Global Optimization Method to Comprise Rotation-Minimizing Euler-Rodrigues Frames of Pythagorean-Hodograph Curve

The rotation-minimizing frame is the main research object for a spatial curve. Although the mathematical description is not complicated, it is not easy to directly make an exact minimizing-rotation frame for the Euler-Rodrigues frame. The condition for the non-normalized Euler-Rodrigues frame of the Pythagorean-Hodograph curve to become the rotation-minimizing frame is given in this article, which is an ordinary differential equation with rational form, the analytical solution that does not always exist. To avoid calculating the solution of ordinary differential equations, a global optimization algorithm for the conditions is proposed, that has a weight function in the objective function. The quintic Pythagorean-Hodograph curve is analyzed concretely with the method, and its objective function and constraint conditions of optimization are clarified. The example is analyzed by using this method with different weight functions and contrasting that approach with its exact value.

Pythagorean-hodograph曲线的最小旋转Euler-Rodrigues标架优化方法

针对空间Pythagorean-hodograph(PH)曲线的有理最小旋转标架(RMF)问题,基于五次空间PH曲线的Euler-Rodrigues(ER)标架提出一种最小旋转标架的优化方法。PH曲线由Bézier方法来构造,再利用Bernstein多项式及四元数来表示,曲线的ER标架得到简单表示。当PH曲线的ER标架沿曲线弧的旋转角最小时,此时最小旋转ER标架也称曲线的RMF。在计算曲线的RMF的过程中,关键问题是求解旋转角度函数。由于有较多有理多项式的积分,一般难以找到角度函数的具体函数形式。运用最佳平方逼近的方法,构造一个多项式来近似表示旋转角度函数,对比不同次数多项式与角度函数的误差,得到合适次数的多项式近似角度函数。将多项式近似角度函数与直接计算角度函数求解曲线最小旋转ER标架所用时间对比,分析各自的计算量大小。数据结果证明,最佳平方逼近的方法可大大减少计算量,同时实现较小误差的目的。

Rotation of the Earth as a Triaxial Rigid Body

The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96; (C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation: the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.

Rotating magnetic field inhibits Aβ protein aggregation and alleviates cognitive impairment in Alzheimer’s disease mice

Amyloid beta(Aβ)monomers aggregate to form fibrils and amyloid plaques,which are critical mechanisms in the pathogenesis of Alzheimer’s disease(AD).Given the important role of Aβ1-42 aggregation in plaque formation,leading to brain lesions and cognitive impairment,numerous studies have aimed to reduce Aβaggregation and slow AD progression.The diphenylalanine(FF)sequence is critical for amyloid aggregation,and magnetic fields can affect peptide alignment due to the diamagnetic anisotropy of aromatic rings.In this study,we examined the effects of a moderate-intensity rotating magnetic field(RMF)on Aβaggregation and AD pathogenesis.Results indicated that the RMF directly inhibited Aβamyloid fibril formation and reduced Aβ-induced cytotoxicity in neural cells in vitro.Using the AD mouse model APP/PS1,RMF restored motor abilities to healthy control levels and significantly alleviated cognitive impairments,including exploration and spatial and non-spatial memory abilities.Tissue examinations demonstrated that RMF reduced amyloid plaque accumulation,attenuated microglial activation,and reduced oxidative stress in the APP/PS1 mouse brain.These findings suggest that RMF holds considerable potential as a non-invasive,high-penetration physical approach for AD treatment.

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

Anomalies identification of Earth’s rotation rate time series (2012-2017) for possible correlation with strong earthquakes occurrence

The analysis of the Earth’s rotation rate time series,from January 1,2012 till December 31,2017,is performed using two different time series analysis methods,both based on signal decomposition joined with forecasting approach.Anomalies in the time series are detected making the comparison between the raw signal and the forecasting one at the 95% confidence interval.The two methods show consistent results and the best is selected according to the evaluation of the prediction uncertainty.Both methods highlight correlations between detected anomalies in the Earth’s rotation rate time series and the world’s earthquakes occurrence with magnitude≥7 and/or number of events≥150 per day,within a time interval of ±10 days from each earthquake event.This study brings an innovation in the analysis of such time series and helps to better understand the extent of this relationship.

Strain data recorded in Xinjiang and their bearing on Tianshan’s uplift/shortening and Tarim basin’s rotation

Based on the continuous strain data recorded in Xinjiang since 1985, we discuss the mechanisms of Tianshan＇ s uplift and Tarim basin＇ s clockwise rotation. The results indicate ： 1 ） The principal - compression directions in Tianshan are nearly NS, and their intersection angles with regional structures and mountains are nearly perpendicular, which is in accordance with Tianshan＇ s uplift and crustal shortening. 2）The principal compressions around Tarim basin tend to facilitate the regional faults＇ left-lateral strike-slip movements and the basin＇ s clockwise rotation. These phenomena of uplift/shortening and rotation are fundamentally the re- suits of India plate＇ s northward push on Euro-Asia plate, and the associated Pamir arc ＇ s rapid northward movement and regional blocks＇ interaction.

Relationship between Earth’s Rotation and Several Strong Earthquakes and Moderate-small Earthquakes Occurring around the Epicenter Regions Prior to Strong Earthquakes

The relationships between Earth＇s rotation and the 1975 Haicheng, Liaoning Ms7.3 earthquake, 2008 Wenchuan, Sichuan Ms8.0 earthquake and the 2004 Sumatra Msg. 0 earthquake, as well as moderate-small earthquakes occurring around the epicenter regions prior to them are investigated in this study. The obtained results could benefit the further understanding of the relationship between the Earth＇s rotation and earthquakes.

Relationships between Earth’s Rotation or Revolution and Geographical Extent of the Global Surface Monsoons

Monsoon seasons, occasionally also known as wet seasons or trade-wind littoral seasons, are found in the regions where there is a complete seasonal reversal of the prevailing surface winds. Accompanying these shifts in the prevailing surface winds are modulations in rainfall activity. Given the fact that our knowledge of the monsoons is mainly based on the interpretation of the mean values of precipitation, cloudiness and winds;relationships between earth’s rotation or revolution and geographical extent of the global surface monsoons deserve to be highlighted. In the abundant literary and audiovisual production devoted to monsoons worldwide and despite the fact that everyone agrees with physical law which shows that Coriolis force acts to the right in the northern hemisphere (to the left in the southern hemisphere), there is no reference to the relationship between Coriolis force (due to earth’s rotation) effects on troposphere general circulation and geographical extent of the global surface monsoons. Furthermore knowing that the ITCZ oscillations on either side of the equators (due to earth’s revolution) determine the seasons (mainly winter and summer), it is clear that earth’s revolution also plays a crucial role in the seasonal reversal of the prevailing surface winds observed in the regions where monsoons are found. Our main objective is to provide a rational answer to the question: what is a monsoon?

Variations of the Earth＇s rotation rate and cyclic processes in geodynamics

The authors analyzed the relationship between variations of the Earth＇s rotation rate and the geodynamic processes within the Earth＇s body, including seismic activity, The rotation rate of a planet determines its uniaxial compression along the axis of rotation and the areas of various surface elements of the body. The Earth＇s ellipticity variations, caused naturally by the rotation rate variations, are manifested in vertical components of precise GPS measurements. Comparative analysis of these variations is considered in view of modern theoretical ideas concerning the Earth＇s figure. The results justify further research that is of interest for improvement of space svstems and technologiesi.

Dynamic Formulations and Beating Phenomena of Rotating Euler-Bernoulli Flexible Shafts

In this paper, the intrinsic behavior of rotating Euler Benoulli flexible shafts was studied due to coupled bending and torsional vibrations. The equations of motion of the shaft with unbalanced eccentricity and viscous material damping were derived by the Hamilton principle. The numerical solution was obtained using the perturbation approach and mode assuming method. The influences of the coupled vibrations between the bending and torsion, the rotating speed, material damping and the slenderness ratio of the shaft were analyzed. It is clearly shown that the beating phenomena can occur when the interaction of torsion and flexure is considered.

Effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids by using the Lord-Shulman and dual-phase-lag models

The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.

The g-factors and magnetic rotation in ^(82)Rb

The g-factors of the intra-band states 12, 13, 14, 15 in a magnetic-rotational band built on the 11 state in S2Rb are measured for the first time by using a transient magnetic field-ion implantation perturbed angular distribution （TMF-IMPAD） method. The magnetic-rotational band in ^82Rb is populated by the ^60Ni（27A1,4pn）^82Rb reaction, and the time-integral Larmor precessions are measured after recoil implantation into a polarized Fe foil. The calculation of g-factors is also carried out in terms of a semi-classical model of independent particle angular momentum coupling on the basis of the four-quasiparticle configuration π（99/2）^2 Оπ（p3/2, f5/2） О v （g9/2）. The measured and calculated g-factors are in good agreement with each other. The g-factors and deduced shear angles decrease with the increase of spin along the band. This clearly illustrates the shear effect of a step-by-step alignment of the valence protons and neutrons in magnetic rotation. The semi-classical calculation also shows that the alignment of the valence neutron angular momentum is faster than that of the valence protons, which results in a decrease of g-factors with increasing spin. The present results provide solid evidence of the shear mechanism of magnetic rotation.

Revolving scheme for solving a cascade of Abel equations in dynamics of planar satellite rotation

The main objective for this research was the analytical exploration of the dynamics of planar satellite rotation during the motion of an elliptical orbit around a planet. First, we revisit the results of J. Wisdom et al. （1984）, in which, by the elegant change of variables （considering the true anomaly f as the independent variable）, the governing equation of satellite rotation takes the form of an Abel ordinary differential equation （ODE） of the second kind, a sort of generalization of the Riccati ODE. We note that due to the special character of solutions of a Riccati-type ODE, there exists the possibility of sudden jumping in the magnitude of the solution at some moment of time. In the physical sense, this jumping of the Riccati-type solutions of the governing ODE could be associated with the effect of sudden acceleration[deceleration in the satellite rotation around the chosen principle axis at a definite moment of parametric time. This means that there exists not only a chaotic satellite rotation regime （as per the results of J. Wisdom et al. （1984））, but a kind of gradient catastrophe （Arnold, 1992） could occur during the satellite rotation process. We especially note that if a gradient catastrophe could occur, this does not mean that it must occur： such a possibility depends on the initial conditions. In addition, we obtained asymptotical solutions that manifest a quasi-periodic character even with the strong simplifying assumptions e → 0, p -- 1, which reduce the governing equation of J. Wisdom et al. （1984） to a kind of Beletskii＇s equation.

Combined distal tibial rotational osteotomy and proximal growth plate modulation for treatment of infantile Blount's disease

Infantile Blount's disease is a condition that causes genu varum and internal tibial torsion. Treatment options include observation, orthotics, corrective osteotomy, elevation of the medial tibial plateau, resection of a physeal bar, lateral hemi-epiphysiodesis, and guided growth of the proximal tibial physis. Each of these treatment options has its disadvantages. Treating the coronal deformity alone(genu varum) will result in persistence of the internal tibial torsion(the axial deformity). In this report, we describe the combination of lateral growth modulation and distal tibial external rotation osteotomy to correct all the elements of the disease. This has not been described before for treatment of Blount's disease. Both coronal and axial deformities were corrected in this patient. We propose this combination(rather than the lateral growth modulation alone) as the method of treatment for early stages of Blount's disease as it corrects both elements of the disease and in the same time avoids the complications of proximal tibial osteotomy.

Behavior of quantum search algorithm with small phase rotations

When the Grover＇ s original algorithm is applied to search an unordered database, the success probability decreases rapidly with the increase of marked items. Aiming at this problem, a general quantum search algorithm with small phase rotations is proposed. Several quantum search algorithms can be derived from this algorithm according to different phase rotations. When the size of phase rotations are fixed at 0. 01π, the success probability of at least 99. 99% can be obtained in 0（√N/M） iterations.

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.

Rotational Eustasy as Understood in Physics

Global sea level has today become widely understood merely in terms of glacial eustasy and thermal expansion. Although this is good in theory, it is not enough to explain observational facts in nature. We know that the 17th century was characterized by cold climate, Little Ice Age conditions, and low solar activity during the Maunder Grand Solar Minimum. In contrast, the 18th century was characterized by warm climate conditions and a Grand Solar Maximum (with the Polar front located north of Svalbard). In terms of glacial eustasy, one would expect to find a low sea level in the 17th century and a high sea level in the 18th century. This is not the case in the equatorial regions, however. In the Indian Ocean and the Pacific, there was a 60 - 70 cm higher sea level in the 17th century, and a sea level well below the present one in the 18th century. This can only be understood in terms of “rotational eustasy”. This is a novel concept, here for the first time addressed with respect to physical interpretation. It is shown that planetary beat affects Earth’s rate of rotation and that this leads to oscillations of the equatorial water bulge with amplitudes of up to ±70 cm.

基于Euler/N-S方程的跨音速非线性静气动弹性问题研究

在C-H网格的基础上,采用Jam eson的中心差分有限体积法求解Eu ler/N-S方程,采用结构影响系数法计算结构的弹性变形,用三角元面积加权法和常体积转换法(CVT)实现流固耦合。

任意曲线坐标系Euler方程S2流面的计算方法

为提高S2流面计算方法对涡轮复杂几何的适应性和计算能力,详细推导了任意正交曲线坐标系下应用于流道中心S2流面计算的Euler方程,提出了任意曲线坐标系Euler方程S2流面的计算方法,发展了适用于三阶精度总变差减小的差分格式的数学模型,结合了隐格式时间推进、Riemann问题求解等技术。在应用于带弧形凸起的流道及某直叶栅气动参数计算,并对某三级低压涡轮进行性能预测的结果表明:所提方法对激波具有较高的捕捉精度,能够较准确地获得叶栅气动参数分布,且与实验结果吻合良好;对于多级涡轮总性能参数和气动参数分布均有较高的计算精度,是一种可为涡轮设计提供快速、可靠的计算方法。