Transparent boundary conditions for wave propagation on unbounded domains

The numerical solution of the time dependent wave equation in an unbounded domain generally leads to a truncation of this domain, which requires the introduction of an artificial boundary with associated boundary conditions. Such nonreflecting conditions ensure the equivalence between the solution of the original problem in the unbounded region and the solution inside the artificial boundary. We consider the acoustic wave equation and derive exact transparent boundary conditions that are local in time and can be directly used in explicit methods. These conditions annihilate wave harmonics up to a given order on a spherical artificial boundary, and we show how to combine the derived boundary condition with a finite difference method. The analysis is complemented by a numerical example in two spatial dimensions that illustrates the usefulness and accuracy of transparent boundary conditions.

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.

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.

A distributed equivalent magnetic current based FDTD method for the calculation of E-fields induced by gradient coils

This paper evaluates a new, low-frequency finite-difference time-domain method applied to the problem of induced E-fields/eddy currents in the human body resulting from the pulsed magnetic field gradients in MRI. In this algorithm, a distributed equivalent magnetic current is proposed as the electromagnetic source and is obtained by quasistatic calculation of the empty coil's vector potential or measurements therein. This technique circumvents the discretization of complicated gradient coil geometries into a mesh of Yee cells, and thereby enables any type of gradient coil modelling or other complex low frequency sources. The proposed method has been verified against an example with an analytical solution. Results are presented showing the spatial distribution of gradient-induced electric fields in a multi-layered spherical phantom model and a complete body model. (C) 2004 Elsevier Inc. All rights reserved.

GCMC-surface area of carbonaceous materials with N-2 and Ar adsorption as an alternative to the classical BET method

In this paper we apply a new method for the determination of surface area of carbonaceous materials, using the local surface excess isotherms obtained from the Grand Canonical Monte Carlo simulation and a concept of area distribution in terms of energy well-depth of solid–fluid interaction. The range of this well-depth considered in our GCMC simulation is from 10 to 100 K, which is wide enough to cover all carbon surfaces that we dealt with (for comparison, the well-depth for perfect graphite surface is about 58 K). Having the set of local surface excess isotherms and the differential area distribution, the overall adsorption isotherm can be obtained in an integral form. Thus, given the experimental data of nitrogen or argon adsorption on a carbon material, the differential area distribution can be obtained from the inversion process, using the regularization method. The total surface area is then obtained as the area of this distribution. We test this approach with a number of data in the literature, and compare our GCMC-surface area with that obtained from the classical BET method. In general, we find that the difference between these two surface areas is about 10%, indicating the need to reliably determine the surface area with a very consistent method. We, therefore, suggest the approach of this paper as an alternative to the BET method because of the long-recognized unrealistic assumptions used in the BET theory. Beside the surface area obtained by this method, it also provides information about the differential area distribution versus the well-depth. This information could be used as a microscopic finger-print of the carbon surface. It is expected that samples prepared from different precursors and different activation conditions will have distinct finger-prints. We illustrate this with Cabot BP120, 280 and 460 samples, and the differential area distributions obtained from the adsorption of argon at 77 K and nitrogen also at 77 K have exactly the same patterns, suggesting the characteristics of this carbon.

An object-oriented designed finite-difference time-domain simulator for electromagnetic analysis and design in MRI - application to high field analyses

This paper presents a finite-difference time-domain (FDTD) simulator for electromagnetic analysis and design applications in MRI. It is intended to be a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The pro-ram has been constructed in an object-oriented framework. The design procedure is detailed and the numerical solver has been verified against analytical solutions for simple cases and also applied to various field calculation problems. In particular, the simulator is demonstrated for inverse RF coil design, optimized source profile generation, and parallel imaging in high-frequency situations. The examples show new developments enabled by the simulator and demonstrate that the proposed FDTD framework can be used to analyze large-scale computational electromagnetic problems in modern MRI engineering. (C) 2004 Elsevier Inc. All rights reserved.

Analysis of transient eddy currents in MRI using a cylindrical FDTD method

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B-0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet.

Monitoring the condition of savanna riparian zones in Northern Australia using high spatial resolution imagery and a field based rapid assessment method

Government agencies responsible for riparian environments are assessing the combined utility of field survey and remote sensing for mapping and monitoring indicators of riparian zone condition. The objective of this work was to compare the Tropical Rapid Appraisal of Riparian Condition (TRARC) method to a satellite image based approach. TRARC was developed for rapid assessment of the environmental condition of savanna riparian zones. The comparison assessed mapping accuracy, representativeness of TRARC assessment, cost-effectiveness, and suitability for multi-temporal analysis. Two multi-spectral QuickBird images captured in 2004 and 2005 and coincident field data covering sections of the Daly River in the Northern Territory, Australia were used in this work. Both field and image data were processed to map riparian health indicators (RHIs) including percentage canopy cover, organic litter, canopy continuity, stream bank stability, and extent of tree clearing. Spectral vegetation indices, image segmentation and supervised classification were used to produce RHI maps. QuickBird image data were used to examine if the spatial distribution of TRARC transects provided a representative sample of ground based RHI measurements. Results showed that TRARC transects were required to cover at least 3% of the study area to obtain a representative sample. The mapping accuracy and costs of the image based approach were compared to those of the ground based TRARC approach. Results proved that TRARC was more cost-effective at smaller scales (1-100km), while image based assessment becomes more feasible at regional scales (100-1000km). Finally, the ability to use both the image and field based approaches for multi-temporal analysis of RHIs was assessed. Change detection analysis demonstrated that image data can provide detailed information on gradual change, while the TRARC method was only able to identify more gross scale changes. In conclusion, results from both methods were considered to complement each other if used at appropriate spatial scales.