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
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.
14(Fri.) 4:00, 5W254
Wanho Lee (Inha Univ.)
Title : Applications of the immersed boundary method: valveless pumping and heart modeling
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.
25(Fri.) 4:00, 5W254
Q-Han Park (Korea University)
Title : New Wave of Nano Metal
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
2012, May 4(Fri.) 4:00, 5W254
Chang Kwon HWANGBO (Inha Univ.)
Title : Introduction to Plasmonics
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.
13(Fri.) 4:00, 5W254
Giulio Ciraolo (Palermo, Italy)
Title : Symmetry of minimizers with a level surface parallel to the boundary
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
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
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
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.