The Observations of Type Ia Supernovae

The past ten years have seen a tremendous increase in the number of Type Ia supernovae discovered and in the quality of the basic data presented. The cosmological results based on distances to Type Ia events have been spectacular, leading to statistically accurate values of the Hubble constant, Omega_M, and Omega_Lambda. However, in spite of the recent advances, a number of mysteries continue to remain in our understanding of these events. In this short review, I will concentrate on unresolved problems and curious correlations in the data on Type Ia SNe, whose resolution may lead to a deeper understanding of the physical mechanism of the Type Ia supernova explosions.Comment: 10 pages, aipproc LaTeX, two eps figures, to be published in "Cosmic Explosions! The Proceedings of the Tenth Maryland Conference on Astrophysics," eds, Steven S. Holt and William W. Zhang, AI

Teardrop and heart orbits of a swinging Atwood's Machine

An exact solution is presented for a swinging Atwood's machine. This teardrop-heart orbit is constructed using Hamilton-Jacobi theory. The example nicely illustrates the utility of the Hamilton-Jacobi method for finding solutions to nonlinear mechanical systems when more elementary techniques fail.Comment: CYCLER Paper 93feb00

Probing Local Structure in Glass by the Application of Shear

The glass transition remains one of the great unsolved mysteries of contemporary condensed matter physics. When crystallization is bypassed by rapid cooling, a supercooled liquid, retaining amorphous particle arrangment, results. The physical phenomenology of supercooled liquids is as vast as it is interesting. Most significant, the viscosity of the supercooled liquid displays an incredible increase over a narrow temperature range. Eventually, the supercooled liquid ceases to flow, becomes a glass, and gains rigidity and solid-like behaviors. Understanding what underpins the monumental growth of viscosity, and how rigidity results without long range order is a long-sought goal. Many theories of the glassy slowdown require the growth of static lengthscale related to structure with lowering of the temperature. To that end, we have proposed a new, natural lengthscale- "the shear penetration depth". This lengthscale quantifies the structural connectivity of the supercooled liquid. The shear penetration depth is defined as the distance up to which a shear perturbation applied to the boundary propagates into the liquid. We provide numerical data, based on the simulations of $NiZr_2$, illustrating that this length scale exhibits dramatic growth and eventual divergence upon approach to the glass transition. We further discuss this in relation to percolating structural connectivity and a new theory of the glass transition.Comment: 9 pages, 4 figures, special journal articl