"Modes of the universe" study of two-photon deterministic, passive quantum logical gates

We use the "modes of the universe" approach to study a cavity-mediated two-photon logical gate recently proposed by Koshino, Ishizaka and Nakamura. We clarify the relationship between the more commonly used input-output formalism, and that of Koshino et al., and show that some elements of this gate had been anticipated by other authors. We conclude that their proposed gate can work both in the good and bad cavity limits, provided only that the pulses are long enough. Our formalism allows us to estimate analytically the size of the various error terms, and to follow the spectral evolution of the field + cavity system in the course of the interaction.Comment: 9 pages, 8 figure

Positive Psychology Within a Cultural Context

As our capacity for communication with nations across the globe increases through the advances of technology, our interactions with others with different worldviews also become more frequent. This exposure to diversity on so many levels requires a better understanding of the multiple contexts in which people from different cultural backgrounds live and the strengths they possess that help them experience well-being. In order to define the characteristics that my be viewed as strengths in different groups, we must make efforts to remember that cultural rules and norms often dictate what can be called a strength versus a weakness. It is imperative that we are able to recognize that strengths may look very different in different contexts and that these diverse manifestations may come from a variety of worldviews. More work must be done in order to develop a better understanding of the way that cultural context plays a role in the operationalization, manifestation, and measurement of strengths in diverse groups. The following chapter provides a history of the connections between culture and positive psychology and discusses current issues regarding the link between cultural context and various personal characteristics. Examples from culturally sensitive positive psychology theory and research are also given in order to illustrate how researchers are better exploring positive psychology within a cultural context

Photon Statistics of a Single Atom Laser

We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as β, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for β are 0.01\u3cβ\u3c1.0. We find that for large enough β, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as β is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with β values in the range considered here. As β is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results

CHROMITE: FROM THE MINERAL TO THE COMMODITY

Chromite belongs to the spinel group with the general chemical formula XY2O4, where X and Y represent divalent and trivalent metal ions, respectively. Four types of chromite ore deposits occur as either lode or secondary deposits. Lode chromite ore deposits comprise stratiform and podiform deposits, whereas secondary chromite ore deposits comprise laterite and placer deposits. Chromite is an important industrial mineral used in the refractory industry. Moreover it is the only industrial source of chromium for chemical and metallurgical industries and to be marketed as a valuable commodity it requires very demanding quality parameters that differ according to the kind of application. Chromite ore cannot be usually sold as it is and, therefore, some kind of ore beneficiation is required in order to separate chromite from gangue minerals. The most commonly used beneficiation methods for chromite ores are the gravity methods, such as the shaking table, jig, spiral and Reichert cone methods. The present work deals with the geologic studies that, coming after prospection, lead to the evaluation of the chromite ore quality and to planning and/or improvement of beneficiation plants. The quality of chromite ore deposits, in order to rank them for possible exploitation, was studied in five deposits of Madagascar (Andriamena, Antanimbary, North Befandriana, North Belobaka and North Toamasina), in collaboration with UT Group s.r.l., for the development of chromite mining in the country. The basic geological, mineralogical and geochemical study of the deposits led to the reconstruction of genetic models for each of them. This was the starting point for a more detailed study on the quality of the chromite ore. The five most important chromite ore localities, investigated for this work, are all characterized by outcropping chromitite bodies hosted within mafic/ultramafic intrusions of probable Neoproterozoic to Cambrian age. Metamorphism and alteration affected, at different degrees, all chromitites, but never completely obliterate their primary characters. Chromitite host rocks are peridotite, orthopyroxenite or orthoamphibolite, while primary gangue phases are orthopyroxene, olivine, rare plagioclase, ilmenite, rutile, pyrrhotite and pentlandite. Secondary assemblage comprises serpentine, talc, Cr-chlorite, tremolitic to actinolitic amphibole and magnetite. Geologic, textural, mineralogical and mineral chemistry data are compatible with an ophiolite origin for North Befandriana chromitites and a layered intrusion origin for Andriamena, North Toamasina, North Belobaka and Antanimbary chromitites. These latter show differences that can be related to a different position of the chromitite bodies within the stratigraphic sequence of a layered intrusion. North Befandriana is a high quality deposit that could be exploited without any beneficiation of the ore, Andriamena needs beneficiation to reach market standard, Antanimbary and North Belobaka is low quality for metallurgical or chemical use but could be a good prospect for refractory market. Finally North Toamasina chromite ore is not suitable for any market even after beneficiation. An innovative study of geologic processes that can affect chromite ore beneficiation was applied to Vavdos chromite deposit (Greece) hosted in the Vavdos ultramafic massif belonging to the Halkidiki ophiolite of the Circum-Rhodope orogenic belt. Here metamorphic modification of chromite led to redistribution of Cr2O3 from chromite to silicates. The effect of the redistribution is to lower the efficiency of gravity plants as Cr2O3 contained in silicate phases will be preferentially discharged into the tailing during enrichment. The influence of this process that is widespread in chromite ores, on chromite enrichment was evaluated quantitatively. Generally accepted assumption that chromite ores do host Cr only in chromite is misleading as metamorphosed chromite ores host significative amounts of Cr in gangue phases and especially in Cr-chlorite. This study, of a completely metasomatized chromite ore, shows that about 3 wt% of total Cr2O3 in the rock is hosted in Cr-chlorite; while only about 0.2 wt% of total Cr2O3 is hosted in serpentine. As Cr-chlorite can host even more Cr2O3 than at Vavdos, and as the deepest alteration of chromite due to metasomatism occurs for ores containing about 34% chromite, the amount of Cr2O3 redistributed within the gangue can be even higher than at Vavdos, especially in low grade disseminated ores, where probably about 5-6% of Cr2O3 can be hosted in the gangue, a value that could rise to 7-8 wt% for high Cr2O3 Cr-chlorite. The effect of this wrong assumption is a mistake in the calculation of plant efficiency that will be overestimated. Mistakes due to redistribution of Cr2O3 during metamorphism can be easily avoided through mineralogical analysis that can detect the presence of Cr-chlorite in the ore. Planning of beneficiation in Cr-chlorite-bearing chromite ores requires additional investigation, concerning Cr2O3 content in Cr-chlorite and Cr-chlorite amount in the ore. A procedure to evaluate efficiency and results of gravity chromite enrichment plants was tested on Brieville enrichment plant (Madagascar), which belongs to Kraomita Malagasy mining company. Here a detailed study of chromite sand quality parameters at each step within the plant together with the measuring of all sand flow rates led to the reconstruction of separation efficiency at each step of chromite processing. The results of grain size, XRD, XRF, EMP and grain counting analyses together with separation efficiency (SE) and liberation degree (LD) evaluation allow to conclude that Brieville plant does not properly work due to the low sorting of sands feeding shaking tables that negatively affects their separation efficiency. Moreover the low degree of liberation of chromite, especially in the coarsest grain sizes, negatively affects the re-cycling process of mix materials. Plant efficiency and quality of final product can be improved by: moving the Cr2O3-enriched mixes to the concentrate and the Cr2O3-depleted mixes to the waste; grinding to finer grain size the overall feed of shaking tables and the mixes that will be re-cycled and substituting hydrosizers with screens. The first change, that does not involve any additional operational cost, has been effectively applied to the plant just after publication of the present study. The other changes involve additional operational costs and require a detailed economic analysis before being applied to the plant. Finally a completely new technology for high performance beneficiation of chromite sand that leads to the production of chromite refractory sands was tested. For this work chromite concentrate sand from Krasta enrichment plant (Albania) was used. The innovative beneficiation plant of Omega Foundry Machinery LTD. comprises a drum magnet and the new Inclined Fluidised Separator that uses an air cushion as the fluidizing agent during gravity driven grain separation. Refractory chromite sand chemical and technical requirements are the most demanding in chromite market and no chromite ore can attain them by simple crushing and grinding. On the other hand usual enrichment methodologies either cannot meet the required parameters or have a very low refractory sand recovery. The combination of drum magnet and Inclined Fluidised Separator in the Omega Foundry Machinery LTD. pilot plant not only produces a good quality refractory sand, but the result is reached with a high recovery, making of this plant an optimal solution for the production of refractory chromite sand. The Inclined Fluidised Separator is particularly performing as it combines a very high recovery of silica in the waste with an increase of the grain size of concentrate

Deterministic and Probabilistic Binary Search in Graphs

We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to querying a node $q$, the algorithm learns either that $q$ is the target, or is given an edge out of $q$ that lies on a shortest path from $q$ to the target. We study this problem in a general noisy model in which each query independently receives a correct answer with probability $p > \frac{1}{2}$ (a known constant), and an (adversarial) incorrect one with probability $1-p$. Our main positive result is that when $p = 1$ (i.e., all answers are correct), $\log_2 n$ queries are always sufficient. For general $p$, we give an (almost information-theoretically optimal) algorithm that uses, in expectation, no more than $(1 - \delta)\frac{\log_2 n}{1 - H(p)} + o(\log n) + O(\log^2 (1/\delta))$ queries, and identifies the target correctly with probability at leas $1-\delta$. Here, $H(p) = -(p \log p + (1-p) \log(1-p))$ denotes the entropy. The first bound is achieved by the algorithm that iteratively queries a 1-median of the nodes not ruled out yet; the second bound by careful repeated invocations of a multiplicative weights algorithm. Even for $p = 1$, we show several hardness results for the problem of determining whether a target can be found using $K$ queries. Our upper bound of $\log_2 n$ implies a quasipolynomial-time algorithm for undirected connected graphs; we show that this is best-possible under the Strong Exponential Time Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs with non-uniform node querying costs, the problem is PSPACE-complete. For a semi-adaptive version, in which one may query $r$ nodes each in $k$ rounds, we show membership in $\Sigma_{2k-1}$ in the polynomial hierarchy, and hardness for $\Sigma_{2k-5}$

Conicoid Mirrors

The first order equation relating object and image location for a mirror of arbitrary conic-sectional shape is derived. It is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case of distant sources.Comment: 9 page