Allan Greenleaf
Schrodinger's Hat: Electromagnetic, acoustic and quantum amplifiers via transformation optics.
Tue, 07/26/2011 - 15:01 — SomNambulAuthors: Matti Lassas, Gunther Uhlmann, Allan Greenleaf, Yaroslav Kurylev
Subjects: Mathematical Physics
AbstractThe advent of transformation optics and metamaterials has made possible
devices producing extreme effects on wave propagation. Here we give theoretical
designs for devices, Schr\"odinger hats, acting as invisible concentrators of
waves.A multi-dimensional resolution of singularities with applications to analysis.
Tue, 07/06/2010 - 15:01 — SomNambulAuthors: Allan Greenleaf, Tristan Collins, Malabika Pramanik
Subjects: Classical Analysis and ODEs
AbstractWe formulate a resolution of singularities algorithm for analyzing the zero
sets of real-analytic functions in dimensions $\geq 3$. Rather than using the
celebrated result of Hironaka, the algorithm is modeled on a more explicit and
elementary approach used in the contemporary algebraic geometry literature. As
an application, we compute the critical integrability index for real-analytic
functions and obtain the sharp growth rate of their sublevel sets.Fourier integral operators with open umbrellas and seismic inversion for cusp caustics.
Thu, 01/28/2010 - 16:01 — SomNambulAuthors: Raluca Felea, Allan Greenleaf
Subjects: Analysis of PDEs
AbstractIn general the composition of Fourier integral operators (FIOs) need not be
an FIO. Motivated by the problem of linearized seismic inversion in the
presence of cusp caustics for the background sound speed, we consider FIOs
whose canonical relations have certain two-sided cusp degeneracies, and show
that the resulting compositions have wave-front relations in the union of the
diagonal and an open umbrella, the simplest type of singular Lagrangian
manifold.
User login
