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Event(s) on May 2011
- Saturday, 7th May, 2011
Title: High order numerical methods for conservation laws Speaker: Prof. Shu Chi-Wang, Division of Applied Mathematics, Brown University, USA Time/Place: 10:00 - 12:00
ACC209, Jockey Club Academic Community Centre, Baptist University Road CampusAbstract: In these lectures we will start from a general introduction of hyperbolic conservation laws and basic concepts of their numerical solutions, including first order montone schemes and second order high resolution TVD schemes. We will then move to some of the representative high order schemes, including finite volume and finite difference WENO schemes and discontinuous Galerkin methods. - Saturday, 7th May, 2011
Title: High order numerical methods for conservation laws Speaker: Prof. Shu Chi-Wang, Division of Applied Mathematics, Brown University, USA Time/Place: 14:30 - 16:30
ACC209, Jockey Club Academic Community Centre, Baptist University Road CampusAbstract: In these lectures we will start from a general introduction of hyperbolic conservation laws and basic concepts of their numerical solutions, including first order montone schemes and second order high resolution TVD schemes. We will then move to some of the representative high order schemes, including finite volume and finite difference WENO schemes and discontinuous Galerkin methods. - Thursday, 12th May, 2011
Title: PL: Computational Thinking: A Necessary Subject in Education Speaker: Prof. Walter Gander, ETH, Switzerland Time/Place: 16:15 - 17:15 (Preceded by Reception at 3:45pm)
LT3, Cha Chi-Ming Science Tower, HSH Campus, Hong Kong Baptist UniversityAbstract: Computers comprehensively control, regulate and govern our lives in the 21 Century, whether we like it or not. Our way to obtain and process information has been revolutionized (Google, GPS, Smart phone, digital media, Skype, etc.). Even in the kitchen a meal is cooked in a modern steamer controlled by a computer program. The automatic information processing takes increasingly place in the background. With so-called embedded systems, the computer has become invisible – often we are not even aware that computer science is involved.
It is time to rethink the fundamentals in school curricula. It is definitely not enough to teach our children to use computers. For understanding the world of today we need to teach fundamentals of computer science to everybody as we do with mathematics. We teach mathematics not to produce more mathematicians but because we are convinced that mathematics is important for the development of the mind. The same applies to the fundamentals of computer science. The Center for Computational Thinking at Carnegie Mellon defines: "Computational thinking is a way of solving problems, designing systems, and understanding human behavior that draws on concepts fundamental to computer science. To flourish in today's world, computational thinking has to be a fundamental part of the way people think and understand the world."
Understanding algorithms, problem solving techniques and programming are fundamentals of computer science necessary today for general education. We will solve problems on the computer with different levels of difficulty and so hopefully awaken some enthusiasm for programming also for an audience which has never programmed before. - Tuesday, 24th May, 2011
Title: Lectures on Algebra (1) Speaker: Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA Time/Place: 10:00 - 12:00
ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist UniversityAbstract: 理性文明 (Civilization of rational mind) 乃是世代相承，精益求精對於大自然的本質的認知。概括地來說，大自然的事物與現象是極為多樣而且變化無窮的﹔但是其內在的本質卻又具有精簡的原理和規律。所以唯有穿透表象，探求本質，才能認知其精簡，而這種由表及裡的基本方法就是定量分析(quantitative analysis)。這也就是為什麼基礎數學在理性文明的全程發展中，一直扮演著重要的角色；代數、幾何與分析則是基礎數學的三大支柱。而代數學的根基在於數的運算，是定量分析，有效能算的基本功。幾何學則是對於我們生活所在的空間本質的認知與深入理解。而分析學則是研究變動事物與現象的“變量數學”，它是代數和幾何的自然結合才發展而得的數學，具基礎理論就是微積分。 - Tuesday, 24th May, 2011
Title: DLS: On a Conjecture of C. Sundberg: A Numerical Investigation Speaker: Prof. Roland Glowinski, University of Houston, USA Time/Place: 16:15 - 17:15 (Preceded by Reception at 3:45pm)
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Carl Sundberg from University of Tennessee-Knoxville conjectured that $$ sup_{vin S} frac {displaystyle int^1_0 frac{|v'|^4}{v^6}dx} {displaystyle 1+int^1_0 |v''|^2dx} < + infty, $$ where $$ S = { v | v in H^2 (0,1), , v(0) = v(1), , v'(0) = v'(1), , v ge 1 }. $$ Our goal is to use a computational approach to investigate if (CSI) holds and to compute the related supremum, assuming it is finite. To do so, we observe that the supremum in (CSI) is equal to: $$ sup_{alpha ge 0} frac{F(alpha)}{1+alpha}, $$ where $$ F(alpha) = sup_{v in S_alpha} int^1_0 frac{|v'|^4}{v^6}dx $$ and $$ S_alpha = left{ v | v in S, , int^1_0 |v''|^2 dx = alpha right}. $$ The strategy we advocate at the moment is a pretty crude one, namely, tabulate the function $alpha rightarrow frac{F(alpha)}{1+alpha}$ in order to get information on the boundedness of the supremum in (CSI). In our lecture, we will discuss the numerical computation of $F(alpha)$, the associated problem of Calculus of Variations being solved by a methodology combining a finite difference discretization and an augmented Lagrangian algorithm associated with the following three families of linear constraints $v-q_0=0$, $v'-q_1 =0$ and $v''-q_2 = 0$. The results of numerical experiments (with a in the range $[0,10^6]$) will be presented; we will discuss the conclusions we can draw from them concerning the veracity of (CSI). - Wednesday, 25th May, 2011
Title: Lectures on Algebra (2) Speaker: Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA Time/Place: 10:00 - 12:00
ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist UniversityAbstract: 理性文明 (Civilization of rational mind) 乃是世代相承，精益求精對於大自然的本質的認知。概括地來說，大自然的事物與現象是極為多樣而且變化無窮的﹔但是其內在的本質卻又具有精簡的原理和規律。所以唯有穿透表象，探求本質，才能認知其精簡，而這種由表及裡的基本方法就是定量分析(quantitative analysis)。這也就是為什麼基礎數學在理性文明的全程發展中，一直扮演著重要的角色；代數、幾何與分析則是基礎數學的三大支柱。而代數學的根基在於數的運算，是定量分析，有效能算的基本功。幾何學則是對於我們生活所在的空間本質的認知與深入理解。而分析學則是研究變動事物與現象的“變量數學”，它是代數和幾何的自然結合才發展而得的數學，具基礎理論就是微積分。 - Wednesday, 25th May, 2011
Title: Global and Local Field Modeling and Inversion in Physics and Chemistry and Engineering Speaker: Prof. Ganquan Xie, 湖南省超级计算科学中心, China Time/Place: 16:00 - 17:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: From history to recent, the analytical and numerical method are developing separately. We combine analytical and numerical methods consistently to propose new Global analytical and local numerical GL field modeling and inversion m in physics, chemistry and engineering. Solving large matrix is a serious difficulty in FEM and FD method, There are error reflection from the artificial boundary is the second difficulty in FEM and FD methods. Our GL method overcomes these difficulties in FEM and FD method
1. The GL method combines analytical and numerical approaches together;
2. The GL method does not need any artificial boundary to truncate infinite domain;
3. There are 3x3 or 6x6 small matrices in GL Method;
4. The GL method does not need to solve any large matrix equation;
5. The GL method can be used to obtain the exact wave field;
6. The GL method is available for all frequency and any large material contrast and anisotropic materials;
7. The GL method is self parallelization;
8. The GL method is available for cloak modeling and no scattering inversion;
9. The GL method is available for quantum, photon and condense physical modeling and inversion;
10 The GL method is available for elastic, EM, acoustic, flow physical modeling and inversion;
11. The GL method has super-convergence;
12. GL method is very accurate and fast than FEM and FD method for wave propagation in the infinite domain. - Friday, 27th May, 2011
Title: Novel Practicable GLLH EM Invisible Cloak with Refractive Index N>1 and GL No Scattering Inversion Speaker: Prof. Ganquan Xie, 湖南省超级计算科学中心, China Time/Place: 10:00 - 11:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In this paper, we propose a novel Global and Local (GL) electromagnetic (EM) invisible cloaks with refractive index N(r)>1. Our GLLH EM invisible cloak is discovered from GL modeling and GL No scattering inversion and searched on a distinctive material class. a_{alpha beta} log^alpha (b_{alpha beta} / h)h^beta. So, it is called GLLH Cloak. The GLLH EM invisible cloak has refractive index N(r)>1, it has finite speed and has no exceed light speed violation. The GLLH EM cloak no scattering inversion and electromagnetic integral equation for cloak are presented in other paper. The novel EM wave propagation and front branching in the GLLH cloak by GLLH EM modeling and no scattering inversion are presented in this paper. The EM wave front propagation in GLLH cloak is behind of the front in free space. That shows that the GLLH EM invisible cloak has refractive index N(r)>1, has finite speed and has no exceed light speed violation. At time steps 118 dt, in the GLLH cloak, the wave front is curved as a crescent like and propagates slower than the light in free space. At the time step 119dt, the EM wave inside of the GLLH cloak propagates slower than light speed, in particular, its two crescent front peaks intersect at a front branching point. At the front branching point, the front is split to two fronts. One is forward propagation front with most energy and without exceed light speed, other one is attracting wave front to the inner boundary with small energy and amplitude decay to zero and with speed decay to zero The novel front branching and crescent like wave propagation. The GLLH EM cloaks can be practicable by using conventional materials in all broad frequency band. GLLH cloak patent and copyright are belong to GL Geophysical Laboratory, USA. - Tuesday, 31st May, 2011
Title: Lectures on Algebra (4) Speaker: Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA Time/Place: 10:00 - 12:00
ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist UniversityAbstract: 理性文明 (Civilization of rational mind) 乃是世代相承，精益求精對於大自然的本質的認知。概括地來說，大自然的事物與現象是極為多樣而且變化無窮的﹔但是其內在的本質卻又具有精簡的原理和規律。所以唯有穿透表象，探求本質，才能認知其精簡，而這種由表及裡的基本方法就是定量分析(quantitative analysis)。這也就是為什麼基礎數學在理性文明的全程發展中，一直扮演著重要的角色；代數、幾何與分析則是基礎數學的三大支柱。而代數學的根基在於數的運算，是定量分析，有效能算的基本功。幾何學則是對於我們生活所在的空間本質的認知與深入理解。而分析學則是研究變動事物與現象的“變量數學”，它是代數和幾何的自然結合才發展而得的數學，具基礎理論就是微積分。 - Tuesday, 31st May, 2011
Title: Quantized vortex stability and dynamics in superfluidity and superconductivity Speaker: Prof. Weizhu Bao, Department of Mathematics, National University of Singapore, Singapore Time/Place: 14:30 - 15:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In this talk, I will review our recent work on quantized vortex stability and dynamics in Ginzburg-Landau-Schrodinger and nonlinear wave equations for modeling superfluidity and superconductivity as well as nonlinear optics. The reduced dynamic laws for quantized vortex interaction are reviewed and solved analytically in several cases. Direct numerical simulation results for Ginzburg-Landau-Schrodinger and nonlinear wave equations are reported for quantized vortex dynamics and they are compared with those from the reduced dynamics laws.