The gravitational field of a disk

This note gives the gravitational potential of the disk {(x, y, z):x ² +y ² p ² , z=0} and the gravitational field at the point (x, y, z). Formulas for a ring can be obtained as the difference of our results for two different values ofp. Results are obtained in terms of elliptic integrals and we indicate how these functions can be computed efficiently. Formulas necessary for the computation of partial derivatives are also given.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS7-100, sponsored by the National Aeronautics and Space Administration.     

Evaluating a Model of Evaporation and Transpiration with Observations in a Partially Wet Douglas-Fir Forest

The Penman–Monteith equation is extended to describe evaporation of intercepted rain, transpiration and the interaction between these processes in a single explicit function. This single-layer model simulates the effects of heat exchange, stomatal blocking and changed humidity deficit close to the canopy as a function of canopywater storage. Evaporation depends on the distribution of water over the canopy and the energy exchange between wet and dry parts. Transpiration depends on the dry canopy surface resistance that is described with a Jarvis-type response. The explicit functions obtained for water vapour fluxes facilitate a straightforward identificationof the various processes. Canopy water storage amounts and xylem sapflow were measured simultaneously during drying episodes after rainfall in a dense, partially wet, Douglas-fir forest. Estimates of evaporation and transpiration rates are derived from these observations. The analysis shows that evaporation induced transpirationreduction is mainly caused by energy consumption. Changes in water vapour deficit have a minor effect due to a compensating stomatal reaction. The remaining difference between observed and modelled transpiration reduction can be attributed to partial blocking of stomata by the water layer.     

Spectral reflectance measurements of estuarine waters

Shapes and variations of reflectance spectra in estuarine water were investigated for the purpose of monitoring chlorophyll in situ by optical means. A survey undertaken in an estuarine environment, using reflectance measurements between 400 and 850 nm with a full-width half maximum (FWHM) of about 2 nm, revealed that the first derivative in the neighbourhood of the chlorophyll absorption band shows a defined spectral region which can be used to estimate chlorophyll concentrations. Correlation between chlorophyll and the first derivative was found to be low, but a good relationship exists between the ratio of the reflectance R680/R670 and chlorophyll concentrations. Based on dissolved organic carbon measurements, it is assumed that chromophoric dissolved organic compounds mask the absorption band of chlorophyll in the blue part of the spectrum, resulting in a low correlation coefficient in that spectral range. Therefore, the use of the red bands is an alternative for measuring photosynthetic pigments in coastal water at longer wavelengths. Results presented here demonstrate that the spectral locations of bands in the visible are not adequate and that hyperspectral data are required for positioning the very narrow bands for measuring chlorophyll at longer wavelengths.     

Measuring the level of interstellar inheritance in the solar protoplanetary disk

The timing and extent to which the initial interstellar material was thermally processed provide fundamental constraints for models of the formation and early evolution of the solar protoplanetary disk. We argue that the nonsolar (solar Δ¹⁷O ≈ ?29‰) and near‐terrestrial (Δ¹⁷O ≈ 0‰) O‐isotopic compositions of the Earth and most extraterrestrial materials (Moon, Mars, asteroids, and comet dust) were established very early by heating of regions of the disk that were modestly enriched (dust/gas ≥ 5–10 times solar) in primordial silicates (Δ¹⁷O ≈ ?29‰) and water‐dominated ice (Δ¹⁷O ≈ 24‰) relative to the gas. Such modest enrichments could be achieved by grain growth and settling of dust to the midplane in regions where the levels of turbulence were modest. The episodic heating of the disk associated with FU Orionis outbursts were the likely causes of this early thermal processing of dust. We also estimate that at the time of accretion the CI chondrite and interplanetary dust particle parent bodies were composed of ~5–10% of pristine interstellar material. The matrices of all chondrites included roughly similar interstellar fractions. Whether this interstellar material avoided the thermal processing experienced by most dust during FU Orionis outbursts or was accreted by the disk after the outbursts ceased to be important remains to be established.     

How well do ecosystem indicators communicate the effects of anthropogenic eutrophication?

Anthropogenic eutrophication affects the Mediterranean, Black, North and Baltic Seas to various extents. Responses to nutrient loading and methods of monitoring relevant indicators vary regionally, hindering interpretation of ecosystem state changes and preventing a straightforward pan-European assessment of eutrophication symptoms. Here we summarize responses to nutrient enrichment in Europe's seas, comparing existing time-series of selected pelagic (phytoplankton biomass and community composition, turbidity, N:P ratio) and benthic (macro flora and faunal communities, bottom oxygen condition) indicators based on their effectiveness in assessing eutrophication effects. Our results suggest that the Black Sea and Northern Adriatic appear to be recovering from eutrophication due to economic reorganization in the Black Sea catchment and nutrient abatement measures in the case of the Northern Adriatic. The Baltic is most strongly impacted by eutrophication due to its limited exchange and the prevalence of nutrient recycling. Eutrophication in the North Sea is primarily a coastal problem, but may be exacerbated by climatic changes. Indicator interpretation is strongly dependent on sea-specific knowledge of ecosystem characteristics, and no single indicator can be employed to adequately compare eutrophication state between European seas. Communicating eutrophication-related information to policy-makers could be facilitated through the use of consistent indicator selection and monitoring methodologies across European seas. This work is discussed in the context of the European Commission's recently published Marine Strategy Directive.     

Robust H∞ control for aseismic structures With uncertainties in model parameters

This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust ontput feedback controller.The uncertainties of structural stiffness,damping and mass parameters are assumed to be norm-bounded.The proposed control approach is formulated within the framework of linear matrix inequalities,for which existing convex optimization techniques,such as the LMI toolbox in MATLAB,can be used effectively and conveniently.To illustrate the effectiveness of the proposed robust H∞ strategy,a six-story building was subjected both to the 1940 El Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation.The results show that the proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness,damping and mass parameters.