The aim of this text is to develop on the asymptotics of some 1-D nonlinear Schrödinger equations from both the theoretical and the numerical perspectives, when a caustic is formed. We review rigorous results in the field and give some heuristics in cases where justification is still needed. The scattering operator theory is recalled. Numerical experiments are carried out on the focus point sin...

The electron capture gas liquid chromatography test method for chick edema factor has been modified by replacing the alumina column s t ep with an additional sulfuric acid cleanup and a caustic wash which permits a reduction in sample cleanup time. Samples are subjected to double preliminary sulfuric acid cleanup and caustic wash and extracted each time with t r imethyl pentane. The final extra...

We show quantitatively how the collision rate of droplets of visible moisture in turbulent air increases very abruptly as the intensity of the turbulence passes a threshold, due to the formation of fold caustics in their velocity field. The formation of caustics is an activated process, in which a measure of the intensity of the turbulence, termed the Stokes number St, is analogous to temperatu...

Hydrofluoric acid is a strong inorganic acid. It differs from other acids in that the fluoride ion readily penetrates the skin, causing destruction of deep tissue layers and even bone. Burns caused by hydrofluoric acid can be life-threatening. The specific antidote, calcium gluconate, can be applied topically, injected into tissue or infused intra-arterially. Emergency medical teams should be f...

Severe gastrointestinal-tract injury due to ingestion of caustic substances is not an infrequent problem in the emergency department. We report the case of a 57-year-old male who developed massive hemorrhagic, caustic gastric necrosis due to the ingestion of a non-diluted solution containing hydrochloric acid, which propitiated an urgent surgical procedure. The esophago-gastrectomy specimen sho...

This dissertation discusses work that enables the realistic image synthesis of very complex scenes. Some of the work herein describes approaches for modeling more complicated scenes, while other portions describe algorithms for accelerating the rendering of complex scenes. First we propose a simple method for modeling and rendering refractive objects that are nested within each other. The techn...