Geometrical methods in hydrodynamics

Geometrical methods in hydrodynamics

We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.

Topological Methods in Hydrodynamics

Matrix Methods in Geometrical Optics

As well as the geometrical methods used for solving lens problems, and locating the size and position of images in optical systems, there is an alternate, perhaps more versatile, method involving matrix manipulation. Many of you will be familiar with the use of simple 2x2 matrices. Firstly, however, before I consider the use of matrices in optics, I will review the matrix solution of two simult...

WKB-Methods in Multivalued Geometrical Optics

We consider the Cauchy problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of the high-frequency asymptotics of such models is reviewed, in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods. Using Wigner measures we present an alternative approach to such asymptotic problems. We first di...

review of radiographic methods in dental implantology

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