The high speed ow of complex materials can often be modeled by the compressible Euler Equations coupled to (possibly many) additional advection equations. Traditionally, good computational results have been obtained by writing these systems in fully conservative form and applying the general methodology of shock-capturing schemes for systems of hyperbolic conservation laws. In this paper, we sh...

Convergence of a second-order shock-capturing scheme for the system of isentropic gas dynamics with L°° initial data is established by analyzing the entropy dissipation measures. This scheme is modified from the classical MUSCL scheme to treat the vacuum problem in gas fluids and to capture local entropy near shock waves. Convergence of this scheme for the piston problem is also discussed.

For computer graphics applications, capturing the appearance parameters of objects – reflectance, transmittance and small scale surface structures, is as important as capturing the overall shape. We briefly review recent approaches developed by the computer graphics community to solve this problem. Excellent results have been obtained by various researchers measuring spatially varying reflectan...

We present a method for capturing the geometry and parameterization of fast-moving cloth using multiple video cameras, without requiring camera calibration. Our cloth is printed with a multi-scale pattern that allows capture at both high speed and high spatial resolution even though self-occlusion might block any individual camera from seeing the majority of the cloth. We show how to incorporat...

In this Essay, we argue that pluripotent epiblast founder cells in the embryo and embryonic stem (ES) cells in culture represent the ground state for a mammalian cell, signified by freedom from developmental specification or epigenetic restriction and capacity for autonomous self-replication. We speculate that cell-to-cell variation may be integral to the ES cell condition, safe-guarding self-r...