Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

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.

Dynamics of Gray Matter Loss in Alzheimer's Disease

We detected and mapped a dynamically spreading wave of gray matter loss in the brains of patients with Alzheimer's disease (AD). The loss pattern was visualized in four dimensions as it spread over time from temporal and limbic cortices into frontal and occipital brain regions, sparing sensorimotor cortices. The shifting deficits were asymmetric (left hemisphere >right hemisphere) and correlated with progressively declining cognitive status ( p 15% loss). The maps distinguished different phases of AD and differentiated AD from normal aging. Local gray matter loss rates (5.3 +/- 2.3% per year in AD v 0.9 +/- 0.9% per year in controls) were faster in the left hemisphere ( p < 0.029) than the right. Transient barriers to disease progression appeared at limbic/frontal boundaries. This degenerative sequence, observed in vivo as it developed, provides the first quantitative, dynamic visualization of cortical atrophic rates in normal elderly populations and in those with dementia.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.

Nitrogen cycling in degraded Leucaena leucocephala-Brachiaria decumbens pastures on an acid infertile soil in south-east Queensland, Australia

A grazing trial was conducted to quantify N cycling in degraded Leucaena leucocephala (leucaena)-Brachiaria decumbens (signal grass) pastures grown on an acid, infertile, podzolic soil in south-east Queensland. Nitrogen accumulation and cycling in leucaena-signal grass pastures were evaluated for 9 weeks until all of the leucaena on offer (mean 600 kg edible dry matter (EDM)/ha, 28% of total pasture EDM) was consumed. Nitrogen pools in the grass, leucaena, soil, cattle liveweight, faeces and urine were estimated. The podzolic soil (pH 4.8-5.9) was found to be deficient in P, Ca and K. Leucaena leaf tissues contained deficient levels of N, P and Ca. Grass tissues were deficient in N and P. Grazing was found to cycle 65% of N on offer in pasture herbage. However, due to the effect of the plant nutrient imbalances described above, biological N fixation by leucaena contributed only 15 kg/ha N to the pasture system over the 9-month regrowth period, of which 13 kg/ha N was cycled. Cattle retained 1.8 kg/ha N (8% of total N consumed) in body tissue and the remainder was excreted in dung and urine in approximately equal proportions. Mineral soil N concentrations did not change significantly (-3.5 kg/ha N) over the trial period. The ramifications of grazing and fertiliser management strategies, and implications for pasture rundown and sustainability are discussed.

Unsaturated diffusivity functions for concrete derived from NMR images

Deterioration of concrete or reinforcing steel through excessive contaminant concentration is often the result of repeated wetting and drying cycles. At each cycle, the absorption of water carries new contaminants into the unsaturated concrete. Nuclear Magnetic Resonance (NMR) is used with large concrete samples to observe the shape of the wetting profile during a simple one-dimensional wetting process. The absorption of water by dry concrete is modelled by a nonlinear diffusion equation with the unsaturated hydraulic diffusivity being a strongly nonlinear function of the moisture content. Exponential and power functions are used for the hydraulic diffusivity and corresponding solutions of the diffusion equation adequately predict the shape of the experimental wetting profile. The shape parameters, describing the wetting profile, vary little between different blends and are relatively insensitive to subsequent re-wetting experiments allowing universal parameters to be suggested for these concretes.

Nitrate retention under sugarcane in wet tropical Queensland deep soil profiles

Nitrate leaching below the crop root-zone in variable charge soils may be adsorbed at anion exchange sites, thereby temporarily reducing the risk of contamination of water bodies. The objectives of this study were (i) to investigate whether nitrate adsorption, accumulation, and retention in the Johnstone River Catchment of Far North Queensland wet tropics is widespread; (ii) to assess the capacity of soil in the Johnstone River Catchment to retain nitrate; and (iii) to deduce the consequences of nitrate adsorption/desorption on contamination of water bodies. Soil cores ranging from 8 to 12.5 m depth were taken from 28 sites across the catchment, representing 9 Ferrosol soil types under sugarcane (Saccharum officinarum-S) cultivation for at least 50 years and from rainforest. The cores were segmented at 0.5-m depth increments and subsamples were analysed for nitrate-N, cation and anion exchange capacities, pH, exchangeable cations (Ca, Mg, K, Na), soil organic C, electrical conductivity, sulfate-S, and chloride. Nitrate-N concentration under sugarcane ranged from 0 to 72.5 mg/kg, compared with 0 to 0.31 mg/kg under rainforest, both Pin Gin soils. The average N load in 1-12 m depth across 19 highly oxidic profiles of the Pin Gin soil series was 1550 kg/ha, compared with 185 kg/ha under 8 non-Pin Gin soils and 11 kg/ha in rainforest on a Pin Gin soil. Most of the nitrate retention was observed at depth of 2-12 m, particularly at 4-10 m, indicating that the accumulation was well below the crop root-zone. The average maximum potential nitrate retention capacity was 10.8 t/ha for the Pin Gin and 4.7 t/ha for the non-Pin Gin soil. Compared with the current N load, the soils still possess a large capacity to adsorb and retain nitrate in profiles. Retention of large quantities of the leached nitrate deep in most of the profiles has reduced the risk of contamination of water bodies. However, computations show that substantial quantities of the nitrate leached below the root-zone were not adsorbed and remain unaccounted for. This unaccounted nitrate might have entered both on- and off-site water bodies and/or have been denitrified.

Effects of soil water availability on water use efficiency of Eucalyptus cloeziana and Eucalyptus argophloia plants

Effects of soil water availability on transpiration efficiency (WUET), instantaneous water use efficiency (WUEi) and carbon isotope composition (delta(13)C) were investigated in 7-month-old plants of humid coastal (Gympie) and dry inland ( Hungry Hills) provenances of Eucalyptus cloeziana F. Muell. and in a dry inland provenance of E. argophloia Blakely (Chinchilla), supplied with 100 (W-100), 70 (W-70) and 50% (W-50) of their water requirements. At W-100, WUET of the three provenances were not significantly different but as available soil moisture decreased, E. argophloia produced greater biomass and demonstrated significantly higher WUET than either E. cloeziana provenance. Midday WUEi was not significantly affected by watering regime within each provenance but was lowest in E. argophloia. A decrease in soil water availability caused a consistent increase in delta(13)C values in all three provenances; however, delta(13)C values of E. argophloia in all three water regimes were significantly lower than those of E. cloeziana provenances, which did not differ significantly from each other. For all three provenances, delta(13)C was not correlated with WUEi but height and root collar diameter were negatively correlated to delta(13)C. There was little evidence of differences in delta(13)C, WUET and WUEi between E. cloeziana provenances but clear differences between E. cloeziana and E. argophloia. The high WUET, low WUEi and low delta(13)C for E. argophloia may have implications in the selection of Eucalyptus provenances for commercial forestry in low-rainfall regions.

A reduced load approximation accounting for link interactions in a loss network

This paper is concerned with evaluating the performance of loss networks. Accurate determination of loss network performance can assist in the design and dimen- sioning of telecommunications networks. However, exact determination can be difficult and generally cannot be done in reasonable time. For these reasons there is much interest in developing fast and accurate approximations. We develop a reduced load approximation that improves on the famous Erlang fixed point approximation (EFPA) in a variety of circumstances. We illustrate our results with reference to a range of networks for which the EFPA may be expected to perform badly.

Simulation supplements field studies to determine no-till dryland corn population recommendations for semiarid western Nebraska

In a 2-yr multiple-site field study conducted in western Nebraska during 1999 and 2000, optimum dryland corn (Zea mays L.) population varied from less than 1.7 to more than 5.6 plants m(-2), depending largely on available water resources. The objective of this study was to use a modeling approach to investigate corn population recommendations for a wide range of seasonal variation. A corn growth simulation model (APSIM-maize) was coupled to long-term sequences of historical climatic data from western Nebraska to provide probabilistic estimates of dryland yield for a range of corn populations. Simulated populations ranged from 2 to 5 plants m(-2). Simulations began with one of three levels of available soil water at planting, either 80, 160, or 240 mm in the surface 1.5 m of a loam soil. Gross margins were maximized at 3 plants m(-2) when starting available water was 160 or 240 mm, and the expected probability of a financial loss at this population was reduced from about 10% at 160 mm to 0% at 240 mm. When starting available water was 80 mm, average gross margins were less than $15 ha(-1), and risk of financial loss exceeded 40%. Median yields were greatest when starting available soil water was 240 mm. However, perhaps the greater benefit of additional soil water at planting was reduction in the risk of making a financial loss. Dryland corn growers in western Nebraska are advised to use a population of 3 plants m(-2) as a base recommendation.

A technique to assess small-scale heterogeneity of chemical properties in soil aggregates

A new method is presented which allows the separation of the soil aggregate exterior from the aggregate core. The method employs a combination of aggregate freezing with rapid separation of aggregate exteriors using ultrasonic energy. The factors influencing the thickness of the removed aggregate surface layer include water content of the aggregate prior to freezing, temperature difference between that of the frozen aggregate and that of the liquid it is submerged in during sonification, sonification time and energy, and the type of the immersion liquid. The success of the method and the thickness of the removed aggregate surface were examined using barium ( Ba2+) as a tracer. Barium ( as BaCl2) is rapidly absorbed by soil and is present at only very low levels in natural soils. Surface layers of 0.2 - 0.4 cm thickness were successfully removed from aggregates of 1 - 4 cm diameter. Two examples are given from soils in northern NSW to demonstrate the occurrence of small- scale heterogeneity in soil chemical properties. Compared with the surface fraction, a 4 - 7% higher calcium concentration was found in the core fraction of a clay loam soil ( Dermosol). Conversely, on a cracking clay soil ( Vertosol), atrazine concentration was around 15 times greater in the aggregate surface fractions compared with core fractions. Compared with the traditional estimation of soil chemical properties on homogenised bulk soil samples, it is suggested that separate analysis of aggregate surface and core fractions could provide useful additional information on the relationships between soil properties and environmental responses.