Light on dark laser addressed smectic liquid crystal projection displays

Two techniques for producing dense uniform bulk scattering in cells containing smectic A liquid crystals have been examined for use in a large area liquid crystal projection display. Textures obtained using both thermal pulses and by dynamic scattering in the smectic A phase were evaluated for their uniformity and scattering density. The conditions required for optimum scattering are described in terms of the electrical characteristics of the scattering pulses used, the effects of different surface alignment treatments and of the nematic bandwidth of the materials employed. The two techniques are compared with respect to their suitability for large area, high information content, white on black, laser addressed liquid crystal light valves.     

The Extended Probability Generating Functional,with Application to Mixing Properties of Cluster Point Processes

An extended probability generating functional (p. g. fl.) \documentclass{article}\pagestyle{empty}\begin{document}$ \bar{G}[h]\; = \;E\;\left({\exp \;\int\limits_x {\log } \;h(x)\; \times \;N(dx)} \right) $\end{document} is well-defined for any point process N on the complete separable metric space χ over the space V?₀ of measurable functions h: χ → (0, 1) such that inf x cH h(x) > 0. The distribution of N is determined uniquely by the p.g.fl. G[h] ≡ ?[h] over the smaller space V₀ of functions h ε V?₀ for which 1 — h has bounded support. Continuity results for ?[·] involving pointwise convergent sequences {h_n} V₀ or V?₀ or V? ≡ {measurable h: χ → [0, 1]} or V = {h ε V?: 1 — h has bounded support} are reviewed, and used in furnishing a complete p. g. fl. proof of the mixing property of certain stationary cluster processes.     

Bounds for the variance of certain stationary point processes

For the variance of stationary renewal and alternating renewal processes N_n(·) the paper establishes upper and lower bounds of the form

$\text{?B}{}_1\text{?varN}{}_8\text{(0,x–Aλx?B}{}_2\text{(0<x<∞)}$

, where λ=EN₈(0,1), with constants A, B₁ and B₂ that depend on the first three moments of the interval distributions for the processes concerned. These results are consistent with the value of the constant A for a general stationary point process suggested by Cox in 1963 [1].     

Application of non-linear damping to vibration isolation: an experimental study

In a previous study, the authors have proved that in theory the introduction of a cubic non-linear damping can produce ideal vibration isolation such that the system force transmissibility over the resonant frequency region is modified, but the transmissibility over the non-resonant regions remain unaffected. The present study is concerned with both an experimental verification of this theoretical finding and the selection of the cubic damping characteristic parameter required to achieve a desired performance for a single degree of freedom vibration isolation system. These results provide an important basis for the design and practical application of non-linearly damped vibration isolation systems in engineering practice.     

Dark-state cooling of atoms by superfluid immersion

We propose and analyze a scheme to cool atoms in an optical lattice to ultralow temperatures within a Bloch band and away from commensurate filling. The protocol is inspired by ideas from dark-state laser cooling but replaces electronic states with motional levels and spontaneous emission of photons by emission of phonons into a Bose-Einstein condensate, in which the lattice is immersed. In our model, achievable temperatures correspond to a small fraction of the Bloch bandwidth and are much lower than the reservoir temperature. This is also a novel realization of an open quantum optical system, where known tools are combined with new ideas involving cooling via a reservoir.     

An investigation of the Si(111)−(√3 × √3)R30°−Ag surface by Li impact collision ion scattering spectroscopy

The Si(111)−(√3 × √3)R30°−Ag surface has been investigated using the technique of Li⁺ impact collision ion scattering spectroscopy. Typical LEED √3 domain sizes were estimated to be on the order of 150 Å for a 1 ML coverage of Ag, with the √3 structure persisting for coverages of Ag up to 35 ML. Silver islanding was found to influence the appearance of the 5 keV Li⁺ ICISS angular scans even for 1 ML coverages of Ag deposited at 480°C. A detailed structural analysis of the Si(111)−√3−Ag surface (0.25 ML deposition) involved the comparison of 5 keV Li⁺ ICISS experimental data along the [11 ], [ 10] and [2 1] azimuths with computer simulations of the scattered ion intensities based on previously proposed models for the √3 surface. Nine structurally different models were tested, and only the missing-top-layer (MTL) and the honeycomb-chained-trimer (HCT) models were found to be consistent with all the experimental results. An estimate of 0.4 Å for the maximum downward vertical displacement of the Ag atoms with resect to the surface Si atoms in the MTL model is made. The effects of increased thermal vibrational amplitude in the simulation of Si---Ag shadowing effects is also discussed. The interpretations of previous noble gas ICISS results are shown to be inconsistent with the present alkali metal ICISS study of the √3 surface.     

A Note on Bounds for the Supremum Metric for Discrete Random Variables

For positive or negative integer-valued random variables X and Y with finite second moments the inequality sup \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\sup }\limits_n |\Pr \{ X \le n\} - \Pr \{ Y \le n\} |\, \le \,|EX - EY| + \frac{1}{2}(EX(EX - 1) + (EY(Y - 1)) $\end{document} is established by elementary manipulation, and shown to be tight. Use of generating functions and an inversion formula yields the larger bound with 1/2 replaced by 2/π.