# Kyoto University Applied Mathematics Seminar (KUAMS)

## Records of past seminars: year 2018

No. 58:   January 9, 2019 (Wed) 13:30-15:00

Dr. Jan Haskovec (King Abdullah University of Science and Technology, Jeddah)
"Discrete and continuum modeling of biological network formation"

Abstract: Motivated by recent papers describing rules for natural network formation in discrete settings, we propose an elliptic-parabolic system of partial differential equations. The model describes the pressure field due to Darcy’s type equation and the dynamics of the conductance network under pressure force effects with a diffusion rate representing randomness in the material structure. After a short overview of the principles of discrete network modeling, we show how to derive the corresponding macroscopic (continuum) description. The highly unusual structure of the resulting PDE system induces several interesting challenges for its mathematical analysis. We give a short overview of the tools and tricks that can be used to overcome them. In particular, we present results regarding the existence of weak solutions of the system, based on recent results on elliptic regularity theory. Moreover, we study the structure and stability properties of steady states that play a central role to understand the pattern capacity of the system. We present results of systematic numerical simulations of the system that provide further insights into the properties of the network-type solutions.

No. 59:   January 29, 2019 (Tue) 16:30-18:00

Prof. Shoji Ito (Osaka Electro-Communication University)
"Systematic performance evaluation for numerical algorithms of linear equations"

Abstract: This talk was given in Japanese.

No. 60:   May 21, 2019 (Tue) 16:30-18:00

Dr. Tsuyoshi Yoneda (The University of Tokyo)
"A remark on the zeroth law and instantaneous vortex stretching on the incompressible 3D Euler equations"

Abstract: This talk was given in Japanese with slides in English.

No. 61:   June 25, 2019 (Tue) 16:30-18:00

Dr. Eiko Kin (Osaka University)
"Braids and entropies from taffy pulling machines"

Abstract: Taffy pullers are devices for pulling candy. One can build braids from the motion of rods for taffy pullers. According to the article A mathematical history of taffy pullers" by Jean-Luc Thiffeault, all taffy pullers (except the first one) give rise to pseudo-Anosov braids. This means that the devices mix candies effectively. Braids are classified in three categories, periodic, reducible and pseudo-Anosov. The last category is the most important one for the study of dynamical systems. Each pseudo-Anosov braid determines its stretch fact and the logarithm of stretch factor is called the entropy. Following a study of Thiffeault, I discuss which pseudo-Anosov braids are realized by taffy pullers, and how to compute their entropies. I explain an interesting connection between braids coming from taffy pullers and hyperbolic links. Interestingly, the two most common taffy pullers give rise to the complements of the the minimally twisted 4-chain link and 5-chain link which are important examples for the study of cusped hyperbolic 3-manifolds with small volumes. If time permits, I will explain a construction of pseudo-Anosov braids.

Note: This talk will be given in Japanese.

No. 62:   July 30, 2019 (Tue) 15:00-18:00

15:00 - 16:30
Dr. Jordan Hauge (Kyoto University)
"A new transform approach to the complex Helmholtz equation"

Abstract: The complex Helmholtz operator is a ubiquitous operator that arises in multiple fields, ranging from thermal conductivity measurement to electrochemical impedance spectroscopy. Motivated by the absence of analytical tools used to solve the complex Helmholtz equation in non-separable domains, we present a new transform approach to solve the complex Helmholtz equation in convex polygonal domains. We use the approach to obtain new analytical solutions related to electrochemical impedance spectroscopy, and the 3\omega method. [Joint work with Prof. Darren Crowdy]

16:30 - 18:00
Dr. Hiroshi Takeuchi (Chubu University)
"Persistence analysis of sampled maps"

Abstract: This talk was given in Japanese.