Classical (Birkhoff) billiards with full 1-parameter families of periodic orbits are considered. It is shown that construction of a convex billiard with a “rational” caustic (i.e. carrying only periodic orbits ) can be reformulated as the problem of finding a closed curve tangent to a non-integrable distribution on a manifold. The properties of this distribution are described as well as the con...

This paper examines the line profile evolution due to bulk motion in circumstellar envelopes during microlensing fold caustic crossing events. These events have recently been shown to be a sensitive probe of stellar surface brightness profiles, thus providing a means – through both photometric and spectroscopic observations – to constrain and test stellar atmosphere models. Here it is demonstra...

Eosinophilic esophagitis (EoE) is an emerging disease in both pediatric and adult patients. It is a chronic disease of the esophagus and refers to intense eosinophilic infiltration limited to the esophageal epithelium in the absence of gastroesophageal reflux disease. In most patients, EoE is thought to be part of an allergic response to food antigens or aeroallergens. One such trigger could be...

In this work we show an error estimate for a first order Gaussian beam at fold caustic, approximating time-harmonic waves governed by the Helmholtz equation. For caustic that study exact solution can be constructed using Airy functions and there are explicit formulae parameters. Via precise comparisons pointwise on is of O ( k − 5 / 6 ) where wave number in Helmholtz.