BKL oscillations in 2+1 space-time dimensions

We investigate the question whether there are cosmological models in 2+1 space-time dimensions which exhibit dynamics similar to BKL oscillations, as the cosmological singularity is approached. Based on intuition, we conceive a toy model which displays such oscillatory dynamics. We show that in the phase space of this model, the cosmological singularity is represented by a separatrix curve and discuss the model's dynamics within the cosmological billiards picture. Finally, we offer a physical interpretation for a family of similar cosmological models in terms of the topological degrees of freedom of gravity in 2+1 dimensions.Comment: 22 pages, 4 figure

User's guide for the Total-Ozone Mapping Spectrometer (TOMS) instrument first year ozone T data set

The TOMS experiment and algorithms are described. Detailed information on the data available on computer tape is provided

Eisenstein series and automorphic representations

We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adeles A, thereby also paving the way for connections to number theory, representation theory and the Langlands program. Most of the results we present are already scattered throughout the mathematics literature but our exposition collects them together and is driven by examples. Many interesting aspects of these functions are hidden in their Fourier coefficients with respect to unipotent subgroups and a large part of our focus is to explain and derive general theorems on these Fourier expansions. Specifically, we give complete proofs of the Langlands constant term formula for Eisenstein series on adelic groups G(A) as well as the Casselman--Shalika formula for the p-adic spherical Whittaker function associated to unramified automorphic representations of G(Q_p). In addition, we explain how the classical theory of Hecke operators fits into the modern theory of automorphic representations of adelic groups, thereby providing a connection with some key elements in the Langlands program, such as the Langlands dual group LG and automorphic L-functions. Somewhat surprisingly, all these results have natural interpretations as encoding physical effects in string theory. We therefore also introduce some basic concepts of string theory, aimed toward mathematicians, emphasising the role of automorphic forms. In particular, we provide a detailed treatment of supersymmetry constraints on string amplitudes which enforce differential equations of the same type that are satisfied by automorphic forms. Our treatise concludes with a detailed list of interesting open questions and pointers to additional topics which go beyond the scope of this book.Comment: 326 pages. Detailed and example-driven exposition of the subject with highlighted applications to string theory. v2: 375 pages. Substantially extended and small correction

User's guide for SBUV/TOMS ozone derivative products

A series of products are available derived from the total-ozone and ozone vertical profile results for the Solar Backscattered Ultraviolet/Total-Ozone Mapping Spectrometer (SBUV/TOMS) Nimbus-7 operation. Products available are (1) orbital height-latitude cross sections of the SBUV profile data, (2) daily global total ozone contours in polar coordinates, (3) daily averages of total ozone in global 5x5 degree latitude-longitude grid, (4) daily, monthly and quarterly averages of total ozone and profile data in 10 degree latitude zones, (5) tabular presentation of zonal means, (6) daily global total ozone and profile contours in polar coordinates. The ""Derivative Products User's Guide'' describes each of these products in detail, including their derivation and presentation format. Information is provided on how to order the tapes and microfilm from the National Space Science Data Center

User's guide for the Solar Backscattered Ultraviolet (SBUV) instrument first year ozone-S data set

Total-ozone and ozone vertical profile results for Solar Backscattered Ultraviolet/Total Ozone Mapping Spectrometer (SBUV/TOMS) Nimbus 7 operation from November 1978 to November 1979 are available. The algorithm used have been thoroughly tested, the instrument performance has been examined in details, and the ozone results have been compared with Dobson, Umkehr, balloon, and rocket observations. The accuracy and precision of the satellite ozone data are good to at least within the ability of the ground truth to check and are self-consistent to within the specifications of the instrument. The 'SBUV User's Guide' describes the SBUV experiment and algorithms used. Detailed information on the data available on computer tape is provided including how to order tapes from the National Space Science Data Center

Stochastic semi-continuous simulation for extreme flood estimation in catchments with combined rainfall–snowmelt flood regimes

Simulation methods for extreme flood estimation represent an important complement to statistical flood frequency analysis because a spectrum of catchment conditions potentially leading to extreme flows can be assessed. In this paper, stochastic, semi-continuous simulation is used to estimate extreme floods in three catchments located in Norway, all of which are characterised by flood regimes in which snowmelt often has a significant role. The simulations are based on SCHADEX, which couples a precipitation probabilistic model with a hydrological simulation such that an exhaustive set of catchment conditions and responses is simulated. The precipitation probabilistic model is conditioned by regional weather patterns, and a bottom–up classification procedure was used to define a set of weather patterns producing extreme precipitation in Norway. SCHADEX estimates for the 1000-year (Q1000) discharge are compared with those of several standard methods, including event-based and long-term simulations which use a single extreme precipitation sequence as input to a hydrological model, statistical flood frequency analysis based on the annual maximum series, and the GRADEX method. The comparison suggests that the combination of a precipitation probabilistic model with a long-term simulation of catchment conditions, including snowmelt, produces estimates for given return periods which are more in line with those based on statistical flood frequency analysis, as compared with the standard simulation methods, in two of the catchments. In the third case, the SCHADEX method gives higher estimates than statistical flood frequency analysis and further suggests that the seasonality of the most likely Q1000 events differs from that of the annual maximum flows. The semi-continuous stochastic simulation method highlights the importance of considering the joint probability of extreme precipitation, snowmelt rates and catchment saturation states when assigning return periods to floods estimated by precipitation-runoff methods. The SCHADEX methodology, as applied here, is dependent on observed discharge data for calibration of a hydrological model, and further study to extend its application to ungauged catchments would significantly enhance its versatility

On fundamental domains and volumes of hyperbolic Coxeter-Weyl groups

We present a simple method for determining the shape of fundamental domains of generalized modular groups related to Weyl groups of hyperbolic Kac-Moody algebras. These domains are given as subsets of certain generalized upper half planes, on which the Weyl groups act via generalized modular transformations. Our construction only requires the Cartan matrix of the underlying finite-dimensional Lie algebra and the associated Coxeter labels as input information. We present a simple formula for determining the volume of these fundamental domains. This allows us to re-produce in a simple manner the known values for these volumes previously obtained by other methods.Comment: v2: to be published in Lett Math Phys (reference added, typo corrected

COST 733 - WG4: Applications of weather type classification

The main objective of the COST Action 733 is to achieve a general numerical method for assessing, comparing and classifying typical weather situations in the European regions. To accomplish this goal, different workgroups are established, each with their specific aims: WG1: Existing methods and applications (finished); WG2: Implementation and development of weather types classification methods; WG3: Comparison of selected weather types classifications; WG4: Testing methods for various applications. The main task of Workgroup 4 (WG4) in COST 733 implies the testing of the selected weather type methods for various classifications. In more detail, WG4 focuses on the following topics:• Selection of dedicated applications (using results from WG1), • Performance of the selected applications using available weather types provided by WG2, • Intercomparison of the application results as a results of different methods • Final assessment of the results and uncertainties, • Presentation and release of results to the other WGs and external interested • Recommend specifications for a new (common) method WG2 Introduction In order to address these specific aims, various applications are selected and WG4 is divided in subgroups accordingly: 1.Air quality 2. Hydrology (& Climatological mapping) 3. Forest fires 4. Climate change and variability 5. Risks and hazards Simultaneously, the special attention is paid to the several wide topics concerning some other COST Actions such as: phenology (COST725), biometeorology (COST730), agriculture (COST 734) and mesoscale modelling and air pollution (COST728). Sub-groups are established to find advantages and disadvantages of different classification methods for different applications. Focus is given to data requirements, spatial and temporal scale, domain area, specifi

Relações morfométricas para árvores dominantes de Pinus taeda no Estado do Paraná.

Este trabalho objetivou estudar as relações morfométricas de árvores dominantes de Pinus taeda no município de Ponta Grossa, Paraná. Em cada amostra a árvore de maior diâmetro a altura do peito (DAP) foi considerada dominante em relação às suas vizinhas. Destas foram mensuradas dap, altura total, altura da copa e oito raios de copa. As variáveis morfométricas analisadas foram: diâmetro de copa, altura da copa, proporção de copa, grau de esbeltez, índice de saliência, índice de abrangência e formal de copa. Estas foram correlacionadas com o dap e altura através de correlação de Pearson. De acordo com os índices, as árvores analisadas possuem média instabilidade, copas arredondadas e não há necessidade de desbaste na área. O diâmetro a altura do peito se correlacionou melhor com as variáveis morfométricas estudadas, indicando que estas sofrem alterações conforme as árvores incrementam em diâmetro

User's guide for the Solar Backscattered Ultraviolet (SBUV) and the Total Ozone Mapping Spectrometer (TOMS) RUT-S and RUT-T data sets: October 31, 1978 to November 1, 1980

Raw data from the Solar Backscattered Ultrviolet/Total Ozone Mapping Spectrometer (SBUV/TOMS) Nimbus 7 operation are available on computer tape. These data are contained on two separate sets of RUTs (Raw Units Tapes) for SBUV and TOMS, labelled RUT-S and RUT-T respectively. The RUT-S and RUT-T tapes contain uncalibrated radiance and irradiance data, housekeeping data, wavelength and electronic calibration data, instrument field-of-view location and solar ephemeris information. These tapes also contain colocated cloud, terrain pressure and snow/ice thickness data, each derived from an independent source. The "RUT User's Guide" describes the SBUV and TOMS experiments, the instrument calibration and performance, operating schedules, and data coverage, and provides an assessment of RUT-S and -T data quality. It also provides detailed information on the data available on the computer tapes