Optimal Estimation of Several Linear Parameters in the Presence of Lorentzian Thermal Noise

In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand that work to include the optimal estimation of several linear parameters from a continuous time series. We show that working in the basis of the thermal driving force both simplifies the calculations and provides additional insight to why various approximate (not optimal) estimation techniques perform as they do. To illustrate this point, we compare the variance in the optimal estimator that we derive for thermal noise with those of two approximate methods which, like the optimal estimator, suppress the contribution to the variance that would come from the irrelevant, resonant motion of the oscillator. We discuss how these methods fare when the dominant noise process is either white displacement noise or noise with power spectral density that is inversely proportional to the frequency ($1/f$ noise). We also construct, in the basis of the driving force, an estimator that performs well for a mixture of white noise and thermal noise. To find the optimal multi-parameter estimators for thermal noise, we derive and illustrate a generalization of traditional matrix methods for parameter estimation that can accommodate continuous data. We discuss how this approach may help refine the design of experiments as they allow an exact, quantitative comparison of the precision of estimated parameters under various data acquisition and data analysis strategies.Comment: 16 pages, 10 figures. Accepted for publication in Classical and Quantum Gravit

Multi-component Force Balance Control Systems Final Report

Technique and apparatus for drag, lift, and pitch force measurements in hypersonic wind tunnel

State-insensitive bichromatic optical trapping

We propose a scheme for state-insensitive trapping of neutral atoms by using light with two independent wavelengths. In particular, we describe the use of trapping and control lasers to minimize the variance of the potential experienced by a trapped Rb atom in ground and excited states. We present calculated values of wavelength pairs for which the 5s and 5p_{3/2} levels have the same ac Stark shifts in the presence of two laser fields.Comment: 5 pages, 4 figure

Space station structures and dynamics test program

The design, construction, and operation of a low-Earth orbit space station poses challenges for development and implementation of technology. One specific challenge is the development of a dynamics test program for defining the space station design requirements, and identifying and characterizing phenomena affecting the space station's design and development. The test proposal, as outlined, is a comprehensive structural dynamics program to be launched in support of the space station (SS). Development of a parametric data base and verification of the mathematical models and analytical analysis tools necessary for engineering support of the station's design, construction, and operation provide the impetus for the dynamics test program. The four test phases planned are discussed: testing of SS applicable structural concepts; testing of SS prototypes; testing of actual SS structural hardware; and on-orbit testing of SS construction

Accurate determination of electric-dipole matrix elements in K and Rb from Stark shift measurements

Stark shifts of potassium and rubidium D1 lines have been measured with high precision by Miller et al [1]. In this work, we combine these measurements with our all-order calculations to determine the values of the electric-dipole matrix elements for the 4p_j-3d_j' transitions in K and for the 5p_j-4d_j' transitions in Rb to high precision. The 4p_1/2-3d_3/2 and 5p_1/2-4d_3/2 transitions contribute on the order of 90% to the respective polarizabilities of the np_1/2 states in K and Rb, and the remaining 10% can be accurately calculated using the relativistic all-order method. Therefore, the combination of the experimental data and theoretical calculations allows us to determine the np-(n-1)d matrix elements and their uncertainties. We compare these values with our all-order calculations of the np-(n-1)d matrix elements in K and Rb for a benchmark test of the accuracy of the all-order method for transitions involving nd states. Such matrix elements are of special interest for many applications, such as determination of magic wavelengths in alkali-metal atoms for state-insensitive cooling and trapping and determination of blackbody radiation shifts in optical frequency standards with ions.Comment: 5 page

Laboratory Tests of Gravitational Physics Using a Cryogenic Torsion Pendulum

Progress and plans are reported for a program of gravitational physics experiments using cryogenic torsion pendula undergoing large amplitude torsional oscillation. The program includes a UC Irvine project to measure the gravitational constant G and joint UC Irvine - U. Washington projects to test the gravitational inverse square law at a range of about 10 cm and to test the weak equivalence principle.Comment: 17 pages, 11 figures, contribution to the 10th Marcel Grossman Conference Proceedings (Rio de Janeiro, July 20 - 26, 2003) - changed wording in first paragraph of section

Comparison of two fluorescent whiteners, Calcofluor and Blankophor, for the detection of fungal elements in clinical specimens in the diagnostic laboratory

ABSTRACTFluorescent whiteners, such as Blankophor and Calcofluor white, bind to chitin and cellulose, and fluoresce when exposed to UV light. Detection of fungal elements from skin and nail samples was faster and more accurate using Blankophor compared with potassium hydroxide preparations and Calcofluor (sensitivity and specificity 100% and 86% vs. 83–90% and 84–88%, or 80% and 84%, respectively). Visibility was improved, and the procedures were simple, inexpensive and rapid, all of which are important considerations in a busy diagnostic laboratory

Excitation energies, hyperfine constants, E1, E2, M1 transition rates, and lifetimes of (6s2)nl states in Tl I and Pb II

Energies of np (n=6-9), ns (n=7-9), nd (n=6-8), and nf (n=5-6) states in Tl I and Pb II are obtained using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the 72 possible electric-dipole transitions. Electric-quadrupole and magnetic-dipole matrix elements are evaluated to obtain np(3/2) - mp(1/2) (n,m=6,7) transition rates. Hyperfine constants A are evaluated for a number of states in 205Tl. First-, second-, third-, and all-order corrections to the energies and matrix elements and first- and second-order Breit corrections to energies are calculated. In our implementation of the all-order method, single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. These calculations provide a theoretical benchmark for comparison with experiment and theory.Comment: twelve tables, no figure

How many black holes fit on the head of a pin?

The Bekenstein-Hawking entropy of certain black holes can be computed microscopically in string theory by mapping the elusive problem of counting microstates of a strongly gravitating black hole to the tractable problem of counting microstates of a weakly coupled D-brane system, which has no event horizon, and indeed comfortably fits on the head of a pin. We show here that, contrary to widely held beliefs, the entropy of spherically symmetric black holes can easily be dwarfed by that of stationary multi-black-hole ``molecules'' of the same total charge and energy. Thus, the corresponding pin-sized D-brane systems do not even approximately count the microstates of a single black hole, but rather those of a zoo of entropically dominant multicentered configurations.Comment: 4 pages, fourth prize in the Gravity Research Foundation Essay competition 200

Heisenberg exchange in magnetic monoxides

The superexchange intertacion in transition-metal oxides, proposed initially by Anderson in 1950, is treated using contemporary tight-binding theory and existing parameters. We find also a direct exchange for nearest-neighbor metal ions, larger by a factor of order five than the superexchange. This direct exchange arises from Vddm coupling, rather than overlap of atomic charge densities, a small overlap exchange contribution which we also estimate. For FeO and CoO there is also an important negative contribution, related to Stoner ferromagnetism, from the partially filled minority-spin band which broadens when ionic spins are aligned. The corresponding J1 and J2 parameters are calculated for MnO, FeO, CoO, and NiO. They give good accounts of the Neel and the Curie-Weiss temperatures, show appropriate trends, and give a reasonable account of their volume dependences. For MnO the predicted value for the magnetic susceptibility at the Neel temperature and the crystal distortion arising from the antiferromagnetic transition were reasonably well given. Application to CuO2 planes in the cuprates gives J=1220oK, compared to an experimental 1500oK, and for LiCrO2 gives J1=4 50oK compared to an experimental 230oK.Comment: 21 pages, 1 figure, submitted to Phys. Rev. B 1/19/07. Realized J=4V^2/U applies generally, as opposed to J=2V^2/U from one-electron theory (1/28 revision