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.

A new method for analysing the equilibrium and time-dependent behaviour of Markovian models

Many large-scale stochastic systems, such as telecommunications networks, can be modelled using a continuous-time Markov chain. However, it is frequently the case that a satisfactory analysis of their time-dependent, or even equilibrium, behaviour is impossible. In this paper, we propose a new method of analyzing Markovian models, whereby the existing transition structure is replaced by a more amenable one. Using rates of transition given by the equilibrium expected rates of the corresponding transitions of the original chain, we are able to approximate its behaviour. We present two formulations of the idea of expected rates. The first provides a method for analysing time-dependent behaviour, while the second provides a highly accurate means of analysing equilibrium behaviour. We shall illustrate our approach with reference to a variety of models, giving particular attention to queueing and loss networks. (C) 2003 Elsevier Ltd. All rights reserved.

Determination of chromophore charge states in the low pH color transition of the fluorescent protein Rtms5(H146S) via time-dependent DFT

The red fluorescent protein Rtms5H146S displays a transition from blue (absorbance λmax 590 nm) to yellow (absorbance λmax not, vert, similar453 nm) upon titration to low pH. The pKa of the reaction depends on the concentration of halide, offering promise for new expressible halide sensors. The protonation state involved in the low pH form of the chromophore remains, however, ambiguous. We report calculated excitation energies of different protonation states of an RFP chromophore model. These suggest that the relevant titration site is the phenoxy moiety of the chromophore, and the relevant base and conjugate acid are anionic and neutral chromophore species, respectively.

The variety of variables in automated real-time refinement

The refinement calculus is a well-established theory for deriving program code from specifications. Recent research has extended the theory to handle timing requirements, as well as functional ones, and we have developed an interactive programming tool based on these extensions. Through a number of case studies completed using the tool, this paper explains how the tool helps the programmer by supporting the many forms of variables needed in the theory. These include simple state variables as in the untimed calculus, trace variables that model the evolution of properties over time, auxiliary variables that exist only to support formal reasoning, subroutine parameters, and variables shared between parallel processes.

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.

Effects of physical activity on emotional well-being among older Australian women - Cross-sectional and longitudinal analyses

Objective: To explore relationships between physical activity and mental health cross-sectionally and longitudinally in a large cohort of older Australian women. Method: Women in their 70s participating in the Australian Longitudinal Study on Women's Health responded in 1996 (aged 70-75) and in 1999 (aged 73-78). Cross-sectional data were analyzed for 10,063 women and longitudinal data for 6472. Self-reports were used to categorize women into four categories of physical activity at each time point as well as to define four physical activity transition categories across the 3-year period. Outcome variables for the cross-sectional analyses were the mental health component score (MCS) and mental health subscales of the Medical Outcomes Study Short Form (SF-36). The longitudinal analyses focused on changes in these variables. Confounders included the physical health component scale (PCS) of the SF-36, marital status, body mass index (BMI) and life events. Adjustment for baseline scores was included for the longitudinal analyses. Results: Cross-sectionally, higher levels of physical activity were associated with higher scores on all dependent variables, both with and without adjustment for confounders. Longitudinally, the effects were weaker, but women who had made a transition from some physical activity to none generally showed more negative changes in emotional well-being than those who had always been sedentary, while those who maintained or adopted physical activity had better outcomes. Conclusion: Physical activity is associated with emotional well-being among a population cohort of older women both cross-sectionally and longitudinally, supporting the need for the promotion of appropriate physical activity in this age group. (C) 2003 Elsevier Science Inc. All rights reserved.

A time-harmonic target-field method for designing unshielded RF coils in MRI

Time-harmonic methods are required in the accurate design of RF coils as operating frequency increases. This paper presents such a method to find a current density solution on the coil that will induce some desired magnetic field upon an asymmetrically located target region within. This inverse method appropriately considers the geometry of the coil via a Fourier series expansion, and incorporates some new regularization penalty functions in the solution process. A new technique is introduced by which the complex, time-dependent current density solution is approximated by a static coil winding pattern. Several winding pattern solutions are given, with more complex winding patterns corresponding to more desirable induced magnetic fields.

Relations between coping and positive and negative outcomes in carers of persons with multiple sclerosis (MS)

This study examined relations between stress and coping predictors and negative and positive outcomes in MS caregiving. A total of 222 carers and their care-recipients completed questionnaires at Time 1 and three months later, Time 2 ( n = 155). Predictors included care-recipient characteristics ( age, time since diagnosis, course and life satisfaction), and Times 1 and 2 carer problems, stress appraisal and coping. Dependent variables were Time 2 negative ( anxiety, depression) and positive outcomes ( life satisfaction, positive affect, benefits). Regressions indicated that, overall, the hypothesised direct effects of stress appraisal and coping strategies on positive and negative outcomes were supported. The hypothesised stress-buffering effects of positive reframing coping were also supported. All but one of the coping strategies were related to both positive and negative outcomes; specifically, practical assistance coping emerged as a unique predictor of distress. Of the model predictors, care-recipient life satisfaction emerged as the strongest and most consistent predictor of both positive and negative outcomes except benefit finding. Findings support the role of care-recipient characteristics and the carer's appraisal and coping processes in shaping both positive and negative outcomes. The guiding framework and findings have the potential to inform interventions designed to promote well-being in carers.

Investigation of the coping antecedents to positive outcomes and distress in multiple sclerosis (MS)

This study examined relations between stress and coping predictors and distress and positive outcomes in multiple sclerosis (MS). A total of 502 people with MS completed a questionnaire at Time 1 and, 3 months later, Time 2 (n= 404). Predictors included Time 1 illness (duration, number of symptoms, course), number of problems, appraisal and coping (acceptance, problem solving, emotional release, avoidance, personal health control, energy conservation). Dependent variables were Time 2 distress (anxiety, depression) and positive outcomes (life satisfaction, positive affect, benefits). Results indicated that as hypothesised, personal health control, emotional release and physical assistance were related to the positive outcomes, whereas avoidance was related to distress, and acceptance was associated with the positive outcomes and distress. Findings highlight the differential relations between coping strategies and positive and negative outcomes and the role of appraisal and coping in regulating distress and promoting positive psychological states while managing a chronic illness.

Methods for Categorical Longitudinal Survey Data: Understanding Employment Status of Australian Women

Many variables that are of interest in social science research are nominal variables with two or more categories, such as employment status, occupation, political preference, or self-reported health status. With longitudinal survey data it is possible to analyse the transitions of individuals between different employment states or occupations (for example). In the statistical literature, models for analysing categorical dependent variables with repeated observations belong to the family of models known as generalized linear mixed models (GLMMs). The specific GLMM for a dependent variable with three or more categories is the multinomial logit random effects model. For these models, the marginal distribution of the response does not have a closed form solution and hence numerical integration must be used to obtain maximum likelihood estimates for the model parameters. Techniques for implementing the numerical integration are available but are computationally intensive requiring a large amount of computer processing time that increases with the number of clusters (or individuals) in the data and are not always readily accessible to the practitioner in standard software. For the purposes of analysing categorical response data from a longitudinal social survey, there is clearly a need to evaluate the existing procedures for estimating multinomial logit random effects model in terms of accuracy, efficiency and computing time. The computational time will have significant implications as to the preferred approach by researchers. In this paper we evaluate statistical software procedures that utilise adaptive Gaussian quadrature and MCMC methods, with specific application to modeling employment status of women using a GLMM, over three waves of the HILDA survey.

Simulations of Bose fields at finite temperature

We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomized initial wave functions to equilibrium. We compare our numerical data to the predictions of a gapless, second order theory of Bose-Einstein condensation [S. A. Morgan, J. Phys. B 33, 3847 (2000)], and find that we can determine a temperature when the theory is valid. As the Gross-Pitaevskii equation is nonperturbative, we expect that it can describe the correct thermal behavior of a Bose gas as long as all relevant modes are highly occupied. Our method could be applied to other boson fields.

Substrate-inhibited kinetics with catalyst deactivation in an isothermal CSTR

Analytical expressions are developed for the time-dependent reactant concentration and catalyst activity in an isothermal CSTR with Langmuir-Hinshelwood kinetics of deactivation and reaction. Several parallel and series posioning mechanisms are considered for a reactor which, without poisoning, would operate at a unique steady state. The use of matched asymptotic expansions and abandonment of the usual initial-steady-state assumption give results, valid from startup to final loss of activity, whose accuracy can be improved systematically.