Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

A yield architecture framework to explain adaptation of pearl millet to environmental stress

Functional knowledge of the physiological basis of crop adaptation to stress is a prerequisite for exploiting specific adaptation to stress environments in breeding programs. This paper presents an analysis of yield components for pearl millet, to explain the specific adaptation of local landraces to stress environments in Rajasthan, India. Six genotypes, ranging from high-tillering traditional landraces to low-tillering open-pollinated modern cultivars, were grown in 20 experiments, covering a range of nonstress and drought stress patterns. In each experiment, yield components (particle number, grain number, 100 grain mass) were measured separately for main shoots, basal tillers, and nodal tillers. Under optimum conditions, landraces had a significantly lower grain yield than the cultivars, but no significant differences were observed at yield levels around 1 ton ha(-1). This genotype x environment interaction for grain yield was due to a difference in yield strategy, where landraces aimed at minimising the risk of a crop failure under stress conditions, and modem cultivars aimed at maximising yield potential under optimum conditions. A key aspect of the adaptation of landraces was the small size of the main shoot panicle, as it minimised (1) the loss of productive tillers during stem elongation; (2) the delay in anthesis if mid-season drought occurs; and (3) the reduction in panicle productivity of the basal tillers under stress. In addition, a low investment in structural panicle weight, relative to vegetative crop growth rate, promoted the production of nodal tillers, providing a mechanism to compensate for reduced basal tiller productivity if stress occurred around anthesis. A low maximum 100 grain mass also ensured individual grain mass was little affected by environmental conditions. The strategy of the high-tillering landraces carries a yield penalty under optimum conditions, but is expected to minimise the risk of a crop failure, particularly if mid-season drought stress occurs. The yield architecture of low-tillering varieties, by contrast, will be suited to end-of-season drought stress, provided anthesis is early. Application of the above adaptation mechanisms into a breeding program could enable the identification of plant types that match the prevalent stress patterns in the target environments. (C) 2003 E.J. van Oosterom. Published by Elsevier Science B.V. All rights reserved.