Three dimensional steady subsonic Euler flows in bounded nozzles

The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic–sonic flow. Furthermore, when the normal component of vorticity and the variation of Bernoulli function are both small, the existence and uniqueness of subsonic Euler flows with non-zero vorticity are established. The proof of these results is based on a new formulation for the Euler system, a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions, detailed study for a linear div–curl system, and delicate estimate for the transport equations.     

L^2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID （EXCMG）

Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.     

Structures,microstructures, physical and chemical properties of different rice grains

Herein, we demonstrated a well-rounded exploration of the universal structures, microstructures and physical properties of different rice grains. We show that these rice grains are nanocrystalline in nature, have the standard pattern of type A rice crystalline, and can be attributed to the hexagonal crystal structure with space group of P6. These rice grains have uneven surfaces, clusters of the granules, or schistose structure. Carbon, nitrogen and oxygen elements are presented in the rice grains. No significant difference is observed in FTIR spectra in these rice grains, indicating the fundamental chemical structures of these rice grains are analogical. Their microstructural and physical properties were investigated in detail. Moreover, chemical properties (e.g. thermal stability) of the rice grains were explored. This research provides an in-depth understanding on the physical and structural properties on the atomic and molecular level, as well as guidance for food and industry applications.     

由几何反演导出的分形几何

本文介绍了由几何反演而导出的自反分形概念.构造了一个对称的,分叉自反分形曲线和一个自反分形尘集.推广了分形密切的概念而且提出了一个新的概念——分形包络.最后给出了“肥皂”和“鸡蛋”的两个自反分形的实例.     

Efficiency promotion for an on-ramp system based on intelligent transportation system information

<正>The effect of cars with intelligent transportation systems(ITSs) on traffic flow near an on-ramp is investigated by car-following simulations.By numerical simulations,the dependences of flux on the inflow rate are investigated for various proportions of cars with ITSs.The phase diagrams as well as the spatiotemporal diagrams are presented to show different traffic flow states on the main road and the on-ramp.The results show that the saturated flux on the main road increases and the free flow region is enlarged with the increase of the proportion of cars with ITS.Interestingly,the congested regions of the main road disappear completely when the proportion is larger than a critical value.Further investigation shows that the capacity of the on-ramp system can be promoted by 13%by using the ITS information, and the saturated flux on the on-ramp can be kept at an appropriate value by adjusting the proportion of cars with ITS.     

Localization theory of distributed fiber vibration sensor

Based on Sagnac interferometer, a simple distributed optical fiber sensing system with sub-loop is presented to monitor the vibration applied on the sensing fiber. By introducing a sub-loop, three output beams of interference with different delay time are gotten. Location of the vibration is analyzed through mathematical-physical equations. The vibration frequency, amplitude, and location are theoretically simulated. The results agree well with the previous experiments.     

Investigation of nanostructured Fe3O4 polypyrrole core-shell composites by X-ray absorbtion spectroscopy and X-ray diffraction using synchrotron radiation

In this article, we focus on the structural peculiarities of nanosized Fe₃O₄ in the core-shell nanocomposites obtained by polymerization of conducting polypyrrole shell around Fe₃O₄ nanoparticles. The local structure of Fe atoms was determined from the Extended X-ray Absorption Fine Structure analysis using our own package computer programs. An X-ray diffraction method that is capable to determine average particle size, microstrains, as the particle size distribution of Fe₃O₄ nanoparticles is presented. The method is based on the Fourier analysis of a single X-ray diffraction profile using a new fitting method based on the generalized Fermi function facilities. The crystallites size obtained by X-ray diffraction spectra analysis was estimated between 3.2 and 10.3 nm. Significant changes in the first and the second Fe coordination shell in comparison with standard bulk were observed. The global and local structure of the nanosized Fe₃O₄ are correlated with the synthesis conditions of the core-shell polypyrrole nanocomposites.     

Existence and selection of steady bubbles in a Hele–Shaw cell

This paper concerns the existence of a steadily translating bubble in a Hele–Shaw cell for small but non-zero surface tension ². We rigorously conclude that for bubble velocity U relative to the fluid velocity at infinity in the interval (1,2), analytic symmetric solutions exist in the asymptotic limit of surface tension ²→0 if and only if the Stokes constant for a relatively simple nonlinear differential equation is zero. This Stokes constant S depends on the parameter α(0,1) corresponding to bubble size and . Earlier calculations have shown S to be zero for a discrete set of values of a.     

Toughening effect of ferroelectric ceramics induced by domain switching and dislocations

The multi-scale analysis of fracture toughness of ferroelectric ceramics under complicate mechanical–electrical coupling effect is carried out in this paper. The generalized stress intensity factor (SIF) arising from spontaneous strains and polarization transformation in switching domain zones is accurately obtained by using an extended Eshelby theory. Taking BaTiO₃ ferroelectric ceramic for example, it is discovered that the crack propagation can be induced by domain switching arising from negative electrical field when the crack surface is parallel to the isotropic plane, and the obtained critical electric displacement intensity factor (EDIF) approximates closely to that obtained by the Green’s function method. Additionally, as pinning dislocations and slip dislocations can strongly influence properties of ferroelectric devices and induce the property degradation, it is necessary to investigate the dislocation toughening effects on fatigue and fracture mechanisms. The results show that the dislocation shielding and anti-shielding effects on mode II SIF, mode I SIF and EDIF are obviously different when a dislocation locates at a position near the crack tip. Through the calculation of the critical applied EDIF for crack propagation by using mechanical energy release rate (MERR) theory, it is discovered that the slip angles obviously influence fracture toughness, and the mode II SIF arising from dislocation has little influence on fracture toughness, however, the mode I SIF and EDIF arising from dislocation have great influences on fracture toughness.     

On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.