Most natural and industrial processes, and in particular those where species are transported by a turbulent flow, occur in fluctuating environments displaying non-trivial correlations. In such settings, classical methods borrowed from statistical physics, based for instance on near-equilibrium assumptions or mean-field approaches, are unsuccessful to describe the overall dynamical evolution of the system. One often needs to account for rare but important fluctuations in order to estimate global quantities.
Many processes take place in an environment where spatial fluctuations take place at such small scales that they only contribute moderately to the macroscopic properties. The environment is then modeled by introducing a hint of disorder. Also, the temporal variations of the environment are often much slower than the mechanisms in which we are interested (such as diffusion, transport, or wave propagation). This leads to consider a “frozen” disorder, as in the case of directed polymers or wave propagation in random media.
Many processes involve the reaction or collision between different species transported by a carrier flow. Such systems are generally modeled in terms of a reaction-diffusion-advection equation for the concentration field. Such an approach relies on two hypotheses: on the one hand, the volumes over which the concentration field is estimated must contain a sufficiently large number of particles so as to neglect finite-number effects; on the other hand, each particle inside such a volume must have an equal probability of reacting with all the others. It is clear that in situations where the reactants are very diluted, these two conditions cannot be satisfied simultaneously and fluctuations due to a finite number of particles can be large enough to invalidate mean-field kinetic equations.
We have considered the formation of aggregates in the specific case where the particles are in a random landscape which varies over time. Particles concentrate in the valleys of the potential but their finite size and their collisions actually lead them to form aggregates there. To reproduce this phenomenon, we have developed a simple experimental device. A random landscape is created from a ferrofluid set in motion by electromagnets. The surface is covered with an elastic film on which are placed spherical particles with a large coefficient of restitution. The position and speed measurements of the particles are made by tracking the particles using a fast camera. We are particularly interested in the temporal evolution of the mass and the total energy of the aggregates.
As a microswimmer swims towards a target in a dynamically evolving turbulent fluid, it is buffeted by the flow or gets trapped in whirlpools. Naively, one could think that it is sufficient for the swimmer to point its motion toward the target. Can one however develop an optimal path-planning strategy that reduces the average time it takes to reach the target? This challenging question, which is of great importance from both fundamental and applications points of view, can be addressed by using machine-learning methods. A smart-swimming strategy using adversarial Q learning can outperform naive microswimmers.