I investigate the caustics produced by the fall of collisionless dark matter in and out of a galaxy in the limit of negligible velocity dispersion. The outer caustics are spherical shells enveloping the galaxy. The inner caustics are rings. These are located near where the particles with the most angular momentum are at their distance of closest approach to the galactic center. The surface of a...

Oliver Knill July 29, 1996 Abstract There are billiard tables of constant width, for which the billiard map has invariant curves in the phase space which belong to continuous but nowhere di erentiable caustics. We apply this to construct ruled surfaces which have a nowhere di erentiable lines of striction. We use it also to get Riemannian metrics on the sphere such that the caustic belonging at...

Interactivity requires tradeoffs to achieve the right balance between rendering quality and speed. In practice, today’s applications restrict lighting to mainly direct illumination, sometimes augmented by precomputed transfer techniques for diffuse global effects. Dynamic high-frequency specular effects, such as caustics, are largely lacking due to the high costs for recomputation each frame. R...

introduction: caustic ingestions are among the most prevalent causes of toxic exposure. the present 10-year survey aimed to evaluate the epidemiologic features and outcomes of caustic ingestion cases presenting to emergency department. methods: this is a retrospective cross-sectional study on patients who were admitted to a referral toxicology center during 2004 to 2014, following caustic inges...

In this paper we present a method to model and simulate a lens such that its caustic reveals a stereoscopic 3D image when viewed through anaglyph glasses. By interpreting lens dispersion as stereoscopic disparity, our method optimizes the shape and arrangement of prisms constituting the lens, such that the resulting anaglyph caustic corresponds to a given input image defined by intensities and ...

Reflection seismic data continuation is the computation of data at source and receiver locations that differ from those in the original data, using what data are available. Here, we develop a general theory of data continuation in the presence of caustics and illustrate it with two examples: dip moveout (DMO) and azimuth moveout (AMO). This theory does not require knowledge of the reflector pos...

The solution to the Schrödinger equation is highly oscillatory when the rescaled Planck constant ε is small in the semiclassical regime. A direct numerical simulation requires the mesh size to be O(ε). The Gaussian beam method is an efficient way to solve the high frequency wave equations asymptotically, outperforming the geometric optics method in that the Gaussian beam method is accurate even...

It has been recently shown that the lens equation for a binary gravitational lens, which is apparently a coupled system, can be reduced to a real fifth-order (quintic) algebraic equation. Some algebraic properties of the real quintic equation are revealed. We find that the number of images on each side of the separation axis is independent of the mass ratio and separation unless the source cros...

The scattering far zone for light transmitted through a sphere following p - 1 internal reflections by a family of near-grazing incident rays is subdivided into a lit region and a shadow region. The sharpness of the ray theory transition between the lit and the shadow regions is smoothed in wave theory by radiation shed by electromagnetic surface waves. It is shown that when higher-order terms ...