## English page

### ABOUT ACS

The Department of Applied Analysis and Complex Dynamical Systems(ACS) originated with the foundation of the Graduated School of Informatics in April, 1998, to meet demands of analyzing and synthesizing the emergence of certain macroscopic phenomena of complex systems consisiting of microscopic elements, mostly via nonlinear, large-scale interactions. Such phenomena can be observed or created in every aspect of modern science/technology; for example, numerical and inverse problems in mathematics, dynamical and chaotic behaviors in physical systems, neural, computational and control systems. They typically present collective behavior such as self-organization, pattern formation, recognition, learning etc. This department aims at clarifying fundamental principles in such phenomena as well as utilizing and synthesizing the knowledge derived out of them. Emphasis is placed upon general backgrounds in diverse fields as well as a more in-depth grasp of specific branches such as applied analysis, nonlinear dynamics, micro-mesoscopic physics, parallel computing, intelligent control systems. To this end, the department places three chairs, each consisting of two divisions: Applied Analysis (Analysis of Inverse Problems, Nonlinear Analysis), Complex Dynamics(Nonlinear Dynamics, Nonequilibrium Dynamics) and Applied Mathematical Sciences (Computational Mechanics, Intelligent and Control Systems).

### Sub-department of Applied Analysis

Professor
ISO, Yuusuke, D.Sc.(Kyoto Univ.),
Numerical Analysis,
Mathematical Analysis of Inverse and Ill-posed Problems
Professor
KIGAMI, Jun, D.Sc.(Kyoto Univ.),
Analysis and Dynamical System,
Analysis on Fractals
Associate Professor
FUJIWARA, Hiroshi, Ph.D.(Informatics, Kyoto Univ.),
Numerical Analysis of Inverse and Ill-Posed Problems,
Computer Arithmetic
Senior Lecturer
KUBO, Masayoshi, D.Sc.(Kyoto Univ.),
Mathematical Analysis of Inverse and Ill-posed Problems,
Numerical Analysis
Senior Lecturer
SHIRAISHI, Daisuke, Ph.D. (Science, Kyoto Univ.),
Probability Theory
Senior Lecturer
CHEN, I-Kun, Ph.D. (Univ. Maryland),
Mathematical Analysis of Partial Differential Equations

### Sub-department of Nonlinear Physics

Professor
FUNAKOSHI, Mitsuaki, D.Eng.(Kyoto Univ.), Nonlinear Dynamics,
Fluid Dynamics, Dynamics of Complex Systems
Professor
AOYAGI, Toshio, D.Sc.(Kyoto Univ.), Theory of Neural Networks,
Nonlinear Dynamics, Nonequilibrium Statistical Physics
Senior Lecturer
MIYAZAKI, Syuji, D.Sc.(Kyushu Univ.), Large Deviation Theoretical Analysis,
Spatiotemporal Dynamics
Assistant Professor
TUTU, Hiroki, D.Sc.(Kyushu Univ.), Ordering Process and Pattern Formation
Assistant Professor
HARADA, Kenji, D.Eng.(Kyoto Univ.), Computational Physics

Current research activities cover the following fields:

Group of Fluid Dynamics and Computational Physics

(Professor: FUNAKOSHI Mitsuaki, Senior Lecturer: MIYAZAKI Syuji, Assistant Professor: HARADA Kenji）

- Chaotic fluid motion and its relation to mixing process
- Flow patterns of thermal convection in a container
- Generation, interactions and pattern formation of nonlinear waves in fluids
- Chaotic motion and deformation of vortices due to their interactions
- Many-body problem

Group of Nonequilibrium Physics and Theoretical Neuroscience

(Professor: AOYAGI Toshio, Assistant Professor: TUTU Hiroki)

- Theoretical neural science (mathematical modeling of the brain)
- A collection of dynamical systems linked through a network with evolving structure (neurons, social networks, etc.)
- Analysis of rhythm phenomena (entrainment transition)
- Nonlinear dynamics and chaos
- Nonequilibrium statistical physics
- Stochastic modeling for molecular machines
- Modeling social systems based on game dynamics on networks

### Sub-department of Applied Mathematical Sciences

Professor
NISHIMURA, Naoshi, D.Eng.(Kyoto Univ.),
Computational Mechanics, Applied Mechanics,
Boundary Integral Equation Methods, Fast Multipole Methods
Associate Professor
YOSHIKAWA, Hitoshi, D.Eng.(Kyoto Univ.),
Computational Mechanics, Applied Mechanics
Assistant Professor
NIINO, Kazuki, Ph.D.(Informatics, Kyoto Univ.),
Boundary Integral Equation Methods, Computational Electromagnetics

Computer simulations provide powerful means of solving various problems in science and engineering. Computational mechanics is one of such approaches which, along with theoretical and experimental mechanics, investigates mechanical phenomena efficiently. This division develops various approaches of the Boundary Integral Equation Method (BIEM), which is one of major techniques of computational mechanics and is considered suitable for the analyses of phenomena such as waves, fracture, etc. We are currently interested in fast BIEMs and their applications to large scale problems.

#### Industrial Mathematics