Boundary Control of Liquid Film Flowing Down a Fibre

A liquid flowing down a vertical fibre exhibits complex and interesting interfacial dynamics. Driven by the Raleigh-Plateau instability, the liquid film forms droplets or pulses that flow down along the fibre. In this work, the problem of controlling the fluid film profile of such a liquid flowing down a fibre is investigated. The fluid dynamics is governed by a fourth order partial differential equation (PDE) derived from the Navier-Stokes equation. In the figures below, control of the film profile is achieved by dynamically altering the input flux to the fluid system. The input flux appears as a boundary condition to the PDE. Specifically, the panels show that the controlled system, subject to constraints, can be driven to both uniform film profiles and traveling waves. Below, the desired film profile is shown in yellow and the simulated evolution of the controlled film thickness is shown in blue.

Control of Multi-Agent Systems

A scalable approach to control large populations of agents is to make a fluid approximation (or Eulerian frame of reference) of the population. The top panel in the Figure below shows the evolution of the distribution of the Markov process, which represents the continuum approximation of the agent population. Whereas, the bottom panel in the figure shows the stochastic evolution of N-agent system. From the figures, we note that N-agent model closely approximates the Markov process.