology. The key idea is to formulate active fluctuation by stochastic dynamics in a frame comoving and corotating with an active particle. I will show an example of such a model constructed from experimental data and will outline first results of how to derive such dynamics analytically.