37,061 research outputs found
Mean curvature flow in a Ricci flow background
Following work of Ecker, we consider a weighted Gibbons-Hawking-York
functional on a Riemannian manifold-with-boundary. We compute its variational
properties and its time derivative under Perelman's modified Ricci flow. The
answer has a boundary term which involves an extension of Hamilton's Harnack
expression for the mean curvature flow in Euclidean space. We also derive the
evolution equations for the second fundamental form and the mean curvature,
under a mean curvature flow in a Ricci flow background. In the case of a
gradient Ricci soliton background, we discuss mean curvature solitons and
Huisken monotonicity.Comment: final versio
Unlimited simultaneous discrimination intervals in regression Technical report no. 90
Unlimited simultaneous discrimination intervals in linear regression
HST Images and Spectra of the Remnant of SN 1885 in M31
Near UV HST images of the remnant of SN 1885 (S And) in M31 show a 0"70 +-
0"05 diameter absorption disk silhouetted against M31's central bulge, at SN
1885's historically reported position. The disk's size corresponds to a linear
diameter of 2.5 +- 0.4 pc at a distance of 725 +- 70 kpc, implying an average
expansion velocity of 11000 +- 2000 km/s over 110 years. Low-dispersion FOS
spectra over 3200-4800 A; reveal that the absorption arises principally from Ca
II H & K (equivalent width ~215 A;) with weaker absorption features of Ca I
4227 A; and Fe I 3720 A;. The flux at Ca II line center indicates a foreground
starlight fraction of 0.21, which places SNR 1885 some 64 pc to the near side
of the midpoint of the M31 bulge, comparable to its projected 55 pc distance
from the nucleus. The absorption line profiles suggest an approximately
spherically symmetric, bell-shaped density distribution of supernova ejecta
freely expanding at up to 13100 +- 1500 km/s. We estimate Ca I, Ca II, and Fe I
masses of 2.9(+2.4,-0.6) x 10^-4 M_o, 0.005(+0.016,-0.002) M_o, and
0.013(+0.010,-0.005) M_o respectively. If the ionization state of iron is
similar to the observed ionization state of calcium, M_CaII/M_CaI = 16(+42,-5),
then the mass of Fe II is 0.21(+0.74,-0.08) M_o, consistent with that expected
for either normal or subluminous SN Ia.Comment: 8 pages, including 4 embedded EPS figures, emulateapj.sty style file.
Color image at http://casa.colorado.edu/~mcl/sand.shtml . Submitted to Ap
Local light-ray rotation
We present a sheet structure that rotates the local ray direction through an
arbitrary angle around the sheet normal. The sheet structure consists of two
parallel Dove-prism sheets, each of which flips one component of the local
direction of transmitted light rays. Together, the two sheets rotate
transmitted light rays around the sheet normal. We show that the direction
under which a point light source is seen is given by a Mobius transform. We
illustrate some of the properties with movies calculated by ray-tracing
software.Comment: 9 pages, 6 figure
Electric field induced charge noise in doped silicon: ionization of phosphorus donors
We report low frequency charge noise measurement on silicon substrates with
different phosphorus doping densities. The measurements are performed with
aluminum single electron transistors (SETs) at millikelvin temperatures where
the substrates are in the insulating regime. By measuring the SET Coulomb
oscillations, we find a gate voltage dependent charge noise on the more heavily
doped substrate. This charge noise, which is seen to have a 1/f spectrum, is
attributed to the electric field induced tunneling of electrons from their
phosphorus donor potentials.Comment: 4 page, 3 figure
Orbiter Landing Loads Math Model Description and Correlation with ALT Flight Data
Results of the space shuttle approach and landing test are examined in order to assess landing gear characteristics and performance and verify landing dynamic analyses. The landing gears were instrumented with load-calibrated strain gages, a wheel-speed sensor, and strut stroke measurement devices. The mathematical procedure used in predicting the shuttle touchdown loads and dynamics is presented together with the comparisons between measured flight data and the analytical predictions. Conclusions from these data are also presented
Control of the persistent currents in two interacting quantum rings through the Coulomb interaction and inter-ring tunneling
The persistent current in two vertically coupled quantum rings containing few
electrons is studied. We find that the Coulomb interaction between the rings in
the absence of tunneling affects the persistent current in each ring and the
ground state configurations. Quantum tunneling between the rings alters
significantly the ground state and the persistent current in the system.Comment: accepted for publication in Phys. Rev.
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