Effect of non-uniform magnetic field on crystal growth by floating-zone method in microgravity

The magnetic damping effect of the non-uniform magnetic field on the floating-zone crystal growth process in microgravity is studied by numerical simulation. The results show that the non-uniform magnetic field with designed configuration can effectively reduce the flow near the free surface and then in the melt zone. At the same time, the designed magnetic field can improve the impurity concentration non-uniformity along the solidification interface. The primary principles of the magnetic field configuration design are also discussed.

Difference schemes on non-uniform mesh and their application

High order accurate schemes are needed to simulate the multi-scale complex flow fields to get fine structures in simulation of the complex flows with large gradient of fluid parameters near the wall, and schemes on non-uniform mesh are desirable for many CFD (computational fluid dynamics) workers. The construction methods of difference approximations and several difference approximations on non-uniform mesh are presented. The accuracy of the methods and the influence of stretch ratio of the neighbor mesh increment on accuracy are discussed. Some comments on these methods are given, and comparison of the accuracy of the results obtained by schemes based on both non-uniform mesh and coordinate transformation is made, and some numerical examples with non-uniform mesh are presented.

Low-Dimensional Dynamical Systems for a Wake-Type Shear Flow with Vortex Dislocations

Low-dimensional systems are constructed to investigate dynamics of vortex dislocations in a wake-type shear flow. High-resolution direct numerical simulations are employed to obtain flow snapshots from which the most energetic modes are extracted using proper orthogonal decomposition (POD). The first 10 modes are classified into two groups. One represents the general characteristics of two-dimensional wake-type shear flow, and the other is related to the three-dimensional properties or non-uniform characteristics along the span. Vortex dislocations are generated by these two kinds of coherent structures. The results from the first 20 three-dimensional POD modes show that the low- dimensional systems have captured the basic properties of the wake-type shear flow with vortex dislocation, such as two incommensurable frequencies and their beat frequency.

Transverse mode formation in longitudinally pumped miniature slab lasers

The formation of transverse modes in longitudinally pumped miniature slab lasers is investigated theoretically and experimentally. The longitudinally non-uniform gain-guiding is studied by expanding the electric field into the Hermite-Gaussian functions that satisfy boundary conditions of the resonator. Non-Gaussian transversal beam profiles in the near field are found and the beam diameter is reduced when the pump spot becomes smaller. The experimental observation agrees with the theoretical calculation.

Single-mode condition for silicon rib waveguides with trapezoidal cross-section

Single-mode condition for silicon rib waveguides with trapezoidal cross-section was obtained using a numerical method based on imaginary-distance beam propagation method with non-uniform discretization. Both quasi-transverse-electric and quasi-transverse-magnetic modes were investigated. Simulated single-mode condition is given by a modified equation. Comparison with reported results shows that the Marcatili's method is in a better agreement with our results. (C) 2003 Elsevier B.V. All rights reserved.

Effect of dopant concentration on photocatalytic activity of TiO2 film doped by Mn non-uniformly

The thin films of TiO2 doped by Mn non-uniformly were prepared by sol-gel method under process control. In our preceding study, we investigated in detail, the effect of doping mode on the photocatalytic activity of TiO2 films showing that Mn non-uniform doping can greatly enhance the activity. In this study we looked at the effect of doping concentration on the photocatalytic activity of the TiO2 films. In this paper, the thin films were characterized by UV-vis spectrophotometer and electrochemical workstation. The activity of the photocatalyst was also evaluated by photocatalytic degradation rate of aqueous methyl orange under UV radiation. The results illustrate that the TiO2 thin film doped by Mn non-uniformly at the optimal dopant concentration (0.7 at %) is of the highest activity, and on the contrary, the activity of those doped uniformly is decreased. As a comparison, in 80 min, the degradation rate of methyl orange is 62 %, 12 % and 34 % for Mn non-uniform doping film (0.7 at %), the uniform doping film (0.7 at %) and pure titanium dioxide film, respectively. We have seen that, for the doping and the pure TiO2 films, the stronger signals of open circuit potential and transient photocurrent, the better photocatalytic activity. We also discusse the effect of dopant concentration on the photocatalytic activity of the TiO2 films in terms of effective separation of the photon-generated carriers in the semiconductor. (C) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.

Multi-mode Vortex-induced Vibration of Slender Cable Experiencing Shear Flow

The dynamic characteristics of slender cable often present serried modes with low frequencies due to large structure flexibility resulted from high aspect ratio (ratio of length to diameter of cable), while the flow velocity distributes non-uniformly along the cable span actually in practical engineering. Therefore, the prediction of the vertex-induce vibration of slender cable suffered from multi-mode and high-mode motions becomes a challenging problem. In this paper a prediction approach based on modal energy is developed to deal with multi-mode lock-in. Then it is applied to the modified wake-oscillator model to predict the VIV displacement and stress responses of cable in non-uniform flow field. At last, illustrative examples are given of which the VIV response of flexible cable in nonlinear shear flow field is analyzed. The effects of flow velocity on VIV are explored. Our results show that both displacement and stress responses become larger as the flow velocity increasing; especially higher stress response companied with higher frequency vibration should be paid enough attention in practical design of SFT because of its remarkable influence on structure fatigue life.

PREDICTION OF VORTEX-INDUCED VIBRATION OF FLEXIBLE RISER USING AN IMPROVED WAKE-OSCILLATOR MODEL

Based on improving the wake-oscillator model, an analytical model for vortex-induced vibration (VIV) of flexible riser under non-uniform current is presented, in which the variation of added mass at lock-in and the nonlinear relationship between amplitude of response and reduced velocity are considered. By means of empirical formula combining iteration computation, the improved analytical model can be conveniently programmed into computer code with simpler and faster computation process than CFD so as to be suitable to application of practical engineering. This model is validated by comparing with experimental result and numerical simulation. Our results show that the improved model can predict VIV response and lock-in region more accurately. At last, illustrative examples are given in which the amplitude of response of flexible riser experiencing VIV under action of non-uniform current is calculated and effects of riser tension and flow distribution along span of riser are explored. It is demonstrated that with the variation of tension and flow distribution, lock-in region of mode behaves in different way, and thus the final response is a synthesis of response of locked modes.

复杂裂隙岩体统计断裂本构关系与变形参数研究

Rock mass is widely recognized as a kind of geologic body which consists of rock blocks and discontinuities. The deformation and failure of rock mass is not only determined by rock block，but also by discontinuity which is virtually more important. Mutual cutting and combination of discontinuities controlled mechanical property of rock mass. The complex cutting of discontinuities determine the intense anisotropy on mechanical property of rock mass，especially under the effect of ground stress. Engineering practice has show that the brittle failure of hard rock always occurs when its working stress is far lower than the yield strength and compressive strength，the failure always directly related to the fracture propagation of discontinuities. Fracture propagation of discontinuities is the virtue of hard rock’s failure. We can research the rock mass discontinuous mechanical properties precisely by the methods of statistical analysis of discontinuities and Fracture Mechanics. According to Superposition Principle in Fracture Mechanics，A Problem or C Problem could be chosen to research. Problem A mainly calculates the crack-tip stress field and displacement field on internal discontinuities by numerical method. Problem C calculate the crack-tip stress field and displacement field under the assumption of that the mainly rock mass stress field has been known. So the Problem C avoid the complex mutual interference of stress fields of discontinuities，which is called crack system problem in Fracture Mechanics. To solve Problem C, field test on stress field in the rock mass is needed. The linear Superposition of discontinuities strain energies are Scientific and Rational. The difference of Fracture Mechanics between rock mass and other materials can mostly expression as：other materials Fracture Mechanics mostly face the problem A，and can’t avoid multi-crack puzzle, while the Rock mass Fracture Mechanics answer to the Problem C. Problem C can avoid multi-discontinuities mutual interference puzzle via the ground stress test. On the basis of Problem C, Fracture Mechanics could be used conveniently in rock mass. The rock mass statistics fracture constitutive relations, which introduced in this article, are based on the Problem C and the Discontinuity Strain Energy linear superposition. This constitutive relation has several merits: first, it is physical constitutive relation rather than empirical; second, it is very fit to describe the rock mass anisotropy properties; third, it elaborates the exogenous factors such as ground stress. The rock mass statistics fracture constitutive relation is the available approach to answer to the physical, anisotropic and ground stress impacted rock mass problems. This article stand on the foundation of predecessor’s statistics fractures constitutive relation, and improved the discontinuity distributive function. This article had derived the limitation of negative exponential distribution in the course of regression analysis, and advocated to using the two parameter negative exponential distribution for instead. In order to solve the problems of two-dimension stability on engineering key cross-sectional view in rock mass, this article derived the rock mass planar flexibility tensor, and established rock mass two-dimension penetrate statistics fracture constitutive relation on the basis of penetrate fracture mechanics. Based on the crack tip plasticity research production of penetrate fracture, for example the Irwin plasticity equifinality crack, this article established the way to deal with the discontinuity stress singularity and plastic yielding problem at discontinuity tip. The research on deformation parameters is always the high light region of rock mass mechanics field. After the dam foundation excavation of XiaoWan hydroelectric power station, dam foundation rock mass upgrowthed a great deal of unload cracks, rock mass mechanical property gotten intricacy and strong anisotropy. The dam foundation rock mass mostly upgrowthed three group discontinuities： the decantation discontinuity, the steep pitch discontinuity, and the schistosity plane. Most of the discontinuities have got partial unload looseness. In accordance with ground stress field data, the dam foundation stress field greatly non-uniform, which felled under the great impaction of tectonic stress field, self-weight stress field, excavation geometric boundary condition, and excavation, unload. The discontinuity complexity and stress field heterogeneity, created the rock mass mechanical property of dam foundation intricacy and levity. The research on the rock mass mechanics, if not take every respected influencing factor into consideration as best as we can, major errors likely to be created. This article calculated the rock mass elastic modulus that after Xiao Wan hydroelectric power station dam foundation gutter excavation finished. The calculation region covered possession monolith of Xiao Wan concrete double-curvature arch dam. Different monolith were adopted the penetrate fracture statistics constitutive relation or bury fracture statistics constitutive relation selectively. Statistics fracture constitutive relation is fit for the intensity anisotropy and heterogeneity rock mass of Xiao Wan hydroelectric power station dam foundation. This article had contrastive analysis the statistics fracture constitutive relation result with the inclined plane load test actual measurement elastic modulus and RMR method estimated elastic modulus, and find that the three methods elastic modulus have got greatly comparability. So, the statistics fracture constitutive relations are qualified for trust. Generally speaking，this article had finished following works based on predecessors job: “Argumentation the C Problems of superposition principle in Fracture Mechanics, establish two-dimension penetrate statistics fracture constitutive relation of rock mass, argue the negative exponential distribution limitation and improve it, improve of the three-dimension berry statistics fracture constitutive relation of rock mass, discontinuity-tip plastic zone isoeffect calculation, calculate the rock mass elastic modulus on two-dimension cross-sectional view”. The whole research clue of this article inherited from the “statistics rock mass mechanics” of Wu Faquan（1992）.

接收函数方法与中国及邻区上地幔间断面的研究

The receiver function method applied in researching the discontinuities in upper mantle was systematically studied in this paper. Using the theoretical receiver functions, the characteristics of P410S and P660S phases were analyzed, and the influencing factors for detection of these phases were discussed. The stability of receiver function was studied, and a new computational method of receiver function, RFSSMS (Receiver Function of Stack and Smooth of Multi seismic-records at a Single station), was put forward. We built initial reference velocity model for the media beneath each of 18 seismic stations respectively; then estimated the buried depths of 410-km and 660-km discontinuities(simply marked as '410' and '660') under the stations by using the arrive time differences of P410S and P660S with P. We developed a new receiver function inversion method -PGARFI (Peeling-Genetic Algorithm of Receiver Function Inversion), to obtain the whole crust and upper mantle velocity structure and the depths of discontinuities beneath a station. The major works and results could be summarized as follows: (1) By analysis of the theoretical receiver functions with different velocity models and different ray parameters, we obtain the knowledge: The amplitudes of P410S and P660S phases are decreasing with the increasing of epicentral distance A , and the arrival time differences of these phases with P are shorter as A is longer. The multiple refracted and/or reflected waves yielded on Moho and the discontinuities in the crust interfere the identification of P410S. If existing LVZ under the lithosphere, some multiple waves caused by LVZ will interfere the identification of P410S. The multiple waves produced by discontinuity lied near 120km depth will mix with P410s phase in some range of epicentral distance; and the multiple waves concerned with the discontinuity lied near 210km depth will interfere the identification of P660S. The epicentral distance for P4i0s identification is limited, the upper limit is 80° . The identification of P660S is not restricted by the epicenter distance obviously. The identification of P410S and P6gos in the theoretical receiver functions is interfered weakly from the seismic wave attenuation caused by the media absorption if the Q value in a reasonable range. (2) The stability of receiver function was studied by using synthetic seismograms with different kind of noise. The results show that on the condition of high signal-noise-ratio of seismic records, the high frequency background noise and the low frequency microseism noise do not influence the calculating result of receiver function. But the media "scattering noise" influence the stability of receiver function. When the scattering effect reach some level, the identification of P4iOs and P66os is difficult in single receiver function which is yielded from only one seismic record. We provided a new method to calculate receiver function, that is, with a group of earthquake records, stacking the R and Z components respectively in the frequency domain, and weighted smooth the stacked Z component, then compute the complex spectrum ratio of R to Z. This method can improve the stability of receiver function and protrude the P4i0s and P66os in the receiver function curves. (3) 263 receiver functions were provided from 1364 three component broadband seismograms recorded at 18 stations in China and adjacent areas for the tele-earthquakes. The observed arrival time differences of P410S and P660S with P were obtained in these receiver functions. The initial velocity model for every station was built according to the prior research results. The buried depths of '410' and '660' under a station were acquired by the way of adjusting the depths of these two discontinuities in the initial velocity model until the theoretical arrival time differences of P410S and P660S with P well conformed to the observed. The results show an obvious lateral heterogeneity of buried depths of ' 410' and (660' . The depth of '410' is shallower beneath BJI, XAN, LZH and ENH, but deeper under QIZ and CHTO, and the average is 403km . The average depth of '660' is 663km, deeper under MDJ and MAJO, but shallower under QIZ and HYB. (4) For inversing the whole crust and upper mantle velocity structure, a new inversion method -PGARFI (Peeling-Genetic Algorithm of Receiver Function Inversion) has- been developed here. The media beneath a station is divided into segments, then the velocity structure is inversed from receiver function from surface to deep successively. Using PGARFI, the multi reflection / refraction phases of shallower discontinuities are isolated from the first order refraction transform phase of deep discontinuity. The genetic algorithm with floating-point coding was used hi the inversion of every segment, and arithmetical crossover and non-uniform mutation technologies were employed in the genetic optimization. 10 independent inversions are completed for every segment, and 50 most excellent velocity models are selected according to the priority of fitness from all models produced in the inversion process. The final velocity structure of every segment is obtained from the weighted average of these 50 models. Before inversion, a wide range of velocity variation with depth and depth range of the main discontinuities are given according to priori knowledge. PGARFI was verified with numerical test and applied in the inversion of the velocity structure beneath HIA station down to 700km depth.

The Liquefaction and Displacement of Highly Saturated Sand under Water Pressure Oscillation

In order to investigate the characteristics of water wave induced liquefaction in highly saturated sand in vertical direction, a one-dimensional model of highly saturated sand to water pressure oscillation is presented based oil the two-phase continuous media theory. The development of the effective stresses and the liquefaction thickness are analyzed. It is shown that water pressure oscillating loading affects liquefaction severely and the developing rate of liquefaction increases with the decreasing of the sand strength or the increasing of the loading strength. It is shown also that there is obvious phase lag in the sand Column. If the sand permeability is non-uniform, the pore pressure and the strain rise sharply at which the smallest permeability occurs. This solution may explain Why the fracture occurs in the sand column in some conditions.

Experimental Studies of the Material Properties of the Forewing of Cicada (Homoptera, Cicadidae)

Detailed investigations on the structural and mechanical properties of the forewing of the cicada were carried out. Measurement of the structures of the wings showed that the thickness of the membrane of each cell and the diameter of each vein were non-uniform in both the longitudinal and transverse directions, and their means were approximately 12.2 and 133.3 mum, respectively. However, the aspect ratios of the wings and the bodies were quite uniform and were approximately equal to 2.98 and 2.13, respectively. Based on the measured thickness, mass and area of the membranes of the cells, the mean density and the mean area density of the wing were approximately 2.3 g cm(-3) and 2.8 x 10(-3) g cm(-2), respectively. In addition, the diameters of the veins of the wings, including the diameters of the holes in the vein of the leading edge, were examined. The mechanical properties of the wing were investigated separately by nanoindentation and tensile testing. The results indicated that the mean Young's modulus, hardness and yield stress of the membranes of the wings were approximately 3.7 Gpa, 0.2 Gpa and 29 Mpa, respectively, and the mean Young's modulus and strength of the veins along the direction of the venation of wings were approximately 1.9 Gpa and 52 Mpa, respectively. Finally, the relevant results were briefly analyzed and discussed, providing a guideline to the biomimetic design of the aerofoil materials of micro air vehicles.

Mechanism on Progressive Failure of a Faulted Rock Slope Due to Slip-Weakening

Slip-weakening is one of the characteristics of geological materials under certain loadings. Non-uniform rock structure may exist in the vicinity of the slip surface for a rock slope. Some portion of the slip surface may be penetrated but the other not. For the latter case, the crack or the fault surface will undergo shear deformation before it becomes a successive surface under a certain loading. As the slipped portion advances,slip-weakening occurs over a distance behind the crack tip. In the weakening zone, the shear strength will decrease from its peak value to residual friction level. The stress will redistribute along the surface of crack and in the weakening zone. Thus the changed local stress concentration leads the crack to extend and the ratio of penetration of the slip surface to increase. From the view of large-scale for the whole slip surface, the shear strength will decrease due to the damage of interior rock structure, and the faulted rock behaves as a softening material. Such a kind of mechanism performs in a large number of practical landslides in the zones experienced strong earthquakes. It should be noted that the mechanism mentioned above is different from that of the breakage of structural clay,in which the geological material is regarded as a medium containing structural lumps and structural bands. In this paper, the softening behavior of a faulted rock should be regarded as a comprehensive result of the whole complicated process including slip-weakening, redistribution of stress, extension of crack tip, and the penetration of the slip surface. This process is accompanied by progressive failure and abrupt structural damage. The size of slip-weakening zone is related to the undergoing strain. Once the relative slide is initiated (local or integrated), the effect of slip-weakening will behave in a certain length behind the crack tip until the formation of the whole slip surface.

Fourth order accurate compact scheme with group velocity control (GVC)

For solving complex flow field with multi-scale structure higher order accurate schemes are preferred. Among high order schemes the compact schemes have higher resolving efficiency. When the compact and upwind compact schemes are used to solve aerodynamic problems there are numerical oscillations near the shocks. The reason of oscillation production is because of non-uniform group velocity of wave packets in numerical solutions. For improvement of resolution of the shock a parameter function is introduced in compact scheme to control the group velocity. The newly developed method is simple. It has higher accuracy and less stencil of grid points.

Three-Dimensional Propagation of the Transmitted Shock Wave in a Square Cross-Sectional Chamber

An investigation into the three-dimensional propagation of the transmitted shock wave in a square cross-section chamber was described in this paper, and the work was carried out numerically by solving the Euler equations with a dispersion-controlled scheme. Computational images were constructed from the density distribution of the transmitted shock wave discharging from the open end of the square shock tube and compared directly with holographic interferograms available for CFD validation. Two cases of the transmitted shock wave propagating at different Mach numbers in the same geometry were simulated. A special shock reflection system near the corner of the square cross-section chamber was observed, consisting of four shock waves: the transmitted shock wave, two reflection shock waves and a Mach stem. A contact surface may appear in the four-shock system when the transmitted shock wave becomes stronger. Both the secondary shock wave and the primary vortex loop are three-dimensional in the present case due to the non-uniform flow expansion behind the transmitted shock.