Colored diffraction catastrophes.

On fine scales, caustics produced with white light show vividly colored diffraction fringes. For caustics described by the elementary catastrophes of singularity theory, the colors are characteristic of the type of singularity. We study the diffraction colors of the fold and cusp catastrophes. The colors can be simulated computationally as the superposition of monochromatic patterns for different wavelengths. Far from the caustic, where the luminosity contrast is negligible, the fringe colors persist; an asymptotic theory explains why. Experiments with caustics produced by refraction through irregular bathroom-window glass show good agreement with theory. Colored fringes near the cusp reveal fine lines that are not present in any of the monochromatic components; these lines are explained in terms of partial decoherence between rays with widely differing path differences.

Paleoproterozoic snowball Earth: Extreme climatic and geochemical global change and its biological consequences

Geological, geophysical, and geochemical data support a theory that Earth experienced several intervals of intense, global glaciation (“snowball Earth” conditions) during Precambrian time. This snowball model predicts that postglacial, greenhouse-induced warming would lead to the deposition of banded iron formations and cap carbonates. Although global glaciation would have drastically curtailed biological productivity, melting of the oceanic ice would also have induced a cyanobacterial bloom, leading to an oxygen spike in the euphotic zone and to the oxidative precipitation of iron and manganese. A Paleoproterozoic snowball Earth at 2.4 Giga-annum before present (Ga) immediately precedes the Kalahari Manganese Field in southern Africa, suggesting that this rapid and massive change in global climate was responsible for its deposition. As large quantities of O2 are needed to precipitate this Mn, photosystem II and oxygen radical protection mechanisms must have evolved before 2.4 Ga. This geochemical event may have triggered a compensatory evolutionary branching in the Fe/Mn superoxide dismutase enzyme, providing a Paleoproterozoic calibration point for studies of molecular evolution.