A spin polarized disc

We present a solution to the gravitational field equations in a Riemann-Cartan spacetime. The solution describes a disc of infinite radius and finite thickness. The solution has three forms which depend on the size of the acceleration. The matter content of the disc is a rotating spin fluid with a constant z acceleration and a spin density polarized along the axis of rotation. The fluid has zero axial and tangential pressures. There is a radial pressure. The energy density and pressure are finite within the disc.     

中国聚变工程实验堆真空室超压保护系统中爆破片的选型与计算

参照相关标准，对聚变装置真空室超压保护系统(VVPSS)中爆破片进行了选型。结合VVPSS的工作要求，完成了爆破片的设计计算，初步得到爆破片直径为882mm，厚度为1mm。利用有限元分析软件对多种型号爆破片进行结构分析比较，最终选用了反拱环向开缝型爆破片。对最终选定的爆破片进行优化设计，使其达到设计要求。     

Finite Element Aided Tracking of Signal Intensity Changes in Deforming Intervertebral Disc Tissue

Tracking of signal intensity changes in soft tissue over time is often hampered by deformation of the tissue. In this study a method is described that uses finite element modeling to compensate for tissue deformation. The method is applied to the quantification of fluid redistribution in an intervertebral disc that deforms under mechanical load. The clinical importance of this application emerges from the increased susceptibility of the intervertebral disc to damage after a period of mechanical loading. The study shows that the use of the finite element aided approach results in a detailed map of tissue MRI signal changes, where the distorting effects of tissue deformation are eliminated.     

Vibration analysis of variable thickness discs subjected to centrifugal and thermal stresses

The paper presents a numerical technique whereby the natural frequencies of transverse vibration of a disc of varying thickness profile may be determined when the disc is subject to the combined actions of centrifugal loading and complex radial temperature distribution. The study includes an optimizing programme for the generation of the most representative temperature gradient across the disc surface, resulting from peripheral heating and surface convection.In-plane stress levels, arising from the thermal gradient and rotational effects, are determined at a number of radially spaced points across the disc and, by means of annular finite elements, the effect of the resulting stress distribution upon the natural frequencies of the disc is examined.     

Exciton phase transitions in semiconductor quantum wells with disc-shaped electrode

Phase transitions in a system of indirect excitons in semiconductor double quantum wells are studied for a set-up when one of the electrodes is of finite size and, in particular, has the shape of a disc. At voltage a region under the rim of the disc is created where excitons have lower energy, thus providing a macroscopic trap attractive for excitons while being repulsive for charged particles. The theory of the formation of patterns of the excitonic condensed phase under the disc is built based on the assumption of the existence of the inter-exciton range where the interaction between them is attractive. The finite value of the exciton lifetime is taken into account serving as a limiting factor for the size of the islands of the condensed phase. The calculations reveal complex restructuring of the patterns of the spatial distribution of exciton density with increasing pumping intensity: from the structureless gaseous phase to separate islands of the condensed phase within the gaseous phase, then to islands of the gaseous phase in the bulk of the condensed phase and finally to the continuous condensed phase.     

A finite element analysis for the vibration modes of a bladed disc

The coupled vibration modes of a rotating blade-disc system are calculated by a finite element method. It is assumed that a large number of identical blades are present, such that the resulting blade loadings on the disc can be considered continuously distributed around the rim of the disc. The disc may have arbitrary profile, and the blades may be tapered and twisted, thus closely representing practical axial flow turbomachine configurations. The effects of rotation, thermal stress, and transverse shear and rotatory inertia in discs of moderately thick profile are readily incorporated into the finite element model. Calculated values of frequencies are compared with experimental data obtained on non-rotating models, and the convergence of the solution is examined by comparison with exact solutions, which can be obtained for configurations of simple geometry. Excellent agreement with experimental data is obtained when using remarkably few elements in the mathematical model, and convergence of the solution is extremely rapid.     

EAST外杜瓦泄放保护装置中爆破片的分析研究

在外杜瓦系统上设置了爆破片装置,借助大型有限元分析程序ANSYS,对爆破片和托架进行了分析,所得结果与实验结果良好吻合,为同类装置的过压泄放提供了有益的参考。     

Finite element modelling for the investigation of in-plane modes and damping shims in disc brake squeal

Squeal propensity of the in-plane modes and the constrained-layer type damping shims for disc brake system is investigated by using the finite element method. Theoretical formulation is derived for a rotating disc in contact with two stationary vibrating pads attached to the damping shim components. By the conversion from the theoretical to FE brake model, the full equations of motion for the actual disc brake system describes the disc rotation, the in-plane friction characteristics and damping shims in association with squeal vibration. It is concluded from the results that the in-plane torsion modes can be generated by the negative friction slope, but they cannot be controlled by the damping shims. The in-plane radial mode is also investigated and found to be very insensitive in squeal generation.     

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在外杜瓦系统上设置了爆破片装置,借助大型有限元分析程序ANSYS,对爆破片和托架进行了分析,所得结果与实验结果良好吻合,为同类装置的过压泄放提供了有益的参考。     

Finite element modelling of dense and porous piezoceramic disc hydrophones

The acoustic characteristics of dense and porous piezoceramic disc hydrophones have been studied by finite element modelling (FEM). The FEM results are validated initially by an analytical model for a simple disc of dense piezoceramic material and then it is extended to a porous piezoceramic disc replicating a foam-reticulated sample. Axisymmetric model was used for dense piezoceramic hydrophone due its regular geometric shape. 3-dimensional model was used for the porous piezoceramics, since the unit cell model is inadequate to fully represent transducers of finite lateral dimensions. The porous PZT discs have been synthesised by foam-reticulation technique. The electrical impedance and the receiving sensitivity of the hydrophones in water are evaluated in the frequency range 10-100 kHz. The model results are compared with the experimental data. The receiving sensitivity of piezocomposite hydrophones is found to be reasonably constant over the frequency range studied. The sharp resonance peaks observed for the dense piezoceramic hydrophone has broadened to a large extent for porous piezoceramic hydrophones, indicating higher losses. The flat frequency response suggests that the 3-3 piezocomposites are useful for wide-band hydrophone applications.     

Analysis of a Disc-Loaded Circular Waveguide for Interaction Impedance of a Gyrotron Amplifier

A rigorous electromagnetic analysis of a circular waveguide loaded with axially periodic annular discs was developed in the fast-wave regime, considering finite axial disc thickness and taking into account the effect of higher order space harmonics in the disc-free region and higher order modal harmonics in the disc-occupied region of the structure. The quality of the disc-loaded circular waveguide was evaluated with respect to its azimuthal interaction impedance that has relevance to the gain of a gyrotron millimeter-wave amplifier (gyro-traveling-wave tube) in which such a loaded waveguide finds application as a wideband interaction structure. The results of electromagnetic analysis of the structure with respect to both the dispersion and azimuthal interaction impedance characteristics were validated against the commercially available code: high frequency structure simulator (HFSS). The analysis predicts that the value of the interaction impedance at a given frequency decreases with the increase of the disc hole radius and disc periodicity. The change of the axial disc thickness does not significantly change the value of the interaction impedance though it shifts the frequency range over which appreciable interaction impedance is obtained. Out of the three disc parameters, namely the disc hole radius, thickness and periodicity, the lattermost is most effective in controlling the value of the azimuthal interaction impedance. However, the passband of frequencies and the center frequency of the passband both decrease with the increase of the disc periodicity. Moreover, the disc periodicity that provides large azimuthal interaction impedance would in general be different from that giving the desired dispersion shape for wideband interaction in a gyro-TWT, suggesting a trade-off in the value of the disc periodicity to be chosen.     

The use of roving discs and orthogonal natural frequencies for crack identification and location in rotors

A variety of approaches that have been developed for the identification and localisation of cracks in a rotor system, which exploit natural frequencies, require a finite element model to obtain the natural frequencies of the intact rotor as baseline data. In fact, such approaches can give erroneous results about the location and depth of a crack if an inaccurate finite element model is used to represent an uncracked model. A new approach for the identification and localisation of cracks in rotor systems, which does not require the use of the natural frequencies of an intact rotor as a baseline data, is presented in this paper. The approach, named orthogonal natural frequencies (ONFs), is based only on the natural frequencies of the non-rotating cracked rotor in the two lateral bending vibration x–z and y–z planes. The approach uses the cracked natural frequencies in the horizontal x–z plane as the reference data instead of the intact natural frequencies. Also, a roving disc is traversed along the rotor in order to enhance the dynamics of the rotor at the cracked locations. At each spatial location of the roving disc, the two ONFs of the rotor–disc system are determined from which the corresponding ONF ratio is computed. The ONF ratios are normalised by the maximum ONF ratio to obtain normalised orthogonal natural frequency curves (NONFCs). The non-rotating cracked rotor is simulated by the finite element method using the Bernoulli–Euler beam theory. The unique characteristics of the proposed approach are the sharp, notched peaks at the crack locations but rounded peaks at non-cracked locations. These features facilitate the unambiguous identification and locations of cracks in rotors. The effects of crack depth, crack location, and mass of a roving disc are investigated. The results show that the proposed method has a great potential in the identification and localisation of cracks in a non-rotating cracked rotor.     

Impact of nonlinearity on a homopolar oscillating-disc dynamo

A numerical method is developed to investigate the effect of the nonlinear factors on a homopolar oscillating-disc dynamo. Our results show that all the nonlinear factors of the oscillating-disc dynamo have no significant effect on the kinematic regime of the disc dynamo. But as the magnetic field grows larger, the nonlinear factors begin to take effect. The role of the nonlinear factor involving the cube of the magnetic flux is to make the dynamo magnetic flux tend to an oscillating solution with finite amplitude. For the case that the mean rotation rate vanishes the nonlinear factor involving the magnetic flux rate can only affect the manner of the magnetic flux tending to infinity; for another case that the disc rotation rate takes a strongly subcritical value, it may have two kinds of effects just mentioned above on the disc dynamo and its specific effect is dependent on the values of the amplitude and frequency of the oscillatory disc rotation rate.     

Brake squeal reduction of vehicle disc brake system with interval parameters by uncertain optimization

An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively.     

Feasibility of MR elastography of the intervertebral disc

Low back pain (LBP) is a costly and widely prevalent health disorder in the U.S. One of the most common causes of LBP is degenerative disc disease (DDD). There are many imaging techniques to characterize disc degeneration; however, there is no way to directly assess the material properties of the intervertebral disc (IVD) within the intact spine. Magnetic resonance elastography (MRE) is an MRI-based technique for non-invasively mapping the mechanical properties of tissues in vivo. The purpose of this study was to investigate the feasibility of using MRE to detect shear wave propagation in and determine the shear stiffness of an axial cross-section of an ex vivo baboon IVD, and compare with shear displacements from a finite element model of an IVD motion segment in response to harmonic shear vibration. MRE was performed on two baboon lumbar spine motion segments (L3–L4) with the posterior elements removed at a range of frequencies (1000–1500 Hz) using a standard clinical 1.5 T MR scanner. Propagating waves were visualized in an axial cross-section of the baboon IVDs in all three motion-encoding directions, which resembled wave patterns predicted using finite element modeling. The baboon nucleus pulposus showed an average shear stiffness of 79 ± 15 kPa at 1000 Hz. These results suggest that MRE is capable of visualizing shear wave propagation in the IVD, assessing the stiffness of the nucleus of the IVD, and can differentiate the nucleus and annulus regions.     

Quantum scattering by nonspherical objects

The problem of scattering by spherically asymmetric potentials is considered where angular momentum not only ceases to be a conserved quantity but is also not a convenient basis for the expansion of wave functions and scattering amplitudes. Numerical solutions of the two-dimensional differential equation for the scattering amplitude of a particle and a coupled pair on a semitransparent disc of finite thickness are obtained. The effect of resonant diffraction is shown. A numerical scheme can be used to describe the scattering of a particle by deformed atomic nuclei.     

Thermal Modelling of Edge-Cooled Single Disc Gyrotron Windows Using a One-Dimensional Finite Difference Computer Code

A one - dimensional finite - difference computer code has been developed and shown to be quite effective in thermal design and analysis of various plane edge-cooled single - disc windows for gyrotrons with Gaussian rf beam output. The program has a modular structure and is flexible enough to suit specific requirements of users; it can handle nonlinearity. Results obtained for various CVD diamond window cases compare well with the experiment and with the results obtained using ABACUS, a well-established 3-D Finite Element code. Results indicate that a CVD diamond disc with 94 mm diameter and edge cooled by water at 293 K will ensure the passage of 1 MW CW at 140 GHz. A fused quartz window, with 60 mm diamter and operating at 165 GHZ on a 1.5 MW pulsed coaxial gyrotron has also been analysed for its transient characteristics and results are presented.     

Hastings–Levitov Aggregation in the Small-Particle Limit

We establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one particle. We study the limit of small particle size and rapid aggregation. The process of growing clusters converges, in the sense of Carathéodory, to an inflating disc. A more refined analysis reveals, within the cluster, a tree structure of branching fingers, whose radial component increases deterministically with time. The arguments of any finite sample of fingers, tracked inwards, perform coalescing Brownian motions. The arguments of any finite sample of gaps between the fingers, tracked outwards, also perform coalescing Brownian motions. These properties are closely related to the evolution of harmonic measure on the boundary of the cluster, which is shown to converge to the Brownian web.     

The hydrogen atom confined in both Debye screening potential and impenetrable spherical box

The ground state energy, some low-lying excited state energies and oscillator strengths for a hydrogen atom confined in both a Debye screening potential and finite impenetrable spherical box have been calculated. These have been calculated using a linear variational method based on B-spline basis functions. The results have been compared with those of other authors. The evaluated energies and oscillator strengths with respect to different plasma screening parameters with a certain confinement radii are discussed.     

Experimental analysis of transverse vibration in thermally stressed rotating discs

Details and results are presented of an experimental analysis of the natural frequencies of free transverse vibration of two annular discs subjected to the combined action of centrifugal and thermal stressing. One disc is of constant thickness form, whilst the other is of linearly varying thickness form. The results obtained experimentally are subsequently compared with those as predicted by a finite element technique previously described by the first two authors. In general the comparisons are found to be favourable, when account is taken of the sources of error in the experimental analysis.