 |
|
Event(s) on September 2011
- 6/9/2011
| 題目: |
Numerical simulation of detonation waves |
| 講員: |
Dr. GAO Zhen, School of Mathematical Sciences, Ocean University of China |
| 時間/地點: |
11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Bapitst University
|
| | |
| 摘要: |
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.
|
- 7/9/2011
| 題目: |
How to Tame CDOs? |
| 講員: |
Prof. Wolfgang Härdle, Center for Applied Statistics and Economics, Humboldt-Universitat zu Berlin, Germany |
| 時間/地點: |
15:30 - 16:30
RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist University
|
| | |
| 摘要: |
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.
|
- 20/9/2011
| 題目: |
A Family of Models in X-ray Dark-field Tomography |
| 講員: |
Prof. Weimin HAN, Department of Mathematics, University of Iowa, USA |
| 時間/地點: |
16:30 - 17:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
|
| | |
| 摘要: |
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
|
|
|
|
|
