Small Rotation Research Articles

Ultra-sensitive measurement of small optical rotation angles using quantum entanglement based on a quasi-Wollaston prism beam splitter

The measurement of optical rotation is fundamental to optical atomic magnetometry. Ultra-high sensitivity has been achieved by employing a quasi-Wollaston prism as the beam splitter within a quantum entanglement state, complemented by synchronous detection. Initially, we designed a quasi-Wollaston prism and intentionally rotated the crystal axis of the exit prism element by a specific bias angle. A linearly polarized light beam, incident upon this prism, is divided into three beams, with the intensity of each beam correlated through quantum entanglement. Subsequently, we formulated the equations for optical rotation angles by synchronously detecting the intensities of these beams, distinguishing between differential and reference signals. Theoretical analysis indicates that the measurement uncertainty for optical rotation angles, when using quantum entanglement, exceeds the conventional photon shot noise limit. Moreover, we have experimentally validated the effectiveness of our method. In DC mode, the experimental results reveal that the measurement uncertainty for optical rotation angles is 4.7 × 10−9 rad, implying a sensitivity of 4.7 × 10−10 rad/Hz1/2 for each 0.01 s measurement duration. In light intensity modulation mode, the uncertainty is 48.9 × 10−9 rad, indicating a sensitivity of 4.89 × 10−9 rad/Hz1/2 per 0.01 s measurement duration. This study presents a novel approach for measuring small optical rotation angles with unprecedentedly low uncertainty and high sensitivity, potentially playing a pivotal role in advancing all-optical atomic magnetometers and magneto-optical effect research.

The impact of bone marrow stimulation on arthroscopic rotator cuff repair for small to large rotator cuff tears: a randomized controlled trial

BackgroundBone marrow stimulation (BMS), a procedure involving the creation of multiple channels in the greater tuberosity, is often performed alongside arthroscopic rotator cuff repair (ARCR). This study evaluated the effect of BMS on clinical and structural outcomes following ARCR. MethodThis study involved 204 patients with small, medium, and large full-thickness rotator cuff tears. In all, 103 patients who underwent BMS and ARCR made up the BMS group, while the 101 patients who only had ARCR made up the control group with randomization. Clinical and functional outcomes were assessed before and at 3 months, 6 months, 1 year, and 2 years after surgery, using parameters such as range of motion, functional scores (ASES and constant score), and clinical scores (VAS). Tendon integrity was also examined postoperatively via ultrasound at 6 months and 2 years. ResultsThere were no significant differences between the two groups concerning range of motion, functional scores (ASES score and constant score), and clinical score (VAS) during the 2-year post-surgery period (all p>0.05). Similarly, the rotator cuff retear rate, as assessed using ultrasonographic tendon integrity checks over 2 years post-surgery, did not significantly vary between the groups (all p>0.05). ConclusionThere were no significant disparities in functional scores and clinical outcomes between the BMS and control groups. Further, no significant differences were observed in tendon integrity post-surgery. Therefore, the inclusion or exclusion of BMS is not anticipated to influence the postoperative outcome in ARCR for patients with small, medium, or large rotator cuff tears.

Descriptive Analysis of the Long Head of the Biceps Abnormalities in Distal Isolated Supraspinatus Tears Based on Video Records: A Study From the SFA Biceps Study Group Using the “Biceps Box” Concept

Background: Considering the long head of biceps (LHB) management, important cultural differences exist among the surgeons around the world, especially when repairing small isolated distal supraspinatus tears under arthroscopy. In the perspective of an international survey to analyze our practice regarding biceps management in small rotator cuff tears, the aim is to collect all the possible LHB abnormalities according to literature review, before considering that the LHB could be normal or pathologic. Indications: The SFA (Société Francophone d’Arthroscopie) behind its research biceps group summarized these abnormalities in a description analysis called the “biceps box” concept, which was validated with a strong inter-rater reliability. The aim is to present the description analysis using a common language with short video records for each abnormality described to reproduce “intraoperatively” the different possible scenarios the surgeon has to encounter during arthroscopic evaluation. Technique Description: The description of the “biceps box” concept classifies lesions of the LHB, with so-called intrinsic lesions, for which the LHB should be considered pathological: partial rupture or delamination, fissuring, lateral or medial instability or subluxation, hypertrophy with an hourglass figure; and so-called extrinsic lesions, for which the LHB should be considered healthy: damage to the pulley without bicipital instability, exposure of the articular portion of the biceps by rupture of the supraspinatus tendon, inflammation of the superficial surface of the tendon, presence of type 1 or 2 superior labral anterior to posterior (SLAP) lesions, or a chondral print. Results: We present the 10 possible scenarios with video records according to our description analysis. Discussion/Conclusion: The LHB could be considered as a pain generator in certain situations which are still not completely clear. The indication of biceps tenotomy or tenodesis depends on the interpretation of the surgeon of these abnormalities as a pathologic or a normal condition. The next step is to use these videos in an international survey to assess cultural differences regarding the management and eventually find a consensus regarding treatment options for each abnormality. Patient Consent Disclosure Statement: The author(s) attests that consent has been obtained from any patient(s) appearing in this publication. If the individual may be identifiable, the author(s) has included a statement of release or other written form of approval from the patient(s) with this submission for publication.

High-precision measurements of terahertz polarization states with a fiber coupled time-domain THz spectrometer

We present a new method for high precision measurements of polarization rotation in the frequency range from 0.2 to 2.2 THz using a fiber coupled time-domain THz spectrometer. A free standing wire-grid polarizer splits THz light into orthogonal components that are then measured by two separate detectors simultaneously. We theoretically model the uncertainties introduced by optical component non-idealities and predict that we may expect to achieve accuracies of 0.8% when anti-symmetrizing the response with respect to an applied field. Anti-symmetrization improves accuracy by more than four orders of magnitude. We demonstrate this method on a 2D electron gas in magnetic field and show that we achieve a precision of 20 μrad (1.1 mdeg) for small polarization rotation angles. A detailed description of the technique and data analysis procedure is provided, demonstrating its capability to precisely measure polarization states in the 0.2 to 2.2 THz range.

A novel camera calibration method based on known rotations and translations

It is often difficult to align the camera optical center with the rotation center of the motion mechanism during active vision calibration, and this dis-alignment could lead to inaccuracy of the constraint equations and calibration results. To circumvent such issues, this paper proposes a novel method for active vision camera calibration and facilitates its real-world implementation. In this method, the rotational motion axis is assumed not necessarily to pass through the camera’s optical center, and the constraint equations are established by correlating image matched points before and after camera motions. The displacements caused by rotation are incorporated into the constraint equations to improve the accuracy of calibration. Numerical simulation and experiments are conducted. The feasibility of this proposed method is justified by using both synthetic and experimental data, and the results show that this method could estimate camera intrinsic parameters with high accuracy. Furthermore, it is found that small rotation angles can better the calibration accuracy even under the influence of external noises. This study suggests that this novel method has great potential for visual and image applications.

Quantum vortex phases of charged pion condensates induced by rotation in a magnetic field

Using the relativistic complex scalar field model with a repulsive self-interaction, we discuss the ground state structure of charged pion condensation under the coexistence of parallel rotation and magnetic field. Our previous study found that the density distribution profile of the condensates is a supergiant quantum vortex phase and change with rotational speed and coupling constant. In this work, we further discover vortex lattice structures in the condensates under conditions of small rotation and strong coupling constant. This mechanism can be thought of as electrical superconductivity: Vortex lattices are created to better adapt to changes in rotation and interaction. Furthermore, large rotation and weak coupling constant are more likely to cause the vortex lattices to be destroyed and form a giant quantum vortex similar to a doughnut. We expect this phenomenon can be observed in the relativistic noncentral heavy ion collisions with large rotation and strong magnetic field. Published by the American Physical Society 2024

Rotation effect on the deconfinement phase transition in holographic QCD

The impact of rotation on the deconfinement phase transition under the Einstein-Maxwell system of the soft and the hard wall models in holographic quantum chromodynamics is studied in this paper. The metric by cylindrical coordinates with rotation is introduced into the system to calculate the Hawking temperature. The first holographic study on the influence of the radius of a homogeneous rotating system on the phase diagram is proposed. It is found that the phase transition temperature hardly changes with the rotation angular velocity for a small rotation radius. Only with a larger rotation radius can the change in rotational angular velocity significantly alter the phase transition temperature. The phase transition temperature decreases rapidly with the increase of rotation angular velocity as the rotation radius increases. Published by the American Physical Society 2024

Challenges in quantifying Pt concentrations in Pd alloys by using secondary ion mass spectrometry: Strong grain orientation effects

Palladium–platinum alloys were analysed by dynamic secondary ion mass spectrometry (SIMS) to investigate grain orientation effects that gave differences of up to 400% in the Pt/Pd count rate ratios, even within the same grain upon small rotations of a Pd sample with 1 wt% Pt. The sample had been homogenized by annealing, and the homogeneity was confirmed by X‐ray analysis in scanning electron microscopy (SEM). Grain orientations were determined by electron backscatter diffraction (EBSD). Crater depths were measured by white light interferometry (WLI). SEM images from the bottom of SIMS craters made in the same grain after small rotations around the sample surface normally showed different patterns of microfaceting for some rotation angles, probably exposing low‐index crystallographic planes. A complete understanding of the observed grain orientation effect is still lacking. However, factors such as ion mass, sputter rate, ion channelling, ion focusing, preferential sputtering, surface height, crater microfaceting and/or angle‐dependent sputtering seem to play a role. For these Pd–Pt alloys, the strong grain orientation effect adds another level of complexity when attempting to quantify concentrations and obtain depth profiles by SIMS. Without proper sampling and/or averaging, one could reach very wrong conclusions when comparing results from different samples.

Altering Spin Distribution of Tb2Pc3 via Molecular Chirality Manipulation.

Manipulating the chirality of the spin-polarized electronic state is pivotal for understanding many unusual quantum spin phenomena, but it has not been achieved at the single-molecule level. Here, using scanning tunneling microscopy and spectroscopy (STM/STS), we successfully manipulate the chirality of spin distribution in a triple-decker single-molecule magnet tris(phthalocyaninato)bis(terbium(III)) (Tb2Pc3), which is evaporated on a Pb(111) substrate via molecular beam epitaxy. The otherwise achiral Tb2Pc3 becomes chiral after being embedded into the self-assembled monolayer films of bis(phthalocyaninato)terbium(III) (TbPc2). The chirality of the spin distribution in Tb2Pc3 is manifested via the spatial mapping of its Kondo resonance state from its ligand orbital. Our first-principles calculations revealed that the spin and molecular chirality are associated with a small rotation followed by a structural distortion of the top Pc, consistent with the experimental observation. By constructing tailored molecular clusters with the STM tip, a single Tb2Pc3 molecule can be manipulated among achiral and differently handed chiral configurations of spin distributions reversibly. This paves the way for designing chiral spin enantiomers for fundamental studies and developing functional spintronic devices.

Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes

We study linear scalar perturbations of slowly accelerating Kerr-Newman-anti-de Sitter black holes using the method of isomonodromic deformations. The conformally coupled Klein-Gordon equation separates into two second-order ordinary differential equations with five singularities. Nevertheless, the angular equation can be transformed into a Heun equation, for which we provide an asymptotic expansion for the angular eigenvalues in the small acceleration and rotation limit. In the radial case, we recast the boundary value problem in terms of a set of initial conditions for the isomonodromic tau function of Fuchsian systems with five regular singular points. For the sake of illustration, we compute the quasi-normal modes frequencies.

Enhancing large-scale motions and turbulent transport in rotating plane Poiseuille flow

Based on the characteristics of large-scale plume currents in rotating plane Poiseuille flows (RPPF), an injection/suction control strategy is introduced to augment the intensity of plume currents and improve the turbulent transport of passive scalar. The control strategy maintains the conventional non-penetrative condition on the stable side, and applies a wall-normal velocity that varies in the spanwise direction on the unstable side. For comparison, the control with non-penetrative condition on the unstable side and injection/suction on the stable side is also examined. The RPPF at $Re_\tau$ ranging from $180$ to $300$ and $Ro_\tau$ ranging from $0$ to $30$ are studied. Injection/suction with fixed root-mean-squared wall-normal velocity (below $1\,\%$ of the bulk mean velocity) at the wall is considered. Direct numerical simulations reveal that the injection/suction on the stable side has minor effect for all cases studied, whereas the injection/suction with properly distributed slots on the unstable side can significantly enhance the large-scale plume currents and the turbulent transport efficiency at small or moderate rotation numbers. This is attributed to the fact that plumes are generated on the unstable side, and controlling the origin of plumes is more effective. A proper strategy for maximum enhancement of turbulent transport is limiting the distance between injection slots equal to or slightly larger than the intrinsic distance between plume currents. This strategy is valid for all physical and computational parameters currently considered, and is potentially applicable over a much wider parameter range.

Dual-energy computed tomography quality control: Initial experiences with a semi-automatic analysis tool

PurposeA quality control (QC) system for dual-energy CT (DECT) was developed. The scope of the QC system was to monitor both the constancy of the CT images and the software used in calculating the DECT derived maps. Longitudinal analysis was based on a standard imaging protocol, a commercial multi-energy phantom, and a semi-automatic analysis tool. MethodsThe phantom consisted of an elliptical body section with round slots for interchangeable inserts. It was scanned with 90kVp/Sn150kVp, automatic tube current modulation, and 9.6 mGy CTDIvol. From the two conventional CT images, scanner manufacturer’s software was used to provide virtual monoenergetic images at two different energies, effective atomic number (Zeff) maps, and iodine concentration maps. The images were analyzed using an open-source tool allowing user-selected statistics of interest. The means and standard deviations of the phantom background and the iodine, calcium, and water inserts were recorded. The QC tool is available at github.com/tomakela/dectqatool. ResultsThe obtained results were generally highly consistent over time, except for the smaller diameter iodine inserts. A small change inZeff was observed after a DECT software update. The developed QC tool aided the analysis robustness: the segmentations were modifiable when needed, and small rotations or air bubbles in the water insert were easily corrected. ConclusionThe developed QC system provided easy-to-use workflow for constancy measurements. A small deviation due to change in the post-processing was detected. The proposed imaging protocol and analysis steps, and the reported measurement variations can aid in determining action levels for DECT QC.

Industrial camera model positioned on an effector for automated tool center point calibration

The study presents a novel, full model of an industrial camera suitable for robotic manipulator tool center point (TCP) calibration. The authors propose a new solution which employs a full camera model positioned on the effector of an industrial robotic arm. The proposed full camera model simulates the capture of a calibration pattern for use in automated TCP calibration. The study describes an experimental test robot stand for producing a reference data set, a full camera model, the parameters of a generally known camera obscura model, and a comparison of proposed solution with the camera obscura model. The results are discussed in the context of an innovative approach which features a full camera model to assist the TCP calibration process. The results showed that the full camera model produced greater accuracy, a significant benefit not provided by other state-of-the-art methods. In several cases, the absolute error produced was up to seven times lower than with the state-of-the-art camera obscura model. The error for small rotation (max. of 5^circ ) and small translation (max. of 20 mm) was 3.65 pixels. The results also highlighted the applicability of the proposed solution in real-life industrial processes.

Categorization of Spatial and Temporal Ejecta Outcomes in Binary Systems Based on Variations of the Didymos System

With the increasing number of binary asteroid systems being discovered, ejecta studies must expand from solely investigating single-body systems to modeling more complex multiple-body systems. For example, the Double Asteroid Redirection Test provides an opportunity to study the dynamics of a debris cloud around Didymos and Dimorphos, a near-Earth binary asteroid system. Here we simulate 72 variations on the Didymos system in order to categorize types of ejecta outcomes and analyze the influence of the varying system parameters on each outcome. We have varied five parameters: the system separation, the mass ratio between the two bodies, the impact location, the target-body shape, and the target-body rotation period. The resulting provenance maps of the final ejecta distributions were blindly sorted into five categories, while the resulting cumulative distribution functions (CDFs), describing the rate at which particles hit the surface, were blindly sorted into eight categories. We count the occurrences of the parameter values in each of the categories and apply a Cramer’s V statistical test to evaluate the significance of the association between each varied effect and the overall grouping of the provenance maps and CDFs. We conclude that more dominant effects, such as a small rotation period, produce notably similar ejecta distributions that result in being assigned to the same category. Less dominant effects, such as target-body location, are sorted into several categories due to the larger influence of varying dominant effects.

Evaluation of the Latest Motion Correction Techniques in Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction (PROPELLER) Imaging across Different Vendors

To evaluate the robustness of the latest periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) technology from each vendor against head movements and to investigate their characteristics for effective clinical use. Using a phantom simulating the T2-weighted image of the human brain, images were acquired with devices from CANON MEDICAL SYSTEMS (Tochigi, Japan; hereinafter "Canon"), GE HealthCare (Chicago, IL, USA; hereinafter "GE"), Philips (Amsterdam, Netherlands), and Siemens Healthineers (Forchheim, Germany; hereinafter "SIEMENS"). The head motion patterns were divided into rotation angle dependency (single rotation and multiple rotations) and rotation frequency dependency and evaluated using structural similarity (SSIM). For rotation angle dependency, Canon was robust against small rotation angles and fine movements. Despite the rotation angle, GE was robust against movements, with deep learning reconstruction (DLR) improving correction functionality. Philips could be used with compressed sensitivity encoding (CS), and robustness varied with blade width. SIEMENS was robust against large movements. For rotation frequency dependency, results were similar across the 4 vendors. The rotation angle and rotation frequency dependencies of the PROPELLER technology from the 4 vendors were quantitatively evaluated. Understanding the characteristics of PROPELLER allows for the possibility of providing diagnostic-quality images even for patients who move during head MRI exams by appropriately using PROPELLER.

Vibration characteristic of free-to-rotate elliptical cylinder at low Reynolds number

Investigating the vibration characteristics of elliptical cylinders is important to harvest useful energy or suppress harmful vibration, but there still exist insufficiently understood in freely rotating elliptical cylinders. Herein, this paper investigates the transverse vibration characteristics of a freely rotating elliptical cylinder at Re = 150. The incompressible Navier-Stokes equation and structural dynamics equation are solved separately, and the two-way fluid-structure interaction is performed by exchanging fluid forces and structural displacements. The elliptical cylinder, with varying axial ratios (AR = 1.0–2.5) and mass ratios (m* = 10 or 5), can vibrate transversely and rotate around its center freely. The established numerical model is verified by the published results, and the numerical values are in good agreement with the experimental results. The vibration response and flow field characteristics over a range of reduced velocities (2 ≤ Ur ≤ 14) are explored. The results demonstrate that both the axial ratio and mass ratio significantly affect the vibration characteristics. Increasing the axial ratio or decreasing the mass ratio lead to a wider synchronization region. Within the synchronization region, the elliptical cylinder undergoes significant and unstable rotation, and P + S mode can be observed. Outside the synchronization region, only a small amplitude rotation takes place near the initial position, the transverse vibration amplitude is consistent with that of a non-rotatable elliptical cylinder, and the vortex shedding mode demonstrates 2S. This work provides important guidance in investigating the vibration characteristics of the elliptical cylinder.

Dosimetric impact of rotational errors in trigeminal neuralgia radiosurgery using CyberKnife.

Trigeminal neuralgia (TN) can be treated on the CyberKnife system using two different treatment delivery paths: the general-purpose full path corrects small rotations, while the dedicated trigeminal path improves dose fall-off but does not allow rotational corrections. The study evaluates the impact of uncorrected rotations on brainstem dose and the length of CN5 (denoted as Leff) covered by the prescription dose. A proposed model estimates the delivered dose considering translational and rotational delivery errors for TN treatments on the CyberKnife system. The model is validated using radiochromic film measurements with and without rotational setup error for both paths. Leff and the brainstem dose is retrospectively assessed for 24 cases planned using the trigeminal path. For 15 cases, plans generated using both paths are compared for the target coverage and toxicity to the brainstem. In experimental validations, measured and estimated doses agree at 1%/1mm level. For 24 cases, the treated Leff is 5.3±1.7mm, reduced from 5.9±1.8mm in the planned dose. Constraints for the brainstem are met in 23 cases for the treated dose but require frequent treatment interruption to maintain rotational corrections<0.5° using the trigeminal path. The treated length of CN5, and plan quality metrics are similar for the two paths, favoring the full path where rotations are corrected. We validated an analytical model that can provide patient-specific tolerances on rotations to meet plan objectives. Treatment using the full path can reduce treatment time and allow for rotational corrections.

The Correlation between the Microstructure and the Characteristic Luminescence in the High Crystalline α-Ga2O3 Grown on the Thin-Wall Single Crystal Al2O3

A high-quality alpha-Ga2O3 thin film was grown on an Al2O3 single-crystal thin-wall channel structure. Alpha-Ga2O3 crystals are grown with a 3-fold symmetry template provided by the Al2O3 surface, which forms domain boundaries from the small rotation of the mosaic structure. The anti-phase domain (APD) was confirmed by convergent-beam electron diffraction (CBED), and it is believed to be developed at the stage of nucleation based on the unstable, or uneven Al-O bonding on the Al2O3 surface. The in-phase domain and the APD boundaries exhibit bright contrast in ADF, which originates from a local strain of crystallographic rotation and not from the local elemental fluctuations of gallium. As confirmed by CL measurement in TEM, the bandgap energy of alpha-Ga2O3 is inferred to be 5.56 eV with a near band edge transition of ~ 223 nm. Even though the heights and positions of peaks vary slightly from area to area, 4 distinct luminescence peaks and a long tail of wavelength are commonly observed throughout the crystal. 2-dimensional mapping with the specific wavelength window reveals a clear difference between the inside domain, in-phase domain boundary, and APD boundary. A luminescence peak of distinct 350 nm was observed at the APD boundary. Misorientation between domains was found, which leads to an in-plane mismatch in crystallographic lattices at the boundary when the two misoriented domains grow and the growth front merges. The imperfect lattice structure at the boundary is believed to create strain and intermediate states.

Nonlinear buckling and post-buckling analyses of functionally graded circular shallow arches

Snap-through analysis of thin, functionally graded (FG), fixed, circular shallow arches subjected to uniformly distributed vertical load is examined in this paper. The modulus of elasticity varies gradually along with the normal to the axis of the arch in alliance with the power law form. The solution of the geometrically nonlinear problem is carried out by using a numerical scheme accounting for the moderately large deflections theory based on small strain and moderate rotation in the von Kármán sense. The combined effect of the parameters that is, the power law index, the ratio of the modulus of elasticity and the modified slenderness ratio on the support reactions, the snap-buckling and post-buckling behaviors of the fixed circular shallow arches are examined. It is found that the lowest buckling load is considerably affected by the variation of these parameters. In addition, the effects of the material distribution on internal forces, deformed configurations and rotation angle are presented at various stages of the deformation.

Vortices in multilayer stacks of Bose–Einstein condensates with tilted dipoles

In this paper, we consider the formation of vortices in multilayer stacks of Bose–Einstein condensates with tilted dipoles by numerical simulations of the Gross–Pitaevskii equation. Different dependencies of critical rotation frequency (CRF) and optical lattice height, vortex number, and rotation frequency are studied, depending on the direction of the dipole axis and dipole strength. Our results show that the CRF in z = 0 is minimum. When the optical lattice height is gradually increased, the CRF decreases gradually. Reducing of dipole strength in anisotropic dipole–dipole interaction (DDI) favours the formation of vortices, and such decline in isotropic DDI hinders the creation of vortices. The reason for this difference is that the repulsive interaction is favorable and the attractive interaction is disadvantageous for the vortex formation. In addition, we study the first-order correlation function and focus on variation of coherence. For small rotation frequency, the break of coherence occurs earlier in the case of purely repulsive interaction. With an increase in rotation frequency, the coherence concurrently disappears in layer z = 2. Moreover, we also investigate the quenched dynamics, showing that the increase of angular momentum is induced by changing the direction of dipoles and in this process the vortex number remains unchanged.