# Kyoto University Applied Mathematics Seminar (KUAMS)

## Records of past seminars: year 2019

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.

No. 63:   August 21, 2019 (Wed) 14:30-16:00

Prof. Je-Chiang Tsai (National Tsing Hua University, Taiwan)
"Pulsating Waves in a Dissipative Medium with Delta Sources on a Periodic Lattice"

Abstract: We study a dissipative heat equation with Delta sources of non-linear strength located on a periodic lattice. The model arises from intracellular waves in continuum excitable media with discrete release sites. The existence, uniqueness, and global and exponential stability of pulsating waves are established. Also a new technique is introduced to find the fine structure of the tails of pulsating waves.

No. 64:   October 23, 2019 (Wed) 16:30-18:00

Dr. Keita Iida (Osaka University)
"Analytical solution of a gene expression model with generalized hypergeometric functions and its application"

Abstract: This talk was given in Japanese.

No. 65:   October 29, 2019 (Tue) 15:00-17:45

Prof. John C. Butcher (The University of Auckland)
"Trees, B-series and General Linear Methods"

Abstract: General linear methods are generalizations of both Runge-Kutta and linear multistep methods. This talk will focus on their important properties, especially the analysis of order of accuracy, expressed in terms of B-series. The talk includes an introduction to (rooted) trees and free trees on which B-series are built.

No. 66:   November 22, 2019 (Fri) 14:00-15:30

Dr. Tomoyuki Miyaji (Kyoto University)
"A billiard problem arising from nonlinear and nonequilibrium systems"

Abstract: This talk was given in Japanese.
Note：This seminar was co-hosted by the Kyoto Dynamical Systems seminar.

No. 67:   December 17, 2019 (Tue) 16:30-18:00

Dr. Kazuaki Tanaka (Waseda University)
"Verified numerical computation for partial differential equations and application to sign-change structure analysis"

Abstract: This talk will be given in Japanese with slides in English.

No. 68:   December 27, 2019 (Fri) 14:00-15:30

Dr. Jan Haskovec (King Abdullah University of Science and Technology, Jeddah)
"Asymptotics of alignment and consensus models with delays"

Abstract: We study the impact of communication or reaction delays on the long-time behavior of alignment/consensus models of Cucker-Smale type. For a model where agents interact with each other through normalized communication weights, we provide sufficient conditions for asymptotic flocking, i.e., convergence to a common velocity vector. The proof is based on a construction of a suitable Lyapunov functional. For a model without normalization, we present new stability estimates for the particle flow, relating suitable delayed and non-delayed quantities. We also briefly explain how multiplicative noise affects the long-time dynamics and present results of systematic numerical simulations.