Andreev's Theorem on hyperbolic polyhedra

In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing $C$ with the assigned dihedral angles. Andreev's Theorem also shows that the resulting polyhedron is unique, up to hyperbolic isometry. Andreev's Theorem is both an interesting statement about the geometry of hyperbolic 3-dimensional space, as well as a fundamental tool used in the proof for Thurston's Hyperbolization Theorem for 3-dimensional Haken manifolds. It is also remarkable to what level the proof of Andreev's Theorem resembles (in a simpler way) the proof of Thurston. We correct a fundamental error in Andreev's proof of existence and also provide a readable new proof of the other parts of the proof of Andreev's Theorem, because Andreev's paper has the reputation of being ``unreadable''.Comment: To appear les Annales de l'Institut Fourier. 47 pages and many figures. Revision includes significant modification to section 4, making it shorter and more rigorous. Many new references include

A geostationary imaging spectrometer TOMS instrument

One design for a geostationary Total Ozone Mapping Spectrometer (TOMS) with many desirable features is an imaging spectrometer. A preliminary study makes use of a 0.25 m Czerny-Turner spectrometer with which the Earth is imaged on a charge-coupled device (CCD) in dispersed light. The wavelength is determined by a movable grating which can be set arbitrarily by ground control. The signal integration time depends on wavelength but this system allows arbitrary timing by command. Special circumstances such as a requirement to track a low-lying sulfur dioxide cloud or a need to discriminate high level ozone from total ozone at midlatitudes could be obtained by adding a particular wavelength to the normally pre-programmed time sequence. The incident solar irradiance is measured by deploying a diffuser plate in the field of view. Individual detector elements correspond to scene elements in which the several wavelengths are serially sampled and the Earth radiance is compared to the incident sunlight. Thus the problem of uncorrelated drift of multiple detectors is removed

Electron-Phonon Driven Spin Frustration in Multi-Band Hubbard Models: MX Chains and Oxide Superconductors

We discuss the consequences of both electron-phonon and electron-electron couplings in 1D and 2D multi-band (Peierls-Hubbard) models. After briefly discussing various analytic limits, we focus on (Hartree-Fock and exact) numerical studies in the intermediate regime for both couplings, where unusual spin-Peierls as well as long-period, frustrated ground states are found. Doping into such phases or near the phase boundaries can lead to further interesting phenomena such as separation of spin and charge, a dopant-induced phase transition of the global (parent) phase, or real-space (``bipolaronic'') pairing. We discuss possible experimentally observable consequences of this rich phase diagram for halogen-bridged, transition metal, linear chain complexes (MX chains) in 1D and the oxide superconductors in 2D.Comment: 6 pages, four postscript figures (appended), in regular Te

Batrachospermum Roth. (Rhodophyta), a genus of red algae new to Iowa

Batrachospermum, a floridean red alga, is formally reported from Iowa. Populations have been observed by several workers at nine localities in eight counties: Black Hawk, Bremer, Des Moines, Dickinson, Dubuque, Emmet, Hancock, and Webster. The habitats include permanent and intermittent streams, a distrophic lake, and prairie marshes. To date, the species include B. ectocarpum Sir. from a stream in Webster County , and an undescribed species from a prairie marsh in Black Hawk County. A discussion of the taxonomy and occurrence of Batrachospermum in Iowa in presented. With this report, four genera of freshwater red algae are known from Iowa

Tool for Forecasting Cool-Season Peak Winds Across Kennedy Space Center and Cape Canaveral Air Force Station

The expected peak wind speed for the day is an important element in the daily morning forecast for ground and space launch operations at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS). The 45th Weather Squadron (45 WS) must issue forecast advisories for KSC/CCAFS when they expect peak gusts for >= 25, >= 35, and >= 50 kt thresholds at any level from the surface to 300 ft. In Phase I of this task, the 45 WS tasked the Applied Meteorology Unit (AMU) to develop a cool-season (October - April) tool to help forecast the non-convective peak wind from the surface to 300 ft at KSC/CCAFS. During the warm season, these wind speeds are rarely exceeded except during convective winds or under the influence of tropical cyclones, for which other techniques are already in use. The tool used single and multiple linear regression equations to predict the peak wind from the morning sounding. The forecaster manually entered several observed sounding parameters into a Microsoft Excel graphical user interface (GUI), and then the tool displayed the forecast peak wind speed, average wind speed at the time of the peak wind, the timing of the peak wind and the probability the peak wind will meet or exceed 35, 50 and 60 kt. The 45 WS customers later dropped the requirement for >= 60 kt wind warnings. During Phase II of this task, the AMU expanded the period of record (POR) by six years to increase the number of observations used to create the forecast equations. A large number of possible predictors were evaluated from archived soundings, including inversion depth and strength, low-level wind shear, mixing height, temperature lapse rate and winds from the surface to 3000 ft. Each day in the POR was stratified in a number of ways, such as by low-level wind direction, synoptic weather pattern, precipitation and Bulk Richardson number. The most accurate Phase II equations were then selected for an independent verification. The Phase I and II forecast methods were compared using an independent verification data set. The two methods were compared to climatology, wind warnings and advisories issued by the 45 WS, and North American Mesoscale (NAM) model (MesoNAM) forecast winds. The performance of the Phase I and II methods were similar with respect to mean absolute error. Since the Phase I data were not stratified by precipitation, this method's peak wind forecasts had a large negative bias on days with precipitation and a small positive bias on days with no precipitation. Overall, the climatology methods performed the worst while the MesoNAM performed the best. Since the MesoNAM winds were the most accurate in the comparison, the final version of the tool was based on the MesoNAM winds. The probability the peak wind will meet or exceed the warning thresholds were based on the one standard deviation error bars from the linear regression. For example, the linear regression might forecast the most likely peak speed to be 35 kt and the error bars used to calculate that the probability of >= 25 kt = 76%, the probability of >= 35 kt = 50%, and the probability of >= 50 kt = 19%. The authors have not seen this application of linear regression error bars in any other meteorological applications. Although probability forecast tools should usually be developed with logistic regression, this technique could be easily generalized to any linear regression forecast tool to estimate the probability of exceeding any desired threshold . This could be useful for previously developed linear regression forecast tools or new forecast applications where statistical analysis software to perform logistic regression is not available. The tool was delivered in two formats - a Microsoft Excel GUI and a Tool Command Language/Tool Kit (Tcl/Tk) GUI in the Meteorological Interactive Data Display System (MIDDS). The Microsoft Excel GUI reads a MesoNAM text file containing hourly forecasts from 0 to 84 hours, from one model run (00 or 12 UTC). The GUI then displays e peak wind speed, average wind speed, and the probability the peak wind will meet or exceed the 25-, 35- and 50-kt thresholds. The user can display the Day-1 through Day-3 peak wind forecasts, and separate forecasts are made for precipitation and non-precipitation days. The MIDDS GUI uses data from the NAM and Global Forecast System (GFS), instead of the MesoNAM. It can display Day-1 and Day-2 forecasts using NAM data, and Day-1 through Day-5 forecasts using GFS data. The timing of the peak wind is not displayed, since the independent verification showed that none of the forecast methods performed significantly better than climatology. The forecaster should use the climatological timing of the peak wind (2248 UTC) as a first guess and then adjust it based on the movement of weather features

Tool for Forecasting Cool-Season Peak Winds Across Kennedy Space Center and Cape Canaveral Air Force Station (CCAFS)

Peak wind speed is important element in 24-Hour and Weekly Planning Forecasts issued by 45th Weather Squadron (45 WS). Forecasts issued for planning operations at KSC/CCAFS. 45 WS wind advisories issued for wind gusts greater than or equal to 25 kt. 35 kt and 50 kt from surface to 300 ft. AMU developed cool-season (Oct - Apr) tool to help 45 WS forecast: daily peak wind speed, 5-minute average speed at time of peak wind, and probability peak speed greater than or equal to 25 kt, 35 kt, 50 kt. AMU tool also forecasts daily average wind speed from 30 ft to 60 ft. Phase I and II tools delivered as a Microsoft Excel graphical user interface (GUI). Phase II tool also delivered as Meteorological Interactive Data Display System (MIDDS) GUI. Phase I and II forecast methods were compared to climatology, 45 WS wind advisories and North American Mesoscale model (MesoNAM) forecasts in a verification data set

Some effects of argon and helium upon explosions of carbon monoxide and oxygen

Report presents the results of an investigation conducted to study the effects of the inert gases, argon and helium, upon flame speed and expansion ratio in exploding mixtures of carbon monoxide, oxygen and water.For the particular gas mixtures investigated the results show that: (1) With the possible exception of helium in small amounts the addition of inert gas always produces decreased flame speed and expansion ratio; (2) like volumes of argon and helium have very different effects upon flame speed but practically the same effect upon expansion ratio; and (3) the difference in the effect of these two gases upon speed is independent of the ratio of carbon monoxide to oxygen. A discussion of some possible modes by which inert gases may produce the observed effects is included

A Sounding-based Severe Weather Tool to Support Daily Operations at Kennedy Space Center and Cape Canaveral Air Force Station

People and property at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) are at risk when severe weather occurs. Strong winds, hail and tornadoes can injure individuals and cause costly damage to structures if not properly protected. NASA's Launch Services Program and Ground Systems Development and Operations Program and other KSC programs use the daily and weekly severe weather forecasts issued by the 45th Weather Squadron (45 WS) to determine if they need to limit an activity such as working on gantries, or protect property such as a vehicle on a pad. The 45 WS requested the Applied Meteorology Unit (AMU) develop a warm season (May-September) severe weather tool for use in the Meteorological Interactive Data Display System (MIDDS) based on the late morning, 1500 UTC (1100 local time), CCAFS (XMR) sounding. The 45 WS frequently makes decisions to issue a severe weather watch and other severe weather warning support products to NASA and the 45th Space Wing in the late morning, after the 1500 UTC sounding. The results of this work indicate that certain stability indices based on the late morning XMR soundings can depict differences between days with reported severe weather and days with no reported severe weather. The AMU determined a frequency of reported severe weather for the stability indices and implemented an operational tool in MIDDS