Anisotropic focusing characteristics of micro-domain structures within crystalline Sr_0.61Ba_0.39Nb₂O₆ : the crystal ball

We report the anisotropic focusing characteristics of a spherically configured region of micro-domains that have been induced within a cubic shaped crystal of Ce:doped Sr0.61Ba0.39Nb2O6. The internal spherical structure focuses extraordinary polarised light, but not ordinary polarised. The spherical region, which is easily observed via scattering, is formed as the crystal cools down, after a repoling cycle through the Curie temperature, with an applied field. Analytic modelling of the thermal gradients that exist within the crystal during cooling reveals a small (< 1°) temperature difference between the central and outside regions. The similarity in shape between these temperature profiles and the observed scattering region suggests a possible mechanism for the growth of this spherical micro-domained structure

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

ABSTRACT 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 cut-off 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 naïve 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. FANGOHR, PRICE, COX, DE GROOT, AND DANIELL

Convergence issues of non-linear 3D reconstruction in EIT

The convergence of non-linear reconstruction algorithms for Electrical Impedance Tomography (EIT) depends on many factors, such as the noise of the measurement system, the numerical discretization of the object and the starting value of the iterative approximation. We have shown previously that the result can be made independent of the underlying numerical discretization of the object when adaptive mesh refinement methods are used in combination with a logarithmic image smoothness constraint. The non-linear nature of EIT reconstruction and the unavoidable measurement noise, however, cause several differing solutions in the image space to satisfy the conditions for a 'best-fit' conductivity distribution. A verification of the correctness of an obtained image can only be carried out if the true distribution is known. This, however, is not possible when in-vivo measurements are made and hence we need to establish a measure of similarity between the reconstructed result and a simulated object to characterize the algorithmic behaviour for real experiments. By distributing and reconstructing a large number of initial 3D conductivity estimates on a commodity cluster of PCs, we can determine the quality of the final images and correlate the results with the true images within a short time-span. This gives an indication of the quality of image and provides a measure of convergence properties of the tested algorithms. In this paper, we present results from these investigations into the characteristics and efficient reconstruction of the final image and comment on the clinical importance of choice of starting valu

Optimal imaging with adaptive mesh refinement in electrical tomography

In non-linear electrical impedance tomography the goodness of fit of the trial images is assessed by the well-established statistical χ2 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

Long-range forces and data compression in Vortex State simulations

We report on two aspects of simulations of the vortex state in high-temperature superconductors. Firstly, we cover the treatment of the involved long-range forces. Secondly, we suggest improvements on how to compress vortex position data effectively to enable visualisation of complex systems. A number of problems arise when long-range forces such as $K_1(x)$ or $1/x$ are used in particle-particle simulations. If a simple cut-off 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: this is an artefact of the cut-off [1]. We have developed 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 the $K_0(x)$ potential and sums the energy 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 demonstrate how tree methods and space filling curves can be used to store particle data more efficiently. [1] H. Fangohr et. al., Peter A.J. de Groot and Geoffrey J. Daniell and Ken S. Thomas (2000) Efficient Methods for Handling Long-Range Forces in Particle-Particle Simulations. Journal of Computational Physics, 162 p.372-384

Eigenvalue spectrum estimation and photonic crystals

We have developed an algorithm for the estimation of eigenvalue spectra and have applied it to the determination of the density of states in a photonic crystal, which requires the repeated solution of a generalized eigenvalue problem. We demonstrate that the algorithm offers significant advantages in time, memory, and ease of parallelization over conventional subspace iteration algorithms. In particular it is possible to obtain more than two orders of magnitude speedup in time over subspace methods for modestly sized matrices. For larger matrices the savings are even greater, whilst retaining accurate resolution of features of the eigenspectru

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

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