Detection of the 267 GHz J = 1-0 rotational transition of PH3 in Saturn with a new Fourier transform spectrometer

In recent observations at the Caltech Submillimeter Observatory, the highly pressure-broadened (FWHM = 11.2 GHz) J = 1-0 rotational transition of PH3 (phosphine) was detected on Saturn. By modeling the Saturnian atmosphere with a radiative transfer code, the observed line profile was consistent with a constant PH3 mole fraction of 3.0 plus or minus 1.0 ppm in the upper troposphere. A best-fit to the depth of the line implies a cutoff at high altitudes, with no PH3 present at pressures approximately less than 100 mbar. The observed line depth, combined with the lack of a detectable emission core, implies that a cutoff in the PH3 abundance occurs at a pressure between 13 and 140 mbar. PH3 in Jupiter was not detected, nor any other molecular lines between 195 and 295 GHz (1.54 mm and 1.02 mm, respectively) in either Jupiter or Saturn

On the terms violating the custodial symmetry in multi-Higgs-doublet models

We prove that a generic multi-Higgs-doublet model (NHDM) generally must contain terms in the potential that violate the custodial symmetry. This is done by showing that the O(4) violating terms of the NHDM potential cannot be excluded by imposing a symmetry on the NHDM Lagrangian. Hence we expect higher-order corrections to necessarily introduce such terms. We also note, in the case of custodially symmetric Higgs-quark couplings, that vacuum alignment will lead to up-down mass degeneration; this is not true if the vacua are not aligned.Comment: 16 pages, 1 figure. Title and abstract are modified, conclusions remain the same. Section on Yukawa couplings is extended. Published versio

Calculating partial expected value of perfect information via Monte Carlo sampling algorithms

Partial expected value of perfect information (EVPI) calculations can quantify the value of learning about particular subsets of uncertain parameters in decision models. Published case studies have used different computational approaches. This article examines the computation of partial EVPI estimates via Monte Carlo sampling algorithms. The mathematical definition shows 2 nested expectations, which must be evaluated separately because of the need to compute a maximum between them. A generalized Monte Carlo sampling algorithm uses nested simulation with an outer loop to sample parameters of interest and, conditional upon these, an inner loop to sample remaining uncertain parameters. Alternative computation methods and shortcut algorithms are discussed and mathematical conditions for their use considered. Maxima of Monte Carlo estimates of expectations are biased upward, and the authors show that the use of small samples results in biased EVPI estimates. Three case studies illustrate 1) the bias due to maximization and also the inaccuracy of shortcut algorithms 2) when correlated variables are present and 3) when there is nonlinearity in net benefit functions. If relatively small correlation or nonlinearity is present, then the shortcut algorithm can be substantially inaccurate. Empirical investigation of the numbers of Monte Carlo samples suggests that fewer samples on the outer level and more on the inner level could be efficient and that relatively small numbers of samples can sometimes be used. Several remaining areas for methodological development are set out. A wider application of partial EVPI is recommended both for greater understanding of decision uncertainty and for analyzing research priorities

Abundance of unknots in various models of polymer loops

A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of $N$ segments follows a decaying exponential form, $\sim \exp (-N/N_0)$, where $N_0$ marks the crossover from a mostly unknotted (ie topologically simple) to a mostly knotted (ie topologically complex) ensemble. In the present work we use computational simulation to look closer into the variation of $N_0$ for a variety of polymer models. Among models examined, $N_0$ is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power law tail.Comment: 13 pages, 6 color figure

Spatial-temporal modelling and analysis of bacterial colonies with phase variable genes

2015 Copyright is held by the owner/author(s). This article defines a novel spatial-temporal modelling and analysis methodology applied to a systems biology case study, namely phase variation patterning in bacterial colony growth. We employ coloured stochastic Petri nets to construct the model and run stochastic simulations to record the development of the circular colonies over time and space. The simulation output is visualised in 2D, and sector-like patterns are automatically detected and analysed. Space is modelled using 2.5 dimensions considering both a rectangular and circular geometry, and the effects of imposing different geometries on space are measured. We close by outlining an interpretation of the Petri net model in terms of finite difference approximations of partial differential equations (PDEs). One result is the derivation of the “best” nine-point diffusion model. Our multidimensional modelling and analysis approach is a precursor to potential future work on more complex multiscale modelling.EPSRC Research Grant EP I036168/1; German BMBF Research Grant 0315449H

Millimeter/submillimeter fourier transform spectroscopy of Jovian planet atmospheres

A new Fourier transform spectrometer, built for use at the Caltech Submillimeter Observatory, has been used to observe all four of the jovian planets (Jupiter, Saturn, Uranus, and Neptune) in the millimeter-submillimeter wavelength range (0.3- 3.0 mm). The observations have resulted in the detection of the PH_3 1 - 0 rotational line (266.9 GHz) in Saturn. and the PH_3 3 - 2 ( 800.5 GHz) line in both Jupiter and Saturn. Because PH_3 is a disequilibrium species, it is an important tracer of vertical mixing and upper atmospheric photochemistry, and can therefore be used to derive dynamical and chemical properties of the jovian atmospheres. A jovian planet radiative transfer code has been used to model the observed PH_3 lineshapes. Using the FTS, a spectral line survey covering the entire range of submillimeter frequencies observable from the ground has also been performed on Jupiter at Saturn at a resolution of 200 MHz. This survey has yielded the tentative detection of HCl (and possibly HCN) in Saturn and, again with the aid of radiative transfer modeling, provided a great number of improved upper limits on the concentrations of many other species. Finally, Uranus and Neptune have been observed in the 1300 µm atmospheric window which contains the CO 2 - 1 transition. This line was not detected in either planet, placing upper limits on the tropospheric CO mole fraction of 0.5 ppm in Uranus and 1.4 ppm in Neptune

CRC concise encyclopedia of mathematics

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the dedication of author Eric Weisstein to collecting, cataloging, and referencing mathematical facts, formulas, and definitions. He has now updated most of the original entries and expanded the Encyclopedia to include 1000 additional pages of illustrated entries. The accessibility of the Encyclopedia along with its broad coverage and economical price make it attractive to the widest possible range of readers and certainly a must for libraries, from the secondary to the professional and research levels. For mathematical definitions, formulas, figures, tabulations, and references, this is simply the most impressive compendium available.Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the dedication of author Eric Weisstein to collecting, cataloging, and referencing mathematical facts, formulas, and definitions. He has now updated most of the original entries and expanded the Encyclopedia to include 1000 additional pages of illustrated entries. Th

Wolfram Mathworld

Mathworld, hosted and sponsored by Wolfram Research, Inc., is an online mathematics encyclopedia intended for students, educators, math enthusiasts, and researchers. This amazing resource was compiled over 12 years by Eric Weisstein with assistance from the mathematics and Internet communities, and continues to be updated. (Weisstein also authored the ScienceWorld site, which contains material about astronomy, scientific biography, chemistry, and physics and has been reported on in a previous Scout Report). Topics listed in the index include: Algebra, Applied Mathematics, Calculus and Analysis, Discrete Mathematics, Foundations of Mathematics, Geometry, History and Terminology, Number Theory, Probability and Statistics, Recreational Mathematics, and Topology. Visitors can also browse an alphabetical index of subjects and concepts covered on this website. The What's New section highlights current developments in mathematics, and more extensive coverage of select topics is offered in the newsletter. Numerous animated GIFs and 3D graphics pages coupled with links to further references and articles make this an interactive site as well