69,207 research outputs found
The number of ramified coverings of the sphere by the double torus, and a general form for higher genera
An explicit expression is obtained for the generating series for the number
of ramified coverings of the sphere by the double torus, with elementary branch
points and prescribed ramification type over infinity. Thus we are able to
prove a conjecture of Graber and Pandharipande, giving a linear recurrence
equation for the number of these coverings with no ramification over infinity.
The general form of the series is conjectured for the number of these coverings
by a surface of arbitrary genus that is at least two.Comment: 14pp.; revised version has two additional results in Section
A proof of a conjecture for the number of ramified coverings of the sphere by the torus
An explicit expression is obtained for the generating series for the number
of ramified coverings of the sphere by the torus, with elementary branch points
and prescribed ramification type over infinity. This proves a conjecture of
Goulden, Jackson and Vainshtein for the explicit number of such coverings.Comment: 10 page
Transitive factorizations of permutations and geometry
We give an account of our work on transitive factorizations of permutations.
The work has had impact upon other areas of mathematics such as the enumeration
of graph embeddings, random matrices, branched covers, and the moduli spaces of
curves. Aspects of these seemingly unrelated areas are seen to be related in a
unifying view from the perspective of algebraic combinatorics. At several
points this work has intertwined with Richard Stanley's in significant ways.Comment: 12 pages, dedicated to Richard Stanley on the occasion of his 70th
birthda
Propagation of exciton pulses in semiconductors
Using a toy model, we examine the propagation of excitons in CuO, which
form localized pulses under certain experimental conditions. The formation of
these waves is attributed to the effect of dispersion, non-linearity and the
coupling of the excitons to phonons, which acts as a dissipative mechanism.Comment: 5 pages, 4 ps figures, RevTe
Finding the Pion in the Chiral Random Matrix Vacuum
The existence of a Goldstone boson is demonstrated in chiral random matrix
theory. After determining the effective coupling and calculating the scalar and
pseudoscalar propagators, a random phase approximation summation reveals the
massless pion and massive sigma modes expected whenever chiral symmetry is
spontaneously broken.Comment: 3 pages, 1 figure, revte
Vortices in Bose-Einstein condensates with anharmonic confinement
We examine an effectively repulsive Bose-Einstein condensate of atoms, that
rotates in a quadratic-plus-quartic trapping potential. We investigate the
phase diagram of the system as a function of the angular frequency of rotation
and of the coupling constant, demonstrating that there are phase transitions
between multiply- and singly-quantized vortex states. The derived phase diagram
is shown to be universal and exact in the limits of small anharmonicity and
weak coupling constant.Comment: 4 pages, 2 ps figures, RevTe
Quantization and Periodicity of the Axion Action in Topological Insulators
The Lagrangian describing the bulk electromagnetic response of a
three-dimensional strong topological insulator contains a topological `axion'
term of the form '\theta E dot B'. It is often stated (without proof) that the
corresponding action is quantized on periodic space-time and therefore
invariant under '\theta -> \theta +2\pi'. Here we provide a simple, physically
motivated proof of the axion action quantization on the periodic space-time,
assuming only that the vector potential is consistent with single-valuedness of
the electron wavefunctions in the underlying insulator.Comment: 4 pages, 1 figure, version2 (section on axion action quantization of
non-periodic systems added
Wind tunnel model and method
The design and development of a wind tunnel model equipped with pressure measuring devices are discussed. The pressure measuring orifices are integrally constructed in the wind tunnel model and do not contribute to distortions of the aerodynamic surface. The construction of a typical model is described and a drawing of the device is included
Tasting edge effects
We show that the baking of potato wedges constitutes a crunchy example of
edge effects, which are usually demonstrated in electrostatics. A simple model
of the diffusive transport of water vapor around the potato wedges shows that
the water vapor flux diverges at the sharp edges in analogy with its
electrostatic counterpart. This increased evaporation at the edges leads to the
crispy taste of these parts of the potatoes.Comment: to appear in American Journal of Physic
- …