Generalized rayleigh principle and its applications

In this paper, we mainly deal with cigenvalue problems of non-self-adjoint operator. To begin with, the generalized Rayleigh variational principle, the idea of which was due to Morse and Feshbach, is examined in detail and proved more strictly in mathematics. Then, other three equivalent formulations of it are presented. While applying them to approximate calculation we find the condition under which the above variational method can be identified as the same with Galerkin's one. After that we illustrate the generalized variational principle by considering the hydrodynamic stability of plane Poiseuille flow and Bénard convection. Finally, the Rayleigh quotient method is extended to the cases of non-self-adjoint matrix in order to determine its strong eigenvalne in linear algebra.

Practical applications of the likelihood, time transcendence and metadata in virtual models of heritage elements

Contributed to: III Bienal de Restauración Monumental: "Sobre la des-restauración" (Sevilla, Spain, Nov 23-25, 2006)

Depletion of the heaviest stable N isotope is associated with NH4 +/NH3 toxicity in NH4 +-fed plants

Background: In plants, nitrate (NO(3)(-)) nutrition gives rise to a natural N isotopic signature (delta(15)N), which correlates with the delta(15)N of the N source. However, little is known about the relationship between the delta(15)N of the N source and the (14)N/(15)N fractionation in plants under ammonium (NH(4)(+)) nutrition. When NH(4)(+) is the major N source, the two forms, NH(4)(+) and NH(3), are present in the nutrient solution. There is a 1.025 thermodynamic isotope effect between NH(3) (g) and NH(4)(+)(aq) which drives to a different delta(15)N. Nine plant species with different NH(4)(+)-sensitivities were cultured hydroponically with NO(3)(-) or NH(4)(+) as the sole N sources, and plant growth and delta(15)N were determined. Short-term NH(4)(+)/NH(3) uptake experiments at pH 6.0 and 9.0 (which favours NH(3) form) were carried out in order to support and substantiate our hypothesis. N source fractionation throughout the whole plant was interpreted on the basis of the relative transport of NH(4)(+) and NH(3). -- Results: Several NO(3)(-)-fed plants were consistently enriched in (15)N, whereas plants under NH(4)(+) nutrition were depleted of (15)N. It was shown that more sensitive plants to NH(4)(+) toxicity were the most depleted in (15)N. In parallel, N-deficient pea and spinach plants fed with (15)NH(4)(+) showed an increased level of NH(3) uptake at alkaline pH that was related to the (15)N depletion of the plant. Tolerant to NH(4)(+) pea plants or sensitive spinach plants showed similar trend on (15)N depletion while slight differences in the time kinetics were observed during the initial stages. The use of RbNO(3) as control discarded that the differences observed arise from pH detrimental effects. -- Conclusions: This article proposes that the negative values of delta(15)N in NH(4)(+)-fed plants are originated from NH(3) uptake by plants. Moreover, this depletion of the heavier N isotope is proportional to the NH(4)(+)/NH(3) toxicity in plants species. Therefore, we hypothesise that the low affinity transport system for NH(4)(+) may have two components: one that transports N in the molecular form and is associated with fractionation and another that transports N in the ionic form and is not associated with fractionation.

Sediment budget: principals and applications

The framework of sediment budget concepts provides a formalized procedure to account for the various components of sediment flux and the changes of volume that occur within a given region. Sediment budget methodology can be useful in a number of coastal engineering and research applications, including: inferring the amount of onshore sediment transport for a nearshore system that contains an "excess of sediment", determining sediment deficits to downdrift beaches as a result of engineering works at navigational entrances, evaluating the performance of a beach nourishment project, inferring the distribution of longshore sediment transport across the surf zone, etc. This chapter reviews briefly the governing equations for sediment budget calculations, considers various measurement and other bases for determining the sediment flux components necessary to apply the sediment budget concept and finally for illustration purposes, applies the sediment budget concept to several examples. (PDF contains 52 pages.)

Responses of Hyalella azteca and Ceridaphnia dubia to reservoir sediments following Chelated Copper Herbicide Applications

In response to nuisance growths of algae and vascular plants, such as dioecious hydrilla ( Hydrilla verticillata L.f. Royle), copper formulations have been applied in lakes and reservoirs for a number of years. Concerns have arisen regarding the long-term consequences of copper applications and those concerns have appropriately focused on sediment residues. In this study, we evaluated the toxicity of sediments from treated (for a decade) and untreated areas in Lake Murray, South Carolina and estimated the capacity of those sediments to bind additional copper. Two sentinel aquatic invertebrates, Hyalella azteca Saussure and Ceriodaphnia dubia Richard, were used to measure residual toxicity of treated and untreated sediments from the field and after laboratory amendments. (PDF has 5 pages.)