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Extrapolation
Kinds of Extrapolation Terms modified by Extrapolation Selected AbstractsTOWARDS A UNIFORM CONCEPT FOR THE COMPARISON AND EXTRAPOLATION OF ROCKWALL RETREAT AND ROCKFALL SUPPLYGEOGRAFISKA ANNALER SERIES A: PHYSICAL GEOGRAPHY, Issue 1 2007MICHAEL KRAUTBLATTER ABSTRACT. Rates of rockwall retreat and rockfall supply are fundamental components of sediment budgets in steep environments. However, the standard procedure of referencing rockwall retreat rates using only lithology is inconsistent with research findings and results in a variability that exceeds three orders of magnitude. The concept proposed in this paper argues that the complexity inherent in rockfall studies can be reduced if the stages of (i) backweathering, (ii) filling and depletion of intermediate storage on the rock face and (iii) final rockfall supply onto the talus slopes are separated as these have different response functions and controlling factors. Backweathering responds to preweathering and weathering conditions whereas the filling and depletion of intermediate storage in the rock face is mainly a function of internal and external triggers. The noise apparent in backweathering rates and rockfall supply can be reduced by integrating the relevant controlling factors in the response functions. Simple conceptual models for the three stages are developed and are linked by a time-dependent ,rockfall delivery rate', which is defined as the difference between backweathering and rockfall supply, thus reflecting the specific importance of intermediate storage in the rock face. Existing studies can be characterized according to their ,rockfall delivery ratio', a concept similar to the ,sediment delivery ratio' used in fluvial geomorphology. Their outputs can be qualified as trigger-dependent rockfall supply rates or backweathering rates dependent on (pre-)weathering conditions. It is shown that the existing quantitative backweathering and rockfall supply models implicitly follow the proposed conceptual models and can be accommodated into the uniform model. Suggestions are made for how best to incorporate non-linearities, phase transitions, path dependencies and different timescales into rockfall response functions. [source] Temporal Extrapolation of PVA Results in Relation to the IUCN Red List Criterion ECONSERVATION BIOLOGY, Issue 1 2003Oskar Kindvall For a population viability analysis ( PVA) to be useful for assessing a species' threat category, the results must have been expressed as the full extinction probability function over time or at least for the three specified time frames. Often this is not the case, and extrapolations from different kinds of PVA results ( e.g., mean time to extinction ) are often necessary. By means of analytic models, we investigated the possibilities of extrapolation. Based on our results, we suggest that extrapolation is not advisable due to the huge errors that can occur. The extinction probability function is the best kind of summary statistic to use when applying criterion E, but even then the threat categorization may be ambiguous. If the extinction risk is low in the near future but increases rapidly later on, a species may be classified as vulnerable even though it is expected to become extinct within 100 years. To avoid this, we suggest that the guidelines to the IUCN Red List criteria include three reference lines that allow for interpretation of the PVA results in the context of the three threat categories within the entire period of 100 years. If the estimated extinction probability function overshoots one of these functions, the species should be classified accordingly. Resumen: Las categorías de amenaza de la lista roja de la IUCN ( críticamente en peligro, en peligro y vulnerable ) están definidos por un juego de criterios ( A-E ). El criterio E se define cuantitativamente por tres límites especificados de riesgo de extinción ( 50%, 20% y 10% ), cada uno de los cuales se asocia a un marco temporal determinado. Para poder usar el análisis de viabilidad poblacional ( PVA ) durante la evaluación de la categoría de amenaza de una especie, los resultados deben ser expresados en función de probabilidad de extinción total sobre un tiempo o al menos para los tres marcos temporales especificados. Frecuentemente este no es el caso y las extrapolaciones de diferente tipo de resultados de PVA ( tiempo promedio de extinción ) son usualmente necesarias. Por medio de modelos analíticos investigamos las posibilidades de extrapolación. En base a nuestros resultados sugerimos que la extrapolación no es recomendable debido a una enorme cantidad de errores que pueden ocurrir. La función de probabilidad de extinción es el mejor tipo de resumen estadístico a usar cuando se aplica el criterio E, pero, aún así, la categorización de amenaza puede ser ambigua. Si el riesgo de extinción es bajo en un futuro inmediato pero incrementa muy rápidamente después, una especie puede ser clasificada como vulnerable aunque se espere que se extinga dentro de los próximos 100 años. Para evitar esto, sugerimos que los lineamientos de los criterios de la Lista Roja de la UICN incluyan tres lineas de referencia que permitan la interpretación de los resultados del PVA en el contexto de las tres categorías dentro de un periodo completo de 100 años. Si la función de probabilidad de extinción estimada se extiende más allá de una de estas funciones, las especies deberán ser clasificadas según sea el caso. [source] Extrapolation of the W7-X Magnet System to Reactor SizeCONTRIBUTIONS TO PLASMA PHYSICS, Issue 8 2010F. Schauer Abstract The fusion experiment Wendelstein 7-X (W7-X), presently under construction at the Greifswald branch institute of IPP, shall demonstrate the reactor potential of a HELIAS stellarator. HELIAS reactors with three, four and five periods have been studied at IPP since many years. With a plasma axis induction of 5 T, corresponding to about 10 T maximal induction at the coil, it was shown that such reactors are feasible. Now the possibility is being investigated to increase the conductor induction up to the 12 T , range, corresponding to > 5.5 T at the plasma axis. This improves the stellarator confinement properties but does not change the basic physics with respect to the previously analyzed machines. In particular the 5periodic HELIAS type, HSR5, is considered which evolves from W7-X by linear scaling of the main dimensions by a factor of four. Recent progress in superconductor technology and the extensive development work performed for ITER are taken into account. The latter is particularly relevant since by coincidence the circumferences of the HSR5 and the ITER toroidal field coils are practically the same. For the presented 12 T reactor version, the HSR50a, also the conductor and structural requirements are comparable to the corresponding ITER specifications. Therefore, advantage can be taken of these similarities for the stellarator reactor magnet design. The input was provided by the new code "MODUCO" which was developed for interactive coil layout. It is based on Bézier curve approximations and includes the computation of magnetic surfaces and forces (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Phobia of self-injecting and self-testing in insulin-treated diabetes patients: opportunities for screeningDIABETIC MEDICINE, Issue 8 2001E. D. Mollema Abstract Aims To define clinically relevant cut-off points for severe fear of self-injecting (FSI) and self-testing (FST) (phobia) in insulin-treated patients with diabetes, and to estimate the magnitude of these phobias in our research population. Methods, FSI and FST were assessed in a cross-sectional survey using the Diabetes Fear of Injecting and Self-testing Questionnaire (D-FISQ). A sample of 24 insulin-treated adult diabetic patients was selected from the high-scorers on FSI and/or FST (, 95th percentile). FSI and FST were re-assessed, after which patients participated in a behavioural avoidance test (BAT), thereby determining the current level of avoidance of either self-injecting or self-testing. FSI and FST scores were linked to the outcome of the BATs. Cut-off scores for severe FSI/FST were determined and extrapolated to the total study population (n = 1275). Results, Seven patients participated in the self-injecting BAT: two patients refused to perform an extra injection. In the self-testing BAT (n = 17) four patients declined to perform the extra blood glucose self-test. Extrapolation of FSI and FST cut-off scores to the total research population showed that 0.2,1.3% of the population scored in the severe FSI range. In FST, 0.6,0.8% of the total study population obtained scores in the cut-off range. Conclusions, Severe FSI and FST, characterized by emotional distress and avoidance behaviour, seems to occur in a small group of insulin-treated patients with diabetes. The D-FISQ can be of use to health care professionals (physicians, nurse specialists) in quickly providing valuable information on levels of FSI and FST in diabetes patients. Diabet. Med. 18, 671,674 (2001) [source] Internal electrolyte temperatures for polymer and fused-silica capillaries used in capillary electrophoresisELECTROPHORESIS, Issue 22 2005Christopher J. Evenhuis Abstract Polymers are important as materials for manufacturing microfluidic devices for electrodriven separations, in which Joule heating is an unavoidable phenomenon. Heating effects were investigated in polymer capillaries using a CE setup. This study is the first step toward the longer-term objective of the study of heating effects occurring in polymeric microfluidic devices. The thermal conductivity of polymers is much smaller than that of fused silica (FS), resulting in less efficient dissipation of heat in polymeric capillaries. This study used conductance measurements as a temperature probe to determine the mean electrolyte temperatures in CE capillaries of different materials. Values for mean electrolyte temperatures in capillaries made of New Generation FluoroPolymer (NGFP), poly-(methylmethacrylate) (PMMA), and poly(ether ether ketone) (PEEK) capillaries were compared with those obtained for FS capillaries. Extrapolation of plots of conductance versus power per unit length (P/L) to zero power was used to obtain conductance values free of Joule heating effects. The ratio of the measured conductance values at different power levels to the conductance at zero power was used to determine the mean temperature of the electrolyte. For each type of capillary material, it was found that the average increase in the mean temperature of the electrolyte (,TMean) was directly proportional to P/L and inversely proportional to the thermal conductivity (,) of the capillary material. At 7.5,W/m, values for ,TMean for NGFP, PMMA, and PEEK were determined to be 36.6, 33.8, and 30.7°C, respectively. Under identical conditions, ,TMean for FS capillaries was 20.4°C. [source] A Geographic Information Systems,based, weights-of-evidence approach for diagnosing aquatic ecosystem impairmentENVIRONMENTAL TOXICOLOGY & CHEMISTRY, Issue 8 2006Katherine E. Kapo Abstract A Geographic Information Systems,based, watershed-level assessment using Bayesian weights of evidence (WOE) and weighted logistic regression (WLR) provides a method to determine and compare potential environmental stressors in lotic ecosystems and to create predictive models of general or species-specific biological impairment across numerous spatial scales based on limited existing sample data. The WOE/WLR technique used in the present study is a data-driven, probabilistic approach conceptualized in epidemiological research and both developed for and currently used in minerals exploration. Extrapolation of this methodology to a case-study watershed assessment of the Great and Little Miami watersheds (OH, USA) using archival data yielded baseline results consistent with previous assessments. The method additionally produced a quantitative determination of physical and chemical watershed stressor associations with biological impairment and a predicted comparative probability (i.e., favorability) of biological impairment at a spatial resolution of 0.5 km2 over the watershed study region. Habitat stressors showed the greatest spatial association with biological impairment in low-order streams (on average, 56% of total spatial association), whereas water chemistry, particularly that of wastewater effluent, was associated most strongly with biological impairment in high-order reaches (on average, 79% of total spatial association, 28% of which was attributed to effluent). Significant potential stressors varied by land-use and stream order as well as by species. This WOE/WLR method provides a highly useful "tier 1" watershed risk assessment product through the integration of various existing data sources, and it produces a clear visual communication of areas favorable for biological impairment and a quantitative ranking of candidate stressors and associated uncertainty. [source] Extrapolation of metabolic pathways as an aid to modelling completely sequenced nonSaccharomyces yeastsFEMS YEAST RESEARCH, Issue 1 2008Florian Iragne Abstract Mathematical models of biological processes for the model yeast Saccharomyces cerevisiae are the subject of intensive effort and are available in increasing numbers. An open question is whether such models are informative for related yeasts of biotechnological and medical interest that will not themselves benefit from an equivalent effort. In this study, we assess a method for extrapolating reference models to other completely sequenced yeasts, using a combination of graph-theoretic analysis and reliable identification of homologous genes using Génolevures protein families. In this first assessment, we focus on subtractive modeling, identified through the correlated loss of input and output ports in metabolic pathways. We confirm that the major, highly connected, pathways of central metabolism are conserved and might be universal. In 60,80% of our results, further analysis is not required to determine whether the pathway is lost or conserved, so that our method can be systematically applied as a first step in developing species-specific models. [source] Evolution of Electrical, Chemical, and Structural Properties of Transparent and Conducting Chemically Derived Graphene Thin FilmsADVANCED FUNCTIONAL MATERIALS, Issue 16 2009Cecilia Mattevi Abstract A detailed description of the electronic properties, chemical state, and structure of uniform single and few-layered graphene oxide (GO) thin films at different stages of reduction is reported. The residual oxygen content and structure of GO are monitored and these chemical and structural characteristics are correlated to electronic properties of the thin films at various stages of reduction. It is found that the electrical characteristics of reduced GO do not approach those of intrinsic graphene obtained by mechanical cleaving because the material remains significantly oxidized. The residual oxygen forms sp3 bonds with carbon atoms in the basal plane such that the carbon sp2 bonding fraction in fully reduced GO is ,0.80. The minority sp3 bonds disrupt the transport of carriers delocalized in the sp2 network, limiting the mobility, and conductivity of reduced GO thin films. Extrapolation of electrical conductivity data as a function of oxygen content reveals that complete removal of oxygen should lead to properties that are comparable to graphene. [source] A one-way wave equation for modelling seismic waveform variations due to elastic heterogeneityGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2005D. A. Angus SUMMARY The application of a new one-way narrow-angle elastic wave equation to isotropic heterogeneous media is described. This narrow-angle finite-difference propagator should provide an efficient and accurate method of simulating primary body wave(s) passing through smoothly varying heterogeneous media. Although computationally slower than ray theory, the narrow-angle propagator can model frequency-dependent forward diffraction and scattering as well as the averaging effects due to smooth variations in medium parameters that vary on the sub-Fresnel zone level. Example waveforms are presented for the propagation of body waves in deterministic as well as stochastic heterogeneous 3-D Earth models. Extrapolation within deterministic media will highlight various familiar wave-diffraction and pulse-distortion effects associated with large-scale inhomogeneities, such as geometrical spreading, wavefront folding and creeping-wave diffraction by a compact object. Simulation within stochastic media will examine the effects of varying the correlation lengths of random heterogeneities on wave propagation. In particular, wave phenomena such as frequency-dependent forward scattering, the appearance of random caustics and the generation of seismic coda will be shown. [source] Carbon flow in an upland grassland: effect of liming on the flux of recently photosynthesized carbon to rhizosphere soilGLOBAL CHANGE BIOLOGY, Issue 12 2004J. Ignacio Rangel-Castro Abstract The effect of liming on the flow of recently photosynthesized carbon to rhizosphere soil was studied using 13CO2 pulse labelling, in an upland grassland ecosystem in Scotland. The use of 13C enabled detection, in the field, of the effect of a 4-year liming period of selected soil plots on C allocation from plant biomass to soil, in comparison with unlimed plots. Photosynthetic rates and carbon turnover were higher in plants grown in limed soils than in those from unlimed plots. Higher ,13C, values were detected in shoots from limed plants than in those from unlimed plants in samples clipped within 15 days of the end of pulse labelling. Analysis of the aboveground plant production corresponding to the 4-year period of liming indicated that the standing biomass was higher in plots that received lime. Lower ,13C, values in limed roots compared with unlimed roots were found, whereas no significant difference was detected between soil samples. Extrapolation of our results indicated that more C has been lost through the soil than has been gained via photosynthetic assimilation because of pasture liming in Scotland during the period 1990,1998. However, the uncertainty associated with such extrapolation based on this single study is high and these estimates are provided only to set our findings in the broader context of national soil carbon emissions. [source] Causes and consequences of fire-induced soil water repellencyHYDROLOGICAL PROCESSES, Issue 15 2001J. Letey Abstract A wettable surface layer overlying a water-repellent layer is commonly observed following a fire on a watershed. High surface temperatures ,burn' off organic materials and create vapours that move downward in response to a temperature gradient and then condense on soil particles causing them to become water repellent. Water-repellent soils have a positive water entry pressure hp that must be exceeded or all the water will runoff. Water ponding depths ho that exceeds hp will cause infiltration, but the profile is not completely wetted. Infiltration rate and soil wetting increase as the value of ho/hp increases. The consequence is very high runoff, which also contributes to high erosion on fire-induced water-repellent soils during rain storms. Grass establishment is impaired by seeds being eroded and lack of soil water for seeds that do remain and germinate. Extrapolation of these general findings to catchment or watershed scales is difficult because of the very high temporal and spatial variabilities that occur in the field. Copyright © 2001 John Wiley & Sons, Ltd. [source] Downregulation of miR-122 in the rodent and human hepatocellular carcinomasJOURNAL OF CELLULAR BIOCHEMISTRY, Issue 3 2006Huban Kutay Abstract MicroRNAs (miRs) are conserved small non-coding RNAs that negatively regulate gene expression. The miR profiles are markedly altered in cancers and some of them have a causal role in tumorigenesis. Here, we report changes in miR expression profile in hepatocellular carcinomas (HCCs) developed in male Fisher rats-fed folic acid, methionine, and choline-deficient (FMD) diet. Comparison of the miR profile by microarray analysis showed altered expression of some miRs in hepatomas compared to the livers from age-matched rats on the normal diet. While let-7a, miR-21, miR-23, miR-130, miR-190, and miR-17-92 family of genes was upregulated, miR-122, an abundant liver-specific miR, was downregulated in the tumors. The decrease in hepatic miR-122 was a tumor-specific event because it did not occur in the rats switched to the folate and methyl-adequate diet after 36 weeks on deficient diet, which did not lead to hepatocarcinogenesis. miR-122 was also silent in a transplanted rat hepatoma. Extrapolation of this study to human primary HCCs revealed that miR-122 expression was significantly (P,=,0.013) reduced in 10 out of 20 tumors compared to the pair-matched control tissues. These findings suggest that the downregulation of miR-122 is associated with hepatocarcinogenesis and could be a potential biomarker for liver cancers. J. Cell. Biochem. 99: 671,678, 2006. © 2006 Wiley-Liss, Inc. [source] Experimental dehydration kinetics of serpentinite using pore volumometryJOURNAL OF METAMORPHIC GEOLOGY, Issue 4 2007S. LLANA-FÚNEZ Abstract A series of dehydration experiments was carried out on both intact rock and cold-pressed powdered samples of serpentinite at temperatures in the range 535,610 °C, 100,170 °C above the onset of the breakdown temperature of 435 °C. Pore water pressures near 120 MPa were servo-controlled using a pore volumometer that also allowed dehydration reaction progress to be monitored through measurement of the amount of evolved water. Effective hydrostatic confining pressures were varied between 0 and 113 MPa. The reaction rate of intact specimens of initially near-zero porosity was constant up to 50,80% reaction progress at any given temperature, but decreased progressively as transformation approached completion. Water expulsion rates were not substantially affected by elevation of effective pressures that remained insufficient to cause major pore collapse. An Arrhenius relation links reaction rate to temperature with an activation enthalpy of 429 ± 201 and 521 ± 52 kJ mol,1 for powdered and intact specimens, respectively. Microstructural study of intact specimens showed extensive nucleation beginning at pre-existing cracks, veins and grain boundaries, and progressing into the interior of the lizardite grains. Extrapolation of these data towards equilibrium temperature provides an upper bound on the kinetics of this reaction in nature. [source] Comparative Cerebrospinal Fluid Diffusion of Imipenem and Meropenem in RatsJOURNAL OF PHARMACY AND PHARMACOLOGY: AN INTERNATI ONAL JOURNAL OF PHARMACEUTICAL SCIENCE, Issue 9 2000ANTOINE DUPUIS The main objective of this study was to compare the cerebrospinal fluid (CSF) diffusion of imipenem and meropenem at steady state, following intravenous infusions at various rates in rats. A preliminary experiment was conducted to estimate the elimination half-lives of these two carbapenem antibiotics, and then to evaluate the infusion duration necessary to reach steady state. CSF diffusion of imipenem was essentially linear over the wide range of infusion rates (66,1320 ,g min,1) and corresponding steady-state plasma concentrations (11.7,443.0 ,g mL,1). Conversely the CSF diffusion of meropenem was saturable, with a predicted maximum CSF concentration equal to 1.3 ,g mL,1. Extrapolation of these data to the clinical situation may not be possible since the rats had normal blood-brain and blood-CSF barriers whereas patients with diseases such as meningitis may not. However, it is suggested that the observed differences in the diffusion characteristics of imipenem and meropenem may be partly responsible for their differences in toxicity and efficacy at the central level. [source] Effects of nitrogen supply on water-use efficiency of higher plantsJOURNAL OF PLANT NUTRITION AND SOIL SCIENCE, Issue 2 2008Holger Brueck Abstract The worldwide increase of food demand and reduced sweet-water availability in some important food-producing regions raised interest in more efficient water use, which has become one of the central research topics in agriculture. Improved irrigation management and reduced bare-soil evaporation have highest priority to increase agronomic water-use efficiency (WUE). Compared to these technical (irrigation) and basic (crop production) management options, effects of nutrient management on WUE were less frequently considered. Twenty-nine publications on nitrogen (N) effects on biomass WUE of container-grown plants are considered in this review. Most of them indicate positive N effects on WUE, and relevance of N effects on intrinsic WUE and unproductive water and carbon loss is discussed. A plot of 90 published data of percent decreases of WUE and dry mass under variable N supply is presented. Extrapolation of biomass WUE from leaf measurements of intrinsic WUE is critically reviewed. The positive correlation between WUE and dry-mass formation suggests that physiological rather than stomatal effects are more important in order to explain positive N effects on WUE. [source] Functional traits of woody plants: correspondence of species rankings between field adults and laboratory-grown seedlings?JOURNAL OF VEGETATION SCIENCE, Issue 3 2003J.H.C. Cornelissen Castroviejo et al. (1986,2000); Stace (1991) Abstract. Research into interspecific variation in functional traits is important for our understanding of trade-offs in plant design and function, for plant functional type classifications and for understanding ecosystem responses to shifts in species composition. Interspecific rankings of functional traits are a function of, among other factors, ontogenetic or allometric development and environmental effects on phenotypes. For woody plants, which attain large size and long lives, these factors might have strong effects on interspecific trait rankings. This paper is the first to test and compare the correspondence of interspecific rankings between laboratory grown seedlings and field grown adult plants for a wide range of functional leaf and stem traits. It employs data for 90 diverse woody and semiwoody species in a temperate British and a (sub)Mediterranean Spanish flora, all collected according to a strict protocol. For 12 out of 14 leaf and stem traits we found significant correlations between the species ranking in laboratory seedlings and field adults. For leaf size and maximum stem vessel diameter > 50 % of variation in field adults was explained by that in laboratory seedlings. Two important determinants of plant and ecosystem functioning, specific leaf area and leaf N content, had only 27 to 36 and 17 to 31 % of variation, respectively, in field adults explained by laboratory seedlings, owing to subsets of species with particular ecologies deviating from the general trend. In contrast, interspecific rankings for the same traits were strongly correlated between populations of field adults on different geological substrata. Extrapolation of interspecific trait rankings from laboratory seedlings to adult plants in the field, or vice versa, should be done with great caution. [source] Simulation of the three-dimensional distribution of the red:far-red ratio within crop canopiesNEW PHYTOLOGIST, Issue 1 2007Michaël Chelle Summary ,,It is widely recognized that the red:far-red ratio (,) acts as a signal that triggers plant morphogenesis. New insights into photomorphogenesis have been gained through experiments in controlled environments. Extrapolation of such results to field conditions requires characterization of the , signal perceived by plant organs within canopies. This paper presents a modeling approach to characterize this signal. ,,A wheat (Triticum aestivum) architectural model was coupled with a three-dimensional light model estimating the irradiances of virtual sensors. Architectural parameters and , values were measured on two contrasting spring wheat canopies under outdoor conditions. Light simulations were compared with measurements, and an analysis of sensitivity to measurement conditions was carried out. ,,The model results agreed well with measurements and previously published data. The sensitivity analysis showed that , strongly depends on canopy development as well as on sky conditions, sensor orientation, and sensor field of view. ,,This paper shows that modeling enables investigation of , distribution in a canopy over space and time. It also shows that the characterization of light quality strongly depends on measurement conditions, and that any discrepancies in results are likely attributable to different experimental set-ups. The usefulness of this modeling approach for crop photomorphogenesis studies is discussed. [source] Changes in optical properties of MnAs thin films on GaAs(001) induced by ,- to ,-phase transitionPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 4 2008B. Gallas Abstract MnAs layers with 45 nm thickness were grown epitaxially on GaAs(001) substrates. Ellipsometry measurements were made in the spectral range 0.045 eV to 6 eV as a function of temperature (between ,10 °C and 50 °C) at 70° of incidence. In this way the transition from the hexagonal ,-phase to the orthorhombic ,-phase could be monitored. Non-zero off-diagonal elements of the Jones matrix for an azimuth of 38° off the [10] axis of the substrate indicate that the optical functions of MnAs are anisotropic in both phases. The optical conductivity exhibits low-energy interband transitions around 0.3 eV, more clearly seen in the ,-phase than in the ,-phase. Extrapolation of the optical conductivity to zero frequency confirms that the ,-phase is about two times more conducting than the ,-phase. A broad structure is observed in the visible range around 3 eV. The ,-phase is characterised by an anisotropy induced energy difference of this structure with a maximum at 2.8 eV for the extraordinary index and at 3.15 eV for the ordinary index. This difference vanishes in the ,-phase in which anisotropy mainly induces changes in amplitude of the 3 eV structure. The assignment of the structures will be discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] In vitro,in vivo correlations for drugs eliminated by glucuronidation: Investigations with the model substrate zidovudineBRITISH JOURNAL OF CLINICAL PHARMACOLOGY, Issue 5 2002Sam Boase Aims, To investigate the effects of incubation conditions on the kinetic constants for zidovudine (AZT) glucuronidation by human liver microsomes, and whether microsomal intrinsic clearance (CLint) derived for the various conditions predicted hepatic AZT clearance by glucuronidation (CLH) in vivo. Methods, The effects of incubation constituents, particularly buffer type (phosphate, Tris) and activators (Brij58, alamethacin, UDP-N-acetylglucosamine (UDP-NAcG)), on the kinetics of AZT glucuronidation by human liver microsomes was investigated. AZT glucuronide (AZTG) formation by microsomal incubations was quantified by h.p.l.c. Microsomal CLint values determined for the various experimental conditions were extrapolated to a whole organ CLint and these data were used to calculate in vivo CLH using the well-stirred, parallel tube and dispersion models. Results, Mean CLint values for Brij58 activated microsomes in both phosphate (3.66 ± 1.40 µl min,1 mg,1, 95% CI 1.92, 5.39) and Tris (3.79 ± 0.74 µl min,1 mg,1, 95% CI 2.87, 4.71) buffers were higher (P < 0.05) than the respective values for native microsomes (1.04 ± 0.42, 95% CI 0.53, 1.56 and 1.37 ± 0.30 µl min,1 mg,1, 95% CI 1.00, 1.73). Extrapolation of the microsomal data to a whole organ CLint and substitution of these values in the expressions for the well-stirred, parallel tube and dispersion models underestimated the known in vivo blood AZT clearance by glucuronidation by 6.5- to 23-fold (3.61,12.71 l h,1vs 82 l h,1). There was no significant difference in the CLH predicted by each of the models for each set of conditions. A wide range of incubation constituents and conditions were subsequently investigated to assess their effects on GAZT formation, including alamethacin, UDP-NAcG, MgCl2, d -saccharic acid 1,4-lactone, ATP, GTP, and buffer pH and ionic strength. Of these, only decreasing the phosphate buffer concentration from 0.1 m to 0.02 m for Brij58 activated microsomes substantially increased the rate of GAZT formation, but the extrapolated CLH determined for this condition still underestimated known AZT glucuronidation clearance by more than 4-fold. AZT was shown not to bind nonspecifically to microsomes. Analysis of published data for other glucuronidated drugs confirmed a trend for microsomal CLint to underestimate in vivo CLH. Conclusions, AZT glucuronidation kinetics by human liver microsomes are markedly dependent on incubation conditions, and there is a need for interlaboratory standardization. Extrapolation of in vitro CLint underestimates in vivo hepatic clearance of drugs eliminated by glucuronidation. [source] Procedural Sedation in the Community Emergency Department: Initial Results of the ProSCED RegistryACADEMIC EMERGENCY MEDICINE, Issue 1 2007Alfred Sacchetti MD Abstract Objectives Procedural sedation and analgesia (PSA) has been well profiled in experimental studies in university emergency departments. Extrapolation of these practices into the community hospital setting is not well established. This report describes community hospital practices and outcomes in a multicenter PSA registry. Methods The Procedural Sedation in the Community Emergency Department (ProSCED) registry is a prospective observational database composed of consecutive emergency physician,directed procedural sedation cases in community hospitals. Registered procedures described by 15 categorical data fields are collected at the time of the patient encounter and entered into a secure Internet-housed database. Results A total of 1,028 procedural sedations were performed on 980 patients at 14 study sites. The most common specified procedures performed included shoulder relocation (392), hip relocation (102), elbow relocation (70), upper extremity fracture care (69), lower extremity fracture care (66), and facial laceration repair (67). Complications of any description occurred in 42 cases (4.1%), with no patient's disposition changed secondary to a complication. Patients' ages ranged from 1 month to 95 years, with a median age of 31 years. Of procedures attempted, 982 (95.5%) were successfully completed, 21 cases (2.0%) were adequately sedated but unable to have their procedure completed, and 21 cases (2.0%) were believed to be inadequately sedated. Medication use included midazolam in 423 cases (41.1%), propofol in 253 (24.6%), fentanyl in 253 (24.6%), etomidate in 241 (23.4%), and ketamine in 145 (14.1%), as well as several others. Cases using either ketamine or propofol exhibited the fewest complications, while those using fentanyl, hydromorphone, or midazolam demonstrated the highest complication rates. Conclusions Community emergency physicians deliver safe and effective PSA over a wide variety of ages and procedures while using a broad selection of agents. [source] Sediment infiltration traps: their use to monitor salmonid spawning habitat in headwater tributaries of the Cascapédia River, QuébecHYDROLOGICAL PROCESSES, Issue 20 2005André E. Zimmermann Abstract Sediment infiltration can clog salmon nests and reduce egg survival. As a countermeasure, environmental managers often deploy infiltration traps to monitor sediment infiltration. Traps provide a repeatable means of measuring infiltration and enable comparisons to be made between sites. Results from infiltration rates measured with traps have also been used to estimate infilling rates into salmon nests. Application of these data is questionable, as the composition of the bed and the amount of fine sediment within the bed is known to affect infiltration rates. Thus, infiltration rates measured with infiltration traps may differ from the infiltration rates occurring in redd and riffle gravels. To examine how relationships between sediment infiltration rates varied between four watersheds, we continuously monitored suspended sediment transport, shear stress and infiltration rates at four sites over 5 months. We also compared infiltration rates measured with infiltration traps with changes in the hydraulic conductivity and subsurface grain size distribution of adjacent artificially constructed salmon nests and natural riffle gravels. Among the four watersheds, clear differences in sediment infiltration rates were observed. The differences correlated with the subsurface silt content but no strong relationship existed between land-use or basin physiography/geology. Despite observing an average of 30 kg m,2 of sediment finer than 2 mm being deposited in the infiltration traps during the study, no change in redd or riffle substrate was observed. If the deposition rates measured with the traps reflect the processes in redds, enough sediment would have been deposited to inhibit egg emergence. However, no reduction in egg survival to the eyed stage was observed. In summary, our results show that infiltration traps with clean gravels can be used to detect intersite differences in sediment transport regimes. Extrapolations of sediment infiltration rates measured with such collectors to estimate infiltration rates in redds or riffles is, however, flawed. Copyright © 2005 John Wiley & Sons, Ltd. [source] Herpetofaunal Diversity and Abundance in Tropical Upland Forests of Cameroon and Panama,BIOTROPICA, Issue 1 2001Ulrich Hofer ABSTRACT Two tropical upland forests, Mount Kupe in Cameroon and Bosque Protector Palo Seco in Panama, were compared in terms of herpetofaunal species richness and density of individuals. Based on rarefaction, whereby samples are standardized for abundance, Palo Seco had significantly more species of frogs and lizards. Extrapolations to total local species richness, by fitting the Michaelis,Menten equation to the species accumulation curves and by using Chao's estimator, yielded divergent results: more lizard species on Mount Kupe, and an equal number of frogs at both sites. These disparities can be accounted for by differences in evenness, which was higher in Palo Seco. Frog density was significantly higher on Mount Kupe, snake density significantly higher in Palo Seco, and lizards exhibited no density difference. Overall, the results revealed a less consistent pattern and more moderate differences than what is known from southeast Asian,-Central American comparisons. This outcome is discussed in the light of available knowledge, but quantitative data from African forests are too sparse to allow general conclusions. Se comparó la herpetofauna de dos bosques tropicales húmedos ubicados en las montañas, Mount Kupe en Camerún y Bosque Protector Palo Seco en Panamá, en relación a la riqueza especifica y la densidad de individuos. Con base en el método de rarefacción, en el cual los muestreos se estandarizan en base a su abudancia, Palo Seco presenta significativamente mas especies de anuros y lagartos. Extrapolaciones con respecto a la riqueza especifica total de los sitios, mediante un ajuste de la ecuación de Michaelis-Menten a las curvas de acumulación de especies, y utilizando el índice de Chao, produjeron resultados divergentes: más especies de lagartos en Mount Kupe, y el mismo número de especies de anuros en ambos sitios. Dichas diferencias pueden resultar de una equitatividad más alta en Palo Seco. La densidad de anuros resultó significativamente más alta en Mount Kupe, mientras que la densidad de serpientes fue significativamente más alta en Palo Seco, y no se encontró una diferencia entre k densidad de lagartos en ambos sitios. En general los resultados muestran patrones menos consistentes y diferencias mis moderadas de las que se conocen entre el Sureste de Asia y Centroamerica. Se discuten los resultados con base en la información disponible, sin embargo, la existencia de datos cuantitativos para bosques africanos es demasiado escaza como para permitir conclusiones generales. RESUMES Se comparó la herpetofauna de dos bosques tropicales húmedos ubicados en las montañas, Mount Kupe en Camerún y Bosque Protector Palo Seco en Panamá, en relación a la riqueza especifica y la densidad de individuos. Con base en el método de rarefacción, en el cual los muestreos se estandarizan en base a su abudancia, Palo Seco presenta significativamente mas especies de anuros y lagartos. Extrapolaciones con respecto a la riqueza especifica total de los sitios, mediante un ajuste de la ecuación de Michaelis-Menten a las curvas de acumulación de especies, y utilizando el índice de Chao, produjeron resultados divergentes: más especies de lagartos en Mount Kupe, y el mismo número de especies de anuros en ambos sitios. Dichas diferencias pueden resultar de una equitatividad más alta en Palo Seco. La densidad de anuros resultó significativamente más alta en Mount Kupe, mientras que la densidad de serpientes fue significativamente más alta en Palo Seco, y no se encontró una diferencia entre k densidad de lagartos en ambos sitios. En general los resultados muestran patrones menos consistentes y diferencias mis moderadas de las que se conocen entre el Sureste de Asia y Centroamerica. Se discuten los resultados con base en la información disponible, sin embargo, la existencia de datos cuantitativos para bosques africanos es demasiado escaza como para permitir conclusiones generales. [source] Ab initio Study of the Interactions between CO2 and N-Containing Organic HeterocyclesCHEMPHYSCHEM, Issue 2 2009Konstantinos D. Vogiatzis Abstract In the garden of dispersion: High-accuracy ab initio calculations are performed to determine the nature of the interactions and the most favorable geometries between CO2 and heteroaromatic molecules containing nitrogen (see figure). Dispersion forces play a key role in the stabilization of the dimer, because correlation effects represent about 50,% of the total interaction energy. The interactions between carbon dioxide and organic heterocyclic molecules containing nitrogen are studied by using high-accuracy ab initio methods. Various adsorption positions are examined for pyridine. The preferred configuration is an in-plane configuration. An electron donor,electron acceptor (EDA) mechanism between the carbon of CO2 and the nitrogen of the heterocycle and weak hydrogen bonds stabilize the complex, with important contributions from dispersion and induction forces. Quantitative results of the binding energy of CO2 to pyridine (C5H5N), pyrimidine, pyridazine, and pyrazine (C4H4N2), triazine (C3H3N3), imidazole (C3H4N2), tetrazole (CH2N4), purine (C5H4N4), imidazopyridine (C6H5N3), adenine (C5H5N5), and imidazopyridamine (C6H6N4) for the in-plane configuration are presented. For purine, three different binding sites are examined. An approximate coupled-cluster model including single and double excitations with a perturbative estimation of triple excitations (CCSD(T)) is used for benchmark calculations. The CCSD(T) basis-set limit is approximated from explicitly correlated second-order Møller,Plesset (MP2-F12) calculations in the aug-cc-pVTZ basis in conjunction with contributions from single, double, and triple excitations calculated at the CCSD(T)/6-311++G** level of theory. Extrapolations to the MP2 basis-set limit coincide with the MP2-F12 calculations. The results are interpreted in terms of electrostatic potential maps and electron density redistribution plots. The effectiveness of density functional theory with the empirical dispersion correction of Grimme (DFT-D) is also examined. [source] Improving realism of a surgery simulator: linear anisotropic elasticity, complex interactions and force extrapolationCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 3 2002Guillaume Picinbono Abstract In this article, we describe the latest developments of the minimally invasive hepatic surgery simulator prototype developed at INRIA. The goal of this simulator is to provide a realistic training test bed to perform laparoscopic procedures. Therefore, its main functionality is to simulate the action of virtual laparoscopic surgical instruments for deforming and cutting tridimensional anatomical models. Throughout this paper, we present the general features of this simulator including the implementation of several biomechanical models and the integration of two force-feedback devices in the simulation platform. More precisely, we describe three new important developments that improve the overall realism of our simulator. First, we have developed biomechanical models, based on linear elasticity and finite element theory, that include the notion of anisotropic deformation. Indeed, we have generalized the linear elastic behaviour of anatomical models to ,transversally isotropic' materials, i.e. materials having a different behaviour in a given direction. We have also added to the volumetric model an external elastic membrane representing the ,liver capsule', a rather stiff skin surrounding the liver, which creates a kind of ,surface anisotropy'. Second, we have developed new contact models between surgical instruments and soft tissue models. For instance, after detecting a contact with an instrument, we define specific boundary constraints on deformable models to represent various forms of interactions with a surgical tool, such as sliding, gripping, cutting or burning. In addition, we compute the reaction forces that should be felt by the user manipulating the force-feedback devices. The last improvement is related to the problem of haptic rendering. Currently, we are able to achieve a simulation frequency of 25,Hz (visual real time) with anatomical models of complex geometry and behaviour. But to achieve a good haptic feedback requires a frequency update of applied forces typically above 300,Hz (haptic real time). Thus, we propose a force extrapolation algorithm in order to reach haptic real time. Copyright © 2002 John Wiley & Sons, Ltd. [source] Principles of risk assessment for determining the safety of chemicals: Recent assessment of residual solvents in drugs and di(2-ethylhexyl) phthalateCONGENITAL ANOMALIES, Issue 2 2004Ryuichi Hasegawa ABSTRACT Risk assessment of chemicals is essential for the estimation of chemical safety, and animal toxicity data are typically used in the evaluation process, which consists of hazard identification, dose,response assessment, exposure assessment, and risk characterization. Hazard identification entails the collection of all available toxicity data and assessment of toxicity endpoints based on findings for repeated dose toxicity, carcinogenicity or genotoxicity and species-specificity. Once a review is compiled, the allowable lifetime exposure level of a chemical is estimated from a dose,response assessment based on several measures. For non-carcinogens and non-genotoxic carcinogens, the no-observed-adverse-effect-level (NOAEL) is divided by uncertainty factors (e.g. with environmental pollutants) or safety factors (e.g. with food additives) to derive a tolerable daily intake (TDI) or acceptable daily intake (ADI), respectively. These factors include interspecies and individual differences, duration of exposure, quality of data, and nature of toxicity such as carcinogenicity or neurotoxicity. For genotoxic carcinogens, low dose extrapolation is accomplished with mathematical modeling (e.g. linearized multistage model) from the point of departure to obtain exposure levels that will be associated with an excess lifetime cancer risk of a certain level. Data for levels of chemicals in food, water and air, are routinely used for exposure assessment. Finally, risk characterization is performed to ensure that the established ,safe' level of exposure exceeds the estimated level of actual exposure. These principles have led to the evaluation of several existing chemicals. To establish a guideline for residual solvents in medicine, the permitted daily exposure (PDE), equivalent to TDI, of N,N-dimethylformamide was derived on the basis of developmental toxicity (malformation) and of N-methylpyrrolidone on the basis of the developmental neurotoxicity. A TDI for di(2-ethylhexyl)phthalate was derived from assessment of testicular toxicity. [source] Temporal Extrapolation of PVA Results in Relation to the IUCN Red List Criterion ECONSERVATION BIOLOGY, Issue 1 2003Oskar Kindvall For a population viability analysis ( PVA) to be useful for assessing a species' threat category, the results must have been expressed as the full extinction probability function over time or at least for the three specified time frames. Often this is not the case, and extrapolations from different kinds of PVA results ( e.g., mean time to extinction ) are often necessary. By means of analytic models, we investigated the possibilities of extrapolation. Based on our results, we suggest that extrapolation is not advisable due to the huge errors that can occur. The extinction probability function is the best kind of summary statistic to use when applying criterion E, but even then the threat categorization may be ambiguous. If the extinction risk is low in the near future but increases rapidly later on, a species may be classified as vulnerable even though it is expected to become extinct within 100 years. To avoid this, we suggest that the guidelines to the IUCN Red List criteria include three reference lines that allow for interpretation of the PVA results in the context of the three threat categories within the entire period of 100 years. If the estimated extinction probability function overshoots one of these functions, the species should be classified accordingly. Resumen: Las categorías de amenaza de la lista roja de la IUCN ( críticamente en peligro, en peligro y vulnerable ) están definidos por un juego de criterios ( A-E ). El criterio E se define cuantitativamente por tres límites especificados de riesgo de extinción ( 50%, 20% y 10% ), cada uno de los cuales se asocia a un marco temporal determinado. Para poder usar el análisis de viabilidad poblacional ( PVA ) durante la evaluación de la categoría de amenaza de una especie, los resultados deben ser expresados en función de probabilidad de extinción total sobre un tiempo o al menos para los tres marcos temporales especificados. Frecuentemente este no es el caso y las extrapolaciones de diferente tipo de resultados de PVA ( tiempo promedio de extinción ) son usualmente necesarias. Por medio de modelos analíticos investigamos las posibilidades de extrapolación. En base a nuestros resultados sugerimos que la extrapolación no es recomendable debido a una enorme cantidad de errores que pueden ocurrir. La función de probabilidad de extinción es el mejor tipo de resumen estadístico a usar cuando se aplica el criterio E, pero, aún así, la categorización de amenaza puede ser ambigua. Si el riesgo de extinción es bajo en un futuro inmediato pero incrementa muy rápidamente después, una especie puede ser clasificada como vulnerable aunque se espere que se extinga dentro de los próximos 100 años. Para evitar esto, sugerimos que los lineamientos de los criterios de la Lista Roja de la UICN incluyan tres lineas de referencia que permitan la interpretación de los resultados del PVA en el contexto de las tres categorías dentro de un periodo completo de 100 años. Si la función de probabilidad de extinción estimada se extiende más allá de una de estas funciones, las especies deberán ser clasificadas según sea el caso. [source] Treatment of isolated systolic hypertension in diabetes mellitus type 2DIABETES OBESITY & METABOLISM, Issue 4 2006Ingrid Os Age-related arterial stiffness is more pronounced in diabetics compared to non-diabetics, which could explain the prevalence of isolated systolic hypertension (ISH, systolic blood pressure ,140 mmHg and diastolic blood pressure <90 mmHg) being approximately twice that of the general population without diabetes. Large-scale interventional outcome trials have also shown that diabetics usually have higher pulse pressure and higher systolic blood pressure than non-diabetics. Advanced glycation end-product formation has been implicated in vascular and cardiac complications of diabetes including loss of arterial elasticity, suggesting possibilities for new therapeutic options. With increasing age, there is a shift to from diastolic to systolic blood pressure and pulse pressure as predictors of cardiovascular disease. This may affect drug treatment as different antihypertensive drugs may have differential effects on arterial stiffness that can be dissociated from their effects on blood pressure. While thiazide diuretics are associated with little or no change in arterial stiffness despite a robust antihypertensive effect, angiotensin converting enzyme inhibitors, angiotensin II receptor blockers and calcium-channel blockers have been shown to reduce arterial stiffness. However, combination therapy is nearly always necessary to obtain adequate blood pressure control in diabetics. There are no randomized controlled trials looking specifically at treatment of ISH in diabetics. Recommendations regarding treatment of ISH in diabetes mellitus type 2 are based on extrapolation from studies in non-diabetics, post-hoc analyses and prespecified subgroup analysis in large-scale studies, and metaanalysis. These analyses have clearly demonstrated that blood pressure lowering in ISH confers improved prognosis and reduced cardiovascular and renal outcomes in both diabetics and non-diabetics. [source] New prospects for immunotherapy at diagnosis of type 1 diabetesDIABETES/METABOLISM: RESEARCH AND REVIEWS, Issue 4 2009Paolo Pozzilli Immune intervention at diagnosis of type 1 diabetes (T1D) aims to prevent or reverse the disease by blocking autoimmunity, thereby preserving/restoring ,-cell mass and function. Recent clinical trials of non-specific and of antigen-specific immune therapies have demonstrated the feasibility of modulation of islet-specific autoimmunity in patients with partial prevention of loss of insulin secretion. In a series of review articles published in this issue of the journal, some of the most promising approaches of immune intervention in T1D are presented. Here we outline the rationale of such interventions and future prospects in this area. Copyright © 2009 John Wiley & Sons, Ltd. Insulin therapy in type 1 diabetes (T1D) rescues the patient from a certain death but not cure the disease. The goal of any therapeutic intervention in T1D is the preservation of insulin-secreting cells; this is achieved by the abrogation of pathogenic reactivity to beta cell autoantigens while preserving full capacity to generate a normal immune response against foreign antigens. Although several therapeutic candidates have been investigated in experimental models of T1D many of which showed promising results, a successful extrapolation of these findings to human T1D has proved to be difficult. In part, this failure results from the considerable disease heterogeneity associated with diverse genetic and non-genetic disease determinants and the spectrum of clinical phenotype at diagnosis. Thus, a younger age at onset is associated with stronger genetic susceptibility, more intense immune response to ,-cell antigens, shorter duration of symptoms, more severe metabolic derangement at diagnosis and a more rapid rate of ,-cell-destruction 1,3. Therefore, designing therapies that would be effective in all clinical settings is definitely challenging. In this issue five different approaches are discussed ranging from antigen-specific therapies [DiaPep277 and glutamic acid decarboxylase(GAD)], to non-antigen-specific immunoregulation (anti-CD3) and to anti-inflammatory (anti-IL1 receptor antagonist). These approaches are currently being tested in large international multicenter trials, and all of them use very similar outcome in terms of a beneficial effect (C-peptide secretion as evidence of a therapeutic effect on restoration of ,-cell function). The authors have been asked to follow a similar format in presenting their approaches so that the reader can easily compare them in terms of rationale and therapeutic goals. [source] Diabetes trends in EuropeDIABETES/METABOLISM: RESEARCH AND REVIEWS, Issue S3 2002Philippe Passa Abstract Estimates and projections suggest an epidemic expansion of diabetes incidence and prevalence in Europe. To evaluate trends in type 1 and type 2 diabetes in seven European countries (Finland, Denmark, the UK, Germany, France, Spain, and Italy), a variety of information is available, including population-based studies on small or large cohorts of subjects representative of the general population in a particular country, European co-operative studies, and sales figures for insulin and oral hypoglycemic agents that allow extrapolation of the number of pharmacologically treated diabetic patients. The incidence of type 1 diabetes in young people is increasing in most European countries, as is its prevalence in all age groups. Type 2 diabetes is the major contributor to the epidemic rise in diabetes. From 1995 to 1999, the prevalence of type 2 diabetes increased considerably, particularly in the UK, Germany, and France. Costs of ambulatory and in-hospital diabetic care (including antidiabetic, antihypertensive, and hypolipidemic agents) have increased even more rapidly than has the number of affected patients. Diabetes trends in Europe are alarming; health care professionals involved in diabetes care must be made aware of these detrimental trends, and health care delivery to patients with diabetes must be improved. Copyright © 2002 John Wiley & Sons, Ltd. [source] Error estimation of closed-form solution for annual rate of structural collapseEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 15 2008Brendon A. Bradley Abstract With the increasing emphasis of performance-based earthquake engineering in the engineering community, several investigations have been presented outlining simplified approaches suitable for performance-based seismic design (PBSD). Central to most of these PBSD approaches is the use of closed-form analytical solutions to the probabilistic integral equations representing the rate of exceedance of key performance measures. Situations where such closed-form solutions are not appropriate primarily relate to the problem of extrapolation outside of the region in which parameters of the closed-form solution are fit. This study presents a critical review of the closed-form solution for the annual rate of structural collapse. The closed-form solution requires the assumptions of lognormality of the collapse fragility and power model form of the ground motion hazard, of which the latter is more significant regarding the error of the closed-form solution. Via a parametric study, the key variables contributing to the error between the closed-form solution and solution via numerical integration are illustrated. As these key variables cannot be easily measured, it casts doubt on the use of such closed-form solutions in future PBSD, especially considering the simple and efficient nature of using direct numerical integration to obtain the solution. Copyright © 2008 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||||||||||||||||||||||||||||||||||||||