Geoffrey J. Daniell

Adaptive mesh refinement techniques for electrical impedance tomography

Adaptive mesh refinement techniques can be applied to increase the efficiency of electrical impedance tomography reconstruction algorithms by reducing computational and storage cost as well as providing problem-dependent solution structures. A self-adaptive refinement algorithm based on an a posteriori error estimate has been developed and its results are shown in comparison with uniform mesh refinement for a simple head model.

Ferrofluid particle size distributions from magnetisation and small angle neutron scattering data

Abstract The particle size distributions of three ferrofluids have been determined at room temperature from magnetisation and small angle neutron scattering measurements. The distributions were calculated using a data analysis technique based upon the concept of maximum entropy, and their significance estimated using an adaptation of the Backus-Gilbert technique.

Optimal imaging with adaptive mesh refinement in electrical impedance tomography

In non-linear electrical impedance tomography the goodness of fit of the trial images is assessed by the well-established statistical chi2 criterion applied to the measured and predicted datasets. Further selection from the range of images that fit the data is effected by imposing an explicit constraint on the form of the image, such as the minimization of the image gradients. In particular, the logarithm of the image gradients is chosen so that conductive and resistive deviations are treated in the same way. In this paper we introduce the idea of adaptive mesh refinement to the 2D problem so that the local scale of the mesh is always matched to the scale of the image structures. This improves the reconstruction resolution so that the image constraint adopted dominates and is not perturbed by the mesh discretization. The avoidance of unnecessary mesh elements optimizes the speed of reconstruction without degrading the resulting images. Starting with a mesh scale length of the order of the electrode separation it is shown that, for data obtained at presently achievable signal-to-noise ratios of 60 to 80 dB, one or two refinement stages are sufficient to generate high quality images.

A new method for the determination of particle size distributions from superparamagnetic measurements

The maximum entropy and Backus-Gilbert approaches to data analysis have been adapted and applied to superparamagnetic measurements to obtain particle size distributions together with realistic estimates of their significance. The particle size distributions of three alumina supported nickel catalysts are presented as an illustration.

High fidelity imaging and high performance computing in nonlinear EIT

We show that nonlinear EIT provides images with well defined characteristics when smoothness of the image is used as a constraint in the reconstruction process. We use the gradient of the logarithm of resistivity as an effective measure of image smoothness, which has the advantage that resistivity and conductivity are treated with equal weight. We suggest that a measure of the fidelity of the image to the object requires the explicit definition and application of such a constraint. The algorithm is applied to the simulation of intra-ventricular haemorrhaging (IVH) in a simple head model. The results indicate that a 5% increase in the blood content of the ventricles would be easily detectable with the noise performance of contemporary instrumentation. The possible implementation of the algorithm in real time via high performance computing is discussed.

Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction

Non-linear electrical impedance tomography reconstruction algorithms usually employ the Newton-Raphson iteration scheme to image the conductivity distribution inside the body. For complex 3D problems, the application of this method is not feasible any more due to the large matrices involved and their high storage requirements. In this paper we demonstrate the suitability of an alternative conjugate gradient reconstruction algorithm for 3D tomographic imaging incorporating adaptive mesh refinement and requiring less storage space than the Newton-Raphson scheme. We compare the reconstruction efficiency of both algorithms for a simple 3D head model. The results show that an increase in speed of about 30% is achievable with the conjugate gradient-based method without loss of accuracy.

Efficient Methods for Handling Long-Range Forces in Particle—Particle Simulations

A number of problems arise when long-range forces, such as those governed by Bessel functions, are used in particle?particle simulations. If a simple cutoff for the interaction is used, the system may find an equilibrium configuration at zero temperature that is not a regular lattice yet has an energy lower than the theoretically predicted minimum for the physical system. We demonstrate two methods to overcome these problems in Monte Carlo and molecular dynamics simulations. The first uses a smoothed potential to truncate the interaction in a single unit cell: this is appropriate for phenomenological characterisations, but may be applied to any potential. The second is a new method for summing the unmodified potential in an infinitely tiled periodic system, which is in excess of 20,000 times faster than previous naive methods which add periodic images in shells of increasing radius: this is suitable for quantitative studies. Finally, we show that numerical experiments which do not handle the long-range force carefully may give misleading results: both of our proposed methods overcome these problems.

Pyroelectric field assisted ion migration induced by ultraviolet laser irradiation and its impact on ferroelectric domain inversion in lithium niobate crystals

The impact of UV laser irradiation on the distribution of lithium ions in ferroelectric lithium niobate single crystals has been numerically modelled. Strongly absorbed UV radiation at wavelengths of 244–305 nm produces steep temperature gradients which cause lithium ions to migrate and result in a local variation of the lithium concentration. In addition to the diffusion, here the pyroelectric effect is also taken into account which predicts a complex distribution of lithium concentration along the c-axis of the crystal: two separated lithium deficient regions on the surface and in depth. The modelling on the local lithium concentration and the subsequent variation of the coercive field are used to explain experimental results on the domain inversion of such UV treated lithium niobate crystals.

Using maximum entropy to double one's expected winnings in the UK National Lottery

We have used the Maximum Entropy method to estimate the probability of each of the 14 million tickets being chosen by players in the UK National Lottery. As data, we used the numbers of winners in the 3, 4, and 5-match categories and the total number of tickets sold in each of the first 113 draws. We have computed the marginal distributions for players choosing single numbers and pairs of numbers. A striking conclusion is that players preferentially pick numbers towards the centre of the ticket. By choosing unpopular combinations of numbers, one?s expected winnings can be doubled.

Numerical model of the optical stark effect as a mode-locking mechanism for femtosecond vertical-external-cavity surface-emitting semiconductor lasers

A pulse is shortened by repeated transits of a quantum well absorber in which the band-edge is detuned to higher energy. The calculated effect is consistent with the experimentally observed formation of 448-fs transform-limited pulses.