Global Rotation Research Articles

Sparse Data Driven Mesh Deformation.

Example-based mesh deformation methods are powerful tools for realistic shape editing. However, existing techniques typically combine all the example deformation modes, which can lead to overfitting, i.e., using an overly complicated model to explain the user-specified deformation. This leads to implausible or unstable deformation results, including unexpected global changes outside the region of interest. To address this fundamental limitation, we propose a sparse blending method that automatically selects a smaller number of deformation modes to compactly describe the desired deformation. This along with a suitably chosen deformation basis including spatially localized deformation modes leads to significant advantages, including more meaningful, reliable, and efficient deformations because fewer and localized deformation modes are applied. To cope with large rotations, we develop a simple but effective representation based on polar decomposition of deformation gradients, which resolves the ambiguity of large global rotations using an as-consistent-as-possible global optimization. This simple representation has a closed form solution for derivatives, making it efficient for our sparse localized representation and thus ensuring interactive performance. Experimental results show that our method outperforms state-of-the-art data-driven mesh deformation methods, for both quality of results and efficiency.

An International Mutually Beneficial Global Surgery Rotation in Malawi.

An International Mutually Beneficial Global Surgery Rotation in Malawi.

Probing vorticity in heavy ion collision with dilepton production

We study the effect of vorticity present in heavy ion collisions (HICs) on the temperature evolution of hot quark-gluon plasma in the presence of spin-vorticity coupling. The initial global rotation entails a nontrivial dependence of the longitudinal flow velocity on the transverse coordinates and also develops a transverse velocity component that depends upon the longitudinal coordinate. Both of these velocities lead to a 2+1 dimensional expansion of the fireball. It is observed that with finite vorticity and spin-polarization the fireball cools faster as compared to the case without vorticity. Furthermore, we discuss the consequence of this on the production of thermal dileptons.

Hierarchical spherical deformation for cortical surface registration.

We present hierarchical spherical deformation for a group-wise shape correspondence to address template selection bias and to minimize registration distortion. In this work, we aim at a continuous and smooth deformation field to guide accurate cortical surface registration. In conventional spherical registration methods, a global rigid alignment and local deformation are independently performed. Motivated by the composition of precession and intrinsic rotation, we simultaneously optimize global rigid rotation and non-rigid local deformation by utilizing spherical harmonics interpolation of local composite rotations in a single framework. To this end, we indirectly encode local displacements by such local composite rotations as functions of spherical locations. Furthermore, we introduce an additional regularization term to the spherical deformation, which maximizes its rigidity while reducing registration distortion. To improve surface registration performance, we employ the second order approximation of the energy function that enables fast convergence of the optimization. In the experiments, we validate our method on healthy normal subjects with manual cortical surface parcellation in registration accuracy and distortion. We show an improved shape correspondence with high accuracy in cortical surface parcellation and significantly low registration distortion in surface area and edge length. In addition to validation, we discuss parameter tuning, optimization, and implementation design with potential acceleration.

Peak systolic longitudinal rotation: a new tool for detecting left ventricular systolic function in patients with type 2 diabetes mellitus by two-dimensional speckle tracking echocardiography

BackgroundType 2 diabetes mellitus (T2DM) is one of the most prevalent cardiac and cerebrovascular risk factors. The study aimed to find a new way to investigate left ventricle (LV) systolic dysfunction in T2DM patients using two-dimensional speckle tracking echocardiography (2D-STE).MethodsFifty-one untreated T2DM patients and 52 normal control subjects were enrolled for the research. Apical four-chamber view was acquired by two-dimensional echocardiography. Segmental and global peak systolic longitudinal rotation (PSLR) degrees were measured by the software of EchoPAC.ResultsIn T2DM patients, global PSLR prominently rotated clockwise, while in normal subjects, global PSLR degrees were so small and almost had no PSLR. HBA1c negatively correlated with apex and global PSLR, that is, T2DM patients with higher HBA1c had a larger clockwise apex and global PSLR. ROC analysis showed that PSLR could detect the accuracy of LV systolic dysfunction.ConclusionCardiac clockwise global PSLR was found in T2DM patients. The cardiac contractile function in T2DM patients was impaired. The new tool of PSLR can conveniently detect cardiac systolic dysfunction in T2DM patients. HBA1c could predict systolic dysfunction in T2DM patients.

A Global Plate Model Including Lithospheric Deformation Along Major Rifts and Orogens Since the Triassic

AbstractGlobal deep‐time plate motion models have traditionally followed a classical rigid plate approach, even though plate deformation is known to be significant. Here we present a global Mesozoic–Cenozoic deforming plate motion model that captures the progressive extension of all continental margins since the initiation of rifting within Pangea at ~240 Ma. The model also includes major failed continental rifts and compressional deformation along collision zones. The outlines and timing of regional deformation episodes are reconstructed from a wealth of published regional tectonic models and associated geological and geophysical data. We reconstruct absolute plate motions in a mantle reference frame with a joint global inversion using hot spot tracks for the last 80 million years and minimizing global trench migration velocities and net lithospheric rotation. In our optimized model, net rotation is consistently below 0.2°/Myr, and trench migration scatter is substantially reduced. Distributed plate deformation reaches a Mesozoic peak of 30 × 106 km2 in the Late Jurassic (~160–155 Ma), driven by a vast network of rift systems. After a mid‐Cretaceous drop in deformation, it reaches a high of 48 x 106 km2 in the Late Eocene (~35 Ma), driven by the progressive growth of plate collisions and the formation of new rift systems. About a third of the continental crustal area has been deformed since 240 Ma, partitioned roughly into 65% extension and 35% compression. This community plate model provides a framework for building detailed regional deforming plate networks and form a constraint for models of basin evolution and the plate‐mantle system.

Tokamak parameter regimes with low toroidal momentum diffusivity

The strong, sharp flow structures that are seen frequently in tokamak cores, and large amplitude spontaneous global toroidal rotation are both surprising in light of current theories where toroidal flow evolution is dominantly diffusive. Mechanisms for spontaneously generating strong poloidal shear flows have been extensively investigated, but these processes were thought not to apply to toroidal flows. We confirm, however, that there is a regime with near-zero toroidal momentum diffusivity, where toroidal flow structures are spontaneously generated, as shown in earlier global gyrokinetic simulations. This allows strong rotation with negligible applied external torque, and the regime where this occurs is also favourable for strong turbulence stabilisation by rotation. The transition to low momentum diffusivity occurs for tight aspect ratio, low safety factor and at low levels of heat flux, in agreement with a simple zero-dimensional model for the flow–turbulence interaction.

Robust Structure From Motion Based on Relative Rotations and Tie Points

In this article, we present two new approaches for image orientation with a focus on robustness, starting with relative orientations of available image pairs, an incremental and a global one, and compare their performance. For the incremental approach, we first choose a suitable initial image pair, and we then iteratively extend the image cluster by adding new images. The rotations of these newly added images are estimated from relative rotations by single rotation averaging. In the next step, a linear equation system is set up for each new image to solve the translation parameters with triangulated tie points that can be viewed in that new image, followed by a resection for refinement. Finally, we refine the orientation parameters of the images by a local bundle adjustment. We also present a global method that consists of two parts: global rotation averaging, followed by setting up a large linear equation system to solve for all image translation parameters simultaneously; a final bundle adjustment is carried out to refine the results. We compare these two methods by analyzing results on different benchmark sets, including ordered and unordered image data sets from the Internet and two other challenging data sets to demonstrate the performance of our two approaches. We conclude that while the incremental method typically yields results of higher accuracy and performs better on the challenging data sets, our global method runs significantly faster.

An SRTM-Aided Epipolar Resampling Method for Multi-Source High-Resolution Satellite Stereo Observation

Binocular stereo observation with multi-source satellite images used to be challenging and impractical, but is now a valuable research issue with the introduction of powerful deep-learning-based stereo matching approaches. However, epipolar resampling, which is critical for binocular stereo observation, has rarely been studied with multi-source satellite images. The main problem is that, under the multi-source stereo mode, the epipolar-line-direction (ELD) at an image location may vary when computed with different elevations. Thus, a novel SRTM (Shuttle Radar Topography Mission)-aided approach is proposed, where a point is transformed from the original image-space to the epipolar image-space through a global rotation, followed by a block-wise homography transformation. The global rotation transfers the ELDs at the center of the overlapping area to the x-axis, and then block-wise transformation shifts the ELDs of all grid-points to the x-axis and eliminates the y-disparities between the virtual corresponding points. Experiments with both single-source and multi-source stereo images showed that the proposed method is obviously more accurate than the previous methods that do not use SRTM. Moreover, with some of the multi-source image pairs, only the proposed method ensured the y-disparities remained within ±1 pixel.

Testing the rotation versus merger scenario in the galaxy cluster Abell 2107

We search for global rotation of the intracluster medium in the galaxy cluster Abell 2107, where previous studies have detected rotational motion in the member galaxies with a high-significance level. By fitting the centroid of the iron Kα line complex at 6.7–6.9 keV rest frame in Chandra ACIS-I spectra, we identify the possible rotation axis with the line that maximizes the difference between the emission-weighted spectroscopic redshift measured in the two halves defined by the line itself. Then, we measure the emission-weighted redshift in linear regions parallel to the preferred rotation axis, and find a significant gradient as a function of the projected distance from the rotation axis, compatible with a rotation pattern with maximum tangential velocity |${\tt v}_{\rm max}=1380\pm 600$| km s−1 at a radius λ0 ∼ 160 kpc. This result, if interpreted in the framework of hydrostatic equilibrium, as suggested by the regular morphology of Abell 2107, would imply a large mass correction of the order of |$\Delta M = (6 \pm 4)\times 10^{13} \, \mathrm{M}_\odot$| at ∼160 kpc, which is incompatible with the cluster morphology itself. A more conservative interpretation may be provided by an unnoticed off-centre, head-on collision between two comparable haloes. Our analysis confirms the peculiar dynamical nature of the otherwise regular cluster Abell 2107, but is not able to resolve the rotation versus merger scenario, a science case that can be addressed by the next-generation X-ray facilities carrying X-ray bolometers on board.

Displacement: translation and rotation. Differences and Similarities in the Discrete and Continuous Models

The motion (displacement) of the Euclidean space can be decomposed into translation and rotation. The two kinds of motion of the Euclidean space based on two structures of the Euclidean space: The first one is the topological structure, the second one is the idea of distance. The motion is such a (topological) map, that the distance of any two points remains the same. The bounded and closed domain of the Euclidean space is taken as a model of the rigid body. The bounded and closed domain of the Euclidean space is also taken as a model of the deformable solid body. The map – i.e. the displacement field – of the deformable solid body is continuous, but is not (necessarily) motion; the size and the shape of body can change. The material has atomic-molecular structure. In compliance with it, the material can be comprehended as a discrete system. In this case the elements of the material, as an atom, molecule, grain, can be comprehended as either material point, or rigid body. In the first case the kinematical freedom is the translation, in the latter case the translation and the rotation. In the paper we analyse how the kinematical behaviour of the discrete and continuous mechanical system can be characterise by translation and rotation. In the discrete system the two motions are independent variable. At the same time they characterise the movement of the body different way. For instance homogeneous local translation gives the global translation, but the homogeneous local rotation does not give the global rotation. To realise global rotation in a discrete system on one hand global rotation of the position of the discrete elements, on the other hand homogeneous local rotations of the discrete elements in harmony with global rotation are required. In the continuous system the two kinds of movement cannot be interpreted: a point cannot rotate, a rotation of surrounding of a point or direction can be interpreted. The kinematical characteristics, as the displacement (practically this is equal to translation) of (neighbourhood of) point, the rotation of surrounding of that point and the rotation of a direction went through that point are not independent variables: the translation of a point determines the rotation of the surrounding of that point as well as the rotation of a direction went through that point. With accordance this statement the displacement (practically translation) (field) as the only kinematical variable can be interpreted in the continuous medium.

Accurate recovery of 3D local field in FRP laminated beam based on asymptotic dimension reduction model

Abstract Accurate prediction of local field distribution plays an important role in failure analysis of FRP laminates. Based on the variational asymptotic method (VAM), a asymptotic dimensional reduction model (ADRM) of FRP laminated beams that can be implemented in standard finite element programs is developed, which provides a novel idea for local field recovery of FRP laminated beams. The present theory formulates the original 3D elasticity problem in a variational form, which is applicable for arbitrarily large displacement and global rotation. Then, the unknown 3D warping functions are solved asymptotically by the ADRM, resulting in the classical model (zero-order approximation) and asymptotically correct refined model (first-order approximation), respectively. Finally, the refined model is casted into a generalized Timoshenko beam model (GTM) using equilibrium equations, which can be applied conveniently in real applications. Numerical examples of FRP laminated I-beams and box-beams show that the local field distributions obtained from GTM are in good agreement with those of finite element analysis, while the computational cost and modeling effort of VAM-based analysis are significantly lower than those of direct finite element analysis.

Dynamo saturation down to vanishing viscosity: strong-field and inertial scaling regimes

We present analytical examples of fluid dynamos that saturate through the action of the Coriolis and inertial terms of the Navier–Stokes equation. The flow is driven by a body force and is subject to global rotation and uniform sweeping velocity. The model can be studied down to arbitrarily low viscosity and naturally leads to the strong-field scaling regime for the magnetic energy produced above threshold: the magnetic energy is proportional to the global rotation rate and independent of the viscosity $\unicode[STIX]{x1D708}$. Depending on the relative orientations of global rotation and large-scale sweeping, the dynamo bifurcation is either supercritical or subcritical. In the supercritical case, the magnetic energy follows the scaling law for supercritical strong-field dynamos predicted on dimensional grounds by Pétrélis & Fauve (Eur. Phys. J. B, vol. 22, 2001, pp. 271–276). In the subcritical case, the system jumps to a finite-amplitude dynamo branch. The magnetic energy obeys a magneto-geostrophic scaling law (Roberts & Soward, Annu. Rev. Fluid Mech., vol. 4, 1972, pp. 117–154), with a turbulent Elsasser number of the order of unity, where the magnetic diffusivity of the standard Elsasser number appears to be replaced by an eddy diffusivity. In the absence of global rotation, the dynamo bifurcation is subcritical and the saturated magnetic energy obeys the equipartition scaling regime. We consider both the vicinity of the dynamo threshold and the limit of large distance from threshold to put these various scaling behaviours on firm analytical ground.

Angular-momentum conservation in discretization of the Navier-Stokes equation for viscous fluids.

Although the Navier-Stokes equation (NSE) is derived under angular-momentum conservation (AMC), numerical simulation methods often lack it. Here we reveal that AMC violations result from implementation of the degenerated viscous terms of NSE. To maintain AMC, these degenerated terms must be separately integrated in accordance with their stress origins. As observed in particle-based hydrodynamics methods, the violation causes artificial rotations in multicomponent fluids with different viscosities. At the interface between two fluids or with a mobile solid object, AMC must be satisfied, whereas AMC can be neglected in bulk fluids. We also clarify that the condition for constant fluid rotation as a rigid body in a container rotating at a constant speed is not the AMC of the stresses, but the invariance of the viscous forces under a global rotation. To confirm our theory, we simulated the circular laminar flows of single- and binary-component fluids using two-dimensional Lagrangian finite-volume methods. The results show excellent agreement with the analytical predictions for fluids with and without AMC.

A Linear Threshold for Uniqueness of Solutions to Random Jigsaw Puzzles

We consider a problem introduced by Mossel and Ross (‘Shotgun assembly of labeled graphs’, arXiv:1504.07682). Suppose a random n × n jigsaw puzzle is constructed by independently and uniformly choosing the shape of each ‘jig’ from q possibilities. We are given the shuffled pieces. Then, depending on q, what is the probability that we can reassemble the puzzle uniquely? We say that two solutions of a puzzle are similar if they only differ by a global rotation of the puzzle, permutation of duplicate pieces, and rotation of rotationally symmetric pieces. In this paper, we show that, with high probability, such a puzzle has at least two non-similar solutions when 2 ⩽ q ⩽ 2e−1/2n, all solutions are similar when q ⩾ (2+ϵ)n, and the solution is unique when q = ω(n).

Cervical rotation before and after hinge-door cervical laminoplasty for cervical spondylotic myelopathy.

Background:Hinge-Door Cervical laminoplasty is commonly performed procedure in patients with cervical spondylotic myelopathy. Most available studies have established restriction of flexion and extension motion post laminoplasty but the literature on post-laminoplasty axial rotation is sparse.Objective:To study the axial neck rotation on either side following hinge door cervical laminoplasty.Materials and Methods:Twenty consecutive patients of cervical spondylotic myelopathy planned for cervical laminoplasty were included in the study. Preoperative and postoperative radiological data was recorded for each patient and analysed by an experienced neuroradiologist. The clinical and radiological follow-up was recorded at 6 months post surgery. All patients underwent standard hinge door C3-C6 laminoplasty preserving the muscle attachments to C2 and C7 vertebra.Results:There were 13 men and 7 women with a mean age of 60.5 years, age range 58-70 years. The mean preop C1 C2 rotation was 46.5 degrees and mean post-operative C1-C2 rotation was 44.3 degrees. The average subaxial cervical spine rotation was 11.66 degrees preoperatively and 12.47 degrees postoperatively. The global cervical spine rotation was 80.95 degrees preoperatively and 76.82 degrees postoperatively. There is no significant change in segmental, subaxial and global cervical spine rotation following hinge door C3-C6 laminoplasty preserving the muscle attachments to C2 and C7 vertebra.Conclusion:Cervical laminoplasty preserves cervical ROM and is a motion-preserving surgery as far as axial rotation is concerned.

Vortex filamentation and fragmentation phenomena in flapping motion and effect of aspect ratio and frequency on global strain, rotation, and enstrophy

In the present study, flow field around rigid flat plate wings executing main flapping motion has been studied using phase-locked two-dimensional particle image velocimetry measurements. Experiments have been conducted in water as a fluid medium for an asymmetric upper–lower stroke single degree of freedom main flapping motion. Two different aspect ratio (1.5 and 1.0) rectangular wings at 1.5 and 2.0 Hz flapping frequency in hovering flight mode (advance ratio, J = 0), zero wing pitch angle, and chord-based Reynolds number of the order of 104 have been studied. Velocity field and vorticity field with λ2 criterion information have been obtained for the complete stroke in great detail to reveal the minute aspects of flow dynamics. The flow features during the downstroke and upstroke have been observed to be consistent for all four cases investigated. The predominant characteristic of the flow during downstroke and upstroke has been referred to as vortex filamentation and fragmentation phenomena. Quantities such as circulation, rate of strain, rate of rotation, and enstrophy have been studied to identity the effect of minor change in aspect ratio and flapping frequency. It is found that for higher aspect ratio wing hyperbolic behavior is predominant except for end of downstroke and beginning of upstroke where elliptic behavior is observed. For lower aspect ratio, wing elliptic behavior is predominant except for end of upstroke and beginning of downstroke where hyperbolic behavior is seen. The hyperbolic behavior became stronger at higher frequency. From enstrophy distribution it is evident that higher frequencies play a more dominant role than aspect ratio in determining the budget.

Representing local atomic environment using descriptors based on local correlations.

Statistical learning of material properties is an emerging topic of research and has been tremendously successful in areas such as representing complex energy landscapes as well as in technologically relevant areas, like identification of better catalysts and electronic materials. However, analysis of large data sets to efficiently learn characteristic features of a complex energy landscape, for example, depends on the ability of descriptors to effectively screen different local atomic environments. Thus, discovering appropriate descriptors of bulk or defect properties and the functional dependence of such properties on these descriptors remains a difficult and tedious process. To this end, we develop a framework to generate descriptors based on many-body correlations that can effectively capture intrinsic geometric features of the local environment of an atom. These descriptors are based on the spectrum of two-body, three-body, four-body, and higher order correlations between an atom and its neighbors and are evaluated by calculating the corresponding two-body, three-body, and four-body overlap integrals. They are invariant to global translation, global rotation, reflection, and permutations of atomic indices. By systematically testing the ability to capture the local atomic environment, it is shown that the local correlation descriptors are able to successfully reconstruct structures containing 10-25 atoms which was previously not possible.

A Redshift Survey of the Nearby Galaxy Cluster A2107: Global Rotation of the Cluster and Its Connection to Large-scale Structures in the Universe

Abstract We study the rotational motion of the galaxy cluster A2107 at redshift z = 0.04 and its connection to nearby large-scale structures using a large amount of spectroscopic redshift data. By combining 978 new redshifts from the MMT/Hectospec observations with data in the literature, we construct a large sample of 1968 galaxies with measured redshifts at clustercentric radius R < 60′. Our sample has high (80%) and spatially uniform completeness at r-band apparent magnitude . We first apply the caustic method to the sample and identify 285 member galaxies of A2107 at R < 60′. Then the rotation amplitude and the position angle of the rotation axis are measured. We find that the member galaxies show strong global rotation at R < 20′ (v rot/σ v ∼ 0.6) with a significance of >3.8σ, which is confirmed by two independent methods. The rotation becomes weaker in outer regions. There are at least five filamentary structures that are connected to the cluster and that consist of known galaxy groups. These structures are smoothly connected to the cluster, which seem to be inducing the global rotation of the cluster through inflow of galaxies.

2D-3D Point Set Registration Based on Global Rotation Search.

Simultaneously determining the relative pose and correspondence between a set of 3D points and its 2D projection is a fundamental problem in computer vision, and the problem becomes more difficult when the point sets are contaminated by noise and outliers. Traditionally, this problem is solved by local optimization methods, which usually start from an initial guess of the pose and alternately optimize the pose and the correspondence. In this paper, we formulate the problem as optimizing the pose of the 3D points in the SE(3) space to make its 2D projection best align with the 2D point set, which is measured by the cardinality of the inlier set on the 2D projection plane. We propose four geometric bounds for the position of the projection of a 3D point on the 2D projection plane and solve the 2D-3D point set registration problem by combining a global optimal rotation search and a grid search of translation. Compared with existing global optimization approaches, the proposed method utilizes a different problem formulation and more efficiently searches the translation space, which improves the registration speed. Experiments with synthetic and real data showed that the proposed approach significantly outperformed state-of-the-art local and global methods.