2017. Oct. 18. (Wed.) 17:00-18:00, 5E102
Giacomo
Albi (University of Verona)
Title : Boltzmann-type
control for consensus dynamics
Abstract : In
this talk I will present some recent developments on a class of numerical
methods for the optimal control of multi-agent systems. Due to the
high-dimensionality and the nonlinearities of this type of problems, standard
techniques usually fail or they are completely inefficient. In order to reduce
the complexity of the problem, I will propose a general framework based on the
approximation of the constrained microscopic dynamics through the control of a
Boltzmann-type equation, showing that under suitable scaling this is equivalent
to the mean-field description of the original problem. A class of fast
algorithms, based on the simulation of the binary interactions of the Boltzmann
dynamics, is derived, and its consistency with respect to the mean-field
control problem is shown. Several numerical examples will show the
effectiveness of the proposed strategies in the context of opinion formation
and flocking dynamics.
2017. Aug. 17. (Thur.) 16:00-17:30, 5E102
Jinyeong Park (Universidad
de Granada)
Title : Uniform
stability and mean-field limit for the augmented Kuramoto model
Abstract : We
present two uniform estimates on stability and mean-field limit for the
"augmented Kuramoto model(AKM)" arising from the second-order lifting
of the first-order Kuramoto model(KM) for synchronization. In particular, we
address three issues such as synchronization estimate, uniform stability and mean-field
limit which are valid uniformly in time for the AKM. The derived mean-field
equation for the AKM corresponds to the dissipative Vlasov-McKean type
equation. The kinetic Kuramoto equation for distributed natural frequencies is
not compatible with the frequency variance functional approach for the complete
synchronization. In contrast, the kinetic equation for the AKM has a similar
structural similarity with the kinetic Cucker-Smale equation which admits the
Lyapunov functional approach for the variance. We present sufficient frameworks
leading to the uniform stability and mean-field limit for the AKM.
2017. Aug. 2 (Wed.) 16:00-17:30, 5E102
Jaehoon Kang (Seoul
National Univ.)
Title : Tangential
limits for harmonic functions with respect to subordinate Brownian motion:
stable and beyond
Abstract : In
this talk, we discuss boundary limits for regular harmonic functions with
respect to in
the open set
in
,
where
is the complete Bernstein function and
. When the exterior function
is local
-Holder continuous of order
on
with
and
, for a large class of Bernstein
function
, we show that the regular
harmonic function
with respect to
, whose
value is
on
, converges a.e. through a certain
parabola that depends on
and
. Our result includes the case
. Our
proofs use both the probabilistic and analytic methods. In particular, the
Poisson kernel estimates are essential to our approach.
2017. July. 19 (Wed.) 16:00-17:30, 5E102
Xiongtao Zhang (Seoul
National Univ.)
Title : Uniform-in-time
transition from discrete dynamics to continuous dynamics in the Cucker-Smale flocking
Abstract : We
study a uniform-in-time convergence from the discrete-time(in short, discrete)
Cucker-Smale (C-S) model to the continuous-time C-S model, which is valid for
the whole time-interval, as time-step tends to zero. Classical theory yields
the convergence results which are valid only in any finite-time interval. Our
uniform convergence estimate relies on two quantitive estimates
"asymptotic flocking estimate" and "uniform -stability estimate with respect
to initial data". In previous literature, most studies on the C-S flocking
have been devoted to the continuous-time model with general communication
weights, whereas flocking estimates have been done for the discrete-time model
with special network topologies such as the complete network with algebraically
decaying communication weights and rooted leaderships. For the discrete C-S
model with a regular and algebraically decaying communication weight,
asymptotic flocking estimate has been extensively studied in previous
literature. In contrast, for a general decaying communication weight,
corresponding flocking dynamics has not been addressed in literature due to the
difficulty of extending the Lyapunov functional approach to the discrete model.
In this paper, we present asymptotic flocking estimate for the discrete model
using the Lyapunov functional approach. Moreover, we present a uniform
-stability estimate of the
solution for the discrete C-S model with respect to initial data. We combine
asymptotic flocking estimate and uniform stability to derive a uniform-in-time
convergence from the discrete C-S model to the continuous C-S model, as
time-step tends to zero.
2017. June. 19 (Mon.) 16:00-17:30, 5E102
Bongsuk Kwon (UNIST)
Title : Plasma sheath
via the Euler-Poisson system
Abstract : The
purpose of this work is to mathematically justify the formation of plasma
sheaths, and to obtain qualitative information of the sheath boundary layers.
To this end, we investigate the existence, time-asymptotic behavior, and
quasi-neutral limit of the boundary layer solutions for the Euler-Poisson
equations in the three dimensional annular domain. If time permits, some key
features of the proof and related problems will be discussed. This is a joint
work with C.-Y. Jung (UNIST) and M. Suzuki (Nagoya Inst. Tech.).
2017. June. 19 (Mon.) 15:00-16:00, 5E102
Seick Kim (Yonsei Univ.)
Title : Weak
type-(1,1) estimates for linear elliptic operators with variable coefficients.
2015. Oct. 20 (Tue.) 17:00-17:30, 5E102
Kazunori Ando
(Inha Univ.)
Title : Anomalous localized
resonance (ALR) for the Lamé system in
two dimensions and cloaking by ALR
2015. Sep. 18 (Fri.) 17:00-17:30, 5E102
Yonggwan Ji
(Inha Univ.)
Title : Spectral property of the Neumann-Poincaré
operator for the Lame system on smooth planar domains
2015. Sep. 18 (Fri.) 16:00-17:00, 5E102
Hyundae Lee
(Inha Univ.)
Title : Effective properties of elastic composites and
neutral inclusions
2015. June 5 (Fri.) 16:00-17:00, 5E102
Tingting Feng (Inha Univ.)
Title
: Solving integral equations on piecewise
smooth boundaries using the RCIP method
2015. May 14
(Thu.) 17:00-18:00, 5E102
Yun-Che Wang (Department of Civil Engineering, National Cheng Kung University, Tainan,
Taiwan 70101)
Title
: Viscoelastic properties of solid-like
and liquid-like materials measured via a pendulum-type viscoelastic
spectrometer
Abstract
: Viscoelastic properties of solid-like
materials, such as creep compliance, relaxation modulus and dynamic modulus,
are of paramount importance in characterizing the materials, understanding
their underlying deformation mechanisms and predicting their mechanical
behavior with existing mathematical models. Similarly, experimentally
determination of liquid viscosity cannot be overemphasized in the development
of modern science and technology. In this work, a pendulum-type viscoelastic
spectrometer (PVS) is adopted to experimentally determine the viscoelastic
properties at elevated temperatures, up to 100˚C, in a wide frequency
range (1 mHz ~ 100 kHz). The driving force of PVS is generated by magnetic
interactions through a permanent magnet placed inside the Helmholtz coil.
Deformation of the cantilever specimen is obtained with a laser-based
displacement measurement system, consisting of a solid-state laser and
silicon-based position sensor. As for viscosity of liquid, a standard cantilever
solid core, made of PMMA or polymeric foam, is placed in a small container
filled with the liquid under test. Under sinusoidal loading on the solid core
through magnetic interactions, its resonant responses are affected by damping
from the solid core and liquid. Through mathematical treatments on immersed
oscillators, the viscosity of the liquid can be determined at the driving
frequency. Experimental
data of several materials tested by the PVS will be presented, along with
discussions on their implications.
2015. May 8
(Fri.) 17:00-18:00, 5E102
Jijun Liu (Southeast University, Nanjing, China)
Title : Simultaneous recovery of the temperature and species concentration from integral equation model
Abstract
: Absorbtion spectroscopy is a advanced tool for flow diagnostics in
measuring multiple parameters of species. Such kinds of problems can be modeled
by some integral equations with known kernel, aiming to determine the
integrands from their integration values along all possible paths of injected
lasers. We consider the parameters detection problems in combustion
process, with the purpose of recovering the gas temperature and the
concentration of burned gas simultaneously using injected lasers along two
directions with multiple frequencies. For this nonlinear ill-posed
model, we consider its optimization version with some penalty
terms. An alternative iteration scheme (AIS) with convergence analysis is
proposed to solve this problem . Numerical implementations are
presented to show the validity of the proposed scheme.
2015.
Apr. 28(Tue.) 17:00-18:00, 5E102
Shuichi JIMBO (Hokkaido University)
Title : Spectra of domains with a thin tubular hole
Abstract
:
In this talk I deal with a singularly perturbed domains which is given by removing a tubular
neighborhood of a low dimensional set and consider the asymptotic behavior
of the eigenvalue of Laplacian. I present the perturbation formulas of
eigenvalues, which depend on the geometric situations and the important parameters.
2014.
Dec. 2(Tue.) 16:00-17:00, 5E102
Semyon Leontyev (North-Eastern Federal University,
Russia)
Title : Mathematical modeling of the stress-strain state of diamond
2014.
Nov. 28(Fri.) 16:00-17:00, 5E102
Hyeonbae
Kang (Inha Univ.)
Title: Spectral
theory of Neumann Poincare operator and applications
2014.
Nov. 14(Fri.) 17:00-18:00, 5E102
Kazunori
Ando (Inha Univ.)
Title: Spectrum of the Neumann-Poincare domain on polygonal domains
2014.
Nov. 14(Fri.) 16:00-17:00, 5E102
Seonguk
You (Inha Univ.)
Title: Truncated Moment Problems with Cubic Column Relations
2014.
Oct. 17(Fri.) 16:00-17:00, 5W254
Mikyoung
Lim (KAIST)
Title: Bipolar coordinates and applications to gradient estimates
2014.
Oct. 10(Fri.) 16:00-17:00, 5W254
Kyungkeun
Kang (Yonsei Univ.)
Title: Boundary value problems of the Navier-Stokes equations
2014.
Sep. 19(Fri.) 16:00-17:00, 5W253
Kazunori
Ando (Inha Univ.)
Title: Discrete
inverse problem for magnetic Schrodinger networks
2014.
Mar. 28(Fri.) 16:00-17:00, 5W253
Hyunseok
Kim(Sogang Univ.)
Title: On the
stability of plane Couette flows
2014.
Mar. 7(Fri.) 16:00-17:00, 5W253
Seick
Kim(Yonsei Univ.)
Title: On De
Giorgi-Moser type estimates for weakly coupled elliptic systems with measurable
coefficients and its applications.
Abstract: I
will review De Giorgi and Moser estimates for elliptic equations with bounded
measurable coefficients and discuss regularity issue for weakly coupled
elliptic systems arising photo-acousitic imaging in inhomogeneous media.
2014, Feb. 19(Wed.)
15:00-16:00, 16:30-17:30,
20(Thu.) 16:00-17:00
Shigeru Sakaguchi (Tohoku Univ.)
Title: Diffusion and
geometry of domain
Abstract: We deal
with two topics concerning the interaction between diffusion and geometry of
domain. One is to classify the domains in Euclidean 3-space having a stationary
isothermic surface for the solutions of the Cauchy problem of the heat
equation. The point here is to use the theories of properly embedded minimal
surfaces and properly embedded constant mean curvature surfaces in Euclidean
3-space. The other gives the interaction between the short time behavior of the
fast diffusion and the principal curvatures of the boundary of the domain in
Euclidean N-space, where we consider the solutions of the Cauchy problem or the
initial-boundary value problem for some nonlinear fast diffusion equations.
2014, Feb. 6(Thu.) 16:00, 5W253
Jishan Fan (Nanjing Forest Univ.)
Title: Weak solutions for
Ginzburg-Landau equations in superconductivity.
Abstract:
In this talk, we will prove global-in-time existence and uniqueness of weak
solutions for 3D Ginzburg-Landau equations in superconductivity with large
initial data in critical space.
2014, Jan. 28(Tue.) 16:00, 5W253
Kazunori Ando (University of
Tsukuba)
Title: Boundary determination for magnetic Schrödinger
networks
Abstract: We study an inverse boundary value problem
for the magnetic Schrödinger network consisting of a finite graph with
boundary, 1-form on the directed edge set, which is regarded as a discrete
version of magnetic potential, and an electric potential, which is a
real-valued function on the vertex set. Governing equation on the network is
the discrete magnetic Schrödinger equation equipped with the 1-form and the
electric potential. Reconstruction procedure of the 1-form and the electric
potential on the boundary from the Dirichlet-to-Neumann map will be shown. Our
approach is based on the inverse problem for resistor network by Curtis and
Morrow [1]. Moreover, a continuous limit of the discrete magnetic Schrödinger
equation will be considered, which implies that our problem is regarded as a
discrete counterpart of the inverse boundary value problem
for the magnetic Schrödinger
equation on a bounded domain of the Euclidean spaces.
References
[1] Edward B. Curtis and James A. Morrow. The
Dirichlet to Neumann map for a resistor network. SIAM J. Appl.
Math., 51(4):1011-1029, 1991.
2014, Jan. 28(Tue.) 17:00, 5W253
Hiroshi Isozaki (University of
Tsukuba)
Title : Spectral properties for Schrödinger operators on perturbed lattices
Abstract : Spectral properties of Hamiltonians on perturbed lattices are principal subject in mathematical physics, and there are plenty of mathematically open questions. Aiming at the inverse scattering for Schrödinger operators on perturbed lattices, we talk about, as the forward problem, the results on resolvent estimates, spectral representations, spaces for the Helmholtz equation and derive S-matrices. Our theory covers many physical examples such as, square, triangular, hexagonal, Kagome, diamond, subdivision lattices, as well as ladder and graphen. This is a joint work with K. Ando and H. Morioka
2014, Jan. 17(Fri.) 16:00, 5W253
Jaemin Shin (Inha
University)
Title: Pad?/span>
approximant and its applications to shape magnetic forming
Abstract: The
Pad?/span> approximant is a well-known method to approximate a function by a
rational function. In this presentation, we will go over the Pad?/span>
approximant and discuss how this method can possibly be used in inverse source
problems, especially focusing on the magnetic shaping problems.
2013, Nov. 29(Fri.) 16:00, 5W253
Jong Chul Ye (Dept. of Bio/Brain Engineering,
KAIST)
Title:?Joint sparse recovery problem: theory
and biomedical imaging applications
Abstract: In a multiple measurement vector
problem (MMV), where multiple signals share a common sparse support and are
sampled by a common sensing matrix, we can expect that the joint sparsity
enables a further reduction in the number of measurements required. While a
diversity gain from the joint sparsity has been demonstrated earlier in the
case of group LASSO, only recently it was shown by our group that similar
diversity gain can be achieved by greedy algorithms if they are combined with
subspace method. Our theory showed that these new class of hybrid algorithms
are nearly optimal with sufficiently accurate subspace estimate. In this talk,
I will describe the mathematical theory for joint sparse recovery problem.
Then, I will explain how such joint sparse recovery principle can be used?not
only to improve the resolution limit but also to overcome the nonlinearity
originated from inverse scattering problem.
2013, Sept. 27(Fri.) 16:00, 5W253
Andreas Kirsch(Karlsruher Institut fuer
Technologie (KIT) Fakultaet fuer Mathematik )
Title : The Factorization Method for Inverse Scattering
Problems.
2013, July 15(Mon.) 11:00, 5W254
Kiwoon Kwon (Dongguk University)
Title : Diffuse optical tomography and Born expansion
Abstract:
Diffuse optical tomography(DOT) is to find the
absorption and (reduced) scattering coefficient of tissues from a few
photon density measurements illuminated from a few light sources. DOT is
described as three ways: an inverse problem for some elliptic
equation called diffusion approximation in the frequency domain, coefficient
minimization for the diffusion approximation, and inverse Born
approximation. The error analysis for the forward and inverse Born
approximation will be given. Various numerical methods will also be
explained.
2013, June 28(Fri.) 4:00, 5W254
Greg Markowski (Monash University, Australia)
Title : The exit time of planar Brownian motion as a
measure of the size of domains.
Abstract: The time which
Brownian motion takes to exit a region gives us information on the size and
shape of the domain. This in turn can give information on the behavior of
analytic and harmonic functions on the domain. This approach has been studied
in the past by Burkholder, amongst others. I will describe the work done by
earlier researchers, and sketch some recent work that I have been doing in
connection with these methods.
2013, April 26(Fri.) 4:00, 5W254
Junichi Nakagawa (Nippon Steel Company)
Title : Creating
an Interdisciplinary Platform for Taking Aim at Mathematical Innovation
2013, April 23(Tue) 4:00, 5E102
Yasumasa Nishiura
(Tohoku Univ.)
Title : Aiming for Connective Knowledge -on the
activities of Japan Science and Technology Agency Mathematical Program
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 ¡°three-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.