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.

Semisolid microstructural evolution of AlSi7Mg alloy during partial remelting

Different as-cast microstructures of an AlSi7Mg alloy were produced by controlling the solidification conditions. The as-cast grain size ranged from 1.4 mm to 160 mum and the morphology varied from dendritic to rosette-like to globular. The as-cast materials were then partially remelted and isothermally held at 580degreesC for microstructure evolution. The final microstructure depended on the initial as-cast microstructure and the isothermal holding time. After partial remelting and isothermal holding, coarse-grained dendritic structures were not able to evolve to a globular structure, while structures with medium sized dendritic grains evolved to a globular structure with a relatively large particle size after a long isothermal holding time. Fine-grained structures evolved to well-rounded globular grains within times ranging front 10 min to 5 min as the dendritic nature of the starting structure diminished. An empirical equation has been established to describe the relationship between the evolved microstructure and the as-cast microstructure. (C) 2003 Elsevier B.V. All rights reserved.

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Partial regularity of minimizers of a functional involving forms and maps

We discuss the partial regularity of minimizers of energy functionals such as (1)/(p)integral(Omega)[sigma(u)dA(p) + (1)/(2)delu(2p)]dx, where u is a map from a domain Omega is an element of R-n into the m-dimensional unit sphere of Rm+1 and A is a differential one-form in Omega.

Gelatinisation of starch in mixtures of sugars. II. Application of differential scanning calorimetry

Differential scanning calorimetry was used to investigate the effect of mixtures of glucose and fructose, and five types of honeys on starch gelatinisation. At a 1:1 starch:water ratio, glucose generally increased the enthalpy (DeltaH(gel)) and temperatures (T-onset, T-peak and T-end) of gelatinisation more than fructose. Upon mixing, DeltaH(gel) of the low-temperature endotherm decreased in comparison to the sole sugars, but was fairly constant (7.7 +/- 0.33 J/g dry starch). DeltaH(gel) of the high-temperature endotherm increased with the fructose content. For both endotherms, the gelatinisation temperatures were unchanged (CV less than or equal to 3%) for the mixtures. With the honeys (moisture, 14.9-18.0%; fructose, 37.2-44.0%; glucose, 28.3-31.9%) added at 1.1-4.4 g per g dry starch, the enthalpy and temperatures of gelatinisation did not vary significantly (CV less than or equal to 6%). Typical thermograms are presented, and the results are interpreted in the light of the various proposed mechanisms for starch gelatinisation in sugar-water systems, total sugar content and possible sugar-sugar interactions. The thermograms were broader in the presence of the sugars and honeys, and a biphasic character was consistently exhibited. The application of an exponential equation to the gelatinisation temperatures of the starch-honey mixtures revealed an opposing influence of fructose and glucose during gelatinisation. The mechanism of starch gelatinisation may be better understood if techniques could be perfected to quantify breakage and formation of hydrogen bonds in the starch granules, and suggested techniques are discussed. (C) 2004 Elsevier Ltd. All rights reserved.

Specific heat capacity of Australian honeys from 35 to 165C as a function of composition using differential scanning calorimetry

Modulated temperature differential scanning calorimetry was used to investigate the specific heat capacity (C-p) of 10 Australian honeys within the processing and handling temperatures. The values obtained were found to be different from the literature values at certain temperatures, and are not predictable by the additive model. The C-p of each honey exhibited a cubic relationship (P < 0.001) with the temperature (T, C). In addition, the moisture (M, %), fructose (F, %) and glucose (G, %) contents of the honeys influenced their C-p. The following equation (r(2) = 0.92) was proposed for estimating C-p of honey, and is recommended for use in the honey industry and in research: C = 996.7 + 1.4 x 10(-3)T + 5.6 x 10(-5)T(2) - 2.4 x 10(-7)T(3) - 56.5M - 25.8F - 31.0G + 1.5(M * F) + 1.8(M * G) + 0.8(F * G) - 4.6 x 10(-2) (M * F * G).

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Student Difficulties with units in differential equations in modelling contexts

First-year undergraduate engineering students' understanding of the units of factors and terms in first-order ordinary differential equations used in modelling contexts was investigated using diagnostic quiz questions. Few students appeared to realize that the units of each term in such equations must be the same, or if they did, nevertheless failed to apply that knowledge when needed. In addition, few students were able to determine the units of a proportionality factor in a simple equation. These results indicate that lecturers of modelling courses cannot take this foundational knowledge for granted and should explicitly include it in instruction.

From Midden to Sieve: The Impact of Differential Recovery and Quantification Techniques on Interpretations of Shellfish Remains in Australian Coastal Archaeology

Experimental mechanical sieving methods are applied to samples of shellfish remains from three sites in southeast Queensland, Seven Mile Creek Mound, Sandstone Point and One-Tree, to test the efficacy of various recovery and quantification procedures commonly applied to shellfish assemblages in Australia. There has been considerable debate regarding the most appropriate sieve sizes and quantification methods that should be applied in the recovery of vertebrate faunal remains. Few studies, however, have addressed the impact of recovery and quantification methods on the interpretation of invertebrates, specifically shellfish remains. In this study, five shellfish taxa representing four bivalves (Anadara trapezia, Trichomya hirsutus, Saccostrea glomerata, Donax deltoides) and one gastropod (Pyrazus ebeninus) common in eastern Australian midden assemblages are sieved through 10mm, 6.3mm and 3.15mm mesh. Results are quantified using MNI, NISP and weight. Analyses indicate that different structural properties and pre- and postdepositional factors affect recovery rates. Fragile taxa (T. hirsutus) or those with foliated structure (S. glomerata) tend to be overrepresented by NISP measures in smaller sieve fractions, while more robust taxa (A. trapezia and P. ebeninus) tend to be overrepresented by weight measures. Results demonstrate that for all quantification methods tested a 3mm sieve should be used on all sites to allow for regional comparability and to effectively collect all available information about the shellfish remains.

Differential patterns of Male and Female mtDNA exchange across the Atlantic Ocean in the blue mussel, Mytilus edulis

Comparisons among loci with differing modes of inheritance can reveal unexpected aspects of population history. We employ a multilocus approach to ask whether two types of independently assorting mitochondrial DNAs (maternally and paternally inherited: F- and M-mtDNA) and a nuclear locus (ITS) yield concordant estimates of gene flow and population divergence. The blue mussel, Mytilus edulis, is distributed on both North American and European coastlines and these populations are separated by the waters of the Atlantic Ocean. Gene flow across the Atlantic Ocean differs among loci, with F-mtDNA and ITS showing an imprint of some genetic interchange and M-mtDNA showing no evidence for gene flow. Gene flow of F-mtDNA and ITS causes trans-Atlantic population divergence times to be greatly underestimated for these loci, although a single trans-Atlantic population divergence time (1.2 MYA) can be accommodated by considering all three loci in combination in a coalescent framework. The apparent lack of gene flow for M-mtDNA is not readily explained by different dispersal capacities of male and female mussels. A genetic barrier to M-mtDNA exchange between North American and European mussel populations is likely to explain the observed pattern, perhaps associated with the double uniparental system of mitochondrial DNA inheritance.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.