An algebraic method of strain analysis using elliptical markers

Samples of deformed pebbles in the slates from the Manjir Formation were collected from normal and inverted limbs of the Chamba Syncline. The axial ratios and orientation on two dimensional sections were determined from deformed quartz pebbles. The finite strain was calculated using Rf/f technique. The two dimensional data were combined to give three dimensional finite strain and type of strain experienced by the pebbles at each locality. Regional variation in the strain distribution is represented by finite distortional strain (es) for both normal and inverted limbs of the syncline. The results show that the deformation is of flattening type and the amount of strain increases from inner arc to outer arc of the Chamba Syncline. A total of about 28 per cent shortening has been noticed in the Manjir Formation.

A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor to approximate a set of unitary operators to a specified level of precision. We measure how well an operation is performed by the process fidelity between the desired operation and the operation produced by the processor. We show how to find the program for a given processor that produces the best approximation of a particular unitary operation. We also place bounds on the dimension of the program space that is necessary to approximate a set of unitary operators to a specified level of precision.

Estimation of the offset between two network clocks has received a lot of attention in the literature, with the motivating force being data networking applications that require synchronous communication protocols. Statistical modeling techniques have been used to develop improved estimation algorithms, with a recent development being the construction of a confidence interval based on a fixed sample size. Lacking in the fixed sample size confidence interval procedures is a useable relationship between sample size and the width of the resulting confidence interval. Were that available, an optimum sample size could be determined to achieve a specified level of precision in the estimator and thereby improve the efficiency of the estimation procedure by reducing unnecessary overhead in the network that is associated with collecting the data used by the estimation schemes. A fixed sample size confidence interval that has a prescribed width is not available for this problem. However, in this paper we develop and compare alternative sequential intervals with fixed width and demonstrate that an effective solution is available.

Free convection heat transfer inside vertical and inclined elliptic tubes with different axis ratio and different inclination and orientation angles

The present study deals with the Jabal Tays ophiolite area, which was affected by Al Amar-Idsas fault. It is one of the most important tectonic features in the Eastern Arabian Shield. This study aims to accomplish through field investigation, finite strain and microstructural analysis for understanding the nature of tectonic evolution and the deformation in the Jabal Tays area. Field and microscopic investigations indicate that mafic-ultramafic rocks at Jabal Tays include the large amount of serpentinite, subordinate amounts of gabbro intruded by mafic dikes, melange, serpentinite schist, and listwaenite. The serpentinite makes up the bulk of Jabal Tays, is variably sheared and typically consists of relatively massive serpentinite cut by shear zones marked by serpentinite schist. Based on finite strain and microstructural analysis, mafic-ultramafic rocks in the Jabal Tays area are generally confined to brittle-ductile shear zones, which they are sub-parallel to the prevailing NW or NNW structural trends. It is confined mainly to the metamorphic terrains, especially to zones intruded by mafic volcanic rocks. It is concluded that the contacts between the Abt schist and metavolcano-sedimentary rocks were formed during progressive thrusting under brittle to semi-ductile deformation conditions by simple shear that also involved a component of vertical shortening, causing subhorizontal foliation in the Jabal Tays area.

RPHIN—A FORTRAN 77 program for acquiring axial ratios, long axis orientations and centroid positions of elliptical strain markers

We have completed an investigation (preliminary results for which were reported in Oleak et al. 1995) into the shapes of Shakhbazian compact groups of galaxies. Ellipticites for 299 groups in the Shakhbazian survey have been examined using the technique proposed by Rood (1979) for deriving the average “flatness” of a large sample of objects. The distribution of the apparent axial ratios (g = b/a) for the groups is found to be broad with a mean of< b/a > ∽ 0.5. This distribution is compared with randomly generated spherical and elliptical model systems. The results confirm the findings of our earlier study: the frequency distribution of axial ratios for Shakhbazian groups is represented soley by a population of prolate spheroids with low intrinsic axial ratios, < q > = 0.3, σ = ∽0.17 (assuming random true orientations in 3D space). This now provides further strong evidence that the Shakhbazian groups are more highly flattened than either rich clusters or elliptical galaxies, and represent the most elongated systems yet found. The result also provides confirmation of the reality of the groups, since in the case of systems of chance line‐of‐sight superpositions of galaxies we would expect to see much higher axial ratios.

Strain analysis method using the maximum frequency of unimodal deformed orientation distributions: applications to gneissic rocks

Strain analysis method using the maximum frequency of unimodal deformed orientation distributions: applications to gneissic rocks : J Struct Geol V13, N3, 1991, P329–335

Finite strain and strain variation analysis in the Sheeprock Thrust Sheet: an internal thrust sheet in the Provo salient of the Sevier Fold-and-Thrust belt, Central Utah

We revisit the non-sphericity of cluster-mass-scale halos from cosmological N-body simulation on the basis of triaxial modeling. In order to understand the difference between the simulation results and the conventional ellipsoidal collapse model (EC), we first consider the evolution of individual simulated halos. The major difference between EC and the simulation becomes appreciable after the turnaround epoch. Moreover, it is sensitive to the individual evolution history of each halo. Despite such strong dependence on individual halos, the resulting non-sphericity of halos exhibits weak but robust mass dependence in a statistical fashion; massive halos are more spherical up to the turnaround, but gradually become less spherical by z = 0. This is clearly inconsistent with the EC prediction: massive halos are usually more spherical. In addition, at z = 0, inner regions of the simulated halos are less spherical than outer regions; that is, the density distribution inside the halos is highly inhomogeneous and therefore not self-similar (concentric ellipsoids with the same axis ratio and orientation). This is also inconsistent with the homogeneous density distribution that is commonly assumed in EC. Since most of previous fitting formulae for the probability distribution function (PDF) of the axis ratio of triaxial ellipsoids have been constructed under the self-similarity assumption, they are not accurate. Indeed, we compute the PDF of the projected axis ratio a1/a2 directly from the simulation data without the self-similarity assumption, and find that it is very sensitive to the assumption. The latter needs to be carefully taken into account in direct comparison with observations, and therefore we provide an empirical fitting formula for the PDF of a1/a2. Our preliminary analysis suggests that the derived PDF of a1/a2 roughly agrees with the current weak-lensing observations. More importantly, the present results will be useful for future exploration of the non-sphericity of clusters in X-ray and optical observations.

Background: Axillary lymph node (ALN) enlargement with diffuse cortical thickening and conserved echogenic hilum may represent a diagnostic and therapeutic challenge. Sonographic strain elastography may help the characterization of borderline ALN. Aim: To evaluate the strain elastography of borderline ALN and to calculate a cutoff value of strain ratio (SR) that can identify suspicious ALN with the highest sensitivity and specificity to reduce unnecessary invasive procedures. Subjects and Methods: A prospective study included 45 patients who attended the Breast clinic in Oncology Teaching Hospital with borderline axillary lymphadenopathy (intact hilum and diffusely thickened cortex more than 3mm) who had normal ipsilateral breast, suspicious ipsilateral breast lesion, or who had ipsilateral mastectomy. B-mode sonography and elastography were performed for all participants. Four-point elasticity score (ES), and SR were obtained for the targeted lymph node followed by ultrasound-guided fine need aspirate (FNA) biopsy.. Results: Malignant ALN constituted 20% of the cohort. B mode measurements were not able to differentiate between cytologically confirmed benign and malignant ALN in terms of axis ratio (mean ± standard deviation, 0.46 ± 0.08 vs 0.50 ± 0.12) and cortical thickness (4.88 ± 1.93 vs 6.27 ± 2.46). The mean SR of all samples was 2.66 ± 2.25. Metastatic ALN depicted significantly higher SR (P<0.0001), with 88.9% exhibiting ES score 3 and 4. None of the metastatic ALN had ES score 1. ROC curve was used to investigate the utility of SR as a diagnostic tool. The area under the curve (AUC) was 0.906 with a 95% CI of 0.814-0.997, P<0.001. SR cutoff of 2.1 was chosen with 100% sensitivity and 66.7% specificity. Conclusion: High proportion of borderline ALNs are not malignant. Strain elasticity can improve the risk stratification of such cases and prevent unnecessary invasive procedures. We suggested an algorithm that could better tackle borderline ALN which will need further evaluation

A thick-walled cylindrical specimen containing an external circumferential groove was subjected to external pressure. To investigate the maximum pressure sustainable by the reduced wall thickness, strain gage measurements were taken during external pressurization tests. For comparison to experimental results, an elastic-plastic notch stress-strain analysis was conducted based on Neuber’s rule. The analysis utilized multiaxial elastic finite element results along with elastic-plastic tensile test data for the cylinder material. Based on experimental observations, it was necessary to supplement the approach with an additional relation between elastic and elastic-plastic multiaxial strains for the axisymmetric geometry under investigation. Assuming an invariant hoop to radial strain ratio rather than an invariant hoop to axial strain ratio provided better agreement with experimental results. It is demonstrated that the boundary conditions used to model the specimen had a substantial effect on the finite element results, even though the boundary was somewhat removed from the region of concentrated stress. Biaxial strain measurements are presented versus pressure over the elastic and into the plastic regime, and deformation plasticity theory was used to compute stress and radial strain components corresponding to measured strains. It is demonstrated that in order to apply a multiaxial Neuber’s rule to accurately estimate the elastic-plastic stress-strain response (using elastic stress concentration information and elastic-plastic material data), it is necessary to utilize an experimental observation that the ratio of the hoop to radial strain remains invariant from the elastic to the elastic-plastic regime. This differs from published assumptions about invariant hoop-to-axial strain ratios based on analysis of circumferentially grooved solid shafts. The predictions are accurate for moderate plastic strains, but correlation breaks down for bulk plastic deformation.

By modifying the horizontal and vertical scanning circuits of a closed circuit television camera, it is possible to produce, on the TV screen, ellipses with more than five to one axial ratios from circular markers that are being filmed. On some cameras strain ratios of 20:1 are possible. Any shape (complex or simple) being filmed is similarly transformed and the effects of homogeneous pure-shear strain on fossils, sedimentary fabrics, folds, ellipses, ect., can be clearly demonstrated. The complete straining sequence can be followed from the initial state through progressively increasing strain ratios. Reversals of strain can also be performed so that strain estimates can be obtained when deformed materials are studied. By photographing the screen, material for student exercises (e.g., fold profile classification, strain from deformed trilobites and brachiopods, and bedding symmetric fabrics) can be obtained quickly and easily. Amounts of strain can be varied continuously allowing great variation in the p...

We investigate the intrinsic shapes of low-luminosity galaxies in the central 300 kpc of the Virgo Cluster using deep imaging obtained as part of the Next Generation Virgo Cluster Survey (NGVS). We build a sample of nearly 300 red-sequence cluster members in the yet-unexplored −14 < M g < −8 mag range, and we measure their apparent axis ratios, q, through Sérsic fits to their two-dimensional light distribution, which is well described by a constant ellipticity parameter. The resulting distribution of apparent axis ratios is then fit by families of triaxial models with normally distributed intrinsic ellipticities, E = 1 − C/A, and triaxialities, T = (A 2 − B 2)/(A 2 − C 2). We develop a Bayesian framework to explore the posterior distribution of the model parameters, which allows us to work directly on discrete data, and to account for individual, surface-brightness-dependent axis ratio uncertainties. For this population we infer a mean intrinsic ellipticity E ¯ ?> = 0.43 - 0.02 + 0.02 ?> and a mean triaxiality T ¯ ?> = 0.16 - 0.06 + 0.07 ?> . This implies that faint Virgo galaxies are best described as a family of thick, nearly oblate spheroids with mean intrinsic axis ratios 1:0.94:0.57. The core of Virgo lacks highly elongated low-luminosity galaxies, with 95% of the population having q > 0.45. We additionally attempt a study of the intrinsic shapes of Local Group (LG) satellites of similar luminosities. For the LG population we infer a slightly larger mean intrinsic ellipticity E ¯ ?> = 0.51 - 0.06 + 0.07 ?> , and the paucity of objects with round apparent shapes translates into more triaxial mean shapes, 1:0.76:0.49. Numerical studies that follow the tidal evolution of satellites within LG-sized halos are in good agreement with the inferred shape distributions, but the mismatch for faint galaxies in Virgo highlights the need for more adequate simulations of this population in the cluster environment. We finally compare the intrinsic shapes of NGVS low-mass galaxies with samples of more massive quiescent systems, and with field, star-forming galaxies of similar luminosities. We find that the intrinsic flattening in this low-luminosity regime is almost independent of the environment in which the galaxy resides, but there is a hint that objects may be slightly rounder in denser environments. The comparable flattening distributions of low-luminosity galaxies that have experienced very different degrees of environmental effects suggest that internal processes are the main drivers of galaxy structure at low masses, with external mechanisms playing a secondary role.