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.

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.

Stochastic Schrodinger equation approach to quantum noise in resonant tunneling current

We apply the quantum trajectory method to current noise in resonant tunneling devices. The results from dynamical simulation are compared with those from unconditional master equation approach. We show that the stochastic Schrodinger equation approach is useful in modeling the dynamical processes in mesoscopic electronic systems.

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.

Modern scientific methods and their potential in wastewater science and technology

Application of novel analytical and investigative methods such as fluorescence in situ hybridization, confocal laser scanning microscopy (CLSM), microelectrodes and advanced numerical simulation has led to new insights into micro-and macroscopic processes in bioreactors. However, the question is still open whether or not these new findings and the subsequent gain of knowledge are of significant practical relevance and if so, where and how. To find suitable answers it is necessary for engineers to know what can be expected by applying these modern analytical tools. Similarly, scientists could benefit significantly from an intensive dialogue with engineers in order to find out about practical problems and conditions existing in wastewater treatment systems. In this paper, an attempt is made to help bridge the gap between science and engineering in biological wastewater treatment. We provide an overview of recently developed methods in microbiology and in mathematical modeling and numerical simulation. A questionnaire is presented which may help generate a platform from which further technical and scientific developments can be accomplished. Both the paper and the questionnaire are aimed at encouraging scientists and engineers to enter into an intensive, mutually beneficial dialogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

On the importance function in splitting simulation

The splitting method is a simulation technique for the estimation of very small probabilities. In this technique, the sample paths are split into multiple copies, at various stages in the simulation. Of vital importance to the efficiency of the method is the Importance Function (IF). This function governs the placement of the thresholds or surfaces at which the paths are split. We derive a characterisation of the optimal IF and show that for multi-dimensional models the natural choice for the IF is usually not optimal. We also show how nearly optimal splitting surfaces can be derived or simulated using reverse time analysis. Our numerical experiments illustrate that by using the optimal IF, one can obtain a significant improvement in simulation efficiency.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Using crop simulation to generate genotype by environment interaction effects for sorghum in water-limited environments

Multi-environment trials (METs) used to evaluate breeding lines vary in the number of years that they sample. We used a cropping systems model to simulate the target population of environments (TPE) for 6 locations over 108 years for 54 'near-isolines' of sorghum in north-eastern Australia. For a single reference genotype, each of 547 trials was clustered into 1 of 3 'drought environment types' (DETs) based on a seasonal water stress index. Within sequential METs of 2 years duration, the frequencies of these drought patterns often differed substantially from those derived for the entire TPE. This was reflected in variation in the mean yield of the reference genotype. For the TPE and for 2-year METs, restricted maximum likelihood methods were used to estimate components of genotypic and genotype by environment variance. These also varied substantially, although not in direct correlation with frequency of occurrence of different DETs over a 2-year period. Combined analysis over different numbers of seasons demonstrated the expected improvement in the correlation between MET estimates of genotype performance and the overall genotype averages as the number of seasons in the MET was increased.

Parallel simulation system for earthquake generation: Fault analysis modules and parallel coupling analysis

Solid earth simulations have recently been developed to address issues such as natural disasters, global environmental destruction and the conservation of natural resources. The simulation of solid earth phenomena involves the analysis of complex structures including strata, faults, and heterogeneous material properties. Simulation of the generation and cycle of earthquakes is particularly important, but such simulations require the analysis of complex fault dynamics. GeoFEM is a parallel finite-element analysis system intended for solid earth field phenomena problems. This paper describes recent development in the GeoFEM project for the simulation of earthquake generation and cycles.

The modeling of turbulent reactive flows based on multiple mapping conditioning

A new modeling approach-multiple mapping conditioning (MMC)-is introduced to treat mixing and reaction in turbulent flows. The model combines the advantages of the probability density function and the conditional moment closure methods and is based on a certain generalization of the mapping closure concept. An equivalent stochastic formulation of the MMC model is given. The validity of the closuring hypothesis of the model is demonstrated by a comparison with direct numerical simulation results for the three-stream mixing problem. (C) 2003 American Institute of Physics.

Adsorption of Supercritical fluids on graphitised thermal carbon black: Molecular layer structure theory versus grand canonical Monte Carlo simulation

This paper presents a detailed analysis of adsorption of supercritical fluids on nonporous graphitized thermal carbon black. Two methods are employed in the analysis. One is the molecular layer structure theory (MLST), proposed recently by our group, and the other is the grand canonical Monte Carlo (GCMC) simulation. They were applied to describe the adsorption of argon, krypton, methane, ethylene, and sulfur hexafluoride on graphitized thermal carbon black. It was found that the MLST describes all the experimental data at various temperatures well. Results from GCMC simulations describe well the data at low pressure but show some deviations at higher pressures for all the adsorbates tested. The question of negative surface excess is also discussed in this paper.

The transform likelihood ratio method for rare event simulation with heavy tails

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focussed recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the best choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy. (C) 2004 Elsevier B.V. All rights reserved.

Implications of seasonal climate forecasts on world wheat trade: a stochastic, dynamic analysis

Improvements in seasonal climate forecasts have potential economic implications for international agriculture. A stochastic, dynamic simulation model of the international wheat economy is developed to estimate the potential effects of seasonal climate forecasts for various countries' wheat production, exports and world trade. Previous studies have generally ignored the stochastic and dynamic aspects of the effects associated with the use of climate forecasts. This study shows the importance of these aspects. In particular with free trade, the use of seasonal forecasts results in increased producer surplus across all exporting countries. In fact, producers appear to capture a large share of the economic surplus created by using the forecasts. Further, the stochastic dimensions suggest that while the expected long-run benefits of seasonal forecasts are positive, considerable year-to-year variation in the distribution of benefits between producers and consumers should be expected. The possibility exists for an economic measure to increase or decrease over a 20-year horizon, depending on the particular sequence of years.