# Kyoto University Applied Mathematics Seminar (KUAMS)

## Records of past seminars: year 2018

No. 48: January 9, 2018 (Tue) 16:30-18:00

Prof. Shigetoshi Yazaki (Meiji University)

"On a curve tracking method"

**Abstract: **This talk was given in Japanese.

No. 49: February 22, 2018 (Thu) 10:30-12:00

Dr. Elena Luca (University of California San Diego)

"Complex variable techniques for Stokes flows: new transform methods and applications"

**Abstract: **Motivated by modelling challenges arising in microfluidics and low-Reynolds-number swimming, we present a new transform approach for solving biharmonic boundary value problems in two-dimensional polygonal and circular domains and show its implementation in various Stokes flow problems. The method is an extension of earlier work by Crowdy & Fokas [Proc. Roy. Soc. A, 460, (2004)] and provides a unified general approach to finding quasi-analytical solutions to a
wide range of problems in low-Reynolds-number hydrodynamics and plane elasticity. The new approach leads to fast and accurate schemes for evaluation of the solutions. [Joint work with Darren Crowdy (Imperial).]

No. 50: March 13, 2018 (Tue) 10:30-12:00

Dr. Patrick Farrell (Mathematical Institute and Oriel College, University of Oxford)

"Computing disconnected solution branches of nonlinear partial differential equations"

**Abstract: **Computing the solutions of a nonlinear equation as a parameter is varied is a
central task in applied mathematics and engineering. In this talk I will present
a new algorithm, deflated continuation, for this task.

Deflated continuation has two main advantages over previous approaches. First,
it is capable of computing disconnected bifurcation diagrams; previous
algorithms only aimed to compute that part of the bifurcation diagram
continuously connected to the initial data. Second, its implementation is
extremely simple: it only requires a minor modification to any existing
Newton-based solver, and does not require solving any new auxiliary problems.
As a consequence, it can scale to very large discretisations if a good
preconditioner is available.

We will demonstrate the utility of the new algorithm by using it to discover
previously unknown solutions to several problems of physical interest.

No. 51: April 17, 2018 (Tue) 16:00-17:30

Dr. Koya Sakakibara (Kyoto University)

"Numerical analysis of point vortex dynamics by the method of fundamental solutions"

**Abstract: **This seminar was given in Japanese.
**Note**:
This seminar is a joint seminar with iTHEMS ・SUURI COOL lab.

Prior to the applied math seminar, the following iTHEMS/Data assimilation seminar presentation will take place:

＊ Speaker: Dr. Kohei Takatama (RIKEN iTHES/iTHEMS, RIKEN AICS)

＊ Title: "Including an ocean mixing model in atmospheric data assimilation: a
case of Typhoon Soudelor 2015"

＊ Time: 15:00 - 15:30

＊ Venue: Maskawa Hall, 1F, Maskawa Building for Education and Research, Kyoto University

Note that the **time and venue of this seminar are different** from the usual ones. The place is the same as for the above iTHEMS/Data assimilation seminar: Maskawa Hall, 1F, Maskawa Building for Education and Research, Kyoto University (building n. 13 in the campus map).

No. 52: May 29, 2018 (Tue) 16:30-18:00

Dr. Jun-nosuke Teramae (Kyoto University)

"Circuit structure and neural dynamics of local cortical networks"

**Abstract: **This seminar was given in Japanese with slides in English.

No. 53: June 19, 2018 (Tue) 16:30-18:00

Dr. Yasuaki Hiraoka (Kyoto University)

"Topological data analysis and persistent homology"

**Abstract: **Topological data analysis is an emerging concept in applied mathematics in which we characterize “shape of data” using topological methods. In particular, the persistent homology and its persistence diagrams are nowadays applied to a wide variety of scientific and engineering problems including materials science, life science and social networks etc. In my talk, I will give a survey of these concepts both from mathematics and applications. If time is allowed, I will show several future challenges which deepen the mathematical understandings and possible applications.

No. 54: July 24, 2018 (Tue) 16:30-18:00

Dr. Yuto Miyatake (Osaka University)

"Discrete gradient methods for optimization problems"

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

No. 55: September 14, 2018 (Fri) 15:00-16:30

Prof. Uriel Frisch (Laboratoire Lagrange, Observatoire and Universite Cote d'Azur, Nice)

"The mathematical and numerical construction of turbulent solutions for the 3D incompressible Euler equation and its perspectives"

**Abstract: **Starting with Kolmogorov’s 1941 (K41) work, infinite Reynolds number flow is known to have velocity increments over a small distance r that
vary roughly as the cubic root of r. Formally, such flow is expected to
satisfy Euler’s partial differential equation, but the flow being
not spatially differentiable, the equation is satisfied only in
a distributional sense. Since Leray’s 1934 work, such solutions are called
weak. Actually they were already present –very briefly– in
Lagrange’s 1760/1761 work on non-smooth solutions of the wave equation.
A major breakthrough has happened recently: mathematicians succeeded
in constructing rigourously weak solutions of the Euler equation
whose spatial regularity –measured by their Hölder continuity exponent–
is arbitrarily close to the value predicted by K41 (Isett 2018), Buckmaster et
al. 2017). Furthermore these solutions present the anomalous energy dissipation
investigated by Onsager in 1949 (Ons49). We shall highlight some aspects of
the derivation of these results which took about ten years and was started
originally by Camillo de Lellis and Laszlo Szekelyhidi and continued with a
number of collaborators. On the mathematical side the derivation makes
use of techniques developed by Nash (1954) for isometric embedding and by Gromov
(1986, 2017) for convex integration. Fortunately, many features of the
derivation have a significant fluid mechanical content. In particular
the successive introduction of finer and finer flow structures, called Mikados
by Daneri and Szekelyhidi (2017) because they are slender and jetlike.
The Mikados generate Reynolds stresses on larger scales; they can be chosen
to cancel discrepancies between approximate and exact solutions of the Euler
equation. A particular engaging aspect of the construction of weak solutions
is its flexibility. The Mikados can be chosen not only to reproduce K41/Ons49
selfsimilar turbulence, but also to synthesize a large class of
turbulent flows, possessing, for example, small-scale intermittency
and multifractal scaling. This huge playground must of course be explored
numerically for testing all manners of physical phenomena and theories, a
process being started in a collaboration between Leipzig, Nice, Kyoto and Rome.

(in collaboration with Laszlo Szekelyhidi,Department of Mathematics,
University of Leipzig, Germany and Takeshi Matsumoto,Department of
Physics, Kyoto University, Japan)
**Note**: This talk was organized in cooperation with Fluid dynamics seminar at Kyoto University. The venue was Graduate School of Science Building n.5, room 401.

No. 56: October 23, 2018 (Tue) 16:30-18:00

Prof. Takaaki Aoki (Kagawa University, Faculty of Education)

"Cities and roads as pattern formation of their co-evolving dynamics on real-world landscape"

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

No. 57: December 11, 2018 (Tue) 16:30-18:00

Prof. Atsushi Mochizuki (Kyoto University, Institute for Frontier Life and Medical Sciences)

"Controlling cell fate specification system based on network structure"

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