Modification to the Hardisty equation, regarding the relationship between sediment transport rate and particle size

Bagnold-type bed-load equations are widely used for the determination of sediment transport rate in marine environments. The accuracy of these equations depends upon the definition of the coefficient k(1) in the equations, which is a function of particle size. Hardisty (1983) has attempted to establish the relationship between k(1) and particle size, but there is an error in his analytical result. Our reanalysis of the original flume data results in new formulae for the coefficient. Furthermore, we found that the k(1) values should be derived using u(1) and u(1cr) data; the use of the vertical mean velocity in flumes to replace u(1) will lead to considerably higher k(1) values and overestimation of sediment transport rates.

The nonlinear evolution equation on the shallow water wave

Based on the variation principle, the nonlinear evolution model for the shallow water waves is established. The research shows the Duffing equation can be introduced to the evolution model of water wave with time.

Asymptotic periodicity of the Volterra equation with infinite delay

For some species, hereditary factors have great effects on their population evolution, which can be described by the well-known Volterra model. A model developed is investigated in this article, considering the seasonal variation of the environment, where the diffusive effect of the population is also considered. The main approaches employed here are the upper-lower solution method and the monotone iteration technique. The results show that whether the species dies out or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the hereditary effects. The evolution of the population may show asymptotic periodicity, provided a certain condition is satisfied for the above factors. (c) 2006 Elsevier Ltd. All rights reserved.

Asymptotic weighted-periodicity of the impulsive parabolic equation with time delay

The main aim of this paper is to investigate the effects of the impulse and time delay on a type of parabolic equations. In view of the characteristics of the equation, a particular iteration scheme is adopted. The results show that Under certain conditions on the coefficients of the equation and the impulse, the solution oscillates in a particular manner-called "asymptotic weighted-periodicity".

Traveling wave front for the Fisher equation on an infinite band region

Instead of discussing the existence of a one-dimensional traveling wave front solution which connects two constant steady states, the present work deals with the case connecting a constant and a nonhomogeneous steady state on an infinite band region. The corresponding model is the well-known Fisher equation with variational coefficient and Dirichlet boundary condition. (c) 2006 Elsevier Ltd. All rights reserved.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

Modeling gross primary production of alpine ecosystems in the Tibetan Plateau using MODIS images and climate data

The eddy covariance technique provides measurements of net ecosystem exchange (NEE) Of CO2 between the atmosphere and terrestrial ecosystems, which is widely used to estimate ecosystem respiration and gross primary production (GPP) at a number Of CO2 eddy flux tower sites. In this paper, canopy-level maximum light use efficiency, a key parameter in the satellite-based Vegetation Photosynthesis Model (VPM), was estimated by using the observed CO2 flux data and photosynthetically active radiation (PAR) data from eddy flux tower sites in an alpine swamp ecosystem, an alpine shrub ecosystem and an alpine meadow ecosystem in Qinghai-Tibetan Plateau, China. The VPM model uses two improved vegetation indices (Enhanced Vegetation Index (EVI), Land Surface Water Index (LSWI)) derived from the Moderate Resolution Imaging Spectral radiometer (MODIS) data and climate data at the flux tower sites, and estimated the seasonal dynamics of GPP of the three alpine grassland ecosystems in Qinghai-Tibetan Plateau. The seasonal dynamics of GPP predicted by the VPM model agreed well with estimated GPP from eddy flux towers. These results demonstrated the potential of the satellite-driven VPM model for scaling-up GPP of alpine grassland ecosystems, a key component for the study of the carbon cycle at regional and global scales. (c) 2006 Elsevier Inc. All rights reserved.

Molecular phylogeny, recent radiation and evolution of gross morphology of the rhubarb genus Rheum (Polygonaceae) inferred from chloroplast DNA trnL-F sequences

Background and Aims Rheum, a highly diversified genus with about 60 species, is mainly confined to the mountainous and desert regions of the Qinghai-Tibetan plateau and adjacent areas. This genus represents a good example of the extensive diversification of the temperate genera in the Qinghai-Tibetan plateau, in which the forces to drive diversification remain unknown. To date, the infrageneric classification of Rheum has been mainly based on morphological characters. However, it may have been subject to convergent evolution under habitat pressure, and the systematic position of some sections are unclear, especially Sect. Globulosa, which has globular inflorescences, and Sect. Nobilia, which has semi-translucent bracts. Recent palynological research has found substantial contradictions between exine patterns and the current classification of Rheum. Two specific objectives of this research were (1) to evaluate possible relationships of some ambiguous sections with a unique morphology, and (2) to examine possible occurrence of the radiative speciation with low genetic divergence across the total genus and the correlation between the extensive diversification time of Rheum and past geographical events, especially the recent large-scale uplifts of the Qinghai-Tibetan Plateau.Methods The chloroplast DNA trnL-F region of 29 individuals representing 26 species of Rheum, belonging to seven out of eight sections, was sequenced and compared. The phylogenetic relationships were further constructed based on the sequences obtained.Key Results Despite the highly diversified morphology, the genetic variation in this DNA fragment is relatively low. The molecular phylogeny is highly inconsistent with gross morphology, pollen exine patterns and traditional classifications, except for identifying all samples of Sect. Palmata, three species of Sect. Spiciformia and a few species of Sect. Rheum as corresponding monophyletic groups. The monotypic Sect. Globulosa showed a tentative position within the clade comprising five species of Sect. Rheum. All of the analyses revealed the paraphyly of R. nobile and R. alexandrae, the only two species of Sect. Nobilia circumscribed by the possession of large bracts. The crude calibration of lineages based on trnL-F sequence differentiation implied an extensive diversification of Rheum within approx. 7 million years.Conclusions Based on these results, it is suggested that the rich geological and ecological diversity caused by the recent large-scale uplifts of the Qinghai-Tibetan Plateau since the late Tertiary, coupled with the oscillating climate of the Quaternary stage, might have promoted rapid speciation in small and isolated populations, as well as allowing the fixation of unique or rare morphological characters in Rheum. Such a rapid radiation, combined with introgressive hybridization and reticulate evolution, may have caused the transfer of cpDNA haplotypes between morphologically dissimilar species, and might account for the inconsistency between morphological classification and molecular phylogeny reported here.

Seasonal patterns of gross primary production and ecosystem respiration in an alpine meadow ecosystem on the Qinghai-Tibetan Plateau

We measured the net ecosystem CO2 exchange (NEE) in an alpine meadow ecosystem (latitude 37degrees29'-45'N, longitude 101degrees12'-23'E, 3250 m above sea level) on the Qinghai-Tibetan Plateau throughout 2002 by the eddy covariance method to examine the carbon dynamics and budget on this unique plateau. Diurnal changes in gross primary production (GPP) and ecosystem respiration (R-e) showed that an afternoon increase of NEE was highly associated with an increase of R-e. Seasonal changes in GPP corresponded well to changes in the leaf area index and daily photosynthetic photon flux density. The ratio of GPP/R-e was high and reached about 2.0 during the peak growing season, which indicates that mainly autotrophic respiration controlled the carbon dynamics of the ecosystem. Seasonal changes in mean GPP and R-e showed compensatory behavior as reported for temperate and Mediterranean ecosystems, but those of GPP(max) and R-emax were poorly synchronized. The alpine ecosystem exhibited lower GPP (575 g C m(-2) y(-1)) than, but net ecosystem production (78.5 g C m(-2) y(-1)) similar to, that of subalpine forest ecosystems. The results suggest that the alpine meadow behaved as a CO2 sink during the 1-year measurement period but apparently sequestered a rather small amount of C in comparison with similar alpine ecosystems.

An empirical equation for the calculation of retention time with extrapolation of temperature in gas chromatography

An empirical equation is proposed to accurately correlate isothermal data over a wide range of temperature With the equation ln k = A* + B*/T-lambda the retention times of different solutes tested on OV-101, SE-54 and PEG 20M capillary columns have been achieved even when lambda is assigned a constant value of 1.7 Comparison with ln k = A + B/T and in k = c + d/T+ h/T-2, shows that the proposed equation is of higher accuracy and is applicable to extrapolation calculation, especially from data at high temperature to those at low temperature. Parameters A* and B* as well as A and B are also discussed. The linear correlation of A* and B* is weaker than that of A and B.