14,403 research outputs found
Propagation of singularities for weak KAM solutions and barrier functions
This paper studies the structure of the singular set (points of
nondifferentiability) of viscosity solutions to Hamilton-Jacobi equations
associated with general mechanical systems on the n-torus. First, using the
level set method, we characterize the propagation of singularities along
generalized characteristics. Then, we obtain a local propagation result for
singularities of weak KAM solutions in the supercritical case. Finally, we
apply such a result to study the propagation of singularities for barrier
functions
The quantum spin Hall effect and topological insulators
In topological insulators, spin-orbit coupling and time-reversal symmetry
combine to form a novel state of matter predicted to have exotic physical
properties.Comment: 7 pages, 5 figures, an introduction of the quantum spin Hall effect
and topological insulators. For a video introduction of topological
insulators, see http://www.youtube.com/watch?v=Qg8Yu-Ju3V
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