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 áin áthe open set áin ,á where ááis the complete Bernstein function and á. When the exterior function áis local á-Holder continuous of order áon ááwith ááand , for a large class of Bernstein function , we show that the regular harmonic function áwith respect to , whose value is áon , converges a.e. through a certain parabola that depends on áand . 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 LamÚ 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-PoincarÚ 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 :á 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

Abstract

 


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,á

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 Schr÷dinger networks

 

Abstract: We study an inverse boundary value problem for the magnetic Schr÷dinger 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 Schr÷dinger 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 Schr÷dinger equation will be considered, which implies that our problem is regarded as a discrete counterpart of the inverse boundary value problem

for the magnetic Schr÷dinger 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 Schr÷dinger 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 Schr÷dinger 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
í░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.


Seminars in the past