Model Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape

In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.

The Quadric Reference Surface: Theory and Applications

The conceptual component of this work is about "reference surfaces'' which are the dual of reference frames often used for shape representation purposes. The theoretical component of this work involves the question of whether one can find a unique (and simple) mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3D, given (i) few corresponding points in the two views, or (ii) the outline conic of the surface in one view (only) and few corresponding points in the two views. The practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects.