Non-linear shipboard shock analysis of the Tomahawk missile shock isolation system

The identification, quantification, computer modeling and verification of the Tomahawk nonlinear liquid spring shock isolation system in a surface ship Vertical Launch System (VLS) are discussed. The isolation system hardware and mode of operation is detailed in an effort to understand the nonlinearities. These nonlinearities are then quantified and modeled using the MSC/NASTRAN finite element code. The model was verified using experimental data from the Navel Ordnance Systems Center MIL-S-901 medium weight shock tests of August 1986. The model was then used to predict the Tomahawk response to the CG-53 USS Mobile Bay shock trials of May-June 1987. Results indicate that the model is an accurate mathematical representation of the physical system either functioning as designed or in an impaired condition due to spring failure

Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations

Schur-Weyl duality is a ubiquitous tool in quantum information. At its heart is the statement that the space of operators that commute with the tensor powers of all unitaries is spanned by the permutations of the tensor factors. In this work, we describe a similar duality theory for tensor powers of Clifford unitaries. The Clifford group is a central object in many subfields of quantum information, most prominently in the theory of fault-tolerance. The duality theory has a simple and clean description in terms of finite geometries. We demonstrate its effectiveness in several applications: (1) We resolve an open problem in quantum property testing by showing that "stabilizerness" is efficiently testable: There is a protocol that, given access to six copies of an unknown state, can determine whether it is a stabilizer state, or whether it is far away from the set of stabilizer states. We give a related membership test for the Clifford group. (2) We find that tensor powers of stabilizer states have an increased symmetry group. We provide corresponding de Finetti theorems, showing that the reductions of arbitrary states with this symmetry are well-approximated by mixtures of stabilizer tensor powers (in some cases, exponentially well). (3) We show that the distance of a pure state to the set of stabilizers can be lower-bounded in terms of the sum-negativity of its Wigner function. This gives a new quantitative meaning to the sum-negativity (and the related mana) -- a measure relevant to fault-tolerant quantum computation. The result constitutes a robust generalization of the discrete Hudson theorem. (4) We show that complex projective designs of arbitrary order can be obtained from a finite number (independent of the number of qudits) of Clifford orbits. To prove this result, we give explicit formulas for arbitrary moments of random stabilizer states.Comment: 60 pages, 2 figure

Phase-resolved heterodyne holographic vibrometry with a strobe local oscillator

We report a demonstration of phase-resolved vibrometry, in which out-of-plane sinusoidal motion is assessed by heterodyne holography. In heterodyne holography, the beam in the reference channel is an optical local oscillator (LO). It is frequency-shifted with respect to the illumination beam to enable frequency conversion within the sensor bandwidth. The proposed scheme introduces a strobe LO, where the reference beam is frequency-shifted and modulated in amplitude, to alleviate the issue of phase retrieval. The strobe LO is both tuned around the first optical modulation side band at the vibration frequency, and modulated in amplitude to freeze selected mechanical vibration states sequentially. The phase map of the vibration can then be derived from the demodulation of successive vibration states

Large NN Phases of Chiral QCD_2

A matrix model is constructed which describes a chiral version of the large $N$ $U(N)$ gauge theory on a two-dimensional sphere of area $A$. This theory has three separate phases. The large area phase describes the associated chiral string theory. An exact expression for the free energy in the large area phase is used to derive a remarkably simple formula for the number of topologically inequivalent covering maps of a sphere with fixed branch points and degree $n$.Comment: 24 pgs., with 4 (postscript) figures included. MIT-CTP-230

Spatiotemporal heterodyne detection

We describe a scheme into which a camera is turned into an efficient tunable frequency filter of a few Hertz bandwidth in an off-axis, heterodyne optical mixing configuration, enabling to perform parallel, high-resolution coherent spectral imaging. This approach is made possible through the combination of a spatial and temporal modulation of the signal to reject noise contributions. Experimental data obtained with dynamically scattered light by a suspension of particles in brownian motion is interpreted

Imaging velocities of a vibrating object by stroboscopic sideband holography

We propose here to combine sideband holography with stroboscopic illumination synchronized with the vibration of an object. By sweeping the optical frequency of the reference beam such a way the holographic detection is tuned on the successive sideband harmonic ranks, we are able to image the instantaneous velocities of the object. Since the stroboscopic illumination is made with an electronic device, the method is compatible with fast (up to several MHz) vibration motions. The method is demonstrated with a vibrating clarinet reed excited sinusoidally at 2 kHz, and a stroboscopic illumination with cyclic ratio 0.15. Harmonic rank up to n = $\pm$100 are detected, and a movie of the instantaneous velocities is reported