Workshop on Solid and Liquid Crystals

Schedule

Tuesday, April 5 (Room 1409)

09:00 – 09:50   Yasumasa Nishiura (Tohoku University)

                            Frustrated phases of diblock copolymers under three-dimensional confinement

10:00 – 10:50   Jinhae Park

                         Structures of Nematic Liquid Crystals in the Landau-de Gennes Theory 

11:00 – 11:50   Jongmin Han (Kyung Hee University)

 A self-dual system for the gravitational Ginzburg-Landau model 

12:00 – 14:00   Lunch

14:00 – 14:50   Zhouping Xin (The Chinese University of Hong Kong)

                            On Uniqueness of Entropy Weak Solutions to Multi-Dimemsional Balance Laws

15:00 – 15:50   Tomonari Inamura (Tokyo Institute of Technology)

                            Experimental study on martensite microstructure in shape memory alloys

17:00 – 18:00   Special Lecture: Annual Lecture Series by John Ball (University of Oxford)

                             Interfaces in Solid and Liquid Crystals (Rm. 1501, Natural Science B/D E6-1)

Wednesday, April 6 (Room 1409)

09:00 – 09:50   Xian Chen (The Hong Kong University of Science and Technology)

      Conditions of compatibility for martensitic transformation and stressed- free microstructure 

10:00 – 10:50   Youngae Lee (National Taiwan University)

                           Degree counting for Toda system of rank two: one bubbling

11:00 – 12:00   Special Lecture: Annual Lecture Series by John Ball (University of Oxford)

                            Interfaces in Solid and Liquid Crystals (Rm. 1501, Natural Science B/D E6-1)

12:00 – 14:00   Lunch

14:00 – 14:50   Namkwon Kim (Chosun University)
                 Mixed type radial solutions in gauge theories.

15:00 – 16:00   Special Lecture: Annual Lecture Series by John Ball (University of Oxford)

                            Interfaces in Solid and Liquid Crystals (Rm. 1501, Natural Science B/D E6-1)

18:00 -              Bangquet

Title & Abstract 

Xian Chen

The Hong Kong University of Science and Techology

Conditions of compatibility for martensitic transformation and

stressed-free microstructure

Martensitic materials have great potential for emerging applications such as medical de-vices, small scale actuators, sensors and novel energy conversion devices. These applica- tions commonly utilize the feature that the material undergoes first-order solid-solid re- versible phase transformation. Phenomenally, the materials show shape memory effect, superelasticity and giant magneto, electro- and elasto-caloric effects.   In general, there is an elastic transition layer between the two phases due to the lattice mismatch at the phase boundary, which causes the thermal hysteresis and degradation of reversibility of the phase transformation. It strongly confines the application and reduces the effective life-time of the materials.

Based on geometrically nonlinear theory and crystallography of martensite, it has been proven that the satisfaction of the conditions of compatibility by special lattice pa- rameters can completely eliminate the elastic transition layer. As a result, there is no elas- tic energy paid at the austenite/martensite interface during phase transformation. There- fore the reversibility can be enhanced while the hysteresis can be minimized in the mate- rial upon many transformation cycles. In this talk, I will present both theoretical and ex- periment work related to the formal formulation of the conditions of compatibility, their implications to the formation of stressed-free martensite microstructure and the quanti- tative justification of these conditions in real materials by advanced structural characterization techniques.

Kyung Hee University

A self-dual system for the gravitational Ginzburg-Landau model

In this talk, we consider the Ginzburg-Landau model in the space-time. The Ginzburg-Landau equations coupled with the Einstein equations can be reduced to a self-dual system under suitable assumptions and this system is also transformed into a single elliptic equation. We briefly review the model and provide some recent results on the radial solutions of the reduced elliptic equation.

Tokyo Institute of Technology

Experimental study on martensite microstructure in shape memory alloys

Martensitic transformation is a shear-dominant, lattice distortive and diffusionless solid-solid transformation occurring by nucleation and growth. Shape memory alloy is a typical material that has the transformation. At the transformation temperature, a high temperature (high symmetry) phase discontinuously transforms to a low temperature (low symmetry) phase through a cooperative motion of atoms.  The loss of some symmetry elements in the high temperature phase results in the formation of crystallographically equivalent domains of the low temperature phase.  The domains of a low symmetry phase are successfully interfaced with each other to reduce the overall strain; a typical microstructure so called martensite microstructure or self-accommodation microstructure appears. Based on the minimization of free energy, Ball and James have constructed the theory that well explains some geometrical and crystallographic aspects of the microstructure. In this study, the microstructure and its formation process are analyzed in some shape memory alloys by various microscopy techniques including in-situ observation with emphasis on the existence of incompatible interfaces and the nucleation of the domain. The results are contrasted with the theoretical analysis to extract factors to be investigated for the deeper understanding of the microstructure and the mechanism of the transformation.

Namkwon Kim

Chosun University

Mixed type radial solutions in gauge theories.

We present some of our recent results on mixed type solutions. Mixed type solutions are important to analysing phase space of nontopological solutions. We state the sufficient condition for existence and discuss the bubbling behavior of them.

Youngae Lee

National Taiwan University

Degree counting for Toda system of rank two: one bubbling

In this talk, we study the degree counting formula of the rank two Toda system with simple singular sources. The key step is to derive the degree formula of the shadow system, which arises from the bubbling solutions as one of parameters crosses  $4pi$. In order to compute the topological degree of the shadow system, we need to find some suitable deformation. During this deformation, we shall deal with new difficulty arising from the new phenomena: blow up does not necessarily imply concentration of mass. This phenomena occurs due to the collapsing of singularities. 
This talk is based on the joint works with Prof. Chang-Shou Lin, Prof. Juncheng Wei, Prof. Lei Zhang, and Dr. Wen Yang.

 Yasumasa Nishiura

Tohoku University

Frustrated phases of diblock copolymers under three-dimensional confinement

We study a set of coupled Cahn-Hilliard equations as a means to find morphologies of diblock copolymers in three-dimensional spherical confinement.  This approach allows to find a variety of energy minimizers including rings, tennis balls, Janus balls and multipods among several others. Phase diagrams of confined morphologies are presented. We modify the size of the interface between microphases to control the number of holes in multipod morphologies.
Comparison to experimental observation by transmission electron microtomography of multipods in polystyrene-polyisoprene diblock copolymers is also presented.  

Jinhae Park

Chungnam National University

Structures of Nematic Liquid Crystals in the Landau-de Gennes Theory