Local Rotation Research Articles

Tilting of Horizontal Shear Vorticity and the Development of Updraft Rotation in Supercell Thunderstorms

AbstractThe question of how rotation arises in sheared updrafts is analyzed using the shear and curvature vorticity framework. Local rotation exists where the shear and curvature vorticity have a similar magnitude and the same sign, such that parcels are in near-solid-body rotation. It is shown that the tilting terms of the vertical vorticity equation cannot explain the development of local rotation in the canonical cases where the horizontal vorticity is either purely streamwise or purely crosswise. Rather, vertical shear vorticity develops if crosswise vorticity is tilted, and vertical curvature vorticity develops if streamwise vorticity is tilted. To analyze how local rotation develops, two simulations of updrafts in an environment with crosswise and mostly streamwise vorticity, respectively, are discussed. A trajectory analysis is performed and shear and curvature vorticity budgets are analyzed. It is found that much of the horizontal vorticity near the updraft becomes streamwise, which results from pressure gradient accelerations in the vicinity of the updraft. Consequently, in the analyzed scenarios, the tilting mechanism results primarily in vertical curvature vorticity. Local rotation is achieved via an interchange process that facilitates a partial conversion of vertical curvature vorticity to vertical shear vorticity. Updraft rotation in supercells thus does not result from tilting of horizontal vorticity alone, but partial conversion of curvature to shear vorticity is also required.

On the use of SEM correlative tools for in situ mechanical tests

In situ SEM mechanical tests are key to study crystal plasticity. In particular, imaging and diffraction (EBSD) allow microstructure and surface kinematics to be monitored all along the test. However, to get a full benefit from different modalities, it is necessary to register all images and crystallographic orientation maps from EBSD into the same frame. Different correlative approaches tracking either Pt surface markings, crystal orientations or grain boundaries, allow such registrations to be performed and displacement as well as rotation fields to be measured, a primary information for crystal plasticity identification. However, the different contrasts that are captured in different modalities and unavoidable stage motions also give rise to artifacts that are to be corrected to register the different information onto the same material points. The same image correlation tools reveal very powerful to correct such artifacts. Illustrated by an in situ uniaxial tensile test performed on a bainitic-ferritic steel sample, recent advances in image correlation techniques are reviewed and shown to provide a comprehensive picture of local strain and rotation maps.

Holography in Lovelock Chern-Simons AdS gravity

We analyse holographic field theory dual to Lovelock Chern-Simons AdS Gravity in higher dimensions using first order formalism. We first find asymptotic symmetries in the AdS sector showing that they consist of local translations, local Lorentz rotations, dilatations and non-Abelian gauge transformations. Then, we compute $1$-point functions of energy-momentum and spin currents in a dual conformal field theory and write Ward identities. We find that the holographic theory possesses Weyl anomaly and also breaks non-Abelian gauge symmetry at the quantum level.

Continuous-wave THz vector imaging system utilizing two-tone signal generation and self-mixing detection.

We propose and demonstrate a continuous-wave vector THz imaging system utilizing a photonic generation of two-tone THz signals and self-mixing detection. The proposed system measures amplitude and phase information simultaneously without the local oscillator reference or phase rotation scheme that is required for heterodyne or homodyne detection. In addition, 2π phase ambiguity that occurs when the sample is thicker than the wavelength of THz radiation can be avoided. In this work, THz signal having two frequency components was generated with a uni-traveling-carrier photodiode and electro-optic modulator on the emitter side and detected with a Schottky barrier diode detector used as a self-mixer on the receiver side. The proposed THz vector imaging system exhibited a 50-dB signal to noise ratio and 0.012-rad phase fluctuation with 100-μs integration time at 325-GHz. With the system, we demonstrate two-dimensional THz phase contrast imaging. Considering the recent use of two-dimensional arrays of Schottky barrier diodes as a THz image sensor, the proposed system is greatly advantageous for realizing a real-time THz vector imaging system due to its simple receiver configuration.

PySCu: A new python code for analyzing remagnetizations directions by means of small circle utilities

The Small Circle (SC) methods are founded upon two main starting hypotheses: (i) the analyzed sites were remagnetized contemporarily, acquiring the same paleomagnetic direction. (ii) The deviation of the acquired paleomagnetic signal from its original direction is only due to tilting around the bedding strike and therefore the remagnetization direction must be located on a small circle (SC) whose axis is the strike of bedding and contains the in situ paleomagnetic direction. Therefore, if we analyze several sites (with different bedding strikes) their SCs will intersect in the remagnetization direction.The SC methods have two applications: (1) the Small Circle Intersection (SCI) method is capable of providing adequate approximations to the expected paleomagnetic direction when dealing with synfolding remagnetizations. By comparing the SCI direction with that predicted from an apparent polar wander path, the (re)magnetization can be dated. (2) Once the remagnetization direction is known, the attitude of the beds (at each site) can be restored to the moment of the acquisition of the remagnetization, showing a palinspastic reconstructuion of the structure. Some caveats are necessary under more complex tectonic scenarios, in which SC-based methods can lead to erroneous interpretations. However, the graphical output of the methods tries to avoid ‘black-box’ effects and can minimize misleading interpretations or even help, for example, to identify local or regional vertical axis rotations. In any case, the methods must be used with caution and always considering the knowledge of the tectonic frame.In this paper, some utilities for SCs analysis are automatized by means of a new Python code and a new technique for defining the uncertainty of the solution is proposed. With pySCu the SCs methods can be easily and quickly applied, obtaining firstly a set of text files containing all calculated information and subsequently generating a graphical output on the fly.

Imaging the Structural Evolution in Nanocrystalline Metals during Mechanical Deformation

Most of our current understanding of the deformation mechanisms active in nanocrystalline (nc) metals stems from in situ deformation experiments on bulk materials using x-ray diffraction (XRD). However, XRD cannot directly resolve the local deformation processes. For a local analysis, these processes are traditionally investigated using BF/DF TEM. However, varying contrast due to local orientation changes, bending and defects during in situ BF-TEM straining experiments make an accurate interpretation for nanometer sized grains difficult. On the other hand, automated crystal orientation mapping (ACOM-TEM) [1] allows to identify the crystallographic orientation of all crystallites with sizes down to around 10 nm, well below the limit of electron back scatter diffraction (EBSD). Performing ACOM-TEM in µp-STEM mode allows to image grain orientations in situ during straining inside a TEM [2, 3]. This combination was key to a new data evaluation based on orientation maps. By tracking individual crystallites through a straining series the change of their orientation can be evaluated in order to distinguish between local crystallite rotation and sample tilting/bending [2, 3]. In addition, twinning/detwinning and grain growth can be directly followed (Fig. 1, 2) and the automatic data evaluation leads to user independent quantitative statistical information such as grain size distribution and grain rotation statistics [3].

Slip transfer across grain/twin boundaries in polycrystalline Ni-based superalloys

This study focuses on the interactions of slip bands with grain boundaries which is one of the main sources of intergranular cracking in polycrystalline nickel-based superalloys. For specific configurations where the transmission of slip bands from a grain to its neighbor is difficult, a local but significant crystal elastic rotation may appear leading to highly localized stresses in front of the tip of the active slip band in the adjacent grain. In previous works, such regions were found to be at the origin of fatigue cracks. The objective of this work is to focus on slip band activity near grain boundaries and slip transfer processes through them in order to identify which crystallographic conditions (linked to geometrical relationships between slip systems activated on both sides of the grain boundary) are more prone to favor the development of the aforementioned regions. For this purpose, a statistical analysis was carried out over a large dataset of grain boundaries configurations obtained from SEM images and EBSD scans performed on deformed samples of a Udimet™ 720 Li. A special attention was paid to the Σ3 coherent twin boundaries. The twist angle between projections of slip bands on the boundary plane was found to govern slip transfer processes in this case. The influence of the twist angle is also discussed in the case of more complex general grain boundaries but no similar conclusion has been drawn.

Gravitational waves in Friedman–Lemaitre–Robertson–Walker cosmology, material perturbations and cosmological rotation, and the Huygens principle

We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb the density and non-azimuthal components of the velocity of material medium of the Friedman–Lemaitre–Robertson–Walker spacetimes. Axial gravitational waves can influence only the azimuthal velocity, leading to local cosmological rotation. The whole gravitational dynamics reduces to the single ‘master equation’ that has the same form for polar and axial modes. That allows us to conclude that the status of the Huygens principle is the same for axial and polar gravitational waves. In particular, this principle is valid exactly in radiation spacetimes with the vanishing cosmological constant, and it is broken otherwise.

Finite-temperature phase diagram and critical point of the Aubry pinned-sliding transition in a two-dimensional monolayer

The Aubry unpinned--pinned transition in the sliding of two incommensurate lattices occurs for increasing mutual interaction strength in one dimension ($1D$) and is of second order at $T=0$, turning into a crossover at nonzero temperatures. Yet, real incommensurate lattices come into contact in two dimensions ($2D$), at finite temperature, generally developing a mutual Novaco-McTague misalignment, conditions in which the existence of a sharp transition is not clear. Using a model inspired by colloid monolayers in an optical lattice as a test $2D$ case, simulations show a sharp Aubry transition between an unpinned and a pinned phase as a function of corrugation. Unlike $1D$, the $2D$ transition is now of first order, and, importantly, remains well defined at $T>0$. It is heavily structural, with a local rotation of moir\'e pattern domains from the nonzero initial Novaco-McTague equilibrium angle to nearly zero. In the temperature ($T$) -- corrugation strength ($W_0$) plane, the thermodynamical coexistence line between the unpinned and the pinned phases is strongly oblique, showing that the former has the largest entropy. This first-order Aubry line terminates with a novel critical point $T=T_c$, marked by a susceptibility peak. The expected static sliding friction upswing between the unpinned and the pinned phase decreases and disappears upon heating from $T=0$ to $T=T_c$. The experimental pursuit of this novel scenario is proposed.

The KMOS Deep Survey (KDS) – I. Dynamical measurements of typical star-forming galaxies at z ≃ 3.5

We present dynamical measurements from the KMOS (K-band Multi-Object Spectrograph) Deep Survey (KDS), which is comprised of 77 typical star-forming galaxies at z $\simeq$ 3.5 in the mass range 9.0 < log(M$_{\star}$/M$_{\odot}$) < 10.5. These measurements constrain the internal dynamics, the intrinsic velocity dispersions ({\sigma}$_{int}$) and rotation velocities (V$_{C}$) of galaxies in the high redshift Universe. The mean velocity dispersion of the galaxies in our sample is {\sigma}$_{int}$ = $70.8^{+3.3}_{-3.1}$ km s$^{-1}$, revealing that the increasing average {\sigma}$_{int}$ with increasing redshift, reported for z $\lesssim2$, continues out to z $\simeq$ 3.5. Only 34 $\pm$ 8% of our galaxies are rotation-dominated (V$_{C}$/{\sigma}$_{int}$ > 1), with the sample average V$_{C}$/{\sigma}$_{int}$ value much smaller than at lower redshift. After carefully selecting comparable star-forming samples at multiple epochs, we find that the rotation-dominated fraction evolves with redshift with a z$^{-0.2}$ dependence. The rotation-dominated KDS galaxies show no clear offset from the local rotation velocity-stellar mass (i.e. V$_{C}$-M$_{\star}$) relation, although a smaller fraction of the galaxies are on the relation due to the increase in the dispersion-dominated fraction. These observations are consistent with a simple equilibrium model picture, in which random motions are boosted in high redshift galaxies by a combination of the increasing gas fractions, accretion efficiency, specific star-formation rate and stellar feedback and which may provide significant pressure support against gravity on the galactic disk scale.

On Minkowski Functionals of CMB polarization

CMB polarization data is usually analyzed using E and B modes because they are scalar quantities under rotations along the lines of sight and have distinct physical origins. We explore the possibility of using the Stokes parameters Q and U for complementary analysis and consistency checks in the context of searches for non-Gaussianity. We show that the Minkowski Functionals (MFs) of Q, U are invariant under local rotations along the lines of sight even though Q, U are spin-2 variables, for full sky analysis. The invariance does not hold for incomplete sky. For local type primordial non-Gaussianity, when we compare the non-Gaussian deviations of MFs for Q, U to what is obtained for E mode or temperature fluctuations, we find that the amplitude is about an order of magnitude lower and the shapes of the deviations are different. This finding can be useful in distinguishing local type non-Gaussianity from other origins of non-Gaussianity in the observed data. Lastly, we analyze the sensitivity of the amplitudes of the MFs for Q, U and the number density of singularities of the total polarization intensity to the tensor-to-scalar ratio, r, and find that all of them decrease as r increases.

Medical Image Tamper Detection Based on Passive Image Authentication.

Telemedicine has gained popularity in recent years. Medical images can be transferred over the Internet to enable the telediagnosis between medical staffs and to make the patient's history accessible to medical staff from anywhere. Therefore, integrity protection of the medical image is a serious concern due to the broadcast nature of the Internet. Some watermarking techniques are proposed to control the integrity of medical images. However, they require embedding of extra information (watermark) into image before transmission. It decreases visual quality of the medical image and can cause false diagnosis. The proposed method uses passive image authentication mechanism to detect the tampered regions on medical images. Structural texture information is obtained from the medical image by using local binary pattern rotation invariant (LBPROT) to make the keypoint extraction techniques more successful. Keypoints on the texture image are obtained with scale invariant feature transform (SIFT). Tampered regions are detected by the method by matching the keypoints. The method improves the keypoint-based passive image authentication mechanism (they do not detect tampering when the smooth region is used for covering an object) by using LBPROT before keypoint extraction because smooth regions also have texture information. Experimental results show that the method detects tampered regions on the medical images even if the forged image has undergone some attacks (Gaussian blurring/additive white Gaussian noise) or the forged regions are scaled/rotated before pasting.

The local rotation set is an interval

Let $\text{Homeo}_{0}(\mathbb{R}^{2};0)$ be the set of all homeomorphisms of the plane that are isotopic to the identity and which fix zero. Recently, in Le Roux [L’ensemble de rotation autour d’un point fixe. Astérisque (350) (2013), 1–109], Le Roux gave the definition of the local rotation set of an isotopy$I$ in $\text{Homeo}_{0}(\mathbb{R}^{2};0)$ from the identity to a homeomorphism $f$ and he asked if this set is always an interval. In this article, we give a positive answer to this question and to the analogous question in the case of the open annulus.

Facile Anhydrous Proton Transport on Hydroxyl Functionalized Graphane.

Graphane functionalized with hydroxyl groups is shown to rapidly conduct protons under anhydrous conditions through a contiguous network of hydrogen bonds. Density functional theory calculations predict remarkably low barriers to diffusion of protons along a 1D chain of surface hydroxyls. Diffusion is controlled by the local rotation of hydroxyl groups, a mechanism that is very different from that found in 1D water wires in confined nanopores or in bulk water. The proton mean square displacement in the 1D chain was observed to follow Fickian diffusion rather than the expected single-file mobility. A charge analysis reveals that the charge on the proton is essentially equally shared by all hydrogens bound to oxygens, effectively delocalizing the proton.

Homogenization of layered materials with rigid components in single-slip finite crystal plasticity

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense that it admits only local rotations, the other one is softer featuring a single active slip system with linear self-hardening. As a main result, we obtain explicit homogenization formulas by means of Gamma -convergence. Due to the anisotropic nature of the problem, the findings depend critically on the orientation of the slip direction relative to the layers, leading to three qualitatively different regimes that involve macroscopic shearing and blocking effects. The technical difficulties in the proofs are rooted in the intrinsic rigidity of the model, which translates into a non-standard variational problem constraint by non-convex partial differential inclusions. The proof of the lower bound requires a careful analysis of the admissible microstructures and a new asymptotic rigidity result, whereas the construction of recovery sequences relies on nested laminates.

Impact of land surface heterogeneity on urban heat island circulation and sea‐land breeze circulation in Hong Kong

AbstractHong Kong is one of the most high‐rise and highly compact cities in the world. The urban land surface is highly heterogeneous, which creates low‐level convergence zones in urban areas, particularly the Kowloon Peninsula. The low‐level convergence zone is due to the combined effect of urban heat island circulation (UHIC) and sea‐land breeze circulation (SLBC) under weak northeasterly synoptic flow. To study the impacts of anthropogenic fluxes and built‐up areas on the local circulation, the Weather Research and Forecasting (WRF) mesoscale model is combined with the multilayer urban canopy building effect parameterization/building energy model (BEP/BEM) parameterization to produce a 3 day simulation of an air pollution episode in Hong Kong in September 2012. To better represent the city land surface features, building information is assimilated in the central part of the Kowloon Peninsula. The WRF‐BEP‐BEM model captures the 2 m temperature distribution and local wind rotation reasonably well but overestimates the 10 m wind speed with a mean bias error of 0.70 m/s. A dome‐shaped feature with a high level of moisture is captured in the convergence zones due to intensified UHIC and inflowing SLBC. The anthropogenic heat increases the air temperature by around 0.3°C up to 250 m, which in turn modifies the SLBC. A new drag coefficient based on λP, plan area per unit ground area, is tested. Besides the basic physical characteristics captured by the WRF‐BEP‐BEM model, the stagnation of wind in the lower level convergence zone is better captured by this approach than by the traditional constant value coefficient.

Spatial Compounding Technique to Obtain Rotation Elastogram: A Feasibility Study

The perception of stiffness and slipperiness of a breast mass on palpation is used by physicians to assess the level of suspicion of a lesion as being malignant or benign. However, most current ultrasound elastography imaging methods provide only stiffness-related information. There is no existing approach that provides information about the local rigid body rotation undergone by only a loosely bonded, asymmetrically oriented lesion subjected to a small quasi-static compression. The inherent poor lateral resolution in ultrasound imaging poses a limitation in estimating the local rigid body rotation. Several techniques have been reported in the literature to improve the lateral resolution in ultrasound imaging, and among them is spatial compounding. In this study, we explore the feasibility of obtaining better-quality rotation elastograms with spatial compounding through simulations using Field II and experiments on tissue-mimicking phantoms. The phantom was subjected to axial compression (∼1%–2%) from the top, and the angular axial and lateral displacement estimates were obtained using a multilevel 2-D displacement tracking algorithm at different insonification angles. A rotation elastogram (RE) was obtained by taking half of the difference between the lateral gradient of the axial displacement estimates and the axial gradient of the lateral displacement estimates. Contrast-to-noise ratio was used to quantify the improvements in quality of RE. Contrast-to-noise ratio values were calculated by varying the maximum steering angle and the incremental angle, and its effects on RE quality were evaluated. Both simulation and experimental results corroborated and indicated a significant improvement in the quality of RE using compounding technique.

Development of a turbulent boundary layer in a rotating square cross-section channel with relatively high local rotation parameter

The development of turbulent boundary layer in a rotating square cross-section straight channel were experimentally measured using hot wire in a new rotating facility. Measurements were conducted at four streamwise stations to study the development of turbulent boundary layer along the stream wise. The governing parameters of the boundary layer are local Reynolds number uτδ/ν and local rotation parameter Ων/uτ2 (uτ is the friction velocity, δ is the thickness of boundary layer, ν is the kinematic viscosity coefficient and Ω is the angular velocity of the channel, which is defined to be positive near the trailing side wall and negative near the leading side wall). The measurements are performed in the range of 199⩽uτδ/ν⩽367 and -0.0135⩽Ων/uτ2⩽0.0054 (these values correspond to u¯D/ν=19,000 and 0⩽|Ω|D/u¯⩽0.362, here, u¯ means the cross-section averaged streamwise velocity, and D means the hydraulic diameter of the channel). Due to the relatively high local rotation parameter |Ω|ν/uτ2 on the leading side (up to 0.0135), some new phenomena were discovered, such as the critical rotation number phenomenon revealed in the variations of wall friction coefficient (the critical rotation number ranges from 0.145 to 0.362), the so-called relaminarization process near the leading side wall. Moreover, in high local rotation parameter cases, the lower limit of the Coriolis force influenced region is too close to the wall to be recognized with the traditional method, hence a new method to evaluate the influence of Coriolis force was proposed in the present work.

Galactic masers: Kinematics, spiral structure and the disk dynamic state

We applied the currently most comprehensive version of the statistical-parallax technique to derive kinematical parameters of the maser sample with 136 sources. Our kinematic model comprises the overall rotation of the Galactic disk and the spiral density-wave effects. We take into account the variation of radial velocity dispersion with Galactocentric distance. The best description of the velocity field is provided by the model with constant radial and vertical velocity dispersions, $(\sigma U0, \sigma W0) \approx (9.4 \pm 0.9~, 5.9 \pm 0.8)~ km/s$. We compute flat Galactic rotation curve over the Galactocentric distance interval from 3 to 15 kpc and find the local circular rotation velocity to be $ V_0 \approx (235-238)$~ km/s $\pm 7$~ km/s. We also determine the parameters of the four-armed spiral pattern (pitch angle $i \approx (-10.4 \pm 0.3)^\circ$ and the phase of the Sun $\chi_0 \approx (125 \pm 10) ^\circ$). The radial and tangential spiral perturbations are about $f_R \approx (-6.9 \pm 1.4)$~km/s, $f_\Theta \approx (+2.8 \pm 1.0$) ~km/s. The kinematic data yield a solar Galactocentric distance of $R_0 \approx (8.24 \pm 0.12)~kpc$. Based on rotation curve parameters and the asymmetric drift we Infer the exponential disk scale $H_D \approx (2.7 \pm 0.2)$ ~kpc under assumption of marginal stability of the intermediate-age disk, and finally we estimate the minimum local surface disk density, $\Sigma (R_0) > (26 \pm 3) ~ M_\odot pc^{-2}$.

On the mechanics of functionally graded nanobeams with the account of surface elasticity

In this paper, size-dependent bending, buckling and free vibration responses of functionally graded (FG) nanobeams are investigated using an integrated nonclassical continuum model. The integrated model accounts for the simultaneous effects of the microstructure local rotation and the surface energy in the framework of the nonlocal elasticity. The proposed nonlocal-couple stress-surface elasticity (NLCSSE) model is formulated by incorporating the Eringen nonlocal elasticity theory, modified couple stress theory and surface elasticity theory into the classical Euler–Bernoulli beam model. It is assumed that the material properties of the bulk and surface of the FG nanobeam change continuously through the thickness according to a power law. The size-dependent equations of motion and corresponding boundary conditions are derived utilizing the Hamilton's principle. The proposed model is validated by comparing the obtained results with available benchmark results. Numerical results are presented to reveal the effects of nonlocal parameter, material length scale parameter, surface energy, gradient index, Poisson ratio, thickness and length-to-thickness ratio on the deflection, critical buckling load and natural frequency of a FG simply supported nanobeam.