High reflectivity grating waveguide coatings for 1064nm

We propose thin single-layer grating waveguide structures to be used as high-reflectivity, but low thermal noise, alternative to conventional coatings for gravitational wave detector test mass mirrors. Grating waveguide (GWG) coatings can show a reflectivity of up to 100% with an overall thickness of less than a wavelength. We theoretically investigate GWG coatings for 1064nm based on tantala (Ta2O5) on a Silica substrate focussing on broad spectral response and low thickness

The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers

In second-generation, ground-based interferometric gravitational-wave detectors such as Advanced LIGO, the dominant noise at frequencies $f \sim 40$ Hz to $\sim 200$ Hz is expected to be due to thermal fluctuations in the mirrors' substrates and coatings which induce random fluctuations in the shape of the mirror face. The laser-light beam averages over these fluctuations; the larger the beam and the flatter its light-power distribution, the better the averaging and the lower the resulting thermal noise. In semi-infinite mirrors, scaling laws for the influence of beam shape on the four dominant types of thermal noise (coating Brownian, coating thermoelastic, substrate Brownian, and substrate thermoelastic) have been suggested by various researchers and derived with varying degrees of rigour. Because these scaling laws are important tools for current research on optimizing the beam shape, it is important to firm up our understanding of them. This paper (1) gives a summary of the prior work and of gaps in the prior analyses, (2) gives a unified and rigorous derivation of all four scaling laws, and (3) explores, relying on work by J. Agresti, deviations from the scaling laws due to finite mirror size.Comment: 25 pages, 10 figures, submitted to Class. Quantum Gra

A multi-color fast-switching microfluidic droplet dye laser

We describe a multi-color microfluidic dye laser operating in whispering gallery mode based on a train of alternating droplets containing solutions of different dyes; this laser is capable of switching the wavelength of its emission between 580 nm and 680 nm at frequencies up to 3.6 kHz -— the fastest among all dye lasers reported; it has potential applications in on-chip spectroscopy and flow cytometry

Moessbauer and Electron Microprobe Studies of Density Separates of Martian Nakhlite Mil03346: Implications for Interpretation of Moessbauer Spectra Acquired by the Mars Exploration Rovers

Martian meteorite MIL03346 is described as an augite-rich cumulate rock with approx.80%, approx.3%, and approx.21% modal phase proportions of augite (CPX), olivine and glassy mesostasis, respectively, and is classified as a nakhlite [1]. The Mossbauer spectrum for whole rock (WR) MIL 03346 is unusual for Martian meteorites in that it has a distinct magnetite subspectrum (~7% subspectral area) [2]. The meteorite also has products of pre-terrestrial aqueous alteration ("iddingsite") that is associated primarily with the basaltic glass and olivine. The Mossbauer spectrometers on the Mars Exploration Rovers have measured the Fe oxidation state and the Fe mineralogical composition of rocks and soils on the planet s surface since their landing in Gusev Crater and Meridiani Planum in January, 2004 [3,4]. The MIL 03346 meteorite provides an opportunity to "ground truth" or refine Fe phase identifications. This is particularly the case for the so-called "nanophase ferric oxide" (npOx) component. NpOx is a generic name for a ferric rich product of oxidative alteration. On Earth, where we can take samples apart and study individual phases, examples of npOx include ferrihydrite, schwertmannite, akagaaneite, and superparamagnetic (small particle) goethite and hematite. It is also possible for ferric iron to be associated to some unknown extent with igneous phases like pyroxene. We report here an electron microprobe (EMPA) and Moessbauer (MB) study of density separates of MIL 03346. The same separates were used for isotopic studies by [5]. Experimental techniques are described by [6,7]

Self-repair ability of evolved self-assembling systems in cellular automata

Self-repairing systems are those that are able to reconfigure themselves following disruptions to bring them back into a defined normal state. In this paper we explore the self-repair ability of some cellular automata-like systems, which differ from classical cellular automata by the introduction of a local diffusion process inspired by chemical signalling processes in biological development. The update rules in these systems are evolved using genetic programming to self-assemble towards a target pattern. In particular, we demonstrate that once the update rules have been evolved for self-assembly, many of those update rules also provide a self-repair ability without any additional evolutionary process aimed specifically at self-repair

Markov bases and subbases for bounded contingency tables

In this paper we study the computation of Markov bases for contingency tables whose cell entries have an upper bound. In general a Markov basis for unbounded contingency table under a certain model differs from a Markov basis for bounded tables. Rapallo, (2007) applied Lawrence lifting to compute a Markov basis for contingency tables whose cell entries are bounded. However, in the process, one has to compute the universal Gr\"obner basis of the ideal associated with the design matrix for a model which is, in general, larger than any reduced Gr\"obner basis. Thus, this is also infeasible in small- and medium-sized problems. In this paper we focus on bounded two-way contingency tables under independence model and show that if these bounds on cells are positive, i.e., they are not structural zeros, the set of basic moves of all $2 \times 2$ minors connects all tables with given margins. We end this paper with an open problem that if we know the given margins are positive, we want to find the necessary and sufficient condition on the set of structural zeros so that the set of basic moves of all $2 \times 2$ minors connects all incomplete contingency tables with given margins.Comment: 22 pages. It will appear in the Annals of the Institution of Statistical Mathematic

Moessbauer Spectroscopy for Lunar Resource Assessment: Measurement of Mineralogy and Soil Maturity

First-order assessment of lunar soil as a resource includes measurement of its mineralogy and maturity. Soils in which the mineral ilmenite is present in high concentrations are desirable feedstock for the production of oxygen at a lunar base. The maturity of lunar soils is a measure of their relative residence time in the upper 1 mm of the lunar surface. Increasing maturity implies increasing load of solar wind species (e.g., N, H, and He-3), decreasing mean grain size, and increasing glass content. All these physicochemical properties that vary in a regular way with maturity are important parameters for assessing lunar soil as a resource. For example, He-3 can be extracted and potentially used for nuclear fusion. A commonly used index for lunar soil maturity is I(sub s)/FeO, which is the concentration of fine-grained metal determined by ferromagnetic resonance (I(sub s)) normalized to the total iron content (as FeO). I(sub s)/FeO has been measured for virtually every soil returned by the Apollo and Luna missions to the Moon. Because the technique is sensitive to both oxidation state and mineralogy, iron Moessbauer spectroscopy (FeMS) is a viable technique for in situ lunar resource assessment. Its utility for mineralogy is apparent from examination of published FeMS data for lunar samples. From the data published, it can be inferred that FeMS data can also be used to determine soil maturity. The use of FeMS to determine mineralogy and maturity and progress on development of a FeMS instrument for lunar surface use are discussed

Limit theorems for weakly subcritical branching processes in random environment

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the process may at the same time be subcritical and, conditioned on nonextinction, 'supercritical'. This so-called weakly subcritical case is considered in this paper. We study the asymptotic survival probability and the size of the population conditioned on non-extinction. Also a functional limit theorem is proven, which makes the conditional supercriticality manifest. A main tool is a new type of functional limit theorems for conditional random walks.Comment: 35 page