This project is devoted to investigating dynamical behavior of thin liquid films and, more generally, systems driven by energy reduction. Thin liquid films can be described by a single equation for the fluid height --- the thin-film equation. Intermolecular forces can destabilize fluid films and lead to complex dynamical behavior. In some systems, droplet configurations that form coarsen over time; the average size of droplets grows, while their number is decreasing. In others instabilities lead to singularity formation. We will investigate these processes using a combination of novel analytical techniques, asymptotic analysis and computational methods. We will also investigate formation and dynamics of interfaces in models of biological aggregation. Large-scale and long-time behavior will also be investigated. Unifying theme of the above systems is that they are driven by energy dissipation. We intend to both use and further develop modern analytical techniques that utilize the underlying geometric structure of these systems.
The project will generate experimentally verifiable predictions about behavior of thin liquid films. With continuing miniaturization trends, applications in which thin liquid films play a role are becoming more widespread (industrial processes, microfluidic devices). Thus understanding the multitude of phenomena that thin films exhibit becomes ever more important. Systems driven by reduction of the energy are ubiquitous in nature. Many such systems share the common structure of the equation that describes them. We will use recent advances on geometry of such equations to gain direct insights into the syste
