Numerical modelling of thermal effects in rats due to high-field magnetic resonance imaging (0.5-1 GHz)

A finite-difference time-domain (FDTD) thermal model has been developed to compute the temperature elevation in the Sprague Dawley rat due to electromagnetic energy deposition in high-field magnetic resonance imaging (MRI). The field strengths examined ranged from 11.75-23.5 T (corresponding to H-1 resonances of 0.5-1 GHz) and an N-stub birdcage resonator was used to both transmit radio-frequency energy and receive the MRI signals. With an in-plane resolution of 1.95 mm, the inhomogeneous rat phantom forms a segmented model of 12 different tissue types, each having its electrical and thermal parameters assigned. The steady-state temperature distribution was calculated using a Pennes 'bioheat' approach. The numerical algorithm used to calculate the induced temperature distribution has been successfully validated against analytical solutions in the form of simplified spherical models with electrical and thermal properties of rat muscle. As well as assisting with the design of MRI experiments and apparatus, the numerical procedures developed in this study could help in future research and design of tumour-treating hyperthermia applicators to be used on rats in vivo.

A numerical approach to modeling the catalytic voltammetry of surface-confined redox enzymes

A finite difference method for simulating voltammograms of electrochemically driven enzyme catalysis is presented. The method enables any enzyme mechanism to be simulated. The finite difference equations can be represented as a matrix equation containing a nonlinear sparse matrix. This equation has been solved using the software package Mathematica. Our focus is on the use of cyclic voltammetry since this is the most commonly employed electrochemical method used to elucidate mechanisms. The use of cyclic voltammetry to obtain data from systems obeying Michaelis-Menten kinetics is discussed, and we then verify our observations on the Michaelis-Menten system using the finite difference simulation. Finally, we demonstrate how the method can be used to obtain mechanistic information on a real redox enzyme system, the complex bacterial molybdoenzyme xanthine dehydrogenase.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

Numerical modelling of radiating superorbital flows

Experimental aerodynamic studies of the flows around new aerocapture spacecraft configurations are presently being done in the superorbital expansion tubes at The University of Queensland. Short duration flows at speeds of 10--13 km/s are produced in the expansion tube facility and are then applied to the model spacecraft. Although high-temperature effects, such as molecular dissociation, have long been a part of the computational modelling of the expansion tube flows for speeds below 10 km/s, radiation may now be a significant mechanism of energy transfer within the shock layer on the model. This paper will study the coupling of radiation energy transport for an optically thin gas to the flow dynamics in order to obtain accurate predictions of thermal loads on the spacecraft. The results show that the effect of radiation on the flowfields of subscale models for expansion tube experiments can be assessed by measurements of total heat transfer and radiative heat transfer.

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Application of X-ray microtomography to numerical simulations of agglomerate breakage by distinct element method

Computer-aided tomography has been used for many years to provide significant information about the internal properties of an object, particularly in the medical fraternity. By reconstructing one-dimensional (ID) X-ray images, 2D cross-sections and 3D renders can provide a wealth of information about an object's internal structure. An extension of the methodology is reported here to enable the characterization of a model agglomerate structure. It is demonstrated that methods based on X-ray microtomography offer considerable potential in the validation and utilization of distinct element method simulations also examined.

Numerical evaluation of three dimensional effects in planar flow birefringence

The influence of three dimensional effects on isochromatic birefringence is evaluated for planar flows by means of numerical simulation. Two fluid models are investigated in channel and abrupt contraction geometries. In practice, the flows are confined by viewing windows, which alter the stresses along the optical path. The observed optical properties differ therefore from their counterpart in an ideal two-dimensional flow. To investigate the influence of these effects, the stress optical rule and the differential propagation Mueller matrix are used. The material parameters are selected so that a retardation of multiple orders is achieved, as is typical for highly birefringent melts. Errors due to three dimensional effects are mainly found on the symmetry plane, and increase significantly with the flow rate. Increasing the geometric aspect ratio improve the accuracy provided that the error on the retardation is less than one order. (C) 2004 Elsevier B.V. All rights reserved.

Numerical simulation of abrupt contraction flows using the Double Convected Pom-Pom model

The Double Convected Pom-Pom model was recently introduced to circumvent some numerical and theological defects found in other formulations of the Pom-Pom concept. It is used here for the simulation of a benchmark problem: the flow in an abrupt planar contraction. The predictions are compared with birefringence measurements and show reasonable quantitative agreement with experimental data. A parametric study is also carried out with the aim of analysing the effect of the branching parameter on vortex dynamics and extrudate swell. The results show that the Double Convected Pom-Pom model (DCPP) model is able to discriminate between branched and linear macromolecular structures in accordance with experimental observations. In that respect, the role of the extensional properties in determining complex flow behaviour is stressed. Also, the ratio of the first normal stress difference to the shear stress appears to play a major role in die swell observation. For the time being, the role of the second normal stress difference appears to be less obvious to evaluate in this complex flow. (C) 2004 Elsevier B.V. All rights reserved.

Numerical investigation of seawater intrusion at Gooburrum, Bundaberg, Queensland, Australia

Seawater intrusion in coastal agricultural areas due to groundwater abstraction is a major environmental problem along the northeastern coast of Australia. Management options are being explored using numerical modelling, however, questions remain concerning the appropriate level of sophistication in models, choice of seaward boundary conditions, and how to accommodate heterogeneity and data uncertainty. The choice of seaward boundary condition is important since it affects the amount of salt transported into the aquifers and forms the focus of the present study. The impact of this boundary condition is illustrated for the seawater-intrusion problem in the Gooburrum aquifers, which occur within Tertiary sedimentary strata. A two-dimensional variable-density groundwater and solute-transport model was constructed using the computer code 2DFEMFAT (Cheng et al. 1998). The code was tested against an experiment for a steady-state freshwater-saltwater interface and against the Elder (Elder 1967) free-convection problem. Numerical simulations show that the imposition of the commonly-used equivalent hydrostatic freshwater heads, combined with a constant salt concentration at the seaward boundary, results in overestimated seawater intrusion in the lower Gooburrum aquifer. Since the imposition of this boundary condition allows water flow across the boundary, which subsequently takes salt into the aquifer, a careful check is essential to estimate whether too much mass of salt is introduced.

Numerical analysis of capacities for two-qubit unitary operations

We present numerical results on the capacities of two-qubit unitary operations for performing communication and creating entanglement. The capacities for communication considered are based upon the increase in Holevo information of an ensemble. Our results indicate that the capacity may be accurately estimated using ensemble sizes and ancilla dimensions of 4. In addition, the calculated values of these capacities were close to, and in some cases equal to, the similarly defined entangling capacities; this result indicates connections between these capacities.

Effective cell-centred time-domain Maxwell's equations numerical solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed. © 2004 Elsevier Inc. All rights reserved.