Propagation of a pre-existing turbulent fluid fracture

The propagation of rough and smooth wall pre-existing turbulent fluid fractures is investigated. The laminar fluid fracture is included as a special case for comparison. Lubrication theory is assumed to apply in the fracture and turbulence is introduced through the wall shear stress. The Perkins–Kern–Nordgren approximation is made in which the fluid pressure is proportional to the half-width of the fracture. The fracture half-width satisfies a non-linear diffusion equation. By using a linear combination of the Lie point symmetries of the non-linear diffusion equation a group invariant solution for the fracture length, volume and half-width is derived. The evolution of the length, half-width and mean flow velocity is analysed for a range of working conditions at the fracture entry. It is found that the mean flow velocity increases approximately linearly along the fracture.     

Nuclear Structure and Electromagnetic Transitions Investigation in Er Isotopes within Framework of Interacting Boson Model

Interacting Boson Model-2(IBM-2)is used to determine the Hamiltonian for Er nuclei.Fit values of parameters are used to construct the Hamiltonian,energy levels and electromagnetic transitions(B(E2),B(M1))multipole mixing ratios(δ(E2/M1))for some even-even Er nuclei and monopole transition probability are estimated.New ideas are used for counting bosons number at N=64 and results are compared with previous works.     

Shear and extensional rheology of entangled polymer melts: Similarities and differences

This work extends our previous understanding concerning the nonlinear responses of entangled polymer solutions and melts to large external deformation in both simple shear and uniaxial extension. Many similarities have recently been identified for both step strain and startup continuous deformation, including elastic yielding, i.e., chain disentanglement after cessation of shear or extension, and emergence of a yield point during startup deformation that involves a deformation rate in excess of the dominant molecular relaxation rate. At a sufficiently high constant Hencky rate, uniaxial extension of an entangled melt is known to produce window-glass-like rupture. The present study provides evidence against the speculation that chain entanglements tie up into "dead knots" in constant-rate extension because of the exponentially growing chain stretching with time. In particular, it is shown that even Instron-style tensile stretching, i.e., extending a specimen by applying a constant velocity on both ends, results in rupture. Yet, in the same rate range, the same entangled melt only yields in simple shear, and the resulting shear banding is clearly not a characteristic of rupture. Thus, we conclude that chain entanglements respond to simple shear in the manner of yielding whereas uniaxial extension is rather effective in causing some entanglements to lock up, making it impossible for the entanglement network to yield at high rates.     

非线性Black-Scholes模型下算术平均亚式期权定价问题

在非线性Black-Scholes模型下,研究了算术平均亚式期权定价问题.首先利用单参数摄动方法,将亚式期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了算术平均亚式期权的近似定价公式.最后分析了近似结论的误差估计,并通过数值算例验证了所得近似结论的合理性.     

基于傅立叶变换的SVJ模型的欧式期权定价

为了更加精确的计算期权价格,将结合随机波动和跳扩散模型(以下简称SVJ模型)以更好的描述期权标的资产价格过程,然而这样的价格过程无法得到概率密度函数的封闭形式,而只能得到包含特殊函数和无限求和的复杂的表达式.不过它们的特征函数都是封闭且是唯一的,因而可以通过它们的特征函数,并运用两种傅立叶变换的方法来求出期权价格.其中FFT算法计算的结果将与Monte Carlo模拟得出的结果进行比较,然后再将SVJ模型的计算结果和Black-Scholes模型进行比较.     

Growth characteristics of spherical titanium oxide nanoparticles during the rapid gaseous detonation reaction

The nanosize grain growth characteristics of spherical single-crystal titanium oxide (TiO₂) during the rapid gaseous detonation reaction are discussed. Based on the experimental conditions and the Chapman–Jouguet theory, the Kruis model was introduced to simulate the growth characteristics of spherical TiO₂ nanoparticles obtained under high pressure, high temperature and by rapid reaction. The results show that the numerical analysis can satisfactorily predict the growth characteristics of spherical TiO₂ nanoparticles with diameters of 15–300 nm at different affecting factors, such as concentration of particles, reaction temperature and time, which are in agreement with the obtained experimental results. We found that the increase of the gas-phase reaction temperature, time, and particle concentration affects the growth tendency of spherical nanocrystal TiO₂, which provides effective theoretical support for the controllable synthesis of multi-scale nanoparticles.     

TRANSIENT ANALYSIS OF COMPOSITE PLATES BY A LOCAL RADIAL BASIS FUNCTIONS-FINITE DIFFERENCE TECHIQUE

The use of local numerical schemes,such as finite differences produces much better conditioned matrices than global collocation radial basis functions methods.However,finite difference schemes are limi...     

Importance of verifying queue model assumptions before planning with simulation software

This case study uses empirical data gathered at an Australian refinery to verify the assumptions for queue distributions before using special-purpose software to plan the off-road-truck hauling of titanium dioxide to a refinery (n = 773). Easy-to-use spreadsheet software is utilized to verify assumptions for queue models. Managers are able to make decisions based on economic implications of queue models to avoid making costly planning mistakes. Analysts can use nonparametric hypothesis-testing techniques to verify distribution assumptions for optimization without having to write hard-to-maintain and complex algebraic linear equations or nonlinear search routines.     

Experimental study and numerical modeling of brittle fracture of carbonate rock under uniaxial compression

The brittle carbonate rock taken from the Tarim Oilfield is tested in laboratory under uniaxial compression. The acoustic emission (AE) is used to monitor the microcracking activity in rock during the experiment. Moreover, the 3D tomograms of carbonate rock after uniaxial compression are obtained by using CT imaging technology, which indicates that microcracks mutually interconnect and eventually form macroscopic fractures after failure. The PFC2D is used to model the behavior of brittle rock including microcracks propagation. The stress–strain curve and cracks distribution in rock model are obtained from the PFC simulation. The numerical results agree with the experimental test well.