32,019 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
Theory of spin Hall effect
An extension of Drude model is proposed that accounts for spin and spin-orbit
interaction of charge carriers. Spin currents appear due to combined action of
the external electric field, crystal field and scattering of charge carriers.
The expression for spin Hall conductivity is derived for metals and
semiconductors that is independent of the scattering mechanism. In cubic
metals, spin Hall conductivity and charge conductivity
are related through with being
the bare electron mass. Theoretically computed value is in agreement with
experiment.Comment: 4 pages, 0 figures, minor extension and corrections of version
Mode-locked dysprosium fiber laser: picosecond pulse generation from 2.97 to 3.30 {\mu}m
Mode-locked fiber laser technology to date has been limited to sub-3 {\mu}m
wavelengths, despite significant application-driven demand for compact
picosecond and femtosecond pulse sources at longer wavelengths. Erbium- and
holmium-doped fluoride fiber lasers incorporating a saturable absorber are
emerging as promising pulse sources for 2.7--2.9 {\mu}m, yet it remains a major
challenge to extend this coverage. Here, we propose a new approach using
dysprosium-doped fiber with frequency shifted feedback (FSF). Using a simple
linear cavity with an acousto-optic tunable filter, we generate 33 ps pulses
with up to 2.7 nJ energy and 330 nm tunability from 2.97 to 3.30 {\mu}m
(3000--3400 cm^-1)---the first mode-locked fiber laser to cover this spectral
region and the most broadly tunable pulsed fiber laser to date. Numerical
simulations show excellent agreement with experiments and also offer new
insights into the underlying dynamics of FSF pulse generation. This highlights
the remarkable potential of both dysprosium as a gain material and FSF for
versatile pulse generation, opening new opportunities for mid-IR laser
development and practical applications outside the laboratory.Comment: Accepted for APL Photonics, 22nd August 201
Swept-wavelength mid-infrared fiber laser for real-time ammonia gas sensing
The mid-infrared (mid-IR) spectral region holds great promise for new
laser-based sensing technologies, based on measuring strong mid-IR molecular
absorption features. Practical applications have been limited to date, however,
by current low-brightness broadband mid-IR light sources and slow
acquisition-time detection systems. Here, we report a new approach by
developing a swept-wavelength mid-infrared fiber laser, exploiting the broad
emission of dysprosium and using an acousto-optic tunable filter to achieve
electronically controlled swept-wavelength operation from 2.89 to 3.25 {\mu}m
(3070-3460 cm^-1). Ammonia (NH3) absorption spectroscopy is demonstrated using
this swept source with a simple room-temperature single-pixel detector, with
0.3 nm resolution and 40 ms acquisition time. This creates new opportunities
for real-time high-sensitivity remote sensing using simple, compact mid-IR
fiber-based technologies.Comment: Invited article for APL Photonic
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