In this book experts discuss research and applications in interfacial fluid dynamics.

We observed the evolution of unstable fluid interfaces in experiments on viscous fingering, pinch-off, and bouncing jets. If we can first identify classes of universal behavior, then we can begin building a unified framework to understand nonlinear processes. We performed the first experimental test of the harmonic moments of viscous fingering patterns, grown by injecting air into a thin layer of silicone oil, which was confined between two closely spaced plates, called a Hele-Shaw cell. We observed that the predicted decay of the moments was accurate within our measurement uncertainty, which confirmed the predicted conservation of the moments for zero surface tension. With greater forcing, the air bubble will undergo a secondary tip-splitting instability, where the fingers of air fork into two or more fingers. We discovered two selection rules for the changing base width and the nearly invariant opening angle of fjords, which are the regions of oil between the fingers of air. We then compared our experiments on viscous fingering with diffusion-limited aggregation (DLA), a model of un-stable growth. We calculated that DLA and viscous fingering have the same spectrum of singularities [called f([alpha])] within measurement uncertainty. Since the spectrum is a global encapsulation of the growth dynamics and scaling properties, we say that the two processes are in the same scaling universality class. All of these results for viscous fingering are expected to apply to other physical systems which approximate Laplacian growth, a model of an interface where its growth rate is determined by the local gradient of a field [phi] obeying Laplace's equation [gradient2 phi] = 0. Next we present preliminary work on the experimental test of two predictions for flows in Hele-Shaw cells: 1) soliton-like behavior of two viscous domains and 2) self-similar, universal pinch-off of an inviscid bubble in a viscous liquid. Finally, we report our observations and analysis of a liquid stream with constant viscosity (i.e. Newtonian) which rebounds from the free surface of a moving bath. The stream bounces on a thin layer of lubricating air which is replenished by the relative motion of the jet and the bath.

MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

Experimental and theoretical studies of the nonlinear dynamics and control of aeroelastic systems including airfoils and wings have been conducted. Nonlinear geometric stiffness and freeplay have been considered specifically and good theoretical / experimental correlation obtained. Active control systems have been designed, built and tested to increase flutter speed and reduce limit cycle oscillations (LCO). Our most recent work includes theoretical studies of aerodynamic nonlinearities in the transonic range and their effect on flutter and LCO.