The statistical physics of hydrodynamic random walkers: Experiments and theory

From the motion and self-organisation of microscopic biological organisms to the formation of galaxies, far-from-equilibrium physics is a ubiquitous feature of the natural world and a grand challenge in contemporary physical science. Despite myriad examples in science and engineering, there is a relative paucity of established theoretical frameworks to describe non-equilibrium phenomena, in particular those that rationalise universal features across multiple length- and time-scales. Over the last two decades the field of active and driven matter has been the target of intense research focus, in part due to its success in describing myriad biological phenomena and its close connections with soft matter physics. Active systems, such as swimming spermatozoa or flocks of fish and birds, operate far from equilibrium by converting an internal energy supply into mechanical motion that can in turn lead to dramatic and unexpected collective motion. From an experimental perspective, however, biological systems are difficult to control and contain multiple interacting physical processes whose role in the observed dynamics of the system are difficult to quantify. To overcome these difficulties synthetic and artificial experimental systems are gaining popularity due to their high degree of accessibility and parametric control. Among this family of experiments are hydrodynamic systems that are driven out of equilibrium by external forcing of the environment. When particles or objects are placed in these complex flows, they exhibit behaviour that is reminiscent of the random or stochastic dynamics of biological organisms thereby challenging fundamental assumptions of smooth-particle hydrodynamics and in turn forging hitherto unrealised connections between classical fluid mechanics and statistical physics. Driven hydrodynamic systems thus serve as a promising candidate to identify universal features of active and driven matter across scales, with mathematics serving as a bridge between these disparate systems. Identifying such commonalities is an essential task in establishing the much-heralded usefulness of active and driven matter in real-life engineering contexts. The aim of this project is to consider a particular example of a driven hydrodynamic system that explores the dynamics and emergent statistics of floating bodies placed in a field of fluctuating interfacial Faraday waves. The Faraday-wave system is supplied by a practically inexhaustible source of energy and emergent dynamics can be explored over significantly broader parameter regimes in contrast to living systems. The research proposed herewith is anticipated to have far-reaching consequences beyond the realm of active and driven matter. In particular, our lab-scale experimental system promises to shed new light on how large plastic particles are transported and distributed in wavy and turbulent fluid flows, a fundamental challenge in climate-change research and oceanography. Furthermore, the dynamics of many non-equilibrium systems are complicated by the presence of memory wherein the future trajectory of the system is intimately tied to its past. An understanding of such temporally correlated, non-Markovian transport processes remains in its infancy in contrast to its Markovian counterpart. Our fully integrated experimental and theoretical approach is thus uniquely placed to make significant contributions to addressing this major unsolved problem in statistical physics.