2,060 research outputs found
Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors
In this paper the zero modes of fluctuation of cylindrically symmetric
self-dual vortices are analyzed and described in full detail. These BPS
topological defects arise at the critical point between Type II and Type I
superconductors, or, equivalently, when the masses of the Higgs particle and
the vector boson in the Abelian Higgs model are equal. In addition, novel bound
states of Higss and vector bosons trapped by the self-dual vortices at their
core are found and investigated.Comment: 29 pages, 51 figure
Differential Operators for Edge Detection
We present several results characterizing two differential operators used for edge detection: the Laplacian and the second directional derivative along the gradient. In particular, (a)we give conditions for coincidence of the zeros of the two operators, and (b) we show that the second derivative along the gradient has the same zeros of the normal curvature in the gradient direction.
Biological implications are also discussed. An experiment is suggested to test which of the two operators may be used by the human visual system.MIT Artificial Intelligence Laborator
Rotational symmetry of self-similar solutions to the Ricci flow
Let (M,g) be a three-dimensional steady gradient Ricci soliton which is
non-flat and \kappa-noncollapsed. We prove that (M,g) is isometric to the
Bryant soliton up to scaling. This solves a problem mentioned in Perelman's
first paper.Comment: Final version, to appear in Invent. Mat
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