Generalizations of reaction rate integrals with applications to nuclear synthesis in astrophysics and some corrections to published literature

Under the Maxwell-Boltzmann approach, the study of nuclear reactions in dense astrophysical plasmas under various cases (such as resonant, non-resonant, modified non-resonant, non-resonant under electron screening, and so on) leads to a class of complicated reaction rate integrals. It is shown that this general class of integrals can be identified with an integral involving the product of twoH-functions. This latter integral is evaluated in this article, and following Buschman (1979), several similar results in the published literature are shown to be incorrect.     

Chronology of the high-pressure metamorphism of Norwegian garnet peridotites/pyroxenites

Eclogite facies mineral assemblages are variably preserved in mafic and ultramafic rocks within the Western Gneiss Region (WGR) of Norway. Mineralogical and microstructural data indicate that some Mg–Cr-rich, Alpine-type peridotites have had a complex metamorphic history. The metamorphic evolution of these rocks has been described in terms of a seven-stage evolutionary model; each stage is characterized by a specific mineral assemblage. Stages II and III both comprise garnet-bearing mineral assemblages. Garnet-bearing assemblages are also present in Fe–Ti-rich peridotites which commonly occur as layers in mafic complexes. Sm–Nd isotopic results are reported for mineral and whole rock samples from both of these types of peridotites and related rocks. The partitioning of Sm and Nd between coexisting garnet and clinopyroxene is used to assess chemical equilibrium. One sample of Mg–Cr-type peridotite shows non-disturbed partitioning of Sm and Nd between Stage II garnet and clinopyroxene pairs and yields a garnet–clinopyroxene–whole-rock date of 1703 ± 29 Ma (I= 0.51069, MSWD = 0.04). This is the best estimate for the age of the Stage II high-P assemblage. Other Stage II garnet–clinopyroxene pairs reflect later disturbance of the Sm–Nd system and yield dates in the range 1303 to 1040 Ma. These dates may not have any geological significance. Stage III garnet–clinopyroxene pairs typically have equilibrated Sm–Nd partitioning and two samples yield dates of 437 ± 58 and 511 ± 18 Ma. This suggests that equilibration of the Stage III high-P assemblage is related to the Caledonian orogeny and is more or less contemporaneous with high-P metamorphism of ‘country-rock’eclogites in the surrounding gneisses. The Sm–Nd mineral data for the Fe–Ti-rich garnet peridotites and for a superferrian eclogite, which occurs as a dyke within the Gurskebotn Mg–Cr-type peridotite, are consistent with a Palaeozoic high-P metamorphism. Finally a synoptic P–T–t path is proposed for the Mg–Cr-type peridotites which is consistent with the petrological and geochronological data.     

Seepage of groundwater nitrate from a riparian agroecosystem into the Wye River estuary

Intensive research in Chesapeake Bay has indicated that reductions in nitrogen inputs to the bay will be necessary to restore water quality to levels needed for resurgence of bay living resources. Fall-line water quality monitoring efferts have characterized diffuse-source nitrogen inputs from a large percentage of the bay drainage basin, but relatively little information exists regarding rates of nitrogen delivery to tidal waters from coastal plain regions. Extensive nitrate contamination of shallow groundwater due to agricultural activities, coupled with the dominant role of subsurface flow in discharge from Coastal Plain regions of the drainage basin, creates the potential for high rates of nitrogen delivery to tidal waters via groundwater seepage. This study utilized intensive hydrologic and water chemistry monitoring from April 1992 through September 1994 to determine the spatial characteristics of the groundwater-estuarine interface, as well as the rates of subsurface nitrogen transport from an agricultural field into nearshore waters of the Wye River, a subestuary of Chesapeake Bay. The hydrogeologic characteristics of the study site resulted in groundwater discharge to the Wye River occurring almost exclusively within 15 m of the shoreline. Calculated groundwater discharge rates were found to vary widely in the short term due to tidal fluctuations but in the long term were driven by seasonal changes in groundwater recharge rates. The zone of groundwater discharge contracted shoreward during summer months of low discharge, and expanded to a maximum width of approximately 15 m during high discharge periods in late winter. Average discharge rates were more than five times higher in winter versus summer months. Groundwater nitrate concentrations entering the discharge zone were relatively stable throughout the study period, with little evidence of denitrification or nitrate uptake by riparian vegetation. Consequently, nitrogen discharge patterns reflected the strong seasonality in groundwater discharge. Annual nitrate-N discharge was approximately 1.2 kg m^?1 of shoreline, indicating drainage basin rates of nitrogen delivery to tidal waters of approximately 60 kg ha^?1.     

Comparative study of different wavelets for developing parsimonious Volterra model for rainfall-runoff simulation

Although the Volterra models are non-parsimonious ones, they are being used because they can mimic dynamics of complex systems. However, applying and identification of the Volterra models using data may result in overfitting problem and uncertainty. In this investigation we evaluate capability of different wavelet forms for decomposing and compressing the Volterra kernels in order to overcome this problem by reducing the number of the model coefficients to be estimated and generating smooth kernels. A simulation study on a rainfall?runoff process over the Cache River watershed showed that the method performance is successful due to multi-resolution capacity of the wavelet analysis and high capability of the Volterra model. The results also revealed that db2 and sym2 wavelets have the same high potential in improving the linear Volterra model performance. However, QS wavelet was more successful in yielding smooth kernels. Moreover, the probability of overfitting while identifying the nonlinear Volterra model may be less than the linear model.     

Association of proportions

Simple correlation leads to misleading results when applied to the proportions of materials in mixtures, because of the constraint that the total of the proportions is less than one. A simple mainly graphical procedure to determine whether the proportions in mixtures are associated after allowing for the constraint is presented. No assumptions about the form of the underlying probability distributions are required. The technique is extended to problems where other constraints apply.     

Do CRISTA Experiment/Campaign Data Represent a Typical Situation or Not?

Data from four A3 radio wave circuits in central Europe are used to analyse the representativeness of the ionization and gravity wave activity pattern in the lower ionosphere (85 – 100 km) in the CRISTA experiment interval (3 – 12 November 1994) for the given conditions. It has been found that the CRISTA experiment interval was run under conditions, which are highly representative both of October – November 1994 and autumn, low-moderate solar activity, the descending phase of solar cycle conditions, i.e. CRISTA measurements may be considered to provide values identical with, or close to climatological values (at least for central Europe, h = 85 – 100 km).