Wobbling motion for a triaxial rotor plus a single quasiparticle

Wobbling motion in a system comprising a triaxial rotor and a single quasiparticle is studied employing the particle-rotor model.The energy spectra,wobbling frequencies,electromagnetic transition probabilities,g-factors,angular momentum components,spin coherent state maps,and static quadrupole moments are investigated.These investigations were conducted with regard to the Fermi surface transitioning from the lowest h_(11/2) orbit to the highest one.As the Fermi surface increases,notable transformations occur in the wobbling mode.Initially,the mode exhibits a transverse revolution around the short axis of the nucleus.However,as the Fermi surface continues to increase,the mode gradually shifts to a longitudinal revolution around the intermediate axis.Eventually,it transitions to a transverse revolution around the long axis.Notably,the stability of the long axis transverse mode diminishes relative to its counterpart along the short axis as the total angular momentum increases atγ=20∘.

Wobbling Motion in the Even-even Nucleus

The recent progresses on the wobbling motion are briefly introduced.So far 17 wobbling candidates have been reported in odd-A and even-even nuclei that spread over A≈100,130,160 and 190 mass regions.The two-quasiparticle configuration wobbling in 130Ba and the wobbling motion in a triaxial rotor are taken as examples in this paper to show the wobbling motion in even-even nuclei.For the 130Ba,the wobbling are investigated based on the combination of the covariant density functional theory(CDFT)and the particle rotor model(PRM).The CDFT provides crucial information on the configuration and deformation parameters of observed bands,serving as input for PRM calculations.The corresponding experimental energy spectra and electromagnetic transition probabilities are reproduced.An analysis of the angular momentum geometry reveals the enhanced stability of transverse wobbling of a two-quasiparticle configuration compared to a single-quasiparticle one.For the triaxial rotor,the time evolution of wobbling motion is explored through the solution of Euler equations.This investigation yields valuable insights into the evolution of orientation angles(φ and θ)and angular momentum components.Notably,the study reveals that low-energy states of a triaxial rotor predominantly exhibit wobbling motion around the intermediate axis.Moreover,an increase in excitation energy corresponds to a prolonged period of intermediate axis wobbling motion.Conversely,a contrasting trend is observed in the case of long axis wobbling,where an increase in excitation energy leads to a decrease in the wobbling period.

Wobbling geometry in a simple triaxial rotor

The spectroscopic properties and angular momentum geometry of the wobbling motion of a simple triaxial rotor are investigated within the triaxial rotor model. The obtained exact solutions of energy spectra and reduced quadrupole transition probabilities are compared to the approximate analytic solutions from the harmonic approximation formula and Holstein-Primakoff formula. It is found that the low lying wobbling bands can be well described by the analytic formulae. The evolution of the angular momentum geometry as well as the K-distribution with respect to the rotation and the wobbling phonon excitation are studied in detail. It is demonstrated that with the increase of the wobbling phonon number, the triaxial rotor changes its wobbling motions along the axis with the largest moment of inertia to the axis with the smallest moment of inertia. In this process, a specific evolutionary track that can be used to depict the motion of a triaxial rotating nucleus is proposed.

Determining the moment of inertia of triaxial Mars with updated global gravity models

The principal moments of inertia(PMIs)with the principal axes are usually taken as the dynamic figure parameters of Mars;they can be deduced from satellite-observed degree-two gravitational potentials in recent global gravity models and from the dynamic ellipticities resulting from precession observations.These PMIs are natural and significant for the geodetic,geophysical,and geodynamic problems of Mars,which are functions of internal density distributions.In this study,a closed and concise formula for determining the PMIs of the entire planet and its core was developed based on the second invariants of gravity and a multipole expansion.We deduced the polar oblateness J^(2)and the equatorial ellipticity J_(22)of Mars to be 1.9566×10^(−3)and 6.3106×10^(−5),respectively.The preferred principal moments of inertia of Mars are A=2.66589×1036 kg·m^(2),B=2.66775×10^(36)kg·m^(2),and C=2.68125×10^(36)kg·m^(2).These values indicate that Mar is slightly triaxial.The equatorial principal moment of inertia of the Martian core is 1.46008×10^(35)kg·m^(2),accounting for~5.47%of the planet’s PMI;this result is critical for investigating the density and size of the core of Mars,and the planet’s free core nutation.

Remarks about External Forces Acting on Earth’s Rotation Axis

It is well known that a variation in the direction of Earth’s rotation axis is a real astronomical phenomenon, named nutation. It is interesting if a variation of this axis can take place only in intensity, in the simplest theoretical case of only two rigid body dynamics. This paper presents two positions of the Moon during its monthly orbit, where a sudden variation of Earth’s rotation axis in intensity can take place. The duration of this phenomenon is limited in time, maybe an instant or a day, and then a vortex can appear.

论瞬时轴线垂直度、平均回转轴线垂直度与Wobble的关系

用姿态变换的方法推导了平均轴线垂直度、瞬时轴线垂直度和倾角回转误差(Wobble)三者之间的关系,从而得出了瞬时轴线垂直度和平均回转轴线垂直度的数据处理方法。

奇特原子核新转动模式探索

针对最新观测的新转动模式,特别是Wobbling运动,采用基于协变密度泛函理论(CDFT)的核芯-准粒子耦合模型(CQC)研究奇中子核105Pd低激发谱,Wobbling频率等物理量,讨论Wobbling运动的微观机制。

平衡训练对慢性踝关节不稳疗效的研究进展

目的通过文献分析平衡训练对慢性踝关节不稳的疗效。方法检索PubMed和Web of Science数据库2000年1月至2019年4月以"慢性踝关节不稳"和"平衡训练"为主题的英文文献。结果和结论慢性踝关节不稳患者最常应用的平衡训练方法为Wobble Board训练和渐进性跳跃稳定平衡(PHSB)训练;现已形成包含单腿站立重心变化和平衡策略的静态平衡、包含星形偏移平衡测试和功能性跳跃的动态平衡、踝关节自评功能问卷、生活质量和社会参与程度问卷的评估模式,完善了平衡训练对患者损伤情况、功能和参与影响的整体化评价体系。

Clearance angle and evolution of depth of cut in actuated disc cutting

This paper investigates the effect of cutter clearance angle on variation of depth of cut and cutting process with an actuated disc cutting(ADC).ADC is a cyclic cutting method with two main characteristics:(i)a disk-shape cutter is used to attack the rock in an undercutting mechanism;and(ii)the cutter is dynamically actuated as it is moved across the rock.Hence,the cutting process of such system is periodic,each recurrence known as actuation cycle.The first ADC model,developed in 2016,represented an idealization of the technology with a flat disc cutter,where no clearance angle was considered.The evolution of the contact between the disc and the rock was,therefore,computed only on horizontal x-y plane,ignoring the effect of normal component of the force acting on cartridge.This article reports on a study that incorporates the cutter inclination angle in derivation of cutter/rock interface laws.It extends the proposed kinematic and geometry based model to take into account the variable depth of cut in estimating the forces associated with cutting in one actuation cycle.Experiments were conducted using Wobble to test the predictions of the improved model at various operating conditions.The model predictions are matched with the experimental results and effects of various factors are analysed.

某“倒三轮”摩托车高速直线行驶操纵稳定性分析

针对“倒三轮”摩托车在高速行驶时的操纵稳定性,以某种国产CVT“倒三轮”摩托车为研究对象,采用专业的摩托车动力学分析软件Bikesim,对“倒三轮”摩托车在高速直线行驶受到微小干扰时的稳定性进行仿真分析,并利用根轨迹法对系统进行稳定性分析。结果表明:“倒三轮”摩托车在高速行驶受到微小干扰时,整车会发生摆振(wobble)和迂回摆动(weave)现象,严重影响“倒三轮”摩托车高速行驶时的操纵稳定性以及行车安全性,与根轨迹法分析结果一致。研究结果对“倒三轮”摩托车高速行驶时的操纵稳定性研究具有一定的指导意义。

Linearization of the Liouville Equation, Multiple Splits of the Chandler Frequency, Markowitz Wobbles, and Error Analysis

The rotation of the physical Earth is far more complex than the rotation of a biaxial or slightly triaxial rigid body can represent. The linearization of the Liouville equation via the Munk and MacDonal perturbation scheme has oversimplified polar excitation physics. A more conventional linearization of the Liouville equation as the generalized equation of motion for free rotation of the physical Earth reveals: 1) The reference frame is most essential, which needs to be unique and physically located in the Earth;2) Physical angular momentum perturbation arises from motion and mass redistribution to appear as relative angular momentum in a rotating Earth, which excites polar motion and length of day variations;3) At polar excitation, the direction of the rotation axis in space does not change besides nutation and precession around the invariant angular momentum axis, while the principal axes shift responding only to mass redistribution;4) Two inertia changes appear simultaneously at polar excitation;one is due to mass redistribution, and the other arises from the axial near-symmetry of the perturbed Earth;5) The Earth at polar excitation becomes slightly triaxial and axially near-symmetrical even it was originally biaxial;6) At polar excitation, the rotation of a non-rigid Earth becomes unstable;7) The instantaneous figure axis or mean excitation axis around which the rotation axis physically wobbles is not a principal axis;8) In addition to amplitude excitation, the Chandler wobble possesses also multiple frequency-splits and is slow damping;9) Secular polar drift is after the products of inertia and always associated with the Chandler wobble;both belong to polar motion;10) The Earth will reach its stable rotation only after its rotation axis, major principal axis, and instantaneous figure axis or mean excitation axis are all completely aligned with each other to arrive at the minimum energy configuration of the system;11) The observation of the multiple splits of the Chandler frequency is further examined by means of exact-bandwidth filtering and spectral analysis, which confirms the theoretical prediction of the linearized Liouville equation. After the removal of the Gibbs phenomenon from the polar motion spectra, Markowitz wobbles are also observed;12) Error analysis of the ILS data demonstrates that the incoherent noises from the Wars in 1920-1945 are separable from polar motion and removable, so the ILS data are still reliable and useful for the study of the continuation of polar motion.

Design of the Rotation Angle Measurement System for the Atmospheric Dispersion Corrector (ADC)

In order to measure the rotation angle error of the worm and gear mechanisms in the atmospheric dispersion corrector( ADC),a novel measurement system based on the autocollimator is designed in this paper.Based on the position relations between the shaft and spot converged by rays of autocollimator,the rotation angle can be calculated quickly and conveniently using a brief algorithm. An optical wedge is introduced to the measurement system for suppressing the awful measuring error caused by the axial wobbly error. The measurement system can measure the shaft rotation angle at any rotation position,which is the novel usage of the two-dimensional autocollimator. Its optical layout is very simple. Only an optical wedge and two plane mirrors are needed besides the autocollimator. The measurement accuracy of the proposed method is less than±0.5 arcmin. In the measurement of two worms and gears mechanisms in ADC,the rotation angle error are±0.05° and ±0.07° respectively,which all satisfies the design demand( ±0.1°). The proposed measurement system can be also suits for some engineering fields.

Revisiting the period and quality factor of the Chandler wobble and its possible geomagnetic jerk excitation

The period and quality factor of the Chandler wobble(CW)are useful for constraining the Earth’s internal structure properties,such as the mantle elasticity.It has been shown that the CW is mainly excited by a combination of atmospheric and oceanic processes;hence based on a deconvolution method,we can remove them from the excitation sequence of the CW to estimate its period P and quality factor Q.We finally re-estimate P=432.3±0.8 days and Q=85±15 for the CW.Based on those two estimates,we investigate the relationship between the geomagnetic jerks and the excitation sequences of the CW.The geomagnetic jerks or jerk bounds are well consistent with the sudden changes of the excitation sequences of the CW.This demonstrates that the geomagnetic jerks could be a possible excitation source of the CW.It is crucial for understanding the excitation of the CW and for deeper geophysical insights into the geomagnetic jerks.

Automatic calibration for wobble errors in shallow water multibeam bathymetries

The wobble errors caused by the imperfect integration of motion sensors and transducers in multibeam echo-sounder systems(MBES)manifest as high-frequency wobbles in swaths and hinder the accurate expression of high-resolution seabed micro-topography under a dynamic marine environment.There are many types of wobble errors with certain coupling among them.However,those current calibration methods ignore the coupling and are mainly manual adjustments.Therefore,we proposed an automatic calibration method with the coupling.First,given the independence of the transmitter and the receiver,the traditional georeferenced model is modified to improve the accuracy of footprint reduction.Secondly,based on the improved georeferenced model,the calibration model associated with motion scale,time delay,yaw misalignment,lever arm errors,and soundings is constructed.Finally,the genetic algorithm(GA)is used to search dynamically for the optimal estimation of the corresponding error parameters to realize the automatic calibration of wobble errors.The simulated data show that the accuracy of the calibrated data can be controlled within 0.2%of the water depth.The measured data show that after calibration,the maximum standard deviation of the depth is reduced by about 5.9%,and the mean standard deviation of the depth is reduced by about 11.2%.The proposed method has significance in the precise calibration of dynamic errors in shallow water multibeam bathymetrie s.

Chandler Wobble Period and Q Derived by Wavelet Transform

We apply complex Morlet wavelet transform to three polar motion data series,and derive quasi-instantaneous periods of the Chandler and annual wobble by differencing the wavelettransform results versus the scale factor, and then find their zero points. The results show thatthe mean periods of the Chandler (annual) wobble are 430.71+-1.07 (365.24+-0.11) and 432.71+-0.42(365.23+-0.18) mean solar days for the data sets of 1900-2001 and 1940-2001, respectively. Themaximum relative variation of the quasi-instantaneous period to the mean of the Chandler wobble isless than 1.5% during 1900-2001 (3%-5% during 1920-1940), and that of the annual wobble is less than1.6% during 1900-2001. Quasi-instantaneous and mean values of Q are also derived by using theenergy density―period profile of the Chandler wobble. An asymptotic value of Q = 36.7 is obtainedby fitting polynomial of exponential of σ^(-2) to the relationship between Q and σ during1940-2001.

GRACE, the Chandler Wobble and Interpretations of Terrestrial Water Transient Storage

Measuring Terrestrial Water Transient Storage in its various components of Earth by orbiting sensors on satellites has been a quest for more than 40 years. Not only in the Hydrology community but also Climatology and Meteorology, Geology, Geodesy, Geophysics and Oceanography have the challenge to attempt to first learn how to measure, then measure and assess the results. The importance is that Earth’s environments are changing and human communities, local and national governing bodies need ability to assess current hazards and to have predictive capabilities for society both local and international. So too the Gravity Recovery and Climate Experiment (GRACE) has joined the ongoing international space-based missions. There will be more after GRACE. For now is an important juncture in the effort to measure Terrestrial Water Transient Storage to ask, “What can GRACE measure and what is GRACE measuring”? Results of this investigation of the GRACE datasets by spectral methods indicate the detection of the Chandler Wobble but the Annual Wobble is aliased and below significance. Therefore, interpretations of Terrestrial Water Transient Storage are failed.

DFT Calculations on the Effect of Solvation on the Tautomeric Reactions for Wobble Gua-Thy and Canonical Gua-Cyt Base-Pairs

To elucidate the reaction mechanism from wobble Guanine-Thymine (wG-T) to tautomeric G-T base-pairs, we investigate its transition state (TS) by density functional theory (DFT) calculations, in vacuum and in water approximated by continuum solvation model. From the comparison of these results, we attempt to elucidate the effect of solvation on the tautomeric reaction for wG-T. In addition, the same DFT calculations are performed for the canonical G-C base-pair, in order to reveal the difference in the activation energy for the reactions involving wG-T and G-C. The obtained TS structures between wG-T and G*-T/G-T* (asterisk is an enol-form of base) are almost the same in vacuum and in water. However, the activation energy is 16.6 and 19.1 kcal/mol in vacuum and in water, respectively, indicating that the effect of solvation enlarges the energy barrier for the reactions from wG-T to G-T*/G*-T. The activation energy for the tautomeric reaction from G-C to G*-C* is also evaluated to be 15.8 and 12.9 kcal/mol in vacuum and in water, respectively. Therefore, it is expected that the tautomeric reaction from wG-T to G*-T/G-T* can occur in vacuum with a similar probability as that from G-C to G*-C*. We furthermore investigate the TS structure for wG-BrU to reveal the effect of the BrU introduction into wG-T. The activation energy is 14.5 and 16.7 kcal/mol in vacuum and in water, respectively. Accordingly, the BrU introduction is found to increase the probability of the tautomeric reaction producing the enol-form G* and T* bases. Because G* prefers to bind to T rather than to C, and T* to G not A, our calculated results reveal that the spontaneous mutation from C to T or from A to G bases is accelerated by the introduction of wG-BrU base-pair.

Triaxial rotation in atomic nuclei

The Projected Shell Model has been developed to include the spontaneously broken axial symmetry so that the rapidly rotating triaxial nuclei can be described microscopically. The theory provides an useful tool to gain an insight into how a triaxial nucleus rotates, a fundamental question in nuclear structure. We shall address some current interests that are strongly associated with the triaxial rotation. A feasible method to explore the problem has been suggested.

International tidal gravity reference values at Wuhan station

The international tidal gravity reference values at Wuhan station are determined accurately based on the comprehensive analysis of the tidal gravity observations obtained from 8 instruments. By comparing these with those in the tidal models given by Dehant (1997) while considering simultaneously (i) the global satellite altimeters tidal data, and (ii) the Schwiderski global tidal data and the local ones along the coast of China, it is found that the average discrepancy of the amplitude factors and of the phase differences for four main waves are given as 5.2% and 3.6% and as 0.16?and 0.08?respectively. They are improved evidently compared to those determined in early stage, indicating the important procedures in improving the Wuhan international tidal gravity reference values when including the long-series observations obtained with a superconducting gravimeter, and when considering the influence of the ocean loading and of the nearly daily free wobble of the Earth’s core.

Atmospheric,hydrological and oceanic comprehensive contributions to seasonal polar wobble of Earth Rotation

The geophysical quantitative excitation on seasonal polar wobble of Earth Rotation has not been well achieved so far. The atmospheric, hydrologic and oceanic angular momentum variations are investigated from monthly values simulated by a coupled ocean-atmosphere general circulation model. The simulated equatorial AAM functions agree well with that from the JMA operational analysis in 90°E direction, but disagree along Greenwich meridian. As for the annual cycle, not only the hydrologic and oceanic excitations partly match the residuals between geodetic functions of polar wobble and JMA AAM functions, but also the combinations with NCEP and JMA analysis AAM functions are better than those estimated from NCAR-CSM1 climate model.