Angle Anisotropy Research Articles

Objective Bayesian Analysis of Geometrically Anisotropic Spatial Data

Anisotropic models are often used in spatial statistics to analyze spatially referenced data. Within a Bayesian framework we develop default priors for the anisotropic Gaussian random field model with and without including a nugget parameter accounting for the effects of microscale variations and measurement errors. We present Jeffreys priors and a reference prior and study their posterior propriety. Moreover, we obtain that the predictive distributions at ungauged locations have finite variance. We also show that the seemingly uninformative uniform prior for the anisotropy parameters, ratio and angle, yields an improper posterior. Finally, we find that the proposed priors have good frequentist properties and we illustrate our approach by analyzing two data sets for which we discuss model choice as well as predictions and uncertainty estimates.

ACCELERATION OF LOW-ENERGY IONS AT PARALLEL SHOCKS WITH A FOCUSED TRANSPORT MODEL

We present a test particle simulation on the injection and acceleration of low-energy suprathermal particles by parallel shocks with a focused transport model. The focused transport equation contains all necessary physics of shock acceleration, but avoids the limitation of diffusive shock acceleration (DSA) that requires a small pitch angle anisotropy. This simulation verifies that the particles with speeds of a fraction of to a few times the shock speed can indeed be directly injected and accelerated into the DSA regime by parallel shocks. At higher energies starting from a few times the shock speed, the energy spectrum of accelerated particles is a power law with the same spectral index as the solution of standard DSA theory, although the particles are highly anisotropic in the upstream region. The intensity, however, is different from that predicted by DSA theory, indicating a different level of injection efficiency. It is found that the shock strength, the injection speed, and the intensity of an electric cross-shock potential (CSP) jump can affect the injection efficiency of the low-energy particles. A stronger shock has a higher injection efficiency. In addition, if the speed of injected particles is above a few times the shock speed, the produced power-law spectrum is consistent with the prediction of standard DSA theory in both its intensity and spectrum index with an injection efficiency of 1. CSP can increase the injection efficiency through direct particle reflection back upstream, but it has little effect on the energetic particle acceleration once the speed of injected particles is beyond a few times the shock speed. This test particle simulation proves that the focused transport theory is an extension of DSA theory with the capability of predicting the efficiency of particle injection.

Tailoring Colloidal Photonic Crystals with Wide Viewing Angles

Photonic crystal materials are developed from colloidal crystal fibers or beads. As the fibers have cylindrical symmetry, the fiber-composed PhCs show anisotropic angle independence. By contrast, the bead-composed PhCs display angle-independent structural colors because of the spherical symmetry of their bead elements.

Cardiac diffusion tensor imaging: helix angle (HA) healthy statistical average technique for HA quantification in vivo

Background In vivo Cardiac Diffusion Tensor Imaging (cDTI) has great potential to depict the microstructure of the myocardium, with Mean Diffusivity (MD), Fractional Anisotropy (FA), and Helix Angle (HA) maps. Quantitative analysis of these parameters might help disease diagnosis, however HA is particularly difficult to quantify as it varies across the myocardial wall. To overcome this, we developed a method to quantify HA deviation from an average healthy map. This technique, together with quantitative FA and MD analysis, have been applied to healthy volunteer data by varying the number of averages to analyse the improvement of the measurements.

Myocardial diffusion tensor imaging using diffusion-prepared SSFP

Background Diffusion tensor imaging of the myocardium is challenging due to the large bulk motion of the heart relative to the distance water diffuses. One solution is to use diffusion gradients on two consecutive heartbeats, with EPI to readout the stimulated echo [1]. The technique has not been widely adopted, primarily due to the long imaging times required to overcome the low SNR of the technique. Recent new technology such as 3T scanners and 32-channel cardiac arrays improve the SNR, helping to make this approach feasible clinically. SSFP provides reduced distortion and high image quality, therefore we investigated the feasibility of replacing the EPI readout with SSFP for myocardial diffusion tensor imaging at 3T. Methods The modified ECG-gated SSFP sequence including a diffusion preparation module is shown in Figure 1a. A final 90° tip-up pulse was required to enable an SSFP readout module rather than EPI. In order to avoid signal voids due to phase accrued from sub-millimetre bulk motion between the two diffusion gradients, a dephase gradient in the slice direction was included before the tip-up pulse, with this residual phase gradient rewound during each readout [2]. The sequence was tested on a 3T Siemens Trio using a 32-channel coil. Images were acquired in diastole (650 ms after the R-wave). Two heartbeats for T1 recovery were included between each imaging module, and the following readout parameters were used: TR/TE=2.5/1.3 ms,a=120°, bandwidth 1021 Hz/px, GRAPPA (R=2), matrix size 96x92, voxel size 2.7x2.7x10 mm. One b=0 image and 3 directions with prescribed b=300 s/mm 2 were acquired in each 14-heartbeat breathhold, with three averages, requiring six breathholds for a single slice. Data were analysed in Matlab and mean diffusivity (MD), fractional anisotropy (FA) and helix angle (HA) calculated. A mid-ventricular slice was acquired in three normal volunteers and one patient with known hypertrophic cardiomyopathy (HCM). Results

Spatial distributions of ion pitch angle anisotropy in the near‐Earth magnetosphere and tail plasma sheet

We have quantified anisotropy of ion pitch angle distributions observed by the Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft and determined statistically how anisotropy varies with particle energy, as well as spatial distributions and dependences on geomagnetic activity. In the tail plasma sheet, ions from a few keV to a few tens of keV are mostly isotropic. The locations and energy ranges for these isotropic ions and their changes with Dst are consistent with ions being isotropized by current sheet scattering predicted using empirical magnetic field models. Ions of a few hundreds of keV in the tail have cigar‐shaped or unidirectional pitch angle distribution (PAD) and are likely a result of Speiser motion. The majority of ions in the near‐Earth magnetosphere are expected to conserve their first and second adiabatic invariants as they move with pitch angle dependent drift. This gives drift shell splitting, which plays an important role in generating pancake‐shaped PAD observed from ~1 keV up to hundreds of keV. The magnetic local time of the pancake PAD rotates with increasing energy. Loss of near 90° ions due to magnetopause shadowing can further explain the butterfly‐shaped PAD observed at the postmidnight sector at energies above 30 keV. For ions below a few hundreds of eV in the tail plasma sheet and the near‐Earth magnetosphere, their PAD is dominantly bidirectional, which is likely due to ionosphere outflow. High‐energy ions on the dayside become less anisotropic during higher AE, when pitch angle scattering by electromagnetic ion cyclotron waves may play an important role.

Topographical Anisotropy and Wetting of Ground Stainless Steel Surfaces

Microscopic and physico-chemical methods were used for a comprehensive surface characterization of different mechanically modified stainless steel surfaces. The surfaces were analyzed using high-resolution confocal microscopy, resulting in detailed information about the topographic properties. In addition, static water contact angle measurements were carried out to characterize the surface heterogeneity of the samples. The effect of morphological anisotropy on water contact angle anisotropy was investigated. The correlation between topography and wetting was studied by means of a model of wetting proposed in the present work, that allows quantifying the air volume of the interface water drop-stainless steel surface.

TWINS energetic neutral atom observations of local‐time‐dependent ring current anisotropy

Stereo energetic neutral atom (ENA) images from Two Wide‐angle Imaging Neutral‐atom Spectrometers (TWINS) are analyzed using a simple line‐of‐sight (LOS) mapping approximation, for two case studies: 6 April 2010 and 29 May 2010. A previous study first reported a global dawn‐dusk asymmetry favoring anisotropy on the duskside, observed by TWINS on 6 April. This paper extends and refines the previous analysis, and applies it to ENA data from 29 May, to find a second event containing the dawn‐dusk anisotropy asymmetry. Ion pitch angle distributions are retrieved using analytical expressions for anisotropy indices and their associated errors. The analysis is limited to intervals for which TWINS 1 and 2 have similar viewing geometries; i.e., the two spacecraft are at similar magnetic local time (MLT) but different latitudes, to sample two different but overlapping ranges of pitch angle. Application of the method is restricted to portions of the image for which the length of intersection of the LOS with the ENA source distribution is small. For each event, deduced pitch angle anisotropy is higher on the duskside than on the dawnside, a global asymmetry that persists for the hour‐long interval of favorable viewing geometry. The anisotropy generally decreases with energy from 1–30 keV. For 6 April the duskside anisotropy spectrum has a local peak at 12 keV, but exhibits an overall decrease over the measured energy range. For 29 May the duskside anisotropy falls monotonically with energy. Finding this previously unreported system‐level ring current attribute in two different events demonstrates that the global anisotropy is not a one‐time, unique occurrence, and also raises the question of how often and why this new phenomenon occurs. Further work is needed to determine the cause of the dawn‐dusk asymmetry in ion anisotropy. It is well known that multiple mechanisms, such as self‐consistent adiabatic ion drift, Coulomb collisions and charge exchange, influence the global ion pitch angle distribution. However, the degree to which these multiple mechanisms contribute specifically to the observed dawn‐dusk asymmetry will likely require direct comparison between the TWINS observations and simulations of these two events, including self‐consistent fields and realistic densities for the plasmasphere and neutral exosphere.

다중시험편 시험에 의한 평면이방성 암석의 탄성상수 분석연구 제 2 보 - 자료의 통계적 평가와 참값의 결정

한 개의 평면이방성 시험편으로부터 5개의 독립적 탄성상수를 결정할 수 있는 방법을 찾기 위하여 다중 시험편 시험을 수행하였다. 실험에는 유상구조가 뚜렷한 유문암의 7개의 서로 다른 각도를 갖는 총 35개 시험편을 사용하였다. 제 2보인 본 연구에서는 측정된 변형률과 해석된 탄성상수를 통계적으로 분석하고 참값을 결정하는데 중점을 두었다. 통계분석의 결과로서, 측정자료의 신뢰성은 충분히 확보되었으며, 15도 시료를 제외한 시료에서 SV 식의 적용성이 매우 높은 것으로 밝혀졌다. 각도가 증가함에 따라 탄성상수의 상대표준편차는 대체로 작아지는 경향진다. 이는 측정값의 편차가 작아지기 때문에 발생하는 현상이기도 하지만, 각도가 클수록 SV 식이 잘 적용되기 때문이라고 유추할 수 있다. 분석된 5개의 탄성상수의 크기는 높은 신뢰성을 갖고 있어 실험에서 얻을 수 있는 참값이라 할 수 있다. 그러나 이러한 값으로부터 예측한 겉보기 탄성계수는 실측된 크기들을 표현할 수 없는 것으로 판명되었다. 이러한 불일치로 미루어 겉보기 탄성계수의 크기를 감소시키거나 또는 전단변형률이 증가시키는 요인이 실험이나 평면이방성 특성에 존재한다고 판단된다. Multi-specimen uniaxial compression test has been carried out in order to find the method to determine the five independent elastic constants from a single standard specimen of a transversely isotropic rock. Total 35 specimens of 7 different angles from a large block of rhyolite presenting the flow structure obviously are used in tests. This second report is to focus on the statistical evaluation of measured strains and analyzed elastic constants. And the determination of their true or near-true values is discussed. As the result of RSD analysis, it turns out that the reliability of measured strains is sufficiently obtained and Saint-Venant approximation is well applicable except 15 degree angled specimen in tests. RSD is decreasing on the increase of the angle of anisotropy. This tendency may be caused not only by the decreasing of the deviation of measured strains, but also by the better applicability of Saint-Venant approximation on the increase of angle. It can be concluded that the analyzed values are considered the near-true ones of five independent constants on the high reliability. But the variation of the apparent Young's modulus expected by these values is not proved to match the measured tendency. It is inferred that the factor to decrease the apparent Young's modulus and/or to increase the shear strain, is present in the test or in the nature of the anisotropy in consideration of this inconsistency.

Superfluid-insulator transition of two-species bosons with spin-orbit coupling

Motivated by recent experiments [Y.J. Lin {\it et al.}, Nature {\bf 471}, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional square optical lattice with nearest neighbor hopping amplitude $t$ in the presence of a spin-orbit coupling characterized by a tunable strength $\gamma$. Using both strong-coupling expansion and Gutzwiller mean-field theory, we chart out the phase diagrams of the bosons in the presence of such spin-orbit interaction. We compute the momentum distribution of the bosons in the Mott phase near the SI transition point and show that it displays precursor peaks whose position in the Brillouin zone can be varied by tuning $\gamma$. Our analysis of the critical theory of the transition unravels the presence of unconventional quantum critical points at $t/\gamma=0$ which are accompanied by emergence of an additional gapless mode in the critical region. We also study the superfluid phases of the bosons near the SI transition using a Gutzwiller mean-field theory which reveals the existence of a twisted superfluid phase with an anisotropic twist angle which depends on $\gamma$. Finally, we compute the collective modes of the bosons and point out the presence of reentrant SI transitions as a function of $\gamma$ for non-zero $t$. We propose experiments to test our theory.

In vivo diffusion tensor MRI of the human heart: Reproducibility of breath‐hold and navigator‐based approaches

The aim of this study was to implement a quantitative in vivo cardiac diffusion tensor imaging (DTI) technique that was robust, reproducible, and feasible to perform in patients with cardiovascular disease. A stimulated-echo single-shot echo-planar imaging (EPI) sequence with zonal excitation and parallel imaging was implemented, together with a novel modification of the prospective navigator (NAV) technique combined with a biofeedback mechanism. Ten volunteers were scanned on two different days, each time with both multiple breath-hold (MBH) and NAV multislice protocols. Fractional anisotropy (FA), mean diffusivity (MD), and helix angle (HA) fiber maps were created. Comparison of initial and repeat scans showed good reproducibility for both MBH and NAV techniques for FA (P > 0.22), MD (P > 0.15), and HA (P > 0.28). Comparison of MBH and NAV FA (FAMBHday1 = 0.60 ± 0.04, FANAVday1 = 0.60 ± 0.03, P = 0.57) and MD (MDMBHday1 = 0.8 ± 0.2 × 10(-3) mm(2) /s, MDNAVday1 = 0.9 ± 0.2 × 10(-3) mm(2) /s, P = 0.07) values showed no significant differences, while HA values (HAMBHday1Endo = 22 ± 10°, HAMBHday1Mid-Endo = 20 ± 6°, HAMBHday1Mid-Epi = -1 ± 6°, HAMBHday1Epi = -17 ± 6°, HANAVday1Endo = 7 ± 7°, HANAVday1Mid-Endo = 13 ± 8°, HANAVday1Mid-Epi = -2 ± 7°, HANAVday1Epi = -14 ± 6°) were significantly different. The scan duration was 20% longer with the NAV approach. Currently, the MBH approach is the more robust in normal volunteers. While the NAV technique still requires resolution of some bulk motion sensitivity issues, these preliminary experiments show its potential for in vivo clinical cardiac diffusion tensor imaging and for delivering high-resolution in vivo 3D DTI tractography of the heart.

Modeling and free vibration behavior of rotating composite thin-walled closed-section beams with SMA fibers

Smart structure with active materials embedded in a rotating composite thin-walled beam is a class of typical structure which is using in study of vibration control of helicopter blades and wind turbine blades. The dynamic behavior investigation of these structures has significance in theory and practice. However, so far dynamic study on the above-mentioned structures is limited only the rotating composite beams with piezoelectric actuation. The free vibration of the rotating composite thin-walled beams with shape memory alloy(SMA) fiber actuation is studied. SMA fiber actuators are embedded into the walls of the composite beam. The equations of motion are derived based on Hamilton's principle and the asymptotically correct constitutive relation of single-cell cross-section accounting for SMA fiber actuation. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin's method. The formulation for free vibration analysis includes anisotropy, pitch and precone angle, centrifugal force and SMA actuation effect. Numerical results of natural frequency are obtained for two configuration composite beams. It is shown that natural frequencies of the composite thin-walled beam decrease as SMA fiber volume and initial strain increase and the decrease in natural frequency becomes more significant as SMA fiber volume increases. The actuation performance of SMA fibers is found to be closely related to the rotational speeds and ply-angle. In addition, the effect of the pitch angle appears to be more significant for the lower-bending mode ones. Finally, in all cases, the precone angle appears to have marginal effect on free vibration frequencies. The developed model can be capable of describing natural vibration behaviors of rotating composite thin-walled beam with active SMA fiber actuation. The present work extends the previous analysis done for modeling passive rotating composite thin-walled beam.

Polarimetric Decomposition Analysis of ALOS PALSAR Observation Data before and after a Landslide Event

Radar scattering mechanisms over landslide areas were studied using representative full polarimetric parameters: Freeman–Durden decomposition, and eigenvalue–eigenvector decomposition. Full polarimetric ALOS (Advanced Land Observation Satellite) PALSAR (Phased Array type L-band Synthetic Aperture Radar) datasets were used to examine landslides caused by the 2008 Iwate-Miyagi Nairiku Earthquake in northern Japan. The Freeman–Durden decomposition indicates that areas affected by large-scale landslides show dominance of the surface scattering component in both ascending and descending orbit data. The polarimetric parameters of eigenvalue–eigenvector decomposition, such as entropy, anisotropy, and alpha angle, were also computed over the landslide areas. Unsupervised classification based on the H- plane explicitly distinguishes landslide areas from others such as forest, water, and snow-covered areas, but does not perform well for farmland. A landslide area is difficult to recognize from a single-polarization image, whereas it is clearly extracted on the full polarimetric data obtained after the earthquake. From these results, we conclude that 30-m resolution full polarimetric data are more useful than 10-m resolution single-polarization PALSAR data in classifying land coverage, and are better suited to detect landslide areas. Additional information, such as pre-landslide imagery, is needed to distinguish landslide areas from farmland or bare soil.

Anisotropy of elastic moduli, P-wave velocities, and thermal conductivities of Asan Gneiss, Boryeong Shale, and Yeoncheon Schist in Korea

This paper presents the anisotropic characteristics of the elastic moduli, P-wave velocities, and thermal conductivities of three types of anisotropic rocks, i.e., Asan gneiss, Boryeong shale, and Yeoncheon schist, occurring in Korea. The experiments were conducted on rock samples that show clear evidence of transverse isotropy. Cylindrical core samples with different anisotropy angles were prepared by coring at 15-degree intervals from the transversely isotropic plane using the laboratory directional coring system established for this study. Elastic moduli, P-wave velocities, and thermal conductivities were determined along the sample axis for different anisotropy angles. The anisotropy ratio is defined as the ratio of the properties parallel to the transversely isotropic plane to those perpendicular to the plane, and the anisotropy ratios for the thermal conductivities (K(90°)/K(0°)) of Asan gneiss, Boryeong shale, and Yeoncheon schist were 1.4, 2.1, and 2.5, respectively. The P-wave velocity anisotropy ratios (VP(90°)/VP(0°)) for Asan gneiss, Boryeong shale, and Yeoncheon schist were 1.2, 1.5, and 2.3, respectively. The elastic moduli, P-wave velocities, and thermal conductivities that were obtained were compared with theoretical predictions by mean prediction error (MPE). The correlations between the measured properties were evidently correlated with some minor scatter in the data. The degree of anisotropy measured in this study suggests that ignoring anisotropy in rock properties may mislead to erroneous results. The application of tensorial transformation evaluations revealed that the three types of rocks chosen for this study can be modeled effectively by a transversely isotropic model.

COMPARISON OF MICROWAVE BACKSCATTER ANISOTROPY PARAMETERISATIONS OVER THE ANTARCTIC ICE SHEET

Abstract. The Antarctic Ice Sheet exhibits a strong anisotropy in microwave backscatter, both as a function of azimuth angle and incidence angle. This anisotropy arises as a result of i) the alignment of roughness elements and other wind-related surface and sub-surface features, as well as ii) internal layers and snow grain size gradient within the snowpack. As a result of its antenna configuration, the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) Advanced SCATterometer (ASCAT) satellite instrument is able to observe much of the continent with a large azimuth and incidence angle diversity. A lack of azimuth and incidence diversity has restricted previous backscatter parameterisations to relatively simple bi-sinusoidal (azimuth angle) and linear (incidence angle) parameterisations. Using ASCAT, we show that a better fit can be obtained using a cubic incidence angle function and a Fourier series of up to four terms for parameterisation of the azimuth angle anisotropy. Scatterometer instruments have previously been used in Greenland to retrieve accumulation rate by observing the change in backscatter as a function of incidence angle. Here we present preliminary results of an empirical study linking the isotropic component and incidence angle dependence to snow accumulation rate in Antarctica, using snow stake measurements as ground truthing.

Ductile failure of X100 pipeline steel – Experiments and fractography

Ductile failure of X100 pipeline steel is studied. In order to study the effect of anisotropy, triaxiality factor and Lode angle on the failure, a series of specimens with different geometries are tested. Measurements of deformation in three dimensions are done to check the variation of elongation and lateral deformations during loading. Extensive fractography is done using pictures taken by SEM to study the fracture surfaces completely. The results show that triaxiality causes the failure to occur sooner and Lode angle has no effect on the failure in triaxialities higher than that of simple tension. Moreover, delamination has occurred in some of the specimens. This phenomenon is studied and the causes of delamination are explained in macro scale.

Whistler mode wave growth and propagation in the prenoon magnetosphere

Pitch angle scattering of electrons can limit the stably trapped particle flux in the magnetosphere and precipitate energetic electrons into the ionosphere. Whistler mode waves generated by a temperature anisotropy can mediate this pitch angle scattering over a wide range of radial distances and latitudes, but in order to correctly predict the phase space diffusion, it is important to characterize the whistler mode wave distributions that result from the instability. We use previously published observations of number density, pitch angle anisotropy, and phase space density to model the plasma in the quiet prenoon magnetosphere (defined as periods when AE < 100 nT). We investigate the global propagation and growth of whistler mode waves by studying millions of growing raypaths and demonstrate that the wave distribution at any one location is a superposition of many waves at different points along their trajectories and with different histories. We show that for observed electron plasma properties, very few raypaths undergo magnetospheric reflection; most rays grow and decay within 30 degrees of the magnetic equator. The frequency range of the wave distribution at large L can be adequately described by the solutions of the local dispersion relation, but the range of wave normal angle is different. The wave distribution is asymmetric with respect to the wave normal angle. The numerical results suggest that it is important to determine the variation of magnetospheric parameters as a function of latitude, as well as local time and L‐shell.

Influence of Anisotropic Internal Friction Angle on the Stability of Uniform Soil Slopes

The effect of anisotropy of friction angle in natural deposited soil on the stability of soil slopes was studied in this paper. Stability analysis was performed on a uniform soil slope with anisotropic friction angle. Spencer’s method was used, and the variation of friction angle was assumed to be linear to the change of direction of the slip surface. It was shown that 7-10 percent of change in safety factor might achieve within a 10m-highed anisotropic soil slope. It was also found from the analysis that that frictional anisotropy had no obvious effect on the location of critical slip surface.

An Icon-Based Synoptic Visualization of Fully Polarimetric Radar Data

The visualization of fully polarimetric radar data is hindered by traditional remote sensing methodologies for displaying data due to the large number of parameters per pixel in such data, and the non-scalar nature of variables such as phase difference. In this paper, a new method is described that uses icons instead of image pixels to represent the image data so that polarimetric properties and geographic context can be visualized together. The icons are parameterized using the alpha-entropy decomposition of polarimetric data. The resulting image allows the following five variables to be displayed simultaneously: unpolarized power, alpha angle, polarimetric entropy, anisotropy and orientation angle. Examples are given for both airborne and laboratory-based imaging.

SPATIAL POWER SPECTRUM OF MULTIPLE SCATTERED ORDINARY AND EXTRAORDINARY WAVES IN MAGNETIZED PLASMA WITH ELECTRON DENSITY FLUCTUATIONS

Features of the spatial power spectrum (SPS) of multiple scattered ordinary and extraordinary waves in randomly inhomogeneous magnetized plasma are investigated using the smooth perturbation method taking into account difiraction efiects. Second order statistical moments are derived for arbitrary correlation function of electron density ∞uctuations at oblique illumination of magnetized plasma by mono-directed incident radiation. Numerical calculations have been carried out for anisotropic Gaussian correlation function taking into account anisotropy factor and angle of inclination of prolate irregularities with respect to the external magnetic fleld. It was shown that SPS has a double-peaked shape. External magnetic fleld narrows SPS for ordinary wave and the gap arises in the direction of prolate irregularities. For extraordinary wave the gap increases with a distance passing by the wave in anisotropic magnetized plasma, the width broadens and maximum slightly displaced.