An approximate projection technique for the calculation of electromagnetic properties of deformed nuclei

A three-dimensional angular momentum projection is carried out for cranking model wave functions. The projected matrix elements of electromagnetic operators are evaluated using a method originally developed by Kamlah for the case of projected energy, which is valid for large deformations and weakly triaxial nuclei. The calculated spectroscopic quadrupole moments deviate substantially from the predictions of a rigid rotor model with axial symmetry. For E2 transitions the deviations are small. Projected values of the magnetic moments are almost identical with those of a semiclassical calculation. Cranking model wave functions are decomposed into its components having good angular momentum.     

The structure of the odd-A nuclei withA≈130 and the problem ofγ-softness

The negative parity states in the^{123, 125, 131}Cs and the¹³¹La nuclei are described in the framework of the particle-core coupling model. In order to study the problem of gamma softness, the following two core models are used:(1) the rigid triaxial rotor model, and(2) theγ-unstable model withγ-dependent inertial functions. The properties of the odd-A nuclei with rigid and soft cores are compared with the experimental data. The results do not allow to draw a definite conclusion about the softness. When seeking properties which could help to distinguish between soft and rigid nuclei it has been found that some spectroscopic factors for the proton stripping reaction are sensitive to the gamma softness.     

Analytical Description of Triaxial Deformation in O(6)-Like Nuclei

Udlizing the consistent Q framework via an additional three-body potendal of L=3 in the interacting boson model,ananalytical descdption for the triaxial deformation in the O(6)-like nuclei is given on the basis of the intrinsic frame.The deformation parameters β and γof the even-even Xe,Ba and Ce isotopes are calculated.The calculated results are in good agree nont with the results of the rigid triaxial rotor model.     

Calculation of the static and dynamic triaxial shapes of 24Mg

The Skyrme interaction is used in a Hartree-Fock calculation of ²⁴Mg with triaxial symmetry. A transition between axial and triaxial shapes is studied as a function of the spin-orbit strength. The effect of the other components of the interaction on the shape of ²⁴Mg is examined. Constrained Hartree-Fock calculations of the energy surface and the cranking mass parameter are used for the calculation of the intrinsic γ-vibration. The main result of the dynamical calculation is that despite the different equilibrium shapes obtained with the two forces SIII and SV, the triaxiality obtained by considering the zero-point γ-oscillation is essentially the same for both forces.     

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.     

Triaxial dynamics in the quadrupole-deformed rotor

The triaxial dynamics of the quadrupole-deformed rotor model of both the rigid and the irrotational type are investigated in detail. The results indicate that level patterns of the two types of model can be matched with each other to the leading order of the deformation parameter β. In particular, it is found that the dynamical structure of the irrotational type with most triaxial deformation(γ = 30?) is equivalent to that of the rigid type with oblate deformation(γ = 60?), and the associated spectrum can be classified into the standard rotational bands obeying the rotational L(L+1)-law or regrouped into a new ground- and γ-band with odd–even staggering in the newγ-band, commonly recognized as a signature of the triaxiality. The differences between the two types of the model in this case are emphasized, especially in the E2 transitional characteristics.     

考虑视轴方向的个性化眼模型的构建

包含更多人眼解剖学特性的个性化眼模型具有重要的实验和临床意义。由角膜地形图计算了8只人眼视轴与光轴之间的夹角,水平分量平均值为4.23°±1.51°,竖直分量平均值为-0.40°±1.27°。根据视轴与光轴之间的夹角、角膜地形数据、眼内各部分轴向间距和人眼波像差,运用光学设计软件Zemax分别为这8只人眼构建了考虑视轴方向的个性化眼模型。在此基础上,计算了波前引导的个性化角膜切削深度,并与光程差方法计算的切削深度进行了比较。在切削光区中心处,两者相差不大,平均值为(0.09±0.04)μm;随着半径增大,两者之间的差值逐渐增大。对于所研究的实例,光区外围处的最大差值为0.59μm。个性化眼模型为设计波前引导的个性化角膜切削方案提供了一个有效工具。     

Rotational Property of~(249)Cm in Particle-Triaxial-Rotor Model

We study the rotational energy spectrum and deformation feature of very heavy nucleus 249Cm in the particle-triaxial-rotor model with variable moment of inertia.Such a nucleus is the unique one involving both multiband structure and high spin states and locating very near the superheavy region.By calculating the energy spectrum,we determine the configurations and quadrupole and triaxial deformation parameters β and γ of the nucleus.The calculated results indicate that the high spin band of 249Cm is built upon the ν[620] 12+configuration with deformation parameters β = 0.296 and γ = 7.5 and the bands based on the ν[622] 32+,ν[613] 72+,ν[750] 12 configuration respectively are also the ones with quite large axial deformation but small triaxial deformation.     

The 0(6) limit of the interacting boson model and its relation to triaxial nuclear models

It is shown that the 0(6) limit of the interacting boson model (IBA) corresponds to the γ-unstable model of Jean and Wilets, if one considers an infinite number of bosons in IBA (N → ∞). The rigid triaxial rotor model with γ = 30° satisfies the same selection rules, but differs considerably with respect to B(E2) values and energies.     

Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight

The derivation of a set of non-linear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two-bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead-lag, elastic bending in flap and lead-lag, blade root torsion, and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated by using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.     

超变形核的转动模型

为处理超变形核的转动谱,提出了一个简单的转动模型,即:冻结振动自由度,把超变形核看成是一个刚性转子．将转动哈密顿量在轴对称陀螺波函数所张开的空间中对角化时,进一步考虑了Ｓｉｇｎａｔｕｒｅ为好量子数,重新计算了Ａ～１９０区偶偶核的超变形带,自旋指定与ａｂ公式自旋指定仍然一致．并计算了Ａ～１５０区１５２Ｄｙ的超变形带,结果也与实验值拟合得很好,但自旋指定与ａｂ公式差异较大.To deal with the SD bands, a single rotational model is proposed, i . e. freeze the degree of vibrational freedom, and regard the SD nuclei as a rigid rotor. Also, the Signature is considered to be a good quantum number . 10 SD bands were calculated, all of the assigned nuclear spins are equal to those determined by ab formula. 190 Hg and 152 Dy were also calculated, but the results of assigned nuclear spins are different to the ones of ab formula.     

Experimental investigation of a single-plane automatic balancing mechanism for a rigid rotor

We present an experimental investigation of a single-plane automatic balancer that is fitted to a rigid rotor. Two balls, which are free to travel around a circular race, are used to compensate for the mass imbalance in the plane of the device. The experimental rig possesses both cylindrical and conical rigid body modes and the performance of the automatic balancer is assessed for a variety of different levels of imbalance. A non-planar mathematical model that also includes the observed effect of support anisotropy is developed and numerical simulations are compared with the experimental findings. In the highly supercritical frequency range the balls act to balance the rotor and a good quantitative match is found between the model and the experimental data. However, during the rigid body resonances the dynamics of the ball balancer is highly nonlinear and for this speed range the agreement between theory and experiment is mainly qualitative. Nevertheless, the model is able to successfully reproduce many of the solution types that are found experimentally.     

The molecular vibration-rotation Hamiltonian in the Bargmann-Hilbert space

The molecular vibration-rotation Hamiltonian of polyatomic molecules is developed in the Bargmann-Hilbert space of entire functions. The vibration-rotation eigenvectors of polyatomic molecules are described as polynomials in complex variables where the number of complex variables is equal to the number of degrees of freedom of the molecule. Simple differential operator representations are found for all rotational and vibrational operators. A special procedure is developed, in the new representation, for describing the direction cosine operators of a rigid symmetric rotor.The new basis of molecular states is shown to be very convenient for calculating energy or intensity perturbations of molecules with axial symmetry. The theoretical methods include a treatment of doubly degenerate modes of vibration.     

Chiral bands in odd-odd nuclei with rigid or soft cores

Properties of chiral bands in an odd-odd nucleus, which is treated as a system of an even-even core and a pair of particles in the πh _11/2 ⊗ υh _11/2 ^-1 configuration, are calculated in the frame of the Core-Particle-Hole Coupling (CPHC) model with either a rigid triaxial or a soft core. The results of calculations for the two different cores are compared. The properties of the nucleus with the rigid, maximally triaxial ( γ = 30^°and with the entirely soft core are qualitatively very similar.     

Dynamic analysis of a BLDC motor with mechanical and electromagnetic interaction due to air gap variation

In this study, the dynamic behaviors of a BLDC motor are analyzed, when the motor undergoes mechanical and electromagnetic interaction due to an air gap variation between the stator and rotor. When considering the air gap variation caused by the translational motion of the rotor relative to the stator, the kinetic and potential energies, Rayleigh dissipation function, and the magnetic coenergy are expressed in terms of the rotor displacements and stator currents. With these energies and function, new equations of motion are derived using Lagrange’s equation. The equations for the proposed model are nonlinear equations in which the displacements and currents are coupled. The time responses for the displacements and currents are computed for the proposed and previous models. Furthermore, the effects of rotor eccentricity are also investigated. It is found that, when the air gap varies with time, the time responses for the proposed and previous models have small differences in the stator currents, electromagnetic torques, and rotating speeds. However, the time responses have large differences in the rotor displacements. Therefore, this paper claims that the proposed model describes the dynamic behaviors of the motor more accurately than the previous model. It is also shown that rotor eccentricity increases the stator current period and the electromagnetic torque, while it decreases the rotating speed of the rotor.     

原子核对光电离截面的影响

利用Dirac-Slater相对论平均自洽场理论,研究了不同原子体系光电离截面在不同核模型下的差异.考虑原子核大小时,核的尺寸效应使电子所感受到的有效核电荷减小,并进而影响到电子的概率分布及光电离截面等;对没有考虑原子核大小的点模型,由于不存在核的尺寸效应,出射光电子的波函数有较大相移,从而有可能出现Cooper极小.当入射光子的能量远大于相关电子的电离能时,不同核模型下电子束缚能及平均半径等的差异将相对减小,从而使光电离截面随入射光子能量的变化趋于一致.     

Fracture Model of Anisotropic Rocks under Complex Loading

The paper proposes a deformation and fracture model for anisotropic stratified rocks and presents theoretical and experimental data on how the rock strength and fracture geometry are influenced by principal stresses and their orientation to bedding planes. Two possible mechanisms are considered for rock fracture under true triaxial load: along bedding planes of weakness and along planes in which Mohr-Coulomb stresses reach a critical combination with cohesion coefficients and internal friction angles typical of the rock. The transition of rocks to inelastic deformation is described in the context of two criteria of which one accounts for the above fracture mechanisms and the other, being a semi-empirical analogue of the Hill yield criterion, accounts for the effect of normal stress. The experimental data presented are for the strain and strength properties of rocks sampled from the Fedorovskoye and Talakanskoye oil and gas fields and tested on an original loading system for true triaxial compression with lateral pressure (similar to the Karman scheme) and for generalized shear (three unequal and nonmonotonic principal stresses). The experimental and theoretical results, including total stress-strain curves, are in good qualitative agreement and demonstrate the possibility to evaluate the parameters entered in the model from tests of particular rocks.     

Rotordynamical simulations of a fibre refiner during production

A key component in panel board production is the refiner, whose task is to break raw cellulose wood chips into slender fibres, done by a relative angular motion between stator and rotor. The main problem in predicting the dynamics of these machines is to model the complicated fibre breaking process, since the refining process leads to a three-phase flow (solid wood, water and steam) between the stator and rotor. By modelling the rotor as a rigid body, the process can only contribute by a resulting force and a resulting moment. Through this approach and axial force measurements, it has been shown that the refining process can be treated as a time dependent stiffness matrix and external load. The objective for this paper is to predict and explain dynamical characteristics of fibre refiners during production in such a way that the results can be used already at early stages of the product development process. Two different pressure distribution cases are studied, i.e. one axisymmetric with only radial variations and one non-axisymmetric. It is found that the axisymmetric case only excited forward modes, while the non-axisymmetric case excited all modes. The time dependent stiffness matrix resulted in unstable domains, but also in stable domains with intermittent high amplitudes.     

轴对称超形变和三轴超形变核态性质的研究

利用轴对称超形变和三轴超形变模型研究了¹⁶⁵Lu π[660 1/2]带.两种模型计算的γ跃迁能量都和实验值较好地符合.然而,能量的signature颤动指数,三轴因子,两类动力学电四极矩之比存在明显的差别,这些差别可以用来识别三轴超形变核态.