Kyoto University Applied Mathematics Seminar (KUAMS)

 

Records of past seminars: year 2015

 

 

No.14:   2015. 1. 6. (Tue) 16:30-18:00

Dr. Karel Svadlenka, Associate Professor (Kyoto Univ.)
"Evolutionary free boundary problems: their analysis and numerical solution"

Abstract: A simple model for motion of bubbles on obstacles is given by a free boundary problem of parabolic or hyperbolic type. In this talk, a method of analysis of such equations based on time semi-discretization will be presented, which allows direct application to numerical approximation. Moreover, this method seems promising in studying hyperbolic free boundary problems, a field with almost no established theory. An example of such an application will be explained. Extension to the more general vector-valued case will also be mentioned.

 

No.15:   2015. 2. 17. (Tue) 11:00-12:00

Dr. Sun-Chul Kim, Professor (Chung-Ang Univ., Korea)
"Vortex sheet evolution on the spheroid"

Abstract: Vortex sheet is an interface of discontinuity between two different velocity fluid flow. The dynamics of vortex sheet has been studied a lot for the plane and also for the sphere. In this talk, we study the motion of vortex sheet on the speroid numerically. More precisely, we asymptotically calculate the linear stability and compute the time evolution of roll ups.The effect of eccentricity is also considered.

 

No.16:   2015. 2. 17. (Tue) 13:30-14:30

Dr. Shin-ichi Takehiro, Associate Professor (RIMS, Kyoto Univ.)
"On axial 2-dimensional vortices exited by thermal convection in a rapidly rotating thin spherical shell"

Abstract: Dynamics of axial 2-dimensional vortices in a rapidly rotating thin spherical shell is discussed. It is presented that the vortices excieted by thermal convection in a rotating spherical shell are affected by the inner and outer spherical boundaries and propagte as topographic Rossby waves, which transport momentum and induce a longitudinally banded strcture of mean zonal flows.

 

No.17:   2015. 2. 17. (Tue) 14:30-15:30

Dr.Sung-Ik Sohn, Professor (Gangneung-Wonju National Univ., Korea)
"Singularity and Nonuniqueness of Hydrodynamic Instabilities"

Abstract: In this talk, the singularity and nonuniqueness of the solutions of hydrodynamic instabilities are presented. We discuss the nonuniqueness of the steady-state solution of the bubble evolution in the Rayleigh-Taylor and Saffman-Taylor instabilities,and the selection of the physically significant solution. The Kelvin-Helmholtz instability is known to evolve a finite-time singularity, and the nonuniqueness of weak solutions has been recently established. We study whether the solutions of different regularization models converge to distinct or the same weak solution, and what the weak solutions are.

These three seminars are held as a part of A3 Workshop on Vortex Dynamics supported by A3 Foresight Program (Leaders: Prof. Y. Nishiura, Tohoku Univ., Japan and Prof. H. Kang, Inha Univ., Korea)

 

No.18:   2015. 4. 21. (Tue) 16:30-18:00

Dr. Kaz Makino, Associate Professor (Kyoto Univ.)
"The complexity issues on stochastic games"

Abstract: Stochastic games were introduced in 1953 by Shapley for the discounted case, and extended to the undiscounted case in 1957 by Gillette. Each such game is a dynamic game with probabilistic transitions played by two players on a finite set of states. The game is played in the infinite sequence of rounds. In the round, the game is in some state. The players choose actions. Then they receive payoffs and the game moves to a new random state, where the payoffs and the transition probability depend on the previous state and the actions chosen by the players. The procedure is repeated at the new state. Stochastic games generalize parity games, cyclic games, simple stochastic games, and BWR games, which all belong to NP and coNP, but are not known to be solved in polynomial time. In this talk, I briefly survey the algorithmic issues on these games, as well as the properties on the optimal strategies for them. I also discuss recent works obtained with Endre Boros, Khaled Elbassioni, and Vladimir Gurvich.

 

No.19:   2015. 5. 19. (Tue) 16:30-18:00

Dr. Masakazu Matsumoto, Associate Professor (Okayama Univ.)
"Water as a network"

Abstract: Water is one of the simplest molecule, but its physical properties in the condensed phases are quite complex. For example, there are more than 16 ice polymorphs and hypothetically two liquid phases. Water is the only liquid that expands when cooled. These complexities originate in hydrogen bond network structures. We regard these phases as graphs and investigate the relationship between topology and properties.

 

No.20:   2015. 6. 2. (Tue) 16:30-18:00

Dr. Ippei Ohbayashi, Assistant Professor (Tohoku Univ.)
"Inverse problem on persistence diagrams"

Abstract: This talk will be given in Japanese.

 

No.21:   2015. 7. 14. (Tue) 16:30-18:00

Dr. Kiori Obuse, Assistant Professor (Okayama Univ.)
"Behaviour of a low-Reynolds-number treadmilling microswimmer near a semi-infinite wall"

Abstract: We investigate the behavior of a treadmilling microswimmer in a two-dimensional unbounded domain with a semi-infinite no-slip wall. The wall can also be regarded as a probe or pipette inserted into the flow. We solve the governing evolution equations in an analytical form by utilizing complex analysis, and numerically calculate trajectories of the swimmer for several different initial positions and orientations. We then compute the probability that the treadmilling swimmers can escape the vicinity of the wall. We find that many trajectories in a wedge around the wall are likely to escape. This suggests that inserting a probe or pipette in a suspension of organism may push away treadmilling swimmers.

 

No.22:   2015. 7. 28. (Tue) 16:30-18:00

Dr. Christohpher Green (Queensland Univ. of Technology)
"Using the Schottky-Klein prime function to solve free boundary problems in multiply connected domains"

Abstract: The Schottky-Klein prime function is a special transcendental function which plays a central role in problems involving multiply connected domains. This function can be used to great advantage in many varied applications. In this talk, we will explore two different free boundary problems (arising in fluid mechanics) defined over two distinct multiply connected geometries. For both problems, we will show that it has been expedient to employ the Schottky-Klein prime function and its associated function theory in order to construct analytical solutions.

 

No.23:   2015. 10. 27. (Tue) 16:30-18:00

Dr. Takuya Tsuchiya, Professor (Ehime Univ.)
"Error estimations of Lagrange interpolations on triangles and tetrahedrons"

Abstract: This talk will be given in Japanese.

 

No.24:   2015. 11. 10. (Tue) 16:30-18:00

Dr. Kei-ichi Ishioka, Associate Professor (Kyoto Univ.)
"On the upper bound of the growth of disturbances from an unstable parallel shear flow on a rotating sphere"

Abstract: This talk will be given in Japanese.

 

No.25:   2015. 12. 1. (Tue) 16:30-18:00

Dr. Masato Kimura, Professor (Kanazawa Univ.)
"Unidirectional gradient flow and application to crack propagation model"

Abstract: We consider a nonlinear diffusion equation with irreversible property and construct a unique strong solution by using implicit time discretization. A new regularity estimate for the classical obstacle problem is established and is used in the construction of the strong solution. As an application, we consider a quasi-static fracture model of brittle material using the idea of the phase field model. The Francfort-Marigo energy which is based on the classical Griffith theory is introduced, where the sharp crack profile is approximated by a smooth damage function using the idea of the Ambrosio-Tortorelli regularization. The crack propagation model is derived as a gradient flow of the energy of the damage variable with an irreversible constraint. Some numerical examples in various settings computed by finite element method are also presented in the talk. The contents is based on the joint works with Goro Akagi (Kobe Univ.) and with Takeshi Takaishi (Hiroshima Kokusai Gakuin Univ.).

This talk will be given in Japanese.

 

No.26:   2015. 12. 15. (Tue) 16:30-18:00

Dr. Yoji Kawamura, Scientist (JAMSTEC)
"Phase description of oscillatory convection with a spatially translational mode"

Abstract: This talk will be given in Japanese.

Reference: Y. Kawamura and H. Nakao, Physica D 295-296, 11-29 (2015).