truecm

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Quenching of the Ruthenium Catalyzed BZ Reaction by Light
truecm**

The mechanism by which light interacts with Ruthenium-bipyridyl in the
BZ reaction is studied by quenching of oscillations with a short
monocromatic pulse of light.
truecm *
*

*
T. Lorenzen, P.Graae Sørensen and F. Hynne
truecm*

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Effect of Oxygen on the BZ Reaction
truecm**

The influence of oxygen on the complex transient oscillations in a
closed system is used to elucidate the nature of the involved elementary
reactions.
truecm *
*

*
J. Wang, P. Graae Sørensen and F. Hynne
truecm*

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Generalization of the complex Ginzburg-Landau Equation to Account for
Effects of Transients
truecm**

The complex Ginzburg-Landau equation (c-GLE) applies to description of plane
waves and spirals sufficiently close to a Hopf bifurcation. In order to
describe a real reaction-diffusion system by an amplitude method at larger
distances from the bifurcation the c-GLE is generalized to include effects
of motion out of the plane of oscillations.
truecm *
*

*
M. Ipsen, F. Hynne and P. Graae Sørensen
truecm*

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Quenching Analysis of Complex Chemical Reactions
truecm**

Quenching analysis is a method of determining important
characteristics of the dynamics of an oscillatory chemical reaction
system. Its theoretical and experimental basis was developed by the
research group, and the method is presently being used to study two
reactions.
One is the Belousov-Zhabotinsky reaction with ruthenium bipyridyl as a
catalyst. This system is very important for studying chemical waves
because the reaction is light sensitive so that it is possible to
systematically set up spatially inhomogeneous initial conditions --
which is otherwise impossible.
The other system studied is the reaction of permanganate with
hydroxylamine. This system is extremely complex and little is
known about the kinetics. Quenching analysis is a powerful tool
for solving such complicated problems because it provides kinetically
relevant quantitative data for the entire oscillating reaction at
its actual working point. We have successfully completed the quenching
experiments.
truecm *
*

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P. Graae Sørensen, F. Hynne, (A. Nagy) and T. Lorenzen
*

*
truecm*

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Determination of the Kinetics of Complex Reactions from Quenching Data
truecm**

We have previously shown how it is possible to systematically
determine the kinetics of a complete set of reactions of an
oscillatory chemical system all at once from experimental quenching
data by a method developed by the group.
For a given mechanism, the method generates all possible Hopf
bifurcation points directly without integration of the kinetic
equations, and the properties are compared with experimental quenching
data. Presently we are working on a very complex manganese oscillator,
and we are preparing to study also biochemical oscillators.
truecm *
*

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F. Hynne, P. Graae Sørensen, (A. Nagy) and K. Nielsen
truecm*

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Chaos in Closed Chemical Reactions
truecm**

Complex oscillations have not previously been observed in closed
chemical reactions under controlled conditions. We have discovered
transient complex oscillations, bifurcations, and chaos in the cerium
catalysed Belousov-Zhabotinsky reaction, conducted in a closed system.
For example, chaotic oscillations were associated with successive
transient supercritical period doublings.
The existence of transient complex oscillations has enabled us to
provide a strong support to the assumption that the chaotic-looking
oscillations that are observed in open systems are indeed caused by
the intrinsic chemical dynamics and not by incomplete mixing of feed
chemicals.
We have successfully modelled these new transient phenomena.
truecm *
*

*
J. Wang, K. Nielsen, P. Graae Sørensen and F. Hynne
truecm*

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Chaos in a ``Kicked Chemical Oscillator''
truecm**

When a chemical system exhibiting small oscillations near a
supercritical Hopf bifurcation is periodically perturbed by addition
of species participating in the reaction, the response may be rather
similar to Shilnikov chaos. This we have demonstrated experimentally.
Such simple system is particularly interesting because it is possible
to approximately calculate its behavior, e.g. a Poincare map, using
quenching data for the system.
truecm *
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P. Graae Sørensen, F. Hynne, R. Breiner and (R. Chacón García)
truecm*

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Biochemical Oscillators
truecm**

Biochemical oscillators are generally difficult to work with. We are
acquiring the expertise necessary to run the peroxidase and glycolysis
reactions. We have succeeded in getting the glycolysis reaction
running in a fully open system which has not been done before. This
system can exhibit chaotic oscillations, a new observation. Presently
we are searching for Hopf bifurcations in these two systems.
truecm *
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K. Nielsen, P. Graae Sørensen and F. Hynne
truecm*

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The Complex Geometry of a Period Doubling Bifurcation
truecm**

The geometry of the stable manifold of a saddle cycle near a period doubling bifurcation is extremely complex. Its possible structure has been indicated in three dimensions, but no experiment has supported the assumed form, at least not for a chemical system (which generally is high dimensional). We have carried out experiments with the cerium catalysed Belousov-Zhabotinsky reaction that show that the manifold must have a curled structure. A perspective of the experiments is to characterize complex (period-doubled) oscillations and their embedding in the concentration space and eventually also chaotic oscillations arising from a Feigenbaum sequence of period doublings. In this way one may learn much about the chemistry responsible for the complexity.

A realistic model for the system derived from the Oregonator confirms
the structure and shows that, for a chemical system, the stable
manifold may end on a coordinate hyperplane.
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J. Wang, F. Hynne and P. Graae Sørensen
truecm*

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Quasiperiodic Oscillations
truecm**

We have initiated experiments to study a secondary Hopf bifurcation
appearing in the ruthenium bipyridyl catalysed BZ reaction. The
experiments aim at probing the invariant manifolds associated with a
saddle cycle arising at the bifurcation by perturbation methods
similar to those used in the quenching experiments and for the period
doubling.
truecm *
*

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P. Graae Sørensen, F. Hynne and T. Lorenzen
truecm*

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Experimental Determination of Ginzburg-Landau Parameters
truecm**

Chemical waves are described by a reaction-diffusion equation that is
a partial differential equation in a concentration vector with space
and time as independent variables. Because the concentration space of
essential species usually is of quite high dimension, realistic
chemical reactions are difficult to model.
Close to a Hopf bifurcation of the corresponding homogeneous system,
the problem can be approximately described by a complex
Ginzburg-Landau (cGL) equation which in effect has a two-dimensional
state space. In addition, the cGL equation is an amplitude equation
which greatly facilitates the numerical solution. This approximation
thus results in a drastic reduction in complexity of the problem.
To actually use the cGL equation to describe a real chemical reaction,
one must know the parameters that enter the equation. We have shown
how it is possible to obtain all of the parameters of the cGL from
quenching experiments, provided the diffusion coefficients of the
reacting species are known. We have calculated the parameters for
definite operating points of the cerium and ruthenium bipyridyl
catalysed Belousov-Zhabotinsky reactions.
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F. Hynne and P. Graae Sørensen
truecm*

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Chemical Waves
truecm**

Equipment to study chemical waves has been developed. It includes a
well thermostated reaction cell, protected from external vibrations,
monitored by a video camera. With this equipment, we have observed
waves in the cerium catalysed Belousov-Zhabotinsky reaction in
ultraviolet light. At the operating point used the system shows frozen
structures (spirals), which are compatible with properties expected
from our quenching experiments. We are proceeding to study the rubidium
catalysed BZ reaction for which it may be possible to control initial
conditions.
truecm *
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*
P. Graae Sørensen, F. Hynne and F. Jensen
truecm*

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Turbulence and Spiral Motion in the Complex Ginzburg-Landau Equation
truecm**

We study various properties of the so-called complex Ginzburg- Landau equation which models systems close to a Hopf-bifurcation (where a limit cycle emerges out of a steady state). We study numerically and theoretically issues, such as

1. Defect turbulence and the transition to phase turbulence. 2. Interaction between spirals waves and the formation of shocks. 3. Scaling properties of various quantities near the transition to tubulence and from defect to phase turbulence.

We have close collaborations with the group of CATS chemists at the
H. C. Ørsted Institute, who studies various forms of the
Belousov-Zhabotinsky reaction experimentally.
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T. Bohr, (M. Bazhenov, E. Bosch, G. Huber, E. Ott and W. van de Water)
*

*
truecm*

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Detailed Models of Allosteric Enzyme Control Networks.
truecm**

The usual Monod, Changeux, Wyman model for S-shaped kinetics with
allosteric transitions of the control enzymes(s) is investigated
in detail. Such detailed models for the control of the rate limiting
steps in glycolysis are currently under construction, and the effect
on limit cycle oscillations and chaos studied.
truecm *
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M. Kærn and A. Hunding
truecm*

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Adaptation in autocatalytic nets of macromolecules
truecm**

A cellular automaton model is under development to
describe competition among macromolecules like t-RNA
and peptides. The dynamics of the network under
various external constraints, coupled to specific
classes of internal feedback, is studied.
truecm *
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R. Engelhardt and A. Hunding
truecm*

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Supercomputer calculation of 3 dimensional pattern
formation, simulating spatially deformed echinoderm eggs
truecm**

Theoretical studies (Copenhagen) on numerical and analytical
bifurcations are carried out.
Experimentally (Bordeaux),
spherical echinoderm eggs are geometrically
altered to produce artificially oriented cleavage furrows,
and mitotic organization, related to the theoretically
found patterns.
The project thus analyzes fundamental properties of the
mechanism of biological cell division, which may create new
important knowledge on normal and malignant cell growth.
A. Hunding has already published a series of papers
demonstrating theoretically found patterns, and their
possible connections to these phenomena. The software used in
these studies is directly applicable to the project.
truecm *
*

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A. Hunding and (E. Dulos, Bordeaux)
truecm*

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Turing structures of the second kind
truecm**

Simulation of Turing structures of the second kind , pattern formation in
embryos under gradient control,
and structure formation in biosystems undergoing growth.
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A. Hunding and (T. Lacalli)
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Fri Mar 29 00:13:44 MET 1996