This section contains a brief overview over the ongoing CATS research activities. More details are given in section 8.

** Classical and Quantum Chaos:**

The goal of this research
is the development of a classical and quantum description of chaotic,
non-integrable systems, of analytic and
numerical quality comparable to those obtainable by the traditional
techniques for nearly integrable systems.
The NBI/Nordita group has established that
strongly chaotic systems
can be described surprisingly accurately by means of unstable
periodic orbits.
So far, the most exciting application of the theory has been to
quantum chaos, where one can now experimentally measure
the energy levels that the chaos theory predicts from the classical
unstable orbits; the theory is under rapid development, with recent
and highly impressive advances such as the first periodic-orbit
calculation of the Helium spectrum.
In 1994 the group has extended the theory by inclusion of the diffraction
contributions
to quantal spectra; also the theory has found several unanticipated
applications to the experiments performed at CATS, in particular
to the statistics of acoustic spectra, and the discovery of a classical
orbit modulation of the surface waves power spectrum in the hydraulic
jump.

** Turbulence:**

While today we know much about what is deterministic chaos and
how to characterize it, our understanding of
turbulence is still
rudimentary. Progress in this field is difficult, but a serious
theoretical advance is crucial in its
implications for classical hydrodynamics, statistical
mechanics, and strongly nonlinear field theories. The CATS
groups study turbulence as chaotic phenomena in
spatially extended systems; the main question is to what extent the
methods developed in the context of low-dimensional chaotic
dynamics can be applied to dynamical systems of high intrinsic
dimensions. We investigate transitions from coherent to
incoherent motion, the turbulent motion of vortices in reaction-diffusion
systems, the instability of boundary layers in convective systems,
intermittency, and scaling exponents of turbulence.
This involves
extensive numerical investigations of
spatio-temporal chaos:
coupled-map lattices, cellular automata, and a
variety of discretized models of chemical and hydrodynamical
turbulent phenomena. Such models have enabled us to study the onset of
turbulent vortex
structures in models of inhomogeneous oscillatory
chemical reactions, as well as to discover new types of phase
transitions.
A common thread of all these projects is extensive computer
experimentation; chaos researchers were
among the first to utilize interactive graphical computation, and our
future research will to a high degree rely on the advent of parallelism
and other advances in computation.

** Chemical Reaction-Diffusion Systems:**

Aspects of nonlinear dynamics, such as chaos and the theory of bifurcations,
play an important role in chemical reaction-diffusion systems
where chaotic behavior is by now
an established experimental fact. The HCØ-KI
group was one of the first
to initiate quantitative experimental
measurements of such dynamical systems. The group has shown that
the Turing structures formed in these systems are relevant for
biological pattern formation; the ability to describe complex
chemical systems is
essential for understanding key phenomena in biological control processes.
The goal of the HCØ-KI/NBI collaboration, combining the experimental
and theoretical strengths of the two groups, is to describe
chemical turbulence in spatially extended systems.

** Fractals:**

One of the key notions in nonlinear science is the concept
of fractals. Dendritic growth, dielectric breakdown,
electrochemical deposition, viscous fingering of a fluid penetrating
another fluid are some of the fractals generated in nature.
The goal of the NBI experimental
investigations of fractal structures and their theoretical
descriptions is to discover,
by techniques closely related to statistical mechanics,
new observable consequences of chaoticity, such as universal scalings, phase
transitions, fractal dimensions, and self-organizing critical phenomena.

** Biology:**

One of the most obvious areas in which to apply and further develop
the tools of nonlinear dynamics

is biology.

Unstable phenomena are increasingly being recognized as significant in the regulation and function of living systems. Investigations performed during the last decade have revealed the existence of a large variety of biological rhythms with periods ranging from fractions of a second to hours or even days. Other investigations have demonstrated the occurrence of deterministic chaos in physiological systems. These observations pose a number of fundamental questions concerning possible advantages of complex behavior and the mechanisms of evolutionary processes. A particularly interesting topic is the evolution and development of biological forms.

All of these closely related areas are experiencing dramatic breakthroughs, obtained through crossfertilization of ideas from physics, mathematics, computer science and biology. The computer simulation of self-organization in realistic 3-dimensional systems based on bifurcations in reaction-diffusion systems was pioneered by the HCØ-KI group. Much of the DTU group research in the coming years will focus on collaborations with biologists, medical doctors and chemists in order to study oscillations, chaos and biological form formation in a number of concrete examples.

** Experimental program:**

Experimental investigations are crucial to the development of our
understanding of complex systems, and the establishment of CATS
Center has made it possible to launch an experimental effort
commensurate with the level of already existing theoretical activity.
Currently we have ongoing experiments in
chemical reactions (quenching analysis, invariant manifolds, chemical waves),
fluid dynamics (turbulence in pipe flows, capillary waves, hydraulic jumps,
thin film flows),
acoustics (spectroscopy of high-**Q** resonators of various geometries),
physics of biological systems
(optical tunneling microscopy of proteins, measurement of
protein folding transitions, fractal boundaries evolution in yeasts),
and solid state phenomena
(relaxation oscillators, granular flows).

Mon Mar 6 19:42:06 MET 1995