Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Step size control for efficient discrete element simulation

The step size determines the accuracy of a discrete element simulation. The position and velocity updating calculation uses a pre-calculated table and hence the control of step size can not use the integration formulas for step size control. A step size control scheme for use with the table driven velocity and position calculation uses the difference between the calculation result from one big step and that from two small steps. This variable time step size method chooses the suitable time step size for each particle at each step automatically according to the conditions. Simulation using fixed time step method is compared with that of using variable time step method. The difference in computation time for the same accuracy using a variable step size (compared to the fixed step) depends on the particular problem. For a simple test case the times are roughly similar. However, the variable step size gives the required accuracy on the first run. A fixed step size may require several runs to check the simulation accuracy or a conservative step size that results in longer run times. (C) 2001 Elsevier Science Ltd. All rights reserved.

Stochastic gauges in quantum dynamics for many-body simulations

Quantum dynamics simulations can be improved using novel quasiprobability distributions based on non-orthogonal Hermitian kernel operators. This introduces arbitrary functions (gauges) into the stochastic equations. which can be used to tailor them for improved calculations. A possible application to full quantum dynamic simulations of BEC's is presented. (C) 2001 Elsevier Science B.V. All rights reserved.

A systematic approach to error isolation in computerized wastewater simulation models

Activated sludge models are used extensively in the study of wastewater treatment processes. While various commercial implementations of these models are available, there are many people who need to code models themselves using the simulation packages available to them, Quality assurance of such models is difficult. While benchmarking problems have been developed and are available, the comparison of simulation data with that of commercial models leads only to the detection, not the isolation of errors. To identify the errors in the code is time-consuming. In this paper, we address the problem by developing a systematic and largely automated approach to the isolation of coding errors. There are three steps: firstly, possible errors are classified according to their place in the model structure and a feature matrix is established for each class of errors. Secondly, an observer is designed to generate residuals, such that each class of errors imposes a subspace, spanned by its feature matrix, on the residuals. Finally. localising the residuals in a subspace isolates coding errors. The algorithm proved capable of rapidly and reliably isolating a variety of single and simultaneous errors in a case study using the ASM 1 activated sludge model. In this paper a newly coded model was verified against a known implementation. The method is also applicable to simultaneous verification of any two independent implementations, hence is useful in commercial model development.

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.

Using clusters of computers for large QU-GENE simulation experiments

The QU-GENE Computing Cluster (QCC) is a hardware and software solution to the automation and speedup of large QU-GENE (QUantitative GENEtics) simulation experiments that are designed to examine the properties of genetic models, particularly those that involve factorial combinations of treatment levels. QCC automates the management of the distribution of components of the simulation experiments among the networked single-processor computers to achieve the speedup.

A simulation model for analysing patient activity in dermatology

We developed a general model to assess patient activity within the primary and secondary health-care sectors following a dermatology outpatient consultation. Based on observed variables from the UK teledermatology trial, the model showed that up to 11 doctor-patient interactions occurred before a patient was ultimately discharged from care. In a cohort of 1000 patients, the average number of health-care visits was 2.4 (range 1-11). Simulation analysis suggested that the most important parameter affecting the total number of doctor-patient Interactions is patient discharge from care following the initial consultation. This implies that resources should be concentrated in this area. The introduction of teledermatology (either realtime or store and forward) changes the values of the model parameters. The model provides a quantitative tool for planning the future provision of dermatology health-care.

Predictions of quantum mechanics and stochastic electrodynamics in travelling wave second harmonic generation

We show that stochastic electrodynamics and quantum mechanics give quantitatively different predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semiclassical results are different in the regions where the system performs best in relation to the QND criteria, and that they significantly overestimate the performance in these regions. (C) 2001 Published by Elsevier Science B.V.

The stochastic design of force-minimized compact magnets for high-field magnetic resonance imaging applications

New designs for force-minimized compact high-field clinical MRI magnets are described. The design method is a modified simulated annealing (SA) procedure which includes Maxwell forces in the error function to be minimized. This permits an automated force reduction in the magnet designs while controlling the overall dimensions of the system. As SA optimization requires many iterations to achieve a final design, it is important that each iteration in the procedure is rapid. We have therefore developed a rapid force calculation algorithm. Novel designs for short 3- and 4-T clinical MRI systems are presented in which force reduction has been invoked. The final designs provide large homogeneous regions and reduced stray fields in remarkable short magnets. A shielded 4-T design that is approximately 30% shorter than current designs is presented. This novel magnet generates a full 50-cm diameter homogeneous region.

Increasing profits and reducing risks in crop production using participatory systems simulation approaches

The development of cropping systems simulation capabilities world-wide combined with easy access to powerful computing has resulted in a plethora of agricultural models and consequently, model applications. Nonetheless, the scientific credibility of such applications and their relevance to farming practice is still being questioned. Our objective in this paper is to highlight some of the model applications from which benefits for farmers were or could be obtained via changed agricultural practice or policy. Changed on-farm practice due to the direct contribution of modelling, while keenly sought after, may in some cases be less achievable than a contribution via agricultural policies. This paper is intended to give some guidance for future model applications. It is not a comprehensive review of model applications, nor is it intended to discuss modelling in the context of social science or extension policy. Rather, we take snapshots around the globe to 'take stock' and to demonstrate that well-defined financial and environmental benefits can be obtained on-farm from the use of models. We highlight the importance of 'relevance' and hence the importance of true partnerships between all stakeholders (farmer, scientists, advisers) for the successful development and adoption of simulation approaches. Specifically, we address some key points that are essential for successful model applications such as: (1) issues to be addressed must be neither trivial nor obvious; (2) a modelling approach must reduce complexity rather than proliferate choices in order to aid the decision-making process (3) the cropping systems must be sufficiently flexible to allow management interventions based on insights gained from models. The pro and cons of normative approaches (e.g. decision support software that can reach a wide audience quickly but are often poorly contextualized for any individual client) versus model applications within the context of an individual client's situation will also be discussed. We suggest that a tandem approach is necessary whereby the latter is used in the early stages of model application for confidence building amongst client groups. This paper focuses on five specific regions that differ fundamentally in terms of environment and socio-economic structure and hence in their requirements for successful model applications. Specifically, we will give examples from Australia and South America (high climatic variability, large areas, low input, technologically advanced); Africa (high climatic variability, small areas, low input, subsistence agriculture); India (high climatic variability, small areas, medium level inputs, technologically progressing; and Europe (relatively low climatic variability, small areas, high input, technologically advanced). The contrast between Australia and Europe will further demonstrate how successful model applications are strongly influenced by the policy framework within which producers operate. We suggest that this might eventually lead to better adoption of fully integrated systems approaches and result in the development of resilient farming systems that are in tune with current climatic conditions and are adaptable to biophysical and socioeconomic variability and change. (C) 2001 Elsevier Science Ltd. All rights reserved.

Patchy populations in stochastic environments: Critical number of patches for persistence

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be greater than or equal to1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the persistence of the population. As the magnitude of environmental fluctuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested decreases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environmental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily distributed organisms that are restricted to a small number of habitat patches.