Obliquity Research Articles

Solar Polar Magnetic Fields: Comparing Full-disk and High-resolution Spectromagnetograph Data

This is the first systematic comparison between photospheric polar magnetic field data from a full-disk synoptic observing program, the National Solar Observatory’s Synoptic Optical Long-term Investigations of the Sun Vector Spectromagnetograph (SOLIS/VSM), and a high-resolution vector spectromagnetograph, the Hinode Solar Optical Telescope Spectropolarimeter (SOT/SP). Polar magnetic fluxes derived from longitudinal magnetic field measurements from both telescopes and from SOT/SP full-Stokes vector data are all compared in the form of polar synoptic maps. Measurements taken over 35 day periods with advantageous rotation axis tilt angle are used; observations extend to the poles, and no synthetic pole-filling is needed. Polar fluxes are derived from longitudinal data assuming an approximately radial field, whereas those derived from vector data are based on measured vector magnitude and direction. However, the full-vector measurements may have a detection problem: polar fields are observed as mostly transverse from (near) Earth, and Zeeman sensitivity to transverse fields is significantly lower than for longitudinal fields. Accordingly, the SOT/SP vector-based polar fluxes are lower than the longitudinal-based fluxes from both telescopes, a result driven by pixels without sufficient Q and U signals for the full-Stokes inversions to detect significant radial field but with good Stokes V signal implying a significant field. Furthermore, the SOT/SP longitudinal-based fluxes are significantly higher than their VSM counterparts because of superior seeing-free spatial resolution and longer observation time. The SOT/SP longitudinal-based polar fluxes appear large enough to account for radial interplanetary field measurements whereas the SOT/SP vector-based and the VSM ones are generally too low.

Experimental study on the mechanical response of metro shield tunnels obliquely crossing ground fissures

Whether the shield tunnel can be adopted to cross the ground fissure is an important issue in the field of metro construction in Xi'an, China. To study this issue, the model test and numerical simulation on a metro shield tunnel that obliquely crosses a ground fissure were carried out. The lining internal force, segment deformation and failure characteristics under the action of ground fissure dislocation were investigated. The results show that the shield tunnel obliquely crossing ground fissure exhibits three-dimensional deformation of axial bending, horizontal local torsion, and axial tension–compression, if the ground fissure dislocation takes place. The segments near ground fissure present uneven vertical dislocation, horizontal slight deflection, and axial tilt. The lining is in bias pressure state, and cracks around segment bolts nearby the vault and inverted arch of shield tunnel when the actual ground fissure dislocation reaches 24 cm. The deformation and failure of shield tunnel obliquely intersecting with the ground fissure is in the torsional-shear mode, which affects the 8 rings in the hanging wall and the 5 rings in the footwall respectively, and these segments need to be strengthened. Also, some countermeasures and suggestions are proposed to deal with the adverse impacts of ground fissure on metro shield tunnel.

Assessment of Neck Imbalance in Adolescent Idiopathic Scoliosis Patients: A Cross-Section Study Based on Body Image of 115 Patients with Main or Double Thoracic Curve.

Neck imbalance negatively affects body aesthetics of adolescent idiopathic scoliosis (AIS) patients. The evaluation of neck imbalance is currently limited to radiographic parameters, but lacks visual indicators. Therefore, the purpose of this study was to establish indexes of neck imbalance based on body image and to investigate whether these indexes can truly reflect neck imbalance in AIS patients. We performed a cross-sectional study at a single institution between June 2017 and September 2020 and there were 115 subjects involved in this research. All patients were diagnosed with adolescent idiopathic scoliosis, Lenke type I/II. Radiographic parameters measured included cervical axis tilt (CAT), T1 tilt, first rib angle (FRA), clavicle angle (CA), radiographic shoulder height (RSH), proximal thoracic curve (PTC), apical vertebra translation of proximal thoracic (AVT of PT), main thoracic curve (MTC), apical vertebra translation of main thoracic (AVT of MT) and coronal balance (CB/C7PL-CSVL). Neck imbalance indexes were obtained and measured following a standardized manner. Intra-class correlation coefficient (ICC) analysis was performed for neck imbalance indexes to determine their intra-observer and inter-observer reliability, and correlation tests were performed for neck imbalance indexes with the radiographic parameters mentioned above. Strong intraobserver and interobserver reliability were observed in neck imbalance index (NII) 1 (0.91 and 0.88), neck imbalance index 2 (0.85 and 0.81) and NII 3 (0.82 and 0.80), P < 0.05. Significant correlation was found in cervical axis tilt (R=0.81 for NII 1, R=0.77 for NII 2 and R=0.78 for NII 3), T1 tilt (R=0.43 for NII 1, R=0.52 for NII 2 and R=0.48 for NII 3), first rib angle (R=0.41 for NII 1, R=0.48 for NII 2 and R=0.43 for NII 3), proximal thoracic curve (R=0.36 for NII 2) and apical vertebra translation of proximal thoracic (R=-0.37 for NII 2 and R=-0.35 for NII 3) with neck imbalance indexes. Neck imbalance index 1 showed the highest correlation with cervical axis tilt (R=0.81, P < 0.01). Neck imbalance indexes established in our study were in good correlation with cervical axis tilt (CAT), At the meantime, they showed significant correlations with T1 tilt and first rib angle (FRA). Our study provides a practical method for measurement of neck imbalance regarding realistic perspective and makes up for the lack of photographic indexes about neck imbalance.

3D Finite Element Study of the Physiological Anchorage Control Concept on Anchorage Molars in Lingual Orthodontics.

To study the effect of the physiological anchorage control concept on anchorage molars in lingual and labial orthodontic techniques. Three-dimensional finite element models, including the right maxillary first molar, periodontal ligament, alveolar bone, and buccal tube, were established. The models were divided into the McLaughlin-Bennett-Trevisi (MBT™) straight-wire model with 0-degree maxillary first molar axial inclination and the physiologic anchorage Speewire system (PASS) model with -7-degree maxillary first molar axial inclination. Simulated sliding retraction forces (1 N, 1.5 N, and 2 N) were loaded on the buccal side and lingual side, and retraction forces (0.5 N, 0.75 N, and 1 N) were loaded on the buccal and lingual sides simultaneously. The displacements, principal stresses, and von Mises stresses of the periodontal ligament under different conditions were derived. The anchorage molars showed different degrees of rotation, tipping, intrusion, and extrusion. As the force increased, these displacement trends also increased. The mesial displacement of the buccal + lingual force loading was less than that of the other two groups. Under the same force load method, the mesial displacement of the PASS group was less than that of the MBT group. Tilt movement increases the tensile stress of the distal cervical margin and root mesial apical third and the compressive stress of the mesial cervical margin and root distal apical third. The maximum stress of the periodontal ligament was less than that of the other two groups when the lingual force was loaded. The physiological anchorage control concept in lingual orthodontics provides better sagittal anchorage control than in labial orthodontics, but there is no significant difference numerically. Attention should be given to the control of torsion, torque, and arch width. Tilt movement increases the PDL stress of the cervical margin and root apical third. The sliding retraction force should be loaded lingually to maintain the force value of 1∼1.5 N.

Atomic structures of grain boundaries for Si and Ge: A simulated annealing method with artificial-neural-network interatomic potentials

To accurately predict low-energy structures for symmetric tilt grain boundaries (GBs) in Si and Ge, artificial-neural-network (ANN) interatomic potentials are constructed and are combined with a simulated annealing (SA) method based on molecular dynamics simulations. The ANN-driven SA method is demonstrated to predict GB structures that are in good agreement with previous electron microscopy observations, without prior knowledge about their atomic configurations. Their GB energies also reasonably agree with density-functional-theory (DFT) calculations. By contrast, a conventional empirical potential fails to predict those GB structures. For misorientation angles 2θ≥93.37°, the lowest-energy structures are found to contain atomic configurations that cannot be reproduced by one repeat unit of the perfect crystal along the tilt axis. Such GB structures cannot be obtained using the γ-surface method, although it is most commonly used for exploring low-energy GB structures. These results highlight the importance of using simulation cells with multiple repeat units along the tilt axis and of performing the SA method with high-accuracy interatomic potentials transferable to GBs.

An anisotropic plastic‐damage model for 3D nonlinear simulation of masonry structures

AbstractPredicting the structural response of masonry structures with acceptable accuracy is paramount to safeguard the historical heritage and build new constructions with safety margins adequate to modern standards. However, due to the heterogeneous nature and anisotropic response of masonry, such prediction is still difficult to achieve, where most current masonry representations are based upon homogeneous isotropic material models or even more simplified masonry macro‐elements. In this article, a novel anisotropic constitutive model to be used in detailed 3D continuum FE representations is described. This is based upon the application of the transformed‐tensor method to an isotropic uncoupled plastic‐damage model, which is further enhanced by additional novel features enabling the proper definition of the shear behavior both in terms of yielding surface and damage evolution while increasing local computational robustness. Illustrative examples at different scales are presented, highlighting the characteristics and potential of the developed masonry material model. Focus is placed on the mechanical behavior under uniaxial and biaxial stress states considering pure compression on wallets with varying inclination of the material principal axes and the out‐of‐plane response of wall components. The numerical results confirm the ability of the proposed constitutive model to predict typical masonry anisotropic response characteristics, which cannot be accurately represented by standard isotropic representations commonly used in professional practice and research.

On the Nature and Origin of Atmospheric Annual and Semi-Annual Oscillations

This paper proposes a joint analysis of variations of global sea-level pressure (SLP) and of Earth’s rotation (RP), expressed as the coordinates of the rotation pole (m1, m2) and length of day (lod). We retain iterative singular spectrum analysis (iSSA) as the main tool to extract the trend, periods, and quasi periods in the data time series. SLP components are a weak trend, seven quasi-periodic or periodic components (∼130, 90, 50, 22, 15, 4, 1.8 years), an annual cycle, and its first three harmonics. These periods are characteristic of the space-time evolution of the Earth’s rotation axis and are present in many characteristic features of solar and terrestrial physics. The amplitudes of the annual SLP component and its three first harmonics decrease from 93 hPa for the annual to 21 hPa for the third harmonic. In contrast, the components with pseudo-periods longer than a year range between 0.2 and 0.5 hPa. We focus mainly on the annual and, to a lesser extent, the semi-annual components. The annual RP and SLP components have a phase lag of 152 days (half the Euler period). Maps of the first three components of SLP (that together comprise 85% of the data variance) reveal interesting symmetries. The trend is very stable and forms a triskeles structure that can be modeled as Taylor–Couette flow of mode 3. The annual component is characterized by a large negative anomaly extending over Eurasia in the NH summer (and the opposite in the NH winter) and three large positive anomalies over Australia and the southern tips of South America and South Africa in the SH spring (and the opposite in the SH autumn), forming a triskeles. The semi-annual component is characterized by three positive anomalies (an irregular triskeles) in the NH spring and autumn (and the opposite in the NH summer and winter), and in the SH spring and autumn by a strong stable pattern consisting of three large negative anomalies forming a clear triskeles within the 40–60∘ annulus formed by the southern oceans. A large positive anomaly centered over Antarctica, with its maximum displaced toward Australia, and a smaller one centered over Southern Africa, complement the pattern. Analysis of iSSA components of global sea level pressure shows a rather simple spatial distribution with the principal forcing factor being changes in parameters of the Earth’s rotation pole and velocity. The flow can probably best be modeled as a set of coaxial cylinders arranged in groups of three (triskeles) or four and controlled by Earth topography and continent/ocean boundaries. Flow patterns suggested by maps of the three main iSSA components of SLP (trend, annual, and semi-annual) are suggestive of Taylor–Couette flow. The envelopes of the annual components of SLP and RP are offset by four decades, and there are indications that causality is present in that changes in Earth rotation axis lead force pressure variations.

Remodeling morphology of the subluxated osteotomy vertebra in closing-opening wedge osteotomy in ankylosing spondylitis: would the anterior bony beak blunt?

To investigate the remodeling morphology of subluxated osteotomy vertebra in ankylosing spondylitis (AS) patients with thoracolumbar kyphosis after single-level closing-opening wedge osteotomy (COWO). Standing lateral radiographs were taken to evaluate sagittal parameters including lumbar lordosis (LL), C7 sagittal vertical axis (SVA), global kyphosis (GK), sacral slope (SS), and pelvic tilt (PT). Radiographic parameters of the osteotomy vertebra included osteotomized vertebra angle (OVA), sagittal translation (ST), anterior height (AH), posterior height (PH), and middle height (MH) of the osteotomy vertebrae. Furthermore, lateral projection area of the vertebral body was also measured to evaluate the remodeling of the osteotomy vertebrae. Sixty AS patients who underwent single-level lumbar COWO with a minimal 2-year follow-up were included. The cohort consisted of 54 males and 6 females with an average age of 36.6years. All patients were divided into two groups according to the development of vertebral subluxation (VS): 15 in VS group (ST ≥ 5mm), 45 in non-VS group (ST < 5mm). There was significant difference in the correction of GK, SVA, and the loss of correction of SVA between AS patients with and without VS. Significant difference in vertebra-related parameters regarding AH and OVA was found between VS group and non-VS group (P < 0.05). After COWO, new bone formation narrowing the gap and adaptive resorption of the anterior bony beak at the osteotomy level during follow-up was surprisingly favorable. However, the ability of spinal canal remodeling is limited in patients complicated with VS.

Numerical analysis of nucleate boiling in rolling rod bundle with tilted axis using two-fluid modeling approach

In this study, an Eulerian-Eulerian two-fluid approach was applied to simulate nucleate boiling in a vertical rolling 2 × 2 rod bundle with a tilted axis. For this purpose, the standard multiphaseEulerFoam solver of OpenFOAM was modified to include the fictitious forces necessary in a non-inertial frame of the reference formulation. High-performance computing was then applied to analyze the effects of oscillation on boiling and the physics of the fluids inside the rod bundle. In particular, the effect of a tilted rolling axis was investigated for the first time. The results indicated that the space-averaged void fraction and surface-averaged heat transfer coefficient decrease in the rolling cases compared with the stationary case. Furthermore, it was found that while the tilt angle has a negligible effect on the space-averaged values, it may have a significant impact on the maximum value of the void fraction. The higher the tilt of the rolling axis, the higher the variation in the maximum field values. The results of this study will further improve our understanding of wall nucleate boiling, which is critical for the design, development, and safety of light water-cooled reactors (LWR).

Effects of the inclination angle of oval film holes on the aero-thermal performance of a squealer blade tip

The investigation and study on the characteristics of the flow and wall heat transfer on the squealer tip is of vital importance to the safe and durable operation of a turbine rotor. The numerical model of the blade squealer tip with discrete film cooling holes (round and oval holes) was constructed and validated in this paper. The effects of the radial and axial inclination of oval-holes on aero-thermal performance were systematically investigated, which received little attentions in previous studies. The result shows that the streamline deflection produced by negative inclination structures significantly improves the coverage of film, but the development of the jet vortex leads to an enhancement in leakage flow. The lift-off of film is effectively restrained by positive inclination structures, however, the jet outflow contraction limits the expansion of film coverage. Besides, the scraping between tip cavity flow and leakage flow is also an important factor to the leakage flow control, which can reduce the momentum of leakage flow. Overall, the negative radial inclination structure achieves the optimal performance of film cooling, whose tip average cooling effectiveness at 0.5 blowing ratio is even 132% higher than that in the round hole reference at 1.5 blowing ratio. The highest relative reduction of leakage flow is obtained by the positive axial inclination structure with 62.79% at the blowing ratio of 1.5.

Spiral Groove Machining Through Wire Electrical Discharge Machining with Two Rotary Axes

In wire electrical discharge machining (WEDM) that can perform 2-D or 2.5-D machining, 3-D complex shape machining is also possible via the addition of a rotary axis on the NC table. Several examples of pin-shaped machining using a rotating shaft like spindle have been previously reported. Alternatively, machining using a rotary axis as an indexing device has also been reported. In these machining processes, the rotary axis is not servo controlled. Conversely, a spiral groove is formed on the outer circumference of the round bar by gripping the round bar workpiece on the rotary axis and performing machining in synchronization with the x- and rotary axes. In this machining, the gap control in electrical discharge machining is performed along the x- and rotary axes. Furthermore, complicated shape machining becomes possible by adding a 2-axis rotary axis of rotation and tilt. When the x-axis is synchronized with the rotation and tilt axes, a spiral groove with a variable groove width is formed. In this case, servo control is synchronized with the three axes, and machining proceeds. In this study, we performed spiral groove shape machining through WEDM with the addition of 1-axis or 2-axis rotary axes, consequently verifying the machining accuracy. Moreover, two types of NC program were used for machining, direct input and CAM output, and the accuracy was compared. The results revealed that the groove width was wider in the direct input program. Therefore, there was a possibility that the wire could bend during machining and tilt along the direction of the apparent widening of the groove width. Thus, it is necessary to consider the deflection of the wire in WEDM with a rotary axis, which is different from the conventional one, to realize precision machining.

Multishot tomography for high-resolution in situ subtomogram averaging

Cryo-electron tomography (cryo-ET) and subtomogram averaging (STA) can resolve protein complexes at near atomic resolution, and when combined with focused ion beam (FIB) milling, macromolecules can be observed within their native context. Unlike single particle acquisition (SPA), cryo-ET can be slow, which may reduce overall project throughput. We here propose a fast, multi-position tomographic acquisition scheme based on beam-tilt corrected beam-shift imaging along the tilt axis, which yields sub-nanometer in situ STA averages.

Long-term changes in the Earth's climate: Milankovitch cycles as an exercise in classical mechanics

Long-term changes in the tilt of the Earth's axis, relative to the plane of its orbit, are of great significance to long-term climate change, because they control the size of the arctic and Antarctic circles. These “Milankovitch cycles” have hitherto been calculated by classical perturbation methods or by direct numerical integration of Newton's equations of motion. This paper presents an approximate calculation from simple considerations of angular momentum using similar methods to those used to study the precession of a spinning top. It is an instructive exercise in classical mechanics and gives a simple explanation of the phenomenon in terms of angular momentum. It is shown that the main component of “Milankovitch cycles” has a period of 41,000 yr and is due to one of the modes of precession of the Earth-Venus system. The other mode of this system produces a component of period 29,500 yr, and a third component of period 54,000 yr results from the influence of the precession of the orbits of Jupiter and Saturn. These results agree closely with several of the numerical simulations in the literature and strongly suggest that some other results in the literature are incorrect.

Adjacent Segment Vertebral Body Bone Density Changes as Measured By Hounsfield Units After Lumbar Spine Fusion.

We sought to evaluate Hounsfield units (HU) at the adjacent segment after single-level transforaminal lumbar interbody fusion (TLIF) with preoperative and postoperative computed tomography scans. We performed a retrospective study on a series of patients who underwent L4-5 TLIF, from 2007 to 2017, by 3 spine surgeons at our institution. One-hundred and forty-three total patients were identified, and 41 patients with minimum 1-year follow-up met inclusion criteria. HU values were measured on preoperative and postoperative computed tomography at the adjacent L3 segment and at L1 as a control arm. Lumbar lordosis, pelvic tilt, pelvic incidence, sacral slope, and sagittal vertical axis were also collected preoperatively and postoperatively. Mean preoperative HU value at L3 did not differ from the postoperative value (134.11 ± 47.14 mg/cm3 vs. 141.21 ± 55.14 mg/cm3, P= 0.34). Similarly, the mean preoperative HU value at the L1 control level region of interest did not differ from the postoperative value (150.17 ± 53.91 mg/cm3 vs. 145.78 ± 58.34 mg/cm3, P= 0.634). The interrater reliability of HU measurements was satisfactory with a resulting intraclass correlation coefficient of 0.76. As measured by HU, we did not observe a change in bone density or other signs of adjacent segment disease at the L3 vertebral body 12 months after L4-5 TLIF. Spinopelvic parameters were not shown to be correlated with HU changes.

Study on the tracking error and focused spot trajectory characteristics of the dish concentrator under the azimuth axis tilt error

The dish concentrator is an indispensable optical device for solar dish/stirling power system, which requires accurate tracking sun’s position. However, both the foundation settlement caused by long-term service and installation error can cause the support column tilt, thus destroying the vertical relationship between the column axis (i.e. azimuth axis) and ground plane resulting tracking errors. In this paper, a tracking error model of dish concentrator with elevation–azimuth dual-axis tracking considering column tilt is developed, the radial error angle θ1 and circumferential error angle φ1 are used to describe column tilt angle and tilt direction. The concentrator tracking error and focused spot position under column tilt error are analyzed using several dimensional evaluation indexes for the whole year, every day and every moment, and are verified by a novel virtual experiment of the concentrator tracking and optical simulation. When θ1 is constant, the tracking performance is worst throughout the year at φ1 of 90° and 270°, while the influence of column tilt can be effectively reduced at φ1 of 0° or 180°. The maximum daily tracking error can reach 1.91∼3.49 mrad in whole year at θ1=0.1° and φ1 in 0°∼360°, so θ1 should be controlled within 0.1°.

Investigation on the lubrication characteristics of low-viscosity lubricated micro-grooved bearings considering turbulence and misalignment

This paper numerically investigates the effect of turbulence and journal misalignment on the lubrication characteristics of micro-grooved bearings with low-viscosity lubricant. The generalized average Reynolds equation satisfying the mass conservation cavitation algorithm is developed by integrating the average flow model proposed by Patir and Cheng, the Ng–Pan turbulent model, and the P-Θ model proposed by Elrod and Adams. With this model, the finite difference method is used in the numerical procedure. Moreover, the mathematical models of micro-grooves with different bottom shapes, that is, rectangle, isosceles triangle, left triangle, and right triangle, are given. The validity of the proposed model is verified by the comparisons with the published literature. Based on numerical simulation, the minimum film thickness, eccentricity ratio, attitude angle, maximum film pressure, friction torque, misalignment moment, film thickness, and pressure distributions under different external loads, rotational speeds, radial clearances, misalignment angles, and micro-groove parameters between models with and without turbulence and misalignment are comparatively analyzed. The numerical results reveal that turbulence may occur under heavy external load, high rotational speed, and large radius clearance. Concurrently, turbulence increases the minimum fluid film thickness and attitude angle, decreases the eccentricity ratio and friction torque, and enhances the bearing capacity. Furthermore, the larger misalignment angle results in the smaller minimum film thickness, eccentricity ratio and attitude angle, and the larger maximum film pressure, misalignment moment, and axial tilt of film pressure. Numerical simulations can provide theoretical guidance for the optimization of the geometrical parameters of micro-grooved bearings.

Teaching The Astronomical Visualization Used For The Explanation Of The Ancient Ein-Gedi Archaeological Zodiac And Its Related Inscription

In teaching the history of astronomy, mosaics found at ancient synagogues in the Middle East are invaluable. The ancient Zodiac signs forming such mosaics are related to the seasons indicating the fact that the precession of the Earth axis had been neglected or even unknown. We demonstrate that the sage’s derivations of the patriarch’s ages in the chronology of the Septuagint version of the bible correspond to the signs of the zodiac, an assumption supported, for example, by the inscription found in the ruins of the Jewish synagogue in Ein-Gedi. Through our astronomical calculations we solve the sun-moon conjunctions occurring at the beginning of the zodiac signs – at the Vernal Equinox - considering the real sun's orbit. Since the Septuagint version of the bible is assumed to have been translated into Greek in the 3rd century BC from an earlier existing Hebrew source, the fact that the ages of the patriarchs correspond to the observations of the real sun's motion, leads to the conclusion that the Septuagint version is an important book of the history of science. As a result of our findings, the bible can, thus, be regarded as one of the most ancient detailed scientific teaching sources leading to improved astronomical models which determined the planetary orbits.

High sensitivity tool for geophysical applications: a geometrically locked ring laser gyroscope.

We demonstrate that a middle sized ring laser gyroscope (RLG) can be a very sensitive and robust instrument for rotational seismology, even if it operates in a quite noisy environment. The RLG has a square cavity, 1.60×1.60m 2, and it lies in a plane orthogonal to the Earth's rotational axis. The Fabry-Perot optical cavities along the diagonals of the square were accessed, and their lengths were locked to a reference laser. Through a quite simple locking circuit, we were able to keep the sensor fully operative for 14days. We verified that the prototype properties are compatible with the seismic requirements. The obtained long term stability is of the order of 3nanorad/s, and the short term sensitivity is close to 2n a n o r a d/s⋅H z -1/2. These results are limited only by the noisy environment; our laboratory is located in a building downtown.

Changes of maxillary central incisor and alveolar bone in Class II Division 2 nonextraction treatment with a fixed appliance or clear aligner: A pilot cone-beam computed tomography study

This retrospective clinical study investigated the clinical changes of maxillary central incisor and alveolar bone in Class II Division 2 nonextraction treatment with fixed appliances or clear aligners on the basis of cone-beam computed tomography. Fifty-nine Chinese Han patients with similar demographic characteristics were collected from a conventional bracket group, a self-ligating bracket group, and a clear aligner group. All measurements about root resorption and alveolar bone thickness on the cone-beam computed tomography images were tested. Changes between pretreatment and posttreatment were evaluated by paired-sample t test. The variation among the 3 groups was compared by 1-way analysis of variance. The resistance center of the maxillary central incisor showed upward or forward movement, and the axial inclination was increased in 3 groups (P<0.0001). Root volume loss in the clear aligner group (23.68 ± 4.82 mm3) was significantly less than that in the fixed appliances group (28.24 ± 6.44 mm3 in the conventional bracket group, 28.17 ± 6.07 mm3 in the self-ligating bracket group) (P<0.05). All 3 groups showed a significant decrease in palatal alveolar bone and total bone thickness at all 3 levels at posttreatment. In contrast, labial bone thickness significantly increased except for crestal level l. Among the 3 groups, the clear aligner group had a prominent increase in labial bone thickness at the apical level (P= 0.0235). Clear aligner treatment for Class II Division 2 malocclusions could effectively reduce the incidence of fenestration and root resorption. Our findings will be beneficial to comprehensively understand the effectiveness of different appliances for Class II Division 2 malocclusions treatment.

On Two Formulations of Polar Motion and Identification of Its Sources

Differences in formulation of the equations of celestial mechanics may result in differences in interpretation. This paper focuses on the Liouville-Euler system of differential equations as first discussed by Laplace. In the “modern” textbook presentation of the equations, variations in polar motion and in length of day are decoupled. Their source terms are assumed to result from redistribution of masses and torques linked to Earth elasticity, large earthquakes, or external forcing by the fluid envelopes. In the “classical” presentation, polar motion is governed by the inclination of Earth’s rotation pole and the derivative of its declination (close to length of day, lod). The duration and modulation of oscillatory components such as the Chandler wobble is accounted for by variations in polar inclination. The “classical” approach also implies that there should be a strong link between the rotations and the torques exerted by the planets of the solar system. Indeed there is, such as the remarkable agreement between the sum of forces exerted by the four Jovian planets and components of Earth’s polar motion. Singular Spectral Analysis of lod (using more than 50 years of data) finds nine components, all with physical sense: first comes a “trend”, then oscillations with periods of ∼80 yrs (Gleissberg cycle), 18.6 yrs, 11 yrs (Schwabe), 1 year and 0.5 yr (Earth revolution and first harmonic), 27.54 days, 13.66 days, 13.63 days and 9.13 days (Moon synodic period and harmonics). Components with luni-solar periods account for 95% of the total variance of the lod. We believe there is value in following Laplace’s approach: it leads to the suggestion that all the oscillatory components with extraterrestrial periods (whose origin could be found in the planetary and solar torques), should be present in the series of sunspots and indeed, they are.