129,373 research outputs found
Characterization of Spherical and Plane Curves Using Rotation Minimizing Frames
In this work, we study plane and spherical curves in Euclidean and
Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By
conveniently writing the curvature and torsion for a curve on a sphere, we show
how to find the angle between the principal normal and an RM vector field for
spherical curves. Later, we characterize plane and spherical curves as curves
whose position vector lies, up to a translation, on a moving plane spanned by
their unit tangent and an RM vector field. Finally, as an application, we
characterize Bertrand curves as curves whose so-called natural mates are
spherical.Comment: 8 pages. This version is an improvement of the previous one. In
addition to a study of some properties of plane and spherical curves, it
contains a characterization of Bertrand curves in terms of the so-called
natural mate
Collision-Dependent Atom Tunnelling Rate in Bose-Einstein Condensates
We show that the interaction (cross-collision) between atoms trapped in
distinct sites of a double-well potential can significantly increase the atom
tunneling rate for special trap configurations leading to an effective linear
Rabi regime of population oscillation between the trap wells. The inclusion of
cross-collisional effects significantly extends the validity of the two-mode
model approach allowing it to be alternatively employed to explain the recently
observed increase of tunneling rates due to nonlinear interactions.Comment: 4 pages, 2 figures. Replaced with improved versio
Deterministic Seasonality in Dickey-Fuller Tests: Should We Care?
This paper investigates the properties of Dickey-Fuller tests for seasonally unadjusted quarterly data when deterministic seasonality is present but it is neglected in the test regression. While for the random walk case the answer is straightforward, an extensive Monte Carlo study has to be performed for more realistic processes and testing strategies. The most important conclusion is that the common perception that deterministic seasonality has nothing to do with the long-run properties of the data is incorrect. Further numerical evidence on the shortcomings of the general-to-specific t-sig lag selection method is also presented.unit root; Dickey-Fuller tests; similar tests; seasonality; Monte Carlo
The Order of Integration for Quarterly Macroeconomic Time series: a Simple Testing Strategy
Besides introducing a simple and intuitive definition for the order of integration of quarterly time series, this paper also presents a simple testing strategy to determine that order for the case of macroeconomic data. A simulation study shows that much more attention should be devoted to the practical issue of selecting the maximum admissible order of integration. In fact, it is shown that when that order is too high, one may get (spurious) evidence for an excessive number of unit roots, resulting in an overdifferenced series.
Optimal Conditions for Atomic Homodyne Detection on Bose-Einstein Condensates
The dynamics of a two-mode Bose-Einstein condensate trapped in a double-well
potential results approximately in an effective Rabi oscillation regime of
exchange of population between both wells for sufficiently strong overlap
between the modes functions. Facing this system as a temporal atomic beam
splitter we show that this regime is optimal for a nondestructive atom-number
measurement allowing an atomic homodyne detection, thus yielding indirect
relative phase information about one of the two-mode condensates.Comment: 9 pages, 5 figure
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