An Introduction to Hyperbolic Barycentric Coordinates and their Applications

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.Comment: 66 pages, 3 figure

Comment on "Minimal size of a barchan dune"

It is now an accepted fact that the size at which dunes form from a flat sand bed as well as their `minimal size' scales on the flux saturation length. This length is by definition the relaxation length of the slowest mode toward equilibrium transport. The model presented by Parteli, Duran and Herrmann [Phys. Rev. E 75, 011301 (2007)] predicts that the saturation length decreases to zero as the inverse of the wind shear stress far from the threshold. We first show that their model is not self-consistent: even under large wind, the relaxation rate is limited by grain inertia and thus can not decrease to zero. A key argument presented by these authors comes from the discussion of the typical dune wavelength on Mars (650 m) on the basis of which they refute the scaling of the dune size with the drag length evidenced by Claudin and Andreotti [Earth Pla. Sci. Lett. 252, 30 (2006)]. They instead propose that Martian dunes, composed of large grains (500 micrometers), were formed in the past under very strong winds. We show that this saltating grain size, estimated from thermal diffusion measurements, is not reliable. Moreover, the microscopic photographs taken by the rovers on Martian aeolian bedforms show a grain size of 87 plus or minus 25 micrometers together with hematite spherules at millimetre scale. As those so-called ``blueberries'' can not be entrained by reasonable winds, we conclude that the saltating grains on Mars are the small ones, which gives a second strong argument against the model of Parteli et al.Comment: A six page comment on ``Minimal size of a barchan dune'' by Parteli, Duran and Herrmann [Phys. Rev. E 75, 011301 (2007) arXiv:0705.1778

Gyrations: The Missing Link Between Classical Mechanics with its Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying Hyperbolic Geometry

Being neither commutative nor associative, Einstein velocity addition of relativistically admissible velocities gives rise to gyrations. Gyrations, in turn, measure the extent to which Einstein addition deviates from commutativity and from associativity. Gyrations are geometric automorphisms abstracted from the relativistic mechanical effect known as Thomas precession

On an inequality of Grüss type

We prove an inequality of Grüss type for p-norm, which for $p=infty$ gives an estimate similar to a result of Pachpatte [2]

Optimised Fabry-Perot (AlGa)As quantum well lasers tunable over 105 nm

Uncoated, Fabry-Perot (AlGa)As semiconductor lasers are tuned over 105nm in a grating-coupled external cavity. Broadband tunability is achieved by optimising the resonator loss so as to invoke lasing from both the first and second quantised states of the single quantum well active region

Sonic boom simulation by means of low-pressure sources

Sonic boom simulation by low pressure source

Coherent Quantum Engineering of Free-Space Laser Cooling

We perform a quantitative analysis of the cooling dynamics of three-level atomic systems interacting with two distinct lasers. Employing sparse-matrix techniques, we find numerical solutions to the fully quantized master equation in steady state. Our method allows straightforward determination of laser-cooling temperatures without the ambiguity often accompanied by semiclassical calculations, and more quickly than non-sparse techniques. Our calculations allow us to develop an understanding of the regimes of cooling, as well as a qualitative picture of the mechanism, related to the phenomenon of electromagnetically induced transparency. Effects of the induced asymmetric Fano-type lineshapes affect the detunings required for optimum cooling, as well as the predicted minimum temperatures which can be lower than the Doppler limit for either transition.Comment: 5 pages, 3 figure

Dislocation density and graphitization of diamond crystals

Two sets of diamond specimens compressed at 2 GPa at temperatures varying between 1060 K and 1760 K were prepared; one in which graphitization was promoted by the presence of water and another in which graphitization of diamond was practically absent. X-ray diffraction peak profiles of both sets were analyzed for the microstructure by using the modified Williamson-Hall method and by fitting the Fourier coefficients of the measured profiles by theoretical functions for crystallite size and lattice strain. The procedures determined mean size and size distribution of crystallites as well as the density and the character of the dislocations. The same experimental conditions resulted in different microstructures for the two sets of samples. They were explained in terms of hydrostatic conditions present in the graphitized samples

A systematic review and meta-analysis of childhood health utilities

Background: A common feature of most reviews or catalogues of health utilities has been their focus on adult health states or derivation of values from adult populations. More generally, utility measurement in or on behalf of children has been constrained by a number of methodological concerns. The objective of this study was to conduct the first comprehensive systematic review and meta-analysis of primary utility data for childhood conditions and descriptors and to determine the effects of methodological factors on childhood utilities. Methods: The review followed PRISMA guidelines. PubMed, Embase, Web of Science, PsycINFO, EconLit, CINAHL and Cochrane Library were searched for primary studies reporting health utilities for childhood conditions or descriptors using direct or indirect valuation methods. The Pediatric Economic Database Evaluation (PEDE) was also searched for cost-utility analyses with primary utility values. Mean or median utilities for each of the main samples were catalogued, whilst weighted averages of utilities for each health condition were estimated, by valuation method. Mixed-effects meta-regression using hierarchical linear modelling was conducted for the most common valuation methods to estimate the utility decrement for each health condition category relative to general childhood population health, as well as the independent effects of methodological factors. Results: The literature searches resulted in 272 eligible studies. These yielded 3,414 utilities when all sub-groups were considered, covering all ICD-10 chapters relevant to childhood health, 19 valuation methods, 12 respondent types, 8 modes of administration, and data from 36 countries. A total of 1,191 utility values were obtained when only main study samples were considered and these were catalogued by health condition or descriptor, and methodological characteristics. 1,073 mean utilities for main samples were used for fixed-effects meta-analysis by health condition and valuation method. Mixed-effects meta-regressions estimated that 53 of 76 ICD-10 delineated health conditions valued using the HUI3 were associated with statistically significant utility decrements relative to general population health, whilst 38 of 57 valued using a Visual Analogue Scale (VAS) were associated with statistically significant VAS decrements. For both methods, parental proxy-assessment was associated with overestimation of values, whilst adolescents reported lower values than children under 12 years. VAS responses were more heavily influenced by mode of administration than the HUI3