A high definition, finite difference time domain method

A high definition, finite difference time domain (HD-FDTD) method is presented in this paper. This new method allows the FDTD method to be efficiently applied over a very large frequency range including low frequencies, which are problematic for conventional FDTD methods. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and has been verified against analytical solutions within the frequency range 50 Hz-1 GHz. As an example of the lower frequency range, the method has been applied to the problem of induced eddy currents in the human body resulting from the pulsed magnetic field gradients of an MRI system. The new method only requires approximately 0.3% of the source period to obtain an accurate solution. (C) 2003 Elsevier Science Inc. All rights reserved.

Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Selecting methods to solve multi-well master equations

There are several competing methods commonly used to solve energy grained master equations describing gas-phase reactive systems. When it comes to selecting an appropriate method for any particular problem, there is little guidance in the literature. In this paper we directly compare several variants of spectral and numerical integration methods from the point of view of computer time required to calculate the solution and the range of temperature and pressure conditions under which the methods are successful. The test case used in the comparison is an important reaction in combustion chemistry and incorporates reversible and irreversible bimolecular reaction steps as well as isomerizations between multiple unimolecular species. While the numerical integration of the ODE with a stiff ODE integrator is not the fastest method overall, it is the fastest method applicable to all conditions.

A comparison of two methods for the calculation of accumulated oxygen deficit

The aim of this study was to compare accumulated oxygen deficit data derived using two different exercise protocols with the aim of producing a less time-consuming test specifically for use with athletes. Six road and four track male endurance cyclists performed two series of cycle ergometer tests. The first series involved five 10 min sub-maximal cycle exercise bouts, a (V) over dotO(2peak) test and a 115% (V) over dotO(2peak) test. Data from these tests were used to estimate the accumulated oxygen deficit according to the calculations of Medbo et al. (1988). In the second series of tests, participants performed a 15 min incremental cycle ergometer test followed, 2 min later, by a 2 min variable resistance test in which they completed as much work as possible while pedalling at a constant rate. Analysis revealed that the accumulated oxygen deficit calculated from the first series of tests was higher (P< 0.02) than that calculated from the second series: 52.3 +/- 11.7 and 43.9 +/- 6.4 ml . kg(-1), respectively (mean +/- s). Other significant differences between the two protocols were observed for (V) over dot O-2peak, total work and maximal heart rate; all were higher during the modified protocol (P