Colloquium/Seminar

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Event(s) on September 2011


  • Tuesday, 6th September, 2011

    Title: Numerical simulation of detonation waves
    Speaker: Dr. GAO Zhen, School of Mathematical Sciences, Ocean University of China
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Bapitst University
    Abstract: Detonation is a complex phenomenon that involves a shock front followed by a reaction zone. Physical experiments of detonation are difficult even with the most advances in engineering and sciences existed today. Accurate and efficient computer simulations provide a way to guide researchers to design and validate experiments. By solving the reactive Euler equations with species with the fifth order WENO finite difference scheme with various grid resolutions, the detailed numerical simulation of one- and two- dimensional detonation waves are demonstrated in this talk. An efficient and easily implemented Perfectly Matched Layer (PML) absorbing boundary condition (ABC) are introduced to reduce the computational cost and to avoid wave reflection from the artificial computational boundary for the two-dimensional detonation waves. Numerical schemes for solving the system of hyperbolic conversation laws with a single-mode ZND analytical solution as initial conditions are presented. Numerical simulation agrees well with those in the literature. This is a joint work with Prof. Don, Wai Sun and Mr. Li, Zhiqiu at Hong Kong Baptist University, HK, China.


  • Wednesday, 7th September, 2011

    Title: How to Tame CDOs?
    Speaker: Prof. Wolfgang Härdle, Center for Applied Statistics and Economics, Humboldt-Universitat zu Berlin, Germany
    Time/Place: 15:30  -  16:30
    RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist University
    Abstract: Modelling portfolio credit risk is one of the crucial challenges faced by financial services industry in the last few years. We propose the valuation model of collateralized debt obligations (CDO) based on copula functions with up to three parameters, with default intensities estimated from market data and with a random loss given default that is correlated with default times. The methods presented are used to reproduce the spreads of the iTraxx Europe tranches. We apply hierarchical Archimedean copulae (HAC) whose construction allows for the fact that the risky assets of the CDO pool are chosen from six different industry sectors. The dependence among the assets from the same group is specified with the higher value of the copula parameter, otherwise the lower value of the parameter is ascribed. The copula with two and three parameters models the relation between the loss given default and the default times. Our approach describes the market prices better than the standard pricing procedure based on the Gaussian distribution.


  • Tuesday, 20th September, 2011

    Title: A Family of Models in X-ray Dark-field Tomography
    Speaker: Prof. Weimin HAN, Department of Mathematics, University of Iowa, USA
    Time/Place: 16:30  -  17:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: X-ray mammography is currently the most prevalent imaging modality for screening and diagnosis of breast cancers. However, its success is limited by the poor contrast between healthy and diseased tissues in the mammogram. A potentially prominent imaging modality is based on the significant difference of x-ray scattering behaviors between tumor and normal tissues. Driven by major practical needs for better x-ray imaging, exploration into contrast mechanisms other than attenuation has been active for decades, e.g., in terms of scattering, which is also known as dark-field tomography. In this talk, a theoretical study is provided for the x-ray dark-field tomography (XDT) assuming the spectral x-ray detection technology. The radiative transfer equation (RTE) is usually employed to describe the light propagation within biological medium. It is challenging to solve RTE numerically due to its integro-differential form and high dimension. For highly forward-peaked media, it is even more difficult to solve RTE since accurate numerical solutions require a high resolution of the direction variable, leading to prohibitively large amount of computations. For this reason, various approximations of RTE have been proposed in the literature. For XDT, a family of differential approximations of the RTE is employed to describe the light propagation for highly forward-peaked medium with small but sufficient amount of large-angle scattering. The forward and inverse parameter problems are studied theoretically and approximated numericall