Theory of double resonance magnetometers based on atomic alignment

We present a theoretical study of the spectra produced by optical-radio-frequency double resonance devices, in which resonant linearly polarized light is used in the optical pumping and detection processes. We extend previous work by presenting algebraic results which are valid for atomic states with arbitrary angular momenta, arbitrary rf intensities, and arbitrary geometries. The only restriction made is the assumption of low light intensity. The results are discussed in view of their use in optical magnetometers

Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians

In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to cast a nonlinear system into the classical state-space form, and identify conditions under which input and state observable functions are well separated. We then extend an existing method of dynamic mode decomposition for learning Koopman operators from data known as deep dynamic mode decomposition to systems with controls or disturbances. We illustrate the accuracy of the method in learning an input-state separable Koopman operator for an example system, even when the underlying system exhibits mixed state-input terms. We next introduce a nonlinear decomposition algorithm, based on Koopman Gramians, that maximizes internal subsystem observability and disturbance rejection from unwanted noise from other subsystems. We derive a relaxation based on Koopman Gramians and multi-way partitioning for the resulting NP-hard decomposition problem. We lastly illustrate the proposed algorithm with the swing dynamics for an IEEE 39-bus system.Comment: 8 pages, submitted to IEEE 2018 AC

Tuning Windowed Chi-Squared Detectors for Sensor Attacks

A model-based windowed chi-squared procedure is proposed for identifying falsified sensor measurements. We employ the widely-used static chi-squared and the dynamic cumulative sum (CUSUM) fault/attack detection procedures as benchmarks to compare the performance of the windowed chi-squared detector. In particular, we characterize the state degradation that a class of attacks can induce to the system while enforcing that the detectors do not raise alarms (zero-alarm attacks). We quantify the advantage of using dynamic detectors (windowed chi-squared and CUSUM detectors), which leverages the history of the state, over a static detector (chi-squared) which uses a single measurement at a time. Simulations using a chemical reactor are presented to illustrate the performance of our tools

New Keck Observations of Lithium in Very Metal-poor Stars

Lithium abundances have been determined in more than 100 metal-poor halo stars both in the field and in clusters. From these data we find trends of Li with both temperature and metallicity and a real dispersion in Li abundances in the Spite Li plateau. We attribute this dispersion primarily to Li depletion (presumably due to extra mixing induced by stellar rotation) and to Galactic chemical evolution. We derive a primordial Li of 2.44 $\pm$0.18 for A(Li)$_p$ = log N(Li/H) + 12.00. This agrees with the Li abundances predicted by the $WMAP$ results. For stars cooler than the Li plateau we have evidence that Li depletion sets in at hotter temperatures for the higher metallicity stars than for the low-metal stars. This is the opposite sense of predictions from stellar models. The smooth transition of the Li content from the Li plateau stars to the cool stars adds weight to the inference of Li depletion in the plateau stars.Comment: Invited talk for IAU Symposium 228 "From Lithium to Uranium..." held in Paris in May, 2005. 6 pages, 6 figure

Continuous-time integral dynamics for Aggregative Game equilibrium seeking

In this paper, we consider continuous-time semi-decentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results

Discovery of Super-Li Rich Red Giants in Dwarf Spheroidal Galaxies

Stars destroy lithium (Li) in their normal evolution. The convective envelopes of evolved red giants reach temperatures of millions of K, hot enough for the 7Li(p,alpha)4He reaction to burn Li efficiently. Only about 1% of first-ascent red giants more luminous than the luminosity function bump in the red giant branch exhibit A(Li) > 1.5. Nonetheless, Li-rich red giants do exist. We present 15 Li-rich red giants--14 of which are new discoveries--among a sample of 2054 red giants in Milky Way dwarf satellite galaxies. Our sample more than doubles the number of low-mass, metal-poor ([Fe/H] <~ -0.7) Li-rich red giants, and it includes the most-metal poor Li-enhanced star known ([Fe/H] = -2.82, A(Li)_NLTE = 3.15). Because most of these stars have Li abundances larger than the universe's primordial value, the Li in these stars must have been created rather than saved from destruction. These Li-rich stars appear like other stars in the same galaxies in every measurable regard other than Li abundance. We consider the possibility that Li enrichment is a universal phase of evolution that affects all stars, and it seems rare only because it is brief.Comment: 6 pages, 3 figures, accepted to ApJ Letters, version 3 includes additional references and minor typographical change

Lithium and Lithium Depletion in Halo Stars on Extreme Orbits

We have determined Li abundances in 55 metal-poor (3.6 < [Fe/H] < -0.7) stars with extreme orbital kinematics. We find the Li abundance in the Li-plateau stars and examine its decrease in low-temperature, low-mass stars. The Li observations are primarily from the Keck I telescope with HIRES (spectral resolution of ~48,000 and median signal-to-noise per pixel of 140). Abundances or upper limits were determined for Li for all the stars with typical errors of 0.06 dex. Our 14 stars on the Li plateau give A(Li) = log N(Li)/N(H) + 12.00 of 2.215 +-0.110, consistent with earlier results. We find a dependence of the Li abundance on metallicity as measured by [Fe/H] and the Fe-peak elements [Cr/H] and [Ni/H], with a slope of ~0.18. We also find dependences of A(Li) with the alpha elements, Mg, Ca, and Ti. For the n-capture element, Ba, the relation between A(Li) and [Ba/H] has a shallower slope of 0.13; over a range of 2.6 dex in [Ba/H], the Li abundance spans only a factor of two. We examined the possible trends of A(Li) with the characteristics of the orbits of our halo stars, but find no relationship with kinematic or dynamic properties. The stars cooler than the Li plateau are separated into three metallicity subsets. The decrease in A(Li) sets in at hotter temperatures at high metallicities than at low metallicities; this is in the opposite sense of the predictions for Li depletion from standard and non-standard models.Comment: 29 pages including 3 tables and 12 figures Accepted by The Astrophysical Journal, for the 1 November 2005 issue, v. 63