Computational Techniques From Geometry and Statistical Physics Applied To Fluid Mechanics and Interface Problems

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Chorin 0076510 The investigator an his colleague continue working in the area of interface modeling, level set methods and fast marching methods, with applications to plastic injection moulding, the computation of seismic travel times, semiconductor manufacturing and computer vision. They also continue to develop statistical prediction methods for partial differential equations with underresolution and partial data, with applications to turbulence, climate modeling, and many-body problems. The common thread of these topics is computation and analysis in the presence of uncertainty The main difficulty in many important problems of engineering is to find the exact location of a surface or the exact time a signal arrives at a given point. Well-known examples occur in the manufacture of microchips, where it is important to control exactly various manufacturing processes, and in robotics, where one has to find the optimal way to perform a task. The investigators have developed powerful computer methods for solving such problems; these methods obviate the need for costly and lengthy trial-and-error in a physical laboratory. They continue to improve these tools, with new applications in manufacturing, geology, and computer vision. Many problems in science lack sufficient data for a complete specification, or are so complex that they cannot be solved in full. Examples are weather and climate forecasting as well as problems in biology. The investigators have examined carefully what is the most one can reliably say in such situations, and have developed computer methods for finding effectively the best information one can in problems where a full solution is out of reach. They are also developing ways of telling in advance what the uncertainty in the answers will be when one can estimate the uncertainty in the data.