Distribution of hydraulic conductivity in single scale anisotropy

The cluster statistics of percolation theory are used to find the distributions of hydraulic conductivity, K, of anisotropic (truncated) random fractal media. Rescaling of variables to transform anisotropic to isotropic media also produces deformations of, for example experimental volumes, and the resulting non-equidimensional shapes may generate interesting size effects on K. Previously, the most likely value of K was obtained by comparing the correlation length from percolation theory with system dimensions, a procedure analogous to those developed for hopping conduction in disordered systems to calculate the longitudinal conductivity of thin films. The result probably explains the frequent tendencies of measurements of K in anisotropic fracture networks and agricultural soils to increase with the scale of measurement, similarly to how the longitudinal conductivity of a thick film would be larger than the corresponding conductivity of a thin film (three- rather than two-dimensional conduction). However, the same procedure applied to the conductivity in the perpendicular direction (analogous to the transverse electrical conductivity of a thin film) shows a diminishing function of spatial scale. Collectively, these ‘scale effects’ disappear if the shape of the experimental volume is selected to maintain the relationships of conduction in the various directions as the scale of the experiment is increased analogously to equidimensional volumes in isotropic media. The increase in K is, thus, merely due to an increase in the dimensionality of conduction from one to three with increasing system size. The paper, thus, provides a solid argument against a common assumption in the porous media communities that the connectivity of highly conducting regions of a medium should increase with increasing scale of measurement.     

On the relationship betweenT 1 andT 2 for stochastic relaxation models

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T ₁, the population relaxation rate, and 1/T ₂, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T ₂1/2T ₁, when fourth-order terms are included, in some instances 1/T ₂<1/2T ₁.     

Construction of universal rotations from point-to-point transformations

For a desired range of offsets, universal rotations of arbitrary flip angle can be constructed based on point-to-point rotations of I(y) with half the flip angle. This approach allows, for example, creation of broadband or bandselective refocusing pulses from broadband or bandselective excitation pulses. Furthermore, universal rotations about any axis can be obtained from point-to-point transformations that can easily be optimized using optimal control algorithms. The construction procedure is demonstrated on the examples of a broadband refocusing pulse, a broadband 120(x) degrees rotation and a z-rotation with offset pattern.     

The isotope exchange depth profiling (IEDP) technique using SIMS and LEIS

The determination of the mass transport kinetics of oxide materials for use in electrochemical systems such as fuel cells, sensors and oxygen separators is a significant challenge. Several techniques have been proposed to derive these data experimentally with only the oxygen isotope exchange depth profile technique coupled with secondary ion mass spectrometry (SIMS) providing a direct measure of these kinetic parameters. Whilst this allows kinetic information to be obtained, there is a lack of knowledge of the surface chemistry of these complex processes. The advent of low-energy ion scattering (LEIS) now offers the opportunity of correlating exchange kinetics with chemical processes at materials atomic surfaces, giving unprecedented levels of information on electrochemical systems with isotopic discrimination. Here, the challenges of these techniques, including sample preparation, are discussed and the advantages of the combined approach of SIMS and LEIS illustrated with reference to key literature data.