13,109 research outputs found
Interplay between bending and stretching in carbon nanoribbons
We investigate the bending properties of carbon nanoribbons by combining
continuum elasticity theory and tight-binding atomistic simulations. First, we
develop a complete analysis of a given bended configuration through continuum
mechanics. Then, we provide by tight-binding calculations the value of the
bending rigidity in good agreement with recent literature. We discuss the
emergence of a stretching field induced by the full atomic-scale relaxation of
the nanoribbon architecture. We further prove that such an in-plane strain
field can be decomposed into a first contribution due to the actual bending of
the sheet and a second one due to edge effects.Comment: 5 pages, 6 figure
On the first Gaussian map for Prym-canonical line bundles
We prove by degeneration to Prym-canonical binary curves that the first
Gaussian map of the Prym canonical line bundle is
surjective for the general point [C,A] of R_g if g >11, while it is injective
if g < 12.Comment: To appear in Geometriae Dedicata. arXiv admin note: text overlap with
arXiv:1105.447
Gravity field information from Gravity Probe-B
The Gravity Probe-B Mission will carry the Stanford Gyroscope relativity experiment into orbit in the mid 1990's, as well as a Global Positioning System (GPS) receiver whose tracking data will be used to study the earth gravity field. Estimates of the likely quality of a gravity field model to be derived from the GPS data are presented, and the significance of this experiment to geodesy and geophysics are discussed
Optimized Large-Scale CMB Likelihood And Quadratic Maximum Likelihood Power Spectrum Estimation
We revisit the problem of exact CMB likelihood and power spectrum estimation
with the goal of minimizing computational cost through linear compression. This
idea was originally proposed for CMB purposes by Tegmark et al.\ (1997), and
here we develop it into a fully working computational framework for large-scale
polarization analysis, adopting \WMAP\ as a worked example. We compare five
different linear bases (pixel space, harmonic space, noise covariance
eigenvectors, signal-to-noise covariance eigenvectors and signal-plus-noise
covariance eigenvectors) in terms of compression efficiency, and find that the
computationally most efficient basis is the signal-to-noise eigenvector basis,
which is closely related to the Karhunen-Loeve and Principal Component
transforms, in agreement with previous suggestions. For this basis, the
information in 6836 unmasked \WMAP\ sky map pixels can be compressed into a
smaller set of 3102 modes, with a maximum error increase of any single
multipole of 3.8\% at , and a maximum shift in the mean values of a
joint distribution of an amplitude--tilt model of 0.006. This
compression reduces the computational cost of a single likelihood evaluation by
a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust
likelihood by implicitly regularizing nearly degenerate modes. Finally, we use
the same compression framework to formulate a numerically stable and
computationally efficient variation of the Quadratic Maximum Likelihood
implementation that requires less than 3 GB of memory and 2 CPU minutes per
iteration for , rendering low- QML CMB power spectrum
analysis fully tractable on a standard laptop.Comment: 13 pages, 13 figures, accepted by ApJ
Semi-autonomous Intersection Collision Avoidance through Job-shop Scheduling
In this paper, we design a supervisor to prevent vehicle collisions at
intersections. An intersection is modeled as an area containing multiple
conflict points where vehicle paths cross in the future. At every time step,
the supervisor determines whether there will be more than one vehicle in the
vicinity of a conflict point at the same time. If there is, then an impending
collision is detected, and the supervisor overrides the drivers to avoid
collision. A major challenge in the design of a supervisor as opposed to an
autonomous vehicle controller is to verify whether future collisions will occur
based on the current drivers choices. This verification problem is particularly
hard due to the large number of vehicles often involved in intersection
collision, to the multitude of conflict points, and to the vehicles dynamics.
In order to solve the verification problem, we translate the problem to a
job-shop scheduling problem that yields equivalent answers. The job-shop
scheduling problem can, in turn, be transformed into a mixed-integer linear
program when the vehicle dynamics are first-order dynamics, and can thus be
solved by using a commercial solver.Comment: Submitted to Hybrid Systems: Computation and Control (HSCC) 201
Orbital dynamics of "smart dust" devices with solar radiation pressure and drag
This paper investigates how perturbations due to asymmetric solar radiation pressure, in the presence of Earth shadow, and atmospheric drag can be balanced to obtain long-lived Earth centred orbits for swarms of micro-scale 'smart dust' devices, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified where Sun-synchronous apse-line precession is achieved passively to maintain asymmetric solar radiation pressure. The long-term orbit evolution is characterized by librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Long-lived orbits can then be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the usual short drag lifetime of such high area-to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the rapid end-of-life decay of such devices, thus preventing long-lived orbit debris
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