Intensive Lectures (2013, Mar. 8 -
9)

Roland Potthast (German
Meteorological Service & Univ. of Reading (UK))

Data Assimilation and dynamic Inverse Problems in
Meteorology and Beyond

**Lecture 1**: Mar. 8 (Friday), 1:00-2:00

Data Assimilation, an introduction

**Lecture 2**: Mar. 8, 3:00-4:00

Variational Methods for Data Assimilation

**Lecture 3**: Mar. 8, 5:00-6:00

The Kalman Filter

**Lecture 4**: Mar. 9 (Saturday), 2:00-3:00

Ensemble Methods for Data Assimilation

**Lecture 5**: Mar. 9, 4:00-5:00

Obervation Systems (e.g. Radar, Radiances,
GPS-Tomography and many more)

2013, Feb. 27(Wed.) 4:00, 5W254

Andreas Kirsch (Karlsruhe Institute of Technology)

Title : The Factorization Method for Inverse
Scattering Problems

2013, Jan. 25(Fri.) 4:00, 5W254

Daewon Jung(Inha University)

Title : On the polarizability and
capacitance of the cube

2012, Dec. 18(Tue.) 4:00, 5W253

이정환(기상청
예보기술팀장)

Title :
기상자료의 생산과정과
특성 및 수학적 접근현황
소개

2012, Dec. 14(Fri.) 4:00, 5W254

Xiaofei Li(Inha University)

Title : Asymptotic analysis of narrow escape time
in singular domains

Tingting Feng(Inha
University)

Title : Neutral inclusions

2012, Dec. 7(Fri.) 4:00, 5W254

Seong-Kwan Park (Inha University)

Title : Flow field computation by upwind point
collocation method for simplified high voltage gas circuit breaker model using
virtual interpolation points

We consider the computational problems related to
high voltage (HV) circuit breakers. To effectively design HV circuit breakers,
a point collocation method which was proposed

by
authors is tested. The point collocation method is implemented to a simplified
model for the HV circuit breaker and showed a robust behavior even in severe
boundary condition.

A good shock capturing is shown in the
computations and a delicate gas diffusion through a
slit is also computed, which is usually difficult to catch. Vector splitting
method is employed

to
exploit the merit of point collocation methods in the hyperbolic problems.

2012, Nov. 9(Fri.) 4:00, 5W254

Yangjin Kim (Konkuk
University)

Title :
A mathematical model of glioma invasion and
proliferation

Glioblastoma is a highly invasive brain tumor. This
invasive behavior of tumor cells is responsible for low survival rate and
microenvironment plays an important role in the active migration. A thorough
understanding of the microenvironment would provide a foundation to generate
new strategies in therapeutic drug development. We developed a mathematical
model to better understand the role of microenvironment in creating different
invasion patterns. We analyze the migration patterns of glioma
cells from the main tumor, and show that the various patterns observed in
experiments can be obtained by a model's simulations, by choosing appropriate
values of the key model parameters of the PDE model. These
includes chemotactic sensitivity, haptotactic
strength, and cell-cell adhesion. Cancer is a complex, multiscale
process, in which genetic mutations occurring at a sub-cellular level manifest
themselves as functional changes at the cellular and tissue scale. A multi-scale
model will also be discussed in order to get more detailed information on cell
migration and proliferation under the influence of a particular microRNA
(miR451) and its counterpart, AMPK complex. Biochemical and Biomechanical
control of cell proliferation and migration play a significant role in
regulation of tumor growth overall and might lead to better treatment option of
eradicating the whole tumor population including 'invisible' migratory tumor
cells.

2012, Oct. 19(Fri.) 4:00, 5W254

Seok-Bae Yun (Academia Sinica)

Title :
On the spatially homogeneous Boltzmann equation for relativistic particles

The relativistic Boltzmann equation describes the evolution of the velocity
distribution function of non-ionized particles in Milkowsky
space-time, In this talk, we consider the Cauchy problem, asymptotic behavior
and the propagation of exponential moments of the relativistic Boltzmann
equation in the case when the dynamics does not depend on spatial variables.
This is a joint work with Robert Strain.

2012, Sept.
14(Fri.) 4:00, 5W254

Wanho Lee (Inha Univ.)

Title : Applications of the immersed boundary method: valveless
pumping and heart modeling

Abstract

2012, July 13(Fri.) 4:00, 5W254

Sanghyeon Yu (KAIST)

Title :
Electrostatics of two charged conducting spheres

2012, July 13(Fri.) 5:00, 5W254

Sookkyung Lim (Univ. of Cincinnatti)

Title :
Generalized immersed boundary method applied to mathematical modeling in
biology

A general version of the immersed boundary (IB) method combined with the
unconstrained Kirchhoff rod theory has been developed to study biological fluid
mechanics in the filamentous structure such as bacterial flagella and DNA
strand. A thin elastic filament (rod) in the Kirchhoff model that resists
bending and twisting can be modeled as a กฐthree-dimensional space curve' together with an
orthonormal triad (material frame) at each point of the rod. The triad
indicates how much the filament bends or twists or shears. This is a
well-established theory in the statics and dynamics of thin elastic filaments
without fluid. Combining Kirchhoff rod theory with the standard models of
viscous incompressible fluids will allow us to study the complicated
hydrodynamics of bacterial swimming, DNA supercoiling, and many more.

2012, May
25(Fri.) 4:00, 5W254

Q-Han Park (Korea University)

Title : New Wave of Nano Metal

2012, May
4(Fri.) 1:00, 5W253

Chongam Kim (Seoul National University)

Title : Multi-dimensional limiting strategy for hyperbolic conservation laws:
Finite Volume Methods to Discontinuous Galerkin
Approximations

Abstract

2012, May 4(Fri.) 4:00, 5W254

Chang Kwon HWANGBO (Inha Univ.)

Title : Introduction to Plasmonics

2012,
Apr. 27(Fri.) 4:00, 5W254

Daniele Garrisi (Inha
Univ.)

Title : Standing-waves with a small energy/charge
ratio

Abstract : Standing-waves solutions to the non-linear Klein-Gordon equation
with small energy/charge ratio (hylomorphic charge)
exhibits a non-dispersion behaviour. We discuss
general hypotheses on the non-linear term for the existence of solutions with
small hylomorphic charge to a system of non-linear
Klein-Gordon equations and their dispersive behaviour.

2012, Apr.
13(Fri.) 4:00, 5W254

Giulio Ciraolo (Palermo,
Italy)

Title : Symmetry of minimizers with a level surface parallel to the boundary

Abstract

2012, Mar. 30
(Fri.) 4:00, 5W254

Yuan Ganghua(Northeast Normal Univ., China)

Title : Inverse Problems and Observability
inequalities for Plate Equations and Schrodinger Equations

Abstract: In this talk, I would like to present some results on inverse
coefficient problems and inverse source problems for some plate equations, and
present some results on L^2-level observability
inequalities for a plate equation and a Schrodinger equation with potential.
All of the results are derived by several kinds of Carleman
estimates.

2012, Mar. 23
(Fri.) 4:00, 5W254

Jisun Lim(Inha Univ.)

Title : Crack Nucleation Sensitivity Analysis

I will talk about sensitivity analysis for crack nucleation problemn
in a two-dimensional linear elastic fracture mechanics. The topological
asymptotic expansion of a shape functional associated to the total potential
energy of an elastic cracked body is calculated.

2012, Mar. 23(Fri.) 5:00, 5W254

Se Eun, Noh (Myongji Univ.)

Title : Large Time Behavior of Solutions for the Navier-Stokes equations for compressible fluid in three
dimension

Abstract

2012, Mar. 9 (Fri.) 4:00, 5W254

Tae Gab Ha(Inha Univ.)

Title : Blow-up solutions to a p-Laplace equation

Consider two perfectly conducting spheres in a homogeneous medium where the
current-electric field relation is the power law. Electric field E blows up in
the L^infinite-norm as delta, the disttance
between the conductors tends to zero.

2012, Mar. 9(Fri.) 5:00, 5W254

Taeyoung Ha (NIMS)

Title : Sufficient conditions for the formation of flocking in Cucker-Smale tyoe flocking model

In this presentation, we present a Cucker-Smale type
flocking model with nonlinear velocity couplings, and derive sufficient
conditions for the formation of flocking in terms of communication weight and
initial spatial, velocity standard deviations.

2011, Nov. 30 (Wed.) 4:00, 5W254

Myoungjean Bae(POSTECH)

Title : Free Boundary Problems and Transonic Shocks

My talk will be devoted to introduction of transonic shocks for the Euler
system of inviscid compressible flow, and to
description of how a transonic shock problem is formulated as a free boundary
problem containing nonlinear Mixed type PDEs. I will present various examples
of shock phenomena and contact discontinuity along with recent results.

2011, Nov. 30 (Wed.) 5:00, 5W254

Sun-Sig Byun(Seoul National University)

Title : Higher regularity results for solutions to elliptic and parabolic
systems

We present some recent regularity results and issues for weak solutions of
elliptic and parabolic systems in divergence form with possibly measurable
coefficients in an irregular bounded domain.

2011, Oct. 28 (Fri.) 4:00, 5W254

Deok-Sun Lee(Inha
University)

Title : Network theory for complex systems

Large-scale data-sets that have been made available recently offer an unprecedented
opportunity to study the design and working principle of macroscopic complex
systems in nature and society. Network theory proved to be quite useful
particularly for understanding the system-level behavior of complex systems
that exhibit structural heterogeneity in general. In this talk, we introduce
the network approach taken by physicists to complex systems and its application
to biological systems and medicine.

2011, Sept. 30 (Fri.) 4:00, 5W254

Graeme Milton(The University of Utah)

Title : Spectral super-resolution in metamaterial
composites

We investigate the optical properties of periodic composites containing
inclusions having a frequency dependent negative electrical permittivity, with
a very small imaginary part,in a normal material
matrix. We consider the case where these inclusions have sharp corners, and
following Hetherington and Thorpe, use analytic results to argue that it is
then possible to deduce the shape of the corner (its included angle) by
measurements of the absorptance of such composites
when the scale size of the inclusions and period cell is much finer than the
wavelength. These analytic arguments are supported by highly accurate numerical
results for the effective permittivity function of such composites as a
function of the permittivity ratio of inclusions to matrix. The results show
that this function has a continuous spectral component with limits independent
of the area fraction of inclusions, and with the same limits for both square
and staggered square arrays. In other words, the composite absorbs significant
energy over a range of frequencies with limits controlled by the corner angle.
In this range energy flows towards each corner where it ends up being absorbed
in an infinitesimal neighborhood of the corner. For staggered arrays where the
squares are almost touching, the absorption spectrum is an extremely sensitive
probe of the inclusion separation distance and acts like a Vernier
scale. This is joint work with Johan Helsing (Lund)
and Ross McPhedran (Sydney).

2011, Sept. 16 (Fri.) 4:00, 5W254

Eun-Jae Park (Yonsei
University)

Title : Recent advances in locally conservative finite element methods

This talk deals with locally conservative methods and consists of two parts:
first part on adaptive mixed finite element methods and second on new
discontinuous Galerkin methods. First part is based
on joint work with Dongho Kim. We study adaptive
mixed finite element discretizations for nonlinear
elliptic problems. The mixed method conserves the mass locally and produces
accurate flux even for highly nonhomogeneous media with large jumps in the
physical properties. We derive reliable and efficient a posteriori error
estimators for the error control of our approximation to the nonlinear problem
under consideration. Several numerical simulation will
be presented. Second part is based on joint work with Youngmok
Jeon. A new class of hybrid discontinuous Galerkin methods is introduced and analyzed for
second-order elliptic equations. The main feature of the our method is that
their approximate solutions can be expressed in an element-by-element fashion
in terms of an approximate trace satisfying a global weak formulation, which
reduces globally coupled degrees of freedom dramatically. Several numerical
results will be presented to support the new theory.

2011, Sept. 2(Fri.) 4:00, 5W254

Hyenkyun Woo(Seoul National
University)

Title : A variational method for speckle reduction in
coherent imaging systems

In coherent imaging systems, such as synthetic aperture radar, the observed
images are contaminated by speckle noise. Due to the edge preserving feature of
the total variation, variational models with total
variation regularization have attracted much interest in removing speckle
noise. In this talk, we will introduce several variational
models for speckle reduction and very efficient method to solve the variational models.

2011, May 13 (Fri.) 4:00, 5W254

Min, Chohong(Ewha Woman's University)

Title : Simulation of Solid-fluid interactions

2011, May 13 (Fri.) 5:00, 5W254

Lee, Jihoon(SungKyunKwan
University)

Title : On the coupled system with the Navier-Stokes
equations

We consider the systems coupled with the Navier-Stokes
equations. Especially, we introduce the Navier-Stokes-Vlasov-Fokker-Planck equations which describes
the motion of the fluid and the particle of the spray model and also Navier-Stokes-Keller-Segel
equations which describes the motion of the swimming bacteria in the fluids.
Also we consider Ericksen-Leslie equations which describes the motion of the liquid
crystal.

2011, April 8
(Fri.) 4:00, 5W254

Hyundae Lee(Inha University)

Title : Near-cloaking using transformation optics

Abstract: Cloaking is the technique that make some objects invisible in the way
that cloaking device itself is imperceptible. The transformation optics
approach uses the change of variable by some transformation that blows a point,
so that it is singular. Near-cloaking is a kind of the regularization of this
singular cloaking. We review the results on near-cloaking and techniques used
in it. We propose briefly a near-cloaking technique based on multi-coating.

2011, April 1
(Fri.) 4:00, 5W254

Myungjoo Kang(Seoul National
University)

Title : Unsupervised Multiple Objects Segmentation by the Adaptive Global
Maximum Grouping

Abstract: We propose a new method to segment an image into multiple objects. A
multiple objects segmentation problem is unstable since the result considerably
depends on the number of objects xed a priori. So,
one of the most important tasks in solving the problem is to automatically get
the number. The method we proposed is not only able to find the reasonable
number of distinct regions which form the image, but also able to give us
information about the meaningful objects. It also performs well for noisy
images. Our method is made up of two procedures. First, we deal with the
histogram of the image. By applying the adaptive global maximum searching
process we have developed, we can automatically obtain the number of local
maxima of the histogram, which signifies the number of different regions in the
image. At the same time, we have the centroids of each interval with a local
maximum and these would help us to find the desired objects. In the second
place, we derive a simple calculation to segment the image composed of multiple
objects. Then, we split the image into sets of pixels with similar intensity
values according to the number and centroids obtained above.

2011, Mar. 25
(Fri.) 4:00, 5W254

Jinhae Park(Chungnam
National University)

Title : Analysis of Nematic Liquid Crystals with
Singularities of degree 1/2

Abstract: Although singularities of degree 1 or -1 appear in the energy
minimizers for harmonic maps or Oseen-Frank energy,
there are many situations where singulairties of
degree 1/2 or -1/2 have been observed. But there is no mathematical frame work
to prove such singularities. In a joint with P. Bauman and D. Phillips, we use
Landau-de Gennes Energy to prove that such
singularities do exist. In the proof, we employ a famous well-known theory
developed by Bethuel, Brezis,
and Helein. To the best knowledge of the authors,
this work is the first result in this direction.

2011, Mar. 11
(Fri.) 4:00, 5W254

Kim, Hyunseok(Sogang University)

Title : Mathematical analysis of the stationary motion of an incompressible
viscous fluid

Abstract

2011, Mar. 4
(Fri.) 4:00, 5W254

Yoon, Kihyun(Hankuk University of Foreign
Studies)

Title : Strong influence of a combination of a triple fiber on shear stress in
fiber-reinforced composites

Abstract: Stiff fiber-reinforced composites have very low strength in
longitudinal shear and this has been explained by high stress concentrations in
the narrow regions between neighboring parallel fibers. Until now, much
attention has been focused on the estimate for such high stress concentration,
especially associated with the distance between adjoining fibers. In this talk,
we consider a strong influence of a combination of a triple fiber, as well as
the distance between a pair of fibers, on the blow-up so that the stress
concentration can be significantly accelerated by adding a
small fiber in-between fibers.