9701980 Lathrop This CAREER project is a study of free surface liquid singularities performed in order to characterize nonlinear self-focusing in liquid free surfaces. This information should assist in defining a class of systems exhibiting singularities including turbulent dissipation fluctuations, self-focusing in nonlinear optical systems, cavitation phenomena and sonoluminescence, and gravitational singularities. The experimental surface waves are produced using a Faraday apparatus (vertically oscillated tank). This proposal focuses on three aspects: determination of the threshold value for singularity formation, understanding the time dynamics of states exhibiting singularities, and finally pursuing local models for the structure of the singularities. The continued development of undergraduate research and improvement of the undergraduate course work are at the core of the teaching plans. The research investigating gree surface singularities is integrated with a program of involving undergraduate and graduate students in the experiments. %%% This is a CAREER project to study local singularities or local blow-up of some pare of a system. Such singularities play an important role in the behavior of a number of physical systems such as turbulence, burn-out of lasers and optical fibers, cavitation, and singular objects due to gravity: black holes. Significant mysteries exist about what classes of motion and what types of singularities arise in physical systems. The droplets, spray and foam produced by breaking waves on a beach and in deep water are examples of singularities on a liquid surface. This project studies liquid surface singularities to aid in both the knowledge of liquid motion, and the general understanding of physical sysstems exhibiting singularities. The continued development of undergraduate research and improvement of the undergraduate course work are at the core of the teaching plans. The research investigating liquid singula rities is integrated with a program of involving undergraduate and graduate students in the experiments. ***
