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Event(s) on May 2011
- 7/5/2011
| 題目: |
High order numerical methods for conservation laws |
| 講員: |
Prof. Shu Chi-Wang, Division of Applied Mathematics, Brown University, USA |
| 時間/地點: |
10:00 - 12:00
ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus
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| 摘要: |
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.
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- 7/5/2011
| 題目: |
High order numerical methods for conservation laws |
| 講員: |
Prof. Shu Chi-Wang, Division of Applied Mathematics, Brown University, USA |
| 時間/地點: |
14:30 - 16:30
ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus
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| 摘要: |
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.
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- 12/5/2011
| 題目: |
PL: Computational Thinking: A Necessary Subject in Education |
| 講員: |
Prof. Walter Gander, ETH, Switzerland |
| 時間/地點: |
16:15 - 17:15 (Preceded by Reception at 3:45pm)
LT3, Cha Chi-Ming Science Tower, HSH Campus, Hong Kong Baptist University
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| 摘要: |
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.
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- 24/5/2011
| 題目: |
Lectures on Algebra (1) |
| 講員: |
Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA |
| 時間/地點: |
10:00 - 12:00
ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist University
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| 摘要: |
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。
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- 24/5/2011
| 題目: |
DLS: On a Conjecture of C. Sundberg: A Numerical Investigation |
| 講員: |
Prof. Roland Glowinski, University of Houston, USA |
| 時間/地點: |
16:15 - 17:15 (Preceded by Reception at 3:45pm)
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
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).
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- 25/5/2011
| 題目: |
Lectures on Algebra (2) |
| 講員: |
Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA |
| 時間/地點: |
10:00 - 12:00
ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist University
|
| | |
| 摘要: |
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。
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- 25/5/2011
| 題目: |
Global and Local Field Modeling and Inversion in Physics and Chemistry and Engineering |
| 講員: |
Prof. Ganquan Xie, 湖南省超级计算科学中心, China |
| 時間/地點: |
16:00 - 17:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
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.
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- 27/5/2011
| 題目: |
Novel Practicable GLLH EM Invisible Cloak with Refractive Index N>1 and GL No Scattering Inversion |
| 講員: |
Prof. Ganquan Xie, 湖南省超级计算科学中心, China |
| 時間/地點: |
10:00 - 11:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
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.
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- 31/5/2011
| 題目: |
Lectures on Algebra (4) |
| 講員: |
Prof. HSIANG Wuyi, Department of Mathematics, University of California, Berkeley, USA |
| 時間/地點: |
10:00 - 12:00
ACC209, Jockey Club Academic Community Centre, Baptist University Road Campus, Hong Kong Baptist University
|
| | |
| 摘要: |
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。
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- 31/5/2011
| 題目: |
Quantized vortex stability and dynamics in superfluidity and superconductivity |
| 講員: |
Prof. Weizhu Bao, Department of Mathematics, National University of Singapore, Singapore |
| 時間/地點: |
14:30 - 15:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
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| 摘要: |
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.
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