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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).

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Sub-department of Applied Analysis

ANALYSIS OF INVERSE PROBLEMS and NONLINEAR 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
 HINO, Masanori, D.Sc.(Kyoto Univ.),
 Probability Theory, 
 Stochastic Analysis on Infinite Dimensional Spaces

Senior Lecturer
 KUBO, Masayoshi, D.Sc.(Kyoto Univ.),
 Mathematical Analysis of Inverse and Ill-posed Problems,
 Numerical Analysis

Senior Lecturer
 WAKANO, Isao, Doctor of Informatics (Kyoto Univ.),
 Numerical Analysis,
 Mathematical Analysis of Fracture Mechanics

Assistant Professor
 FUJIWARA, Hiroshi, Doctor of Informatics (Kyoto Univ.),
 Numerical Analysis of Inverse and Ill-Posed Problems,
 Computer Arithmetic

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Sub-department of Complex Dynamics

Nonlinear Dynamics 

Professor
 FUNAKOSHI, Mitsuaki,  D.Eng.(Kyoto Univ.), Nonlinear Dynamics,
 Fluid Dynamics, Dynamics of Complex Systems

Associate Professor
 TANAKA, Hiroaki, D.Eng.(Kyoto Univ.), Structural Reliability,
 Stochastic Mechanics

Assistant Professor
 KANEKO, Yutaka, D.Eng.(Kyoto Univ.), Computational Physics

Current research activities cover the following fields:

  1. Chaotic fluid motion and its relation to mixing process
  2. Controlling and suppression of chaos in coupled systems
  3. Generation, interactions and pattern formation of nonlinear waves in fluids
  4. Chaotic motion and deformation of vortices due to their interactions
  5. Application of stochastic differential equations to system reliability analysis
  6. Differential equations with random fields and their application
  7. Efficient Monte-Carlo simulation for time-dependent reliability analysis
  8. Computer simulation of many-particle systems
  9. Electrodeposition and thin film growth

Nonequilibrium Dynamics

Associate 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

The research concerns theoretical and computational studies of complex dynamics observed in nonlinear, nonequilibrium systems. Our special attention is devoted to the study by utilizing methods of nonequinlibrium statistical physics and numerical computation, by employing mathematical models in hydrodynamic, magnetic, coupled-oscillator, chemical reaction, liquid-crystal systems, etc. Current research activities cover the following fields:

  1. Statistical study of turbulence
  2. Dynamical properties in time-delayed oscillator systems
  3. Large-deviation theoretical analysis of complex dynamics and stochastic processes
  4. Ordering processes associated with phase transitions
  5. Dissipative structures and pattern formations
  6. Stochastic modeling of chaotic evolution
  7. Complex dynamics in coupled-oscillator systems

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Sub-department of Applied Mathematical Sciences

Computational Mechanics

Professor
 NISHIMURA, Naoshi, D.Eng.(Kyoto Univ.), 
 Computational Mechanics, Applied Mechanics, 
 Boundary Integral Equation Methods, Fast Multipole Methods

Senior Lecturer
 YOSHIKAWA, Hitoshi, D.Eng.(Kyoto Univ.),
 Computational Mechanics, Applied Mechanics

Assistant Professor
 HARADA, Kenji, D.Eng.(Kyoto Univ.), Computational Physics

The research concerns analysis and synthesis of complex systems characterized by self-organization, pattern formation and association etc. through interaction in parallel and global perspective, and the complexity theory. It is founded upon applied mathematics and physics, computational mathematics and parallel algorithms. Current reserach is dedicated to phase-field models of phase transition, cluster algorithms in quantum Monte Carlo simulation, immune and enzyme systems, cerebral neural models, global environment problems, and development of intelligent object-oriented software and parallelizer. Subjects are classified into

  1. Fundamental theory of complex systems
  2. Computational mathematics and physics
  3. Complexity
  4. Parallel computers and parallel algorithms
  5. Complex systems in biology, sociology and global environment

Intelligent and Control Systems

Professor 
 YAMAMOTO, Yutaka, Ph.D.(Univ. of Florida),

Assistant Professor 
 NAGAHARA, Masaaki, Doctor of Informatics (Kyoto Univ.),

The division undertakes research and graduate study in the area of intelligent and control systems based on the dynamical system theory. The research interest includes intelligent and control systems, sampled-data control, digital signal processing, learning control, neural networks, and robust control.

Intelligent Systems: The division approaches to intelligent systems with learning process from the viewpoint of the feedback systems theory. Applications include neural networks, learning control systems, and GA optimization.

Digital Systems: Introducing digital computers for the purpose of implementing control/filter algorithms makes the resulting system hybrid in the sense that it contains both analog and digital components. The lifting technique, which is proposed by the division, resolved main difficulties in the study of such digital systems. Current research topics in the division include digital signal processing, digital repetitive control, robust sampled-data control, and object-oriented CAD for sampled-data control systems,

Robust Control: Analysis and synthesis of robust feedback systems is a central theme of control theory with great theoretical and practical importance, since uncertainties in systems and related signals are inevitable. For example, H-infinity control, infinite-dimensional systems, and matrix inequality approach with its computational algorithms are studied in the division within the field of robust control.

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