1,035 research outputs found
Dynamics of the Tippe Top via Routhian Reduction
We consider a tippe top modeled as an eccentric sphere, spinning on a
horizontal table and subject to a sliding friction. Ignoring translational
effects, we show that the system is reducible using a Routhian reduction
technique. The reduced system is a two dimensional system of second order
differential equations, that allows an elegant and compact way to retrieve the
classification of tippe tops in six groups as proposed in [1] according to the
existence and stability type of the steady states.Comment: 16 pages, 7 figures, added reference. Typos corrected and a forgotten
term in de linearized system is adde
Quantization and Compressive Sensing
Quantization is an essential step in digitizing signals, and, therefore, an
indispensable component of any modern acquisition system. This book chapter
explores the interaction of quantization and compressive sensing and examines
practical quantization strategies for compressive acquisition systems.
Specifically, we first provide a brief overview of quantization and examine
fundamental performance bounds applicable to any quantization approach. Next,
we consider several forms of scalar quantizers, namely uniform, non-uniform,
and 1-bit. We provide performance bounds and fundamental analysis, as well as
practical quantizer designs and reconstruction algorithms that account for
quantization. Furthermore, we provide an overview of Sigma-Delta
() quantization in the compressed sensing context, and also
discuss implementation issues, recovery algorithms and performance bounds. As
we demonstrate, proper accounting for quantization and careful quantizer design
has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing
and Its Applications", 201
The PL calibration for Milky Way Cepheids and its implications for the distance scale
The rationale behind recent calibrations of the Cepheid PL relation using the
Wesenheit formulation is reviewed and reanalyzed, and it is shown that recent
conclusions regarding a possible change in slope of the PL relation for
short-period and long-period Cepheids are tied to a pathological distribution
of HST calibrators within the instability strip. A recalibration of the
period-luminosity relation is obtained using Galactic Cepheids in open clusters
and groups, the resulting relationship, described by log L/L_sun =
2.415(+-0.035) + 1.148(+-0.044)log P, exhibiting only the moderate scatter
expected from color spread within the instability strip. The relationship is
confirmed by Cepheids with HST parallaxes, although without the need for
Lutz-Kelker corrections, and in general by Cepheids with revised Hipparcos
parallaxes, albeit with concerns about the cited precisions of the latter. A
Wesenheit formulation of Wv = -2.259(+-0.083) - 4.185(+-0.103)log P for
Galactic Cepheids is tested successfully using Cepheids in the inner regions of
the galaxy NGC 4258, confirming the independent geometrical distance
established for the galaxy from OH masers. Differences between the extinction
properties of interstellar and extragalactic dust may yet play an important
role in the further calibration of the Cepheid PL relation and its application
to the extragalactic distance scale.Comment: Accepted for Publication (Astrophysics & Space Science
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