Flexural vibration band gaps in a thin plate containing a periodic array of hemmed discs

Using a periodic expansion by means of the Bloch theorem, the flexural vibration band gaps are studied in a thin plate with two-dimensional ternary locally resonant structures, i.e. a thin epoxy plate containing a periodic square array of lead discs hemmed around by rubber. The full band gaps of flexural vibration in the thin plate are obtained within which sound and vibration will be forbidden. The numerical results are used to show how the width of the first full band gap depends on the radius ratio of lead disc to hemmed disc, filling fraction, lattice constant (distance between the centers of the nearest lead discs) and thickness of the thin plate. It is observed that the gap width can be changed a lot by modulating these physical parameters.     

Gravitating discs around a Schwarzschild black hole II

A sequence of exact spacetimes is obtained describing the fields of a Schwarzschild black hole surrounded by stable static axisymmetric thin discs having their inner rim at the least possible radius. In the previous paper we only required stability with respect to perturbations in the disc plane, while it turns out that for discs with relative mass >0.23 the perturbations in perpendicular direction are more dangerous. The discs of the resulting sequence have their inner rims just on, or very close to, circular geodesics marginally stable with respect to either of the perturbations. Redshift from static and Keplerian observers in the disc is computed. The inverted first Morgan-Morgan counter-rotating disc, used in superpositions, has a number of satisfactory physical properties, but it has turned out to have a curvature singularity at the inner rim. However, this is only a consequence of a too steep radial start of density, not present in (inverted) “higher” Morgan-Morgan solutions. Dedicated to Professor Jiří Bičák on the occasion of his 60th birthday.     

Simulation of triaxial response of granular materials by modified DEM

A modified discrete element method(DEM)with rolling effect taken into consideration is developed to examine macroscopic behavior of granular materials in this study.Dimensional analysis is firstly performed to establish the relationship between macroscopic mechanical behavior,mesoscale contact parameters at particle level and external loading rate.It is found that only four dimensionless parameters may govern the macroscopic mechanical behavior in bulk.The numerical triaxial apparatus was used to study their influence on the mechanical behavior of granular materials.The parametric study indicates that Poisson’s ratio only varies with stiffness ratio,while Young’s modulus is proportional to contact modulus and grows with stiffness ratio,both of which agree with the micromechanical model.The peak friction angle is dependent on both inter-particle friction angle and rolling resistance.The dilatancy angle relies on inter-particle friction angle if rolling stiffness coefficient is sufficiently large.Finally,we have recommended a calibration procedure for cohesionless soil,which was at once applied to the simulation of Chende sand using a series of triaxial compression tests.The responses of DEM model are shown in quantitative agreement with experiments.In addition,stress-strain response of triaxial extension was also obtained by numerical triaxial extension tests.     

GeSbTe 与 AgInSbTe 体系相变光盘的研究进展

自Ovshinsky把相变材料用于光存储以来 ,一大批具有可逆光存储性能的材料不断出现 ,其中研究较多的是GeSbTe和AgInSbTe两种体系 .文章着重介绍了利用这两种材料制成的相变光盘记录介质的微观结构特点 ,阐述了其晶化机理 ;同时 ,较详细地概述了光盘的堆栈结构及掺杂其他元素对相变光盘性能的影响 ,并对比说明了GeSbTe和AgInSbTe两种体系在蓝光记录方面的各自特点     

聚二甲基硅氧烷润湿各向异性薄膜

利用模板技术制备了聚二甲基硅氧烷光盘沟槽微结构薄膜,采用电子显微镜对材料进行表征并对薄膜的润湿性各向异性进行了研究.结果表明:刻录可以使光盘沟槽加深,利用聚二甲基硅氧烷复制的薄膜表面具有与光盘基本一致的表面微结构,但沟槽深度比原光盘有所降低.平行沟槽方向的接触角大于与垂直沟槽方向的接触角,具有明显的润湿各向异性.     

Optically—thick accretion discs with advection

The structures of optically-thick accretion discs with radial advection have been investigated by the iteration and integration algorithms. The advective cooling term changes mostly the inner part of disc solution, and even results in an optically-thick advection-dominated accretion flow (ADAF). Three distinct branches－the outer Shakura－Sunyaev disc (SSD), the inner ADAF and the middle transition layer－are found for a super-Eddington disc. The SSD－ADAF transition radius can be estimated as 18(\dot{M}/\dot{M}_E)R_G where R_G is the Schwarzschild radius, \dot{M} is the mass accretion rate and \dot{M}_E is the Eddington accretion rate. SSD solutions calculated with the iteration and integration methods are identical, while ADAF solutions obtained by these two methods differ greatly. Detailed algorithms and their differences have been analysed. The iteration algorithm is not self-consistent, since it implies that the dimensionless advection factor ξ is invariant, but in the inner ADAF region the variation of ξ is not negligible. The integration algorithm is always effective for the whole region of an optically-thick disc if the accretion rate is no smaller than 10^-4\dot{M}_E. For optically-thin discs, the validity of these two algorithms is different. We suggest that the integration method be employed to calculate the global solution of a disc model without assuming ξ to be a constant. We also discuss its application to the emergent continuum spectrum in order to explain observational facts.     

A model for solid-state dewetting of a fully-faceted thin film

Owing to their extremely aspect ratios, most thin films are unstable and when they are heated, they will dewet or agglomerate to form islands. This process can occur in the solid state through capillary-driven surface self-diffusion. A key feature of the dewetting process is the retraction of the edges of the film, either natural edges, patterned edges, or edges where holes have formed. Models of edge retraction have been previously developed for isotropic materials and anisotropic materials with differentiable surfaces, but the effects of faceting in highly anisotropic materials have been largely unexplored. Here, we present a two-dimensional model of edge retraction for highly anisotropic, fully-faceted thin films. This model shows generally good agreement with experimental results for edge retraction of single-crystal Ni films on MgO. In both experiments and the model, rims form as the edges retract. The effects of adjusting various physical parameters on the edge retraction rate and the evolving rim geometry were explored using the model. The film thickness, surface self-diffusivity on the top facet of the rim, the equivalent contact angle of the film on the substrate, and the absolute value of the surface energies were found to be the factors that have the greatest influence on the edge retraction rate. In isotropic models and some experimental systems, valleys form ahead of the retracting rims and deepen to contact the substrate and cause pinch-off. Our model suggests that this form of pinch-off will not occur when the rim is fully faceted and the top surface is an equilibrium facet. However, pinch-off can occur through film thinning and for films with top surfaces that do not form flat equilibrium facets.     

Correlation between nucleus zone migration within scoliotic intervertebral discs and mechanical properties distribution within scoliotic vertebrae

Correlations between intervertebral disc degeneration and bone mass were investigated previously, but never on scoliotic patients. Using MRI measurements of intervertebral discs behavior and vertebral bone tomodensitometry, correlations between nucleus zone displacement within intervertebral discs and mechanical center migration within vertebral bodies were investigated in vivo on scoliotic patients.The protocol, performed on eleven scoliotic girls, was composed of a CT scan acquisition of apical and adjacent vertebrae followed by a MRI acquisition of the thoracolumbar spine. The displacement between the vertebral body centroid and inertia center was computed from the CT images and called the mechanical migration. The displacement between nucleus zones and vertebral body centroids was quantified from MRI and called the nucleus zone migration.For apical vertebrae, a significant correlation was found in the coronal plane (r = 0.766, p < 0.01), but not in the sagittal plane (r = -0.349, p > 0.05). For adjacent vertebrae, significant correlations were found in both coronal (r = -0.633, p < 0.05) and sagittal (r = -0.797, p < 0.01) planes. The nucleus zone migration occurred in the convexity of the curvature whereas the mechanical migration occurred in the concavity.Known secondary mechanical phenomenon of scoliosis was quantified using new parameters describing intervertebral discs and vertebral bodies. Further investigations should be performed to explain the mechanical evolution of scoliosis and to use these parameters in predictive criteria of scoliosis.     

The interplay between screening properties and colloid anisotropy: Towards a reliable pair potential for disc-like charged particles

The electrostatic potential of a highly charged disc (clay platelet) in an electrolyte is investigated in detail. The corresponding non-linear Poisson-Boltzmann (PB) equation is solved numerically, and we show that the far-field behaviour (relevant for colloidal interactions in dilute suspensions) is exactly that obtained within linearized PB theory, with the surface boundary condition of a uniform potential. The latter linear problem is solved by a new semi-analytical procedure and both the potential amplitude (quantified by an effective charge) and potential anisotropy coincide closely within PB and linearized PB, provided the disc bare charge is high enough. This anisotropy remains at all scales; it is encoded in a function that may vary over several orders of magnitude depending on the azimuthal angle under which the disc is seen. The results allow to construct a pair potential for discs interaction, that is strongly orientation dependent.     

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.     

Vibration analysis of a new polymer quartz piezoelectric crystal sensor for detecting characteristic materials of volatility liquid

We present a new polymer quartz piezoelectric crystal sensor that takes a quartz piezoelectric crystal as the basal material and a nanometer nonmetallic polymer thin film as the surface coating based on the principle of quartz crystal microbalance (QCM). The new sensor can be used to detect the characteristic materials of a volatile liquid. A mechanical model of the new sensor was built, whose structure was a thin circle plate composing of polytef/quartz piezoelectric/polytef. The mechanical model had a diameter of 8 mm and a thickness of 170 μ. The vibration state of the model was simulated by software ANSYS after the physical parameters and the boundary condition of the new sensor were set. According to the results of experiments, we set up a frequency range from 9.995850 MHz to 9.997225 MHz, 17 kinds of frequencies and modes of vibration were obtained within this range. We found a special frequency f_sp of 9.996358 MHz. When the resonant frequency of the new sensor’s mechanical model reached the special frequency, a special phenomenon occurred. In this case, the amplitude of the center point O on the mechanical model reached the maximum value. At the same time, the minimum absolute difference between the simulated frequency based on the ANSYS software and the experimental measured stable frequency was reached. The research showed that the design of the new polymer quartz piezoelectric crystal sensor perfectly conforms to the principle of QCM. A special frequency value f_sp was found and subsequently became one of the most important parameters in the new sensor design.     

Intervertebral disc modeling using a MRI method: migration of the nucleus zone within scoliotic intervertebral discs.

MRI is increasingly being used for etiologic examination of scoliosis and for intervertebral disc disorder analysis, but until now has not been applied to geometric modeling. The aim of this study was to develop a new geometric model of intervertebral discs using MRI and to quantify the migration of the nucleus zone within scoliotic intervertebral discs. Fourteen lumbar scoliotic children (Cobb angles 22 ± 7°) were examined using MRI. The protocol consisted of sagittal and coronal plane acquisitions of the entire spine. An image processing software allowed the outline detection of the nucleus zone (intervertebral high intensity portion). The vertebral bodies were also reconstructed. Using a pre-post processor, the nucleus zone migration and a wedging angle were quantified. Statistical tests showed the repeatability of the method (p > 0.4). Nucleus zone migration was correlated to the wedging angle (r² = 0.488, p < 0.0001) in the coronal plane. Our results were in agreement with the literature: when two vertebrae move deforming the disc, the nucleus moves into the convexity of the curvature. But should we talk about the nucleus? Despite image processing software allowing the highlighting of image features (automatic color lookup tables applied to grayscale images using pixel intensity measurements), it is impossible to differentiate the nucleus from the annulus on T2 weighting images of adolescent spine. This new geometric model of the intervertebral disc, used for the quantification of the nucleus zone migration, should be of interest for further investigation of stiffness parameters of spine.     

A novel trilayer antireflection coating using dip-coating technique

We report a new structure for broadband antireflection coating by dip-coating technique, which has minimal cost and is compatible with large-scale manufacturing. The coatings are prepared by depositing SiO 2 sol-gel film on a glass substrate, subsequently depositing SiO 2 single-layer particle coating through electrostatic attraction, and depositing a final very thin SiO 2 sol-gel film to improve the mechanical strength of the whole coating structure. The refractive index of the structure changes gradually from the top to the substrate. The transmittance of a glass substrate has been experimentally found to be improved in the spectral range of 400 1 400 nm and in the incidence angle range from 0 to at least 45 . The mechanical strength is immensely improved because of the additional thin SiO 2 sol-gel layer. The surface texture can be applied to the substrates of different materials and shapes as an add-on coating.     

Experimental investigation of wake evolution behind a couple of flat discs in a hydrochannel

The decay of a far wake and its turbulent fluctuations behind two thin discs of the same diameter D, oriented normal to the incident flow, have been studied using the Particle Image Velocimetry (PIV). The experimental study was carried out in a water flume (Re ≈ 2·10⁵) with varying distances between the discs (L _х = 4–8D) and their axes shift relative to each other (0, 0.5D and 1D). It is found that the velocity deficit behind two discs depends weakly on L _x , and at L _х > 40D, it becomes indistinguishable from the level of turbulent fluctuations of the incident flow. It is found that the decay of the average velocity deficit and its turbulent fluctuations in a wake of a tandem of discs can be described by the same analytical dependence with exponent–2/3 as for the wake decay of a single disc. However, at the same distance downstream, the value of deficit behind two discs is substantially higher than the corresponding value behind a single disc. Velocity fluctuations in a far wake behind a pair of discs depend weakly on longitudinal dimension L _x , but at the same time, in contrast to the velocity deficit, their level does not differ significantly from the level of fluctuations behind a single disc.     

The evolution of solar systems

The recent detection of extra-solar planets and the increasing ability of modern instruments to image discs around young stars has brought a renewed interest in the formation of solar systems. In this article, I shall briefly review what we know about extra-solar planets and the physical structure of protostellar discs. One of the most powerful means of studying these disc systems is to observe the rotational line emission from molecules which can give information on physics and dynamics. At present, the observations are relatively crude but future instruments should be able to resolve molecular structures in the disc around nearby stars. As a prelude to these observations, I discuss some conceptually simple, although numerically challenging, models of the physical and chemical processes involved in determining the molecular distributions.     

Land/groove optical recording with GeTe/Sb2Te3 superlattice-like structure

A superlattice-like (SLL) structure was applied to phase-change optical recording. The recording layer consisting of alternating thin layers of two different phase-change materials, GeTe and Sb2Tes, were grown by magnetron sputtering on polycarbonate substrates. Land/groove optical recording was adopted to suppress crosstalk and obtain a large track density. Dynamic properties of the SLL disc were investigated with the shortest 1T pulse duration of 8 ns. Clear eye pattern was observed after 10000 direct overwrite cycles. Erasability above 20 dB was achieved at a constant linear velocity of 19 m/s. Carrier-noise ratio (CNR) kept above 46 dB when the recording frequency reaches 21 MHz. The SLL phase change optical disc demonstrates a better recording performance than the Ge1Sb2Te4 and Ge1Sb4Te7 discs in terms of CNR, erasability, and overwrite jitter.     

Nanoindentation and mechanical properties of solids in submicrovolumes,thin near-surface layers,and films: A Review

This paper presents a review devoted to the specific mechanical behavior of thin near-surface layers of various solids, materials, films, and multilayer coatings under local loading. Analysis is made of the principles, techniques, and instruments used for testing and determining mechanical properties of materials on a nanoscale, which, in recent years, have found a wide application under the general name “nanoindentation.” Information capabilities of this large and multifunctional family of methods employed for mechanical tests are discussed. Different aspects and specific features of the behavior of solids under severely constrained deformation caused by the local application of a microload to the surface of the test object are considered. Special attention is focused on the physical mechanisms of deformation and fracture under these conditions.     

Fractal dimension of Siegel disc boundaries

Using renormalization techniques, we provide rigorous computer-assisted bounds on the Hausdorff dimension of the boundary of Siegel discs. Specifically, for Siegel discs with golden mean rotation number and quadratic critical points we show that the Hausdorff dimension is less than 1.08523. This is done by exploiting a previously found renormalization fixed point and expressing the Siegel disc boundary as the attractor of an associated Iterated Function System. Received: 26 January 1998 / Received in final form: 5 June 1998 / Accepted: 11 June 1998     

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.     

Existence criteria and validity of plate models for graphene-like materials

Graphene-like(GL) materials have enriched the application prospects of two-dimensional materials by virtue of their various structures and properties. However, the following theoretical issues remain unsolved: how can stable GL materials exist and is plate idealization valid for any GL materials? Here we answer these questions based on an atomistic potential-based approach.The existence criteria for GL materials with three common structures, including planar honeycomb(PH), buckled honeycomb(BH), and honeycomb MX_2(2 H-MX_2) structures, were established. Moreover, the validity of classic linear-elastic plate models for these materials was examined. A validity factor, which represents the validity of using thin plate models to investigate the overall mechanical response of GL sheets, was defined. We determined that 2 H-MX_2 sheets can approximately be modeled as thin plates for arbitrary loadings, unlike PH and BH sheets.