Using directional curvatures to visualize folding patterns of the GTM projection manifolds

In data visualization, characterizing local geometric properties of non-linear projection manifolds provides the user with valuable additional information that can influence further steps in the data analysis. We take advantage of the smooth character of GTM projection manifold and analytically calculate its local directional curvatures. Curvature plots are useful for detecting regions where geometry is distorted, for changing the amount of regularization in non-linear projection manifolds, and for choosing regions of interest when constructing detailed lower-level visualization plots

Sign Rules for Anisotropic Quantum Spin Systems

We present new and exact ``sign rules'' for various spin-s anisotropic spin-lattice models. It is shown that, after a simple transformation which utilizes these sign rules, the ground-state wave function of the transformed Hamiltonian is positive-definite. Using these results exact statements for various expectation values of off-diagonal operators are presented, and transitions in the behavior of these expectation values are observed at particular values of the anisotropy. Furthermore, the effects of sign rules in variational calculations and quantum Monte Carlo calculations are considered. They are illustrated by a simple variational treatment of a one-dimensional anisotropic spin model.Comment: 4 pages, 1 ps-figur

SLIP4EX- a program for routine slope stability analysis to include the effects of vegetation, reinforcement and hydrological changes

SLIP4EX is a straightforward computer program developed in connection with the EU funded ECOSLOPES project for routine stability analysis and the assessment of the contribution of vegetation to slope stability. The slope section is drawn up and dimensions and parameters are fed in to the Microsoft Excel based program for stability calculations and comparisons of Factors of Safety using different methods of analysis (Bishop, Janbu, Fellenius, Simple, Greenwood). The background and assumptions involved in the derivation of each of the methods is briefly described. The simplicity of the program enables the user to understand the nature of the analysis, explore the parameter assumptions made and compare the different methods of analysis. Soil reinforcement by geosynthetic layers or anchors, and vegetation effects of enhanced cohesion, changed water pressures, mass of vegetation, wind forces and root reinforcement forces are readily included in the analysis. The program is freely available on request from the author

Ultrasonic Attenuation in Clean d-Wave Superconductors

We calculate the low temperature longitudinal ultrasonic attenuation rate $\alpha_S$ in clean d-wave superconductors. We consider the contribution of previously ignored processes involving the excitation of a pair of quasi-holes or quasi-particles. These processes, which are forbidden by energy conservation in conventional s-wave superconductors, have a finite phase space in d-wave superconductors due to the presence of nodes in the gap which give rise to soft low-energy electronic excitations. We find the contribution to $\alpha_S$ from these processes to be proportional to $T$ in the regime $k_B T\ll Qv_{\Delta} \ll \Delta_0$,(ultra-low temperature regime) and to be proportional to 1/T in the region $Qv_F \ll k_BT \ll \Delta_0$, (low temperature regime) where ${\bf Q}$ is the ultrasound wave-vector and $\Delta_0$ is the maximum gap amplitude. We explicitly evaluate these terms, for parameters appropriate to the cuprates, for ${\bf Q}$ along the nodal and the antinodal directions and compare it with the contribution from processes considered earlier(I.Vekhter et al {\it Phys. Rev.}{\bf B59}, 7123(1999)). In the ultra-low temperature regime, the processes considered by us make a contribution which is smaller by about a factor of 10 for ${\bf Q}$ along the nodal direction, while along the antinodal direction it is larger by a factor of 100 or so. In the low temperature regime on the other hand the contribution made by these terms is small. However taken together with the original terms we describe a possible way to evaluate the parameter $v_F/v_\Delta$.Comment: 9 pages, RevTex, accepted for publication in Physica

Ultrasonic Attenuation in the Vortex State of d-wave Superconductors

We calculate the low temperature quasi-particle contribution to the ultrasonic attenuation rate in the mixed state of d-wave superconductors. Our calculation is performed within the semi-classical approximation using quasi-particle energies that are Doppler shifted, with respect to their values in the Meissner phase, by the supercurrent associated with the vortices. We find that the attenuation at low temperatures and at fields $H_{c1} \leq H \ll H_{c2}$ has a temperature independent contribution which is proportional to $\surd H$ where $H$ is the applied magnetic field. We indicate how our result in combination with the zero-field result for ultrasonic attenuation can be used to calculate one of the parameters $v_F$, $H_{c2}$ or $\xi$ given the values for any two of them.Comment: 10 pages, RevTeX, submitted to Physica

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range r_s=100-150. We have tested different types of orbital for use in the approximate wave functions but none improve upon the simple Gaussian form. The Gaussian exponents are optimized by directly minimizing the diffusion quantum Monte Carlo energy. We have carefully investigated and sought to minimize the potential biases in our Monte Carlo results. We conclude that the uniform electron gas undergoes a transition from a ferromagnetic fluid to a body-centered-cubic Wigner crystal at r_s=106+/-1. The diffusion quantum Monte Carlo results are compared with those from Hartree-Fock and Hartree theory in order to understand the role played by exchange and correlation in Wigner crystals. We also study "floating" Wigner crystals and give results for their pair-correlation functions

Effect of FET geometry on charge ordering of transition metal oxides

We examine the effect of an FET geometry on the charge ordering phase diagram of transition metal oxides using numerical simulations of a semiclassical model including long-range Coulomb fields, resulting in nanoscale pattern formation. We find that the phase diagram is unchanged for insulating layers thicker than approximately twice the magnetic correlation length. For very thin insulating layers, the onset of a charge clump phase is shifted to lower values of the strength of the magnetic dipolar interaction, and intermediate diagonal stripe and geometric phases can be suppressed. Our results indicate that, for sufficiently thick insulating layers, charge injection in an FET geometry can be used to experimentally probe the intrinsic charge ordering phases in these materials.Comment: 4 pages, 4 postscript figure

The architecture of cancellous bone in the hindlimb of moa (Aves: Dinornithiformes), with implications for stance and gait

The extinct, flightless moa of New Zealand included some of the largest birds to have existed and possessed many distinguishing pelvic and hindlimb osteological features. These features may have influenced stance and gait in moa compared with extant birds. One means of assessing locomotor biomechanics, particularly for extinct species, is quantitative analysis of the architecture of cancellous bone, since this architecture is adapted to suit its mechanical environment with high sensitivity. This study investigated the three-dimensional architecture of cancellous bone in the femur, tibiotarsus and fibula of three moa species: Dinornis robustus, Pachyornis elephantopus and Megalapteryx didinus. Using computed tomographic X-ray scanning and previously developed fabric analysis techniques, the spatial variation in cancellous bone fabric patterns in moa was found to be largely comparable with that previously reported for extant birds, particularly large species. Moa hence likely used postures and kinematics similar to those employed by large extant bird species, but this interpretation is tentative on account of relatively small sample sizes. A point of major difference between moa and extant birds concerns the diaphyses; cancellous bone invades the medullary cavity in both groups, but the invasion is far more extensive in moa. Combined with previous assessments of cortical geometry, this further paints a picture of at least some moa species possessing very robust limb bones, for which a convincing explanation remains to be determine

Heritability of specific language impairment depends on diagnostic criteria

Heritability estimates for specific language impairment (SLI) have been inconsistent. Four twin studies reported heritability of 0.5 or more, but a recent report from the Twins Early Development Study found negligible genetic influence in 4-year-olds. We considered whether the method of ascertainment influenced results and found substantially higher heritability if SLI was defined in terms of referral to speech and language pathology services than if defined by language test scores. Further analysis showed that presence of speech difficulties played a major role in determining whether a child had contact with services. Childhood language disorders that are identified by population screening are likely to have a different phenotype and different etiology from clinically referred cases. Genetic studies are more likely to find high heritability if they focus on cases who have speech difficulties and who have been referred for intervention

Self-consistent calculation of total energies of the electron gas using many-body perturbation theory

The performance of many-body perturbation theory for calculating ground-state properties is investigated. We present fully numerical results for the electron gas in three and two dimensions in the framework of the GW approximation. The overall agreement with very accurate Monte Carlo data is excellent, even for those ranges of densities for which the GW approach is often supposed to be unsuitable. The latter seems to be due to the fulfillment of general conservation rules. These results open further prospects for accurate calculations of ground-state properties circumventing the limitations of standard density-functional theory