Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

Decomposition of complete tripartite graphs into gregarious 4-cycles

A 4-cycle in a tripartite graph with vertex partition {V-1, V-2, V-3} is said to be gregarious if it has at least one vertex in each V-i, 1 less than or equal to i less than or equal to 3. In this paper, necessary and sufficient conditions are given for the existence of an edge-disjoint decomposition of any complete tripartite graph into gregarious 4-cycles.

A note on the decomposition of the health concentration index

In recent work, the concentration index has been widely used as a measure of income-related health inequality. The purpose of this note is to illustrate two different methods for decomposing the overall health concentration index using data collected from a Short Form (SF-36) survey of the general Australian population conducted in 1995. For simplicity, we focus on the physical functioning scale of the SF-36. Firstly we examine decomposition 'by component' by separating the concentration index for the physical functioning scale into the ten items on which it is based. The results show that the items contribute differently to the overall inequality measure, i.e. two of the items contributed 13% and 5%, respectively, to the overall measure. Second, to illustrate the 'by subgroup' method we decompose the concentration index by employment status. This involves separating the population into two groups: individuals currently in employment; and individuals not currently employed. We find that the inequality between these groups is about five times greater than the inequality within each group. These methods provide insights into the nature of inequality that can be used to inform policy design to reduce income related health inequalities. Copyright (C) 2002 John Wiley Sons, Ltd.

Thermal characterization of copolymers obtained by radiation grafting of styrene onto poly(tetrafluoroethyleneperfluoropropylvinylether) substrates: thermal decomposition, melting behavior and low-temperature transitions

Differential scanning calorimetric (DSC) and thermogravimetric analysis (TGA) have been used to study the thermal decomposition, the melting behavior and low-temperature transitions of copolymers obtained by radiation-induced grafting of styrene onto poly (tetrafluoroethylene- perfluoropropylvinylether) (PFA) substrates. PFA with different contents of perfluoropropylvinylether (PPVE) as a comonomer have been investigated. A two step degradation pattern was observed from TGA thermograms of all the grafted copolymers, which was attributed to degradation of PSTY followed by the degradation of the PFA backbone at higher temperature. One broad melting peak can be identified for all copolymers, which has two components in the samples with higher PPVE content. The melting peak, crystal-crystal transition and the degree of crystallinity of the grafted copolymers increases with radiation grafting up to 50 kGy, followed by a decrease at higher doses. No such decrease was observed in the ungrafted PFA samples after irradiation. This indicated that the changes in the heats of transitions and crystallinity at low doses are due to the radiation effects on the microstructure of PFA (chain scission), whereas at higher doses the grafted PSTY is the driving force behind these changes. (C) 2001 Elsevier Science Ltd. All rights reserved.

Time-dependent master equation simulation of complex elementary reactions in combustion: Application to the reaction of (CH2)-C-1 with C2H2 from 300-2000 K

Computational simulations of the title reaction are presented, covering a temperature range from 300 to 2000 K. At lower temperatures we find that initial formation of the cyclopropene complex by addition of methylene to acetylene is irreversible, as is the stabilisation process via collisional energy transfer. Product branching between propargyl and the stable isomers is predicted at 300 K as a function of pressure for the first time. At intermediate temperatures (1200 K), complex temporal evolution involving multiple steady states begins to emerge. At high temperatures (2000 K) the timescale for subsequent unimolecular decay of thermalized intermediates begins to impinge on the timescale for reaction of methylene, such that the rate of formation of propargyl product does not admit a simple analysis in terms of a single time-independent rate constant until the methylene supply becomes depleted. Likewise, at the elevated temperatures the thermalized intermediates cannot be regarded as irreversible product channels. Our solution algorithm involves spectral propagation of a symmetrised version of the discretized master equation matrix, and is implemented in a high precision environment which makes hitherto unachievable low-temperature modelling a reality.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Capacity utilisation and profitability: A decomposition of short-run profit efficiency

The principal aim of this paper is to measure the amount by which the profit of a multi-input, multi-output firm deviates from maximum short-run profit, and then to decompose this profit gap into components that are of practical use to managers. In particular, our interest is in the measurement of the contribution of unused capacity, along with measures of technical inefficiency, and allocative inefficiency, in this profit gap. We survey existing definitions of capacity and, after discussing their shortcomings, we propose a new ray economic capacity measure that involves short-run profit maximisation, with the output mix held constant. We go on to describe how the gap between observed profit and maximum profit can be calculated and decomposed using linear programming methods. The paper concludes with an empirical illustration, involving data on 28 international airline companies. The empirical results indicate that these airline companies achieve profit levels which are on average US$815m below potential levels, and that 70% of the gap may be attributed to unused capacity. (C) 2002 Elsevier Science B.V. All rights reserved.

Lexicographic decomposition of chains and the concept of a planar chain

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17-38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example of which is the Debreu chain (R-2, <(l)). (C) 2002 Elsevier Science B.V. All rights reserved.

Calculation of resonances and product state distributions for the unimolecular dissociation of H2S

Resonance phenomena associated with the unimolecular dissociation of H2S --> SH + H have been investigated quantum mechanically by the Lanczos homogeneous filter diagonalization method using a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). Resonance energies, widths (rates), and product state distributions have been obtained. Both dissociation rates and product state distributions of SH show, strong fluctuations, indicating that the dissociation of H2S is essentially irregular. Statistical analysis of neighboring level spacing and width distributions also confirms this behavior. The dissociation rates and product state distributions are compared to the predictions of quantum phase space theory.

Leaf litter decomposition of Piper aduncum, Gliricidia sepium and Imperata cylindrica in the humid lowlands of Papua New Guinea

No information is available on the decomposition and nutrient release pattern of Piper aduncum and Imperata cylindrica despite their importance in shifting cultivation systems of Papua New Guinea and other tropical regions. We conducted a litter bag study (24 weeks) on a Typic Eutropepts in the humid lowlands to assess the rate of decomposition of Piper aduncum, Imperata cylindrica and Gliricidia sepium leaves under sweet potato (Ipomoea batatas). Decomposition rates of piper leaf litter were fastest followed closely by gliricidia, and both lost 50% of the leaf biomass within 10 weeks. Imperata leaf litter decomposed much slower and half-life values exceeded the period of observation. The decomposition patterns were best explained by the lignin plus polyphenol over N ratio which was lowest for piper (4.3) and highest for imperata (24.7). Gliricidia leaf litter released 79 kg N ha(-1), whereas 18 kg N ha(-1) was immobilised in the imperata litter. The mineralization of P was similar for the three species, but piper litter released large amounts of K. The decomposition and nutrient release patterns had significant effects on the soil. The soil contained significantly more water in the previous imperata plots at 13 weeks due to the relative slow decomposition of the leaves. Soil N levels were significantly reduced in the previous imperata plots due to immobilisation of N. Levels of exchangeable K were significantly increased in the previous piper plots due to the large addition of K. It can be concluded that piper leaf litter is a significant and easily decomposable source of K which is an important nutrient for sweet potato. Gliricidia leaf litter contained much N, whereas imperata leaf litter releases relatively little nutrients and keeps the soil more moist. Gliricidia fallow is more attractive than an imperata fallow for it improves the soil fertility and produces fuelwood as additional saleable products.

Quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Future directions in this field are also discussed.