Breeding for improved nitrogen use efficiency in oilseed rape

Oilseed rape has a high requirement for nitrogen (N) fertiliser relative to its seed yield. This paper uses published and unpublished work to explore the extent to which the N use efficiency (seed yield ÷ N supply) of oilseed rape could be improved without reducing seed yield. It was estimated that if the concentration of N in the stem and pod wall at crop maturity could be reduced from 1.0 to 0.6%, the root length density increased to 1 cm/cm3 to 100 cm soil depth and the post flowering N uptake increased by 20 kg N/ha then the fertiliser requirement could be reduced from 191 to 142 kg N/ha and the N use efficiency could be increased from 15.2 to 22.4 kg of seed dry matter per kg N. Genetic variation was found for all of the traits that were estimated to be important for N use efficiency. This indicates that there is significant scope for plant breeders to reduce N use efficiency in oilseed rape

River monitoring from satellite radar altimetry in the Zambezi River basin

Satellite radar altimetry can be used to monitor surface water levels from space. While current and past altimetry missions were designed to study oceans, retracking the waveforms returned over land allows data to be retrieved for smaller water bodies or narrow rivers. The objective of this study is the assessment of the potential for river monitoring from radar altimetry in terms of water level and discharge in the Zambezi River basin. Retracked Envisat altimetry data were extracted over the Zambezi River basin using a detailed river mask based on Landsat imagery. This allowed for stage measurements to be obtained for rivers down to 80m wide with an RMSE relative to in situ levels of 0.32 to 0.72m at different locations. The altimetric levels were then converted to discharge using three different methods adapted to different data-availability scenarios: first with an in situ rating curve available, secondly with one simultaneous field measurement of cross-section and discharge, and finally with only historical discharge data available. For the two locations at which all three methods could be applied, the accuracies of the different methods were found to be comparable, with RMSE values ranging from 4.1 to 6.5% of the mean annual in situ gauged amplitude for the first method and from 6.9 to 13.8% for the second and third methods. The precision obtained with the different methods was analyzed by running Monte Carlo simulations and also showed comparable values for the three approaches with standard deviations found between 5.7 and 7.2% of the mean annual in situ gauged amplitude for the first method and from 8.7 to 13.0% for the second and third methods

Coincidence of length spectra does not imply isospectrality

Penrose--Lifshits mushrooms are planar domains coming in nonisometric pairs with the same geodesic length spectrum. Recently S. Zelditch raised the question whether such billiards also have the same eigenvalue spectrum for the Dirichlet Laplacian (conjecturing ``no''). Here we show that generically (in the class of smooth domains) the two members of a mushroom pair have different spectra.Comment: 8 pages, 5 figure

Invariant sets for discontinuous parabolic area-preserving torus maps

We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter family of maps, the set of noninvertible maps is open and dense. For cases where the entries in the matrix are rational we show that the maximal invariant set has positive Lebesgue measure and we give bounds on the measure. For several examples we find expressions for the measure of the invariant set but we leave open the question as to whether there are parameters for which this measure is zero.Comment: 19 pages in Latex (with epsfig,amssymb,graphics) with 5 figures in eps; revised version: section 2 rewritten, new example and picture adde

Heat kernel coefficients for chiral bag boundary conditions

We study the asymptotic expansion of the smeared L2-trace of fexp(-tP^2) where P is an operator of Dirac type, f is an auxiliary smooth smearing function which is used to localize the problem, and chiral bag boundary conditions are imposed. Special case calculations, functorial methods and the theory of zeta and eta invariants are used to obtain the boundary part of the heat-kernel coefficients a1 and a2.Comment: Published in J. Phys. A38, 2259-2276 (2005). Record without file already exists on the SLAC recor

Classification of phase transitions in small systems

We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the right critical indices. We apply this classification scheme to Bose-Einstein condensates in a harmonic trap as an example of a higher order phase transitions in a finite system and to small Ar clusters.Comment: 12 pages, 4 figures, accepted for publication in Phys. Rev. Let

Classical Dynamics of the Time-Dependent Elliptical Billiard

In this work we study the nonlinear dynamics of the static and the driven ellipse. In the static case, we find numerically an asymptotical algebraic decay for the escape of an ensemble of non-interacting particles through a small hole due to the integrable structure of the phase space of the system. Furthermore, for a certain hole position a saturation value in the decay that can be tuned arbitrarily by varying the eccentricity of the ellipse is observed and explained. When applying harmonic boundary oscillations this saturation value caused by librator type orbits is gradually destroyed via two fundamental processes which are discussed in detail. As a result, an amplitude dependent emission rate is obtained in the long time behavior of the decay, suggesting that the driven elliptical billiard can be used as a controllable source of particles

Deceptive signals of phase transitions in small magnetic clusters

We present an analysis of the thermodynamic properties of small transition metal clusters and show how the commonly used indicators of phase transitions like peaks in the specific heat or magnetic susceptibility can lead to deceptive interpretations of the underlying physics. The analysis of the distribution of zeros of the canonical partition function in the whole complex temperature plane reveals the nature of the transition. We show that signals in the magnetic susceptibility at positive temperatures have their origin at zeros lying at negative temperatures.Comment: 4 pages, 5 figures, revtex4, for further information see http://www.smallsystems.d