Development of a three-dimensional time-dependent flow field model

A three-dimensional, time-dependent mathematical model to represent Mobile Bay was developed. Computer programs were developed which numerically solve the appropriate conservation equations for predicting bay and estuary flow fields. The model is useful for analyzing the dispersion of sea water into fresh water and the transport of sediment, and for relating field and physical model data

9+ Years of CALIOP PSC Data: An Evolving Climatology

Polar stratospheric clouds (PSCs) play key roles in the springtime chemical depletion of ozone at high latitudes. PSC particles provide sites for heterogeneous chemical reactions that transform stable chlorine and bromine reservoir species into highly reactive ozone-destructive forms. Furthermore, large nitric acid trihydrate (NAT) PSC particles can irreversibly redistribute odd nitrogen through gravitational sedimentation, which prolongs the ozone depletion process by slowing the reformation of the stable chlorine reservoirs. However, there are still significant gaps in our understanding of PSC processes, particularly concerning the details of NAT particle formation. Spaceborne observations from the CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) lidar on the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) satellite are providing a rich new dataset for studying PSCs on unprecedented vortex-wide scales. In this paper, we examine the vertical and spatial distribution of PSCs in the Antarctic and Arctic on vortex-wide scales for entire PSC seasons over the more than nine-year data record

A three-dimensional, time-dependent model of Mobile Bay

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries

Algebraic Isomorphisms and Spectra of Triangular Limit Algebras: Erratum

We have found an error in the proof of Theorem 4.1 in [2]. This error affects only Theorems 4.1 and 4.3. As we have been unable to find an alternative proof of Theorem 4.1, we do not know if these theorems are true in full generality. Restricted to limit algebras generated by their order-preserving normalizers, the proof is correct. The theorems are known to be true in this case by somewhat different methods [1]

A principled approach to programming with nested types in Haskell

Initial algebra semantics is one of the cornerstones of the theory of modern functional programming languages. For each inductive data type, it provides a Church encoding for that type, a build combinator which constructs data of that type, a fold combinator which encapsulates structured recursion over data of that type, and a fold/build rule which optimises modular programs by eliminating from them data constructed using the buildcombinator, and immediately consumed using the foldcombinator, for that type. It has long been thought that initial algebra semantics is not expressive enough to provide a similar foundation for programming with nested types in Haskell. Specifically, the standard folds derived from initial algebra semantics have been considered too weak to capture commonly occurring patterns of recursion over data of nested types in Haskell, and no build combinators or fold/build rules have until now been defined for nested types. This paper shows that standard folds are, in fact, sufficiently expressive for programming with nested types in Haskell. It also defines buildcombinators and fold/build fusion rules for nested types. It thus shows how initial algebra semantics provides a principled, expressive, and elegant foundation for programming with nested types in Haskell

Characterization of Polar Stratospheric Clouds With Spaceborne Lidar: CALIPSO and the 2006 Antarctic Season

The role of polar stratospheric clouds in polar ozone loss has been well documented. The CALIPSO satellite mission offers a new opportunity to characterize PSCs on spatial and temporal scales previously unavailable. A PSC detection algorithm based on a single wavelength threshold approach has been developed for CALIPSO. The method appears to accurately detect PSCs of all opacities, including tenuous clouds, with a very low rate of false positives and few missed clouds. We applied the algorithm to CALIPSO data acquired during the 2006 Antarctic winter season from 13 June through 31 October. The spatial and temporal distribution of CALIPSO PSC observations is illustrated with weekly maps of PSC occurrence. The evolution of the 2006 PSC season is depicted by time series of daily PSC frequency as a function of altitude. Comparisons with virtual solar occultation data indicate that CALIPSO provides a different view of the PSC season than attained with previous solar occultation satellites. Measurement-based time series of PSC areal coverage and vertically-integrated PSC volume are computed from the CALIPSO data. The observed area covered with PSCs is significantly smaller than would be inferred from a temperature-based proxy such as TNAT but is similar in magnitude to that inferred from TSTS. The potential of CALIPSO measurements for investigating PSC microphysics is illustrated using combinations of lidar backscatter coefficient and volume depolarization to infer composition for two CALIPSO PSC scenes

Nonaxisymmetric Magnetorotational Instability in Proto-Neutron Stars

We investigate the stability of differentially rotating proto-neutron stars (PNSs) with a toroidal magnetic field. Stability criteria for nonaxisymmetric MHD instabilities are derived using a local linear analysis. PNSs are expected to have much stronger radial shear in the rotation velocity compared to normal stars. We find that nonaxisymmetric magnetorotational instability (NMRI) with a large azimuthal wavenumber $m$ is dominant over the kink mode ($m=1$) in differentially rotating PNSs. The growth rate of the NMRI is of the order of the angular velocity $\Omega$ which is faster than that of the kink-type instability by several orders of magnitude. The stability criteria are analogous to those of the axisymmetric magnetorotational instability with a poloidal field, although the effects of leptonic gradients are considered in our analysis. The NMRI can grow even in convectively stable layers if the wavevectors of unstable modes are parallel to the restoring force by the Brunt-V\"ais\"al\"a oscillation. The nonlinear evolution of NMRI could amplify the magnetic fields and drive MHD turbulence in PNSs, which may lead to enhancement of the neutrino luminosity.Comment: 24pages, 7figures, Accepted for publication in the Astrophysical Journal (December 12, 2005

Heterogeneous formation of polar stratospheric clouds – Part 1: Nucleation of nitric acid trihydrate (NAT)

Satellite-based observations during the Arctic winter of 2009/2010 provide firm evidence that, in contrast to the current understanding, the nucleation of nitric acid trihydrate (NAT) in the polar stratosphere does not only occur on preexisting ice particles. In order to explain the NAT clouds observed over the Arctic in mid-December 2009, a heterogeneous nucleation mechanism is required, occurring via immersion freezing on the surface of solid particles, likely of meteoritic origin. For the first time, a detailed microphysical modelling of this NAT formation pathway has been carried out. Heterogeneous NAT formation was calculated along more than sixty thousand trajectories, ending at Cloud Aerosol Lidar with Orthogonal Polarization (CALIOP) observation points. Comparing the optical properties of the modelled NAT with these observations enabled a thorough validation of a newly developed NAT nucleation parameterisation, which has been built into the Zurich Optical and Microphysical box Model (ZOMM). The parameterisation is based on active site theory, is simple to implement in models and provides substantial advantages over previous approaches which involved a constant rate of NAT nucleation in a given volume of air. It is shown that the new method is capable of reproducing observed polar stratospheric clouds (PSCs) very well, despite the varied conditions experienced by air parcels travelling along the different trajectories. In a companion paper, ZOMM is applied to a later period of the winter, when ice PSCs are also present, and it is shown that the observed PSCs are also represented extremely well under these conditions

An in vitro comparison between two methods of electrical resistance measurement for occlusal caries detection

Because of different measurement techniques and the easier design of the CRM prototype, this in vitro study aimed to compare the diagnostic performance and reproducibility of two electrical methods (Electronic Caries Monitor III, ECM and Cariometer 800, CRM) for occlusal caries detection, and to evaluate the effect of staining/ discoloration of fissures on diagnostic performance. Hundred and seventeen third molars with no apparent occlusal cavitation were selected. Six examiners inspected all specimens independently, using the CRM, and a subgroup of 4 using the ECM. Histological validation using a stereomicroscope was performed after hemisectioning. Intra- and interexaminer reproducibility was assessed by Lin's concordance correlation coefficient (CCC) and Bland and Altman analysis. Diagnostic performance parameters included sensitivity (SE), specificity (SP) and area under the ROC curve (A(z)). The CCC yielded an intra- and interexaminer reproducibility of 0.69/0.62 (ECM) and of 0.79/0.74 (CRM). The mean intra- and interexaminer 95% range of measurements (range between Bland and Altman limits of agreement) given in percentages of the instrument reading were 67%/65% for the ECM and 28%/33% for the CRM. A(z) at the D3-4 level was 0.74 (ECM) and 0.78 (CRM). The CRM showed at least equivalent diagnostic performance to the ECM. However, improvement is still desirable. Diagnostic performance appeared to be enhanced in discolored lesions; however, this may be related to sample lesion distribution characteristics. Copyright (C) 2006 S. Karger AG, Basel

Universally Coupled Massive Gravity

We derive Einstein's equations from a linear theory in flat space-time using free-field gauge invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. We adapt these results to yield universally coupled massive variants of Einstein's equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The Freund-Maheshwari-Schonberg theory is therefore not the unique universally coupled massive generalization of Einstein's theory, although it is privileged in some respects. The theories we derive are a subset of those found by Ogievetsky and Polubarinov by other means. The question of positive energy, which continues to be discussed, might be addressed numerically in spherical symmetry. We briefly comment on the issue of causality with two observable metrics and the need for gauge freedom and address some criticisms by Padmanabhan of field derivations of Einstein-like equations along the way.Comment: Introduction notes resemblance between Einstein's discovery process and later field/spin 2 project; matches journal versio