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Quenching Analysis of Complex Chemical Reactions
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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.
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P. Graae Sørensen, F. Hynne, (A. Nagy) and T. Lorenzen
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Determination of the Kinetics of Complex Reactions from Quenching Data
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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.
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F. Hynne, P. Graae Sørensen, (A. Nagy) and K. Nielsen
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Normal Form Analysis of the BZ Reaction near a Hopf Bifurcation
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We have showed that the behavior of the Belousov-Zhabotinsky (BZ)
reaction observed experimentally away from a Hopf bifurcation can be
described quite well by normal form equations with parameters obtained
experimentally by quenching experiments near the Hopf bifurcation.
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P. Graae Sørensen, F. Hynne, (J. Kosek) and (M. Marek)
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Chaos in Closed Chemical Reactions
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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.
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J. Wang, K. Nielsen, P. Graae Sørensen and F. Hynne
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Chaos in a ``Kicked Chemical Oscillator''
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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.
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P. Graae Sørensen, F. Hynne, R. Breiner and R. Chacón García
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Biochemical Oscillators
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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.
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K. Nielsen, P. Graae Sørensen and F. Hynne
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The Complex Geometry of a Period Doubling Bifurcation
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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
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Quasiperiodic Oscillations
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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.
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P. Graae Sørensen, F. Hynne and T. Lorenzen
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Experimental Determination of Ginzburg-Landau Parameters
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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
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Chemical Waves
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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.
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P. Graae Sørensen, F. Hynne and F. Jensen
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Spontaneous Pattern Formation in Cells and Embryos
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Bifurcations in nonlinear partial differential equations, describing
autocatalytic biochemical control systems and diffusion, show
emergence of well controllable patterns (morphogenetic fields).
The simulation of such processes (Turing structure formation) in
three curvilinear space coordinates and time was pioneered internationally
by us. Subsequently, high performance computer codes were developed,
which run at near peak performance of various supercomputers. These
codes are used by the national computer center to benchmark current
supercomputers, including parallel architectures.
We have established that biological pattern formation is intimately
linked to highly nonlinear control processes. The current view that
pattern formation has arisen through the exploitation of simple
gradient patterns is challenged. The prerequisite for interpretation
of positional information set up by simple gradients is highly
nonlinear response to the gradient, but such high nonlinearities,
experimentally found in gene control systems, are prone to yield
nonlinear oscillations and waves, and even Turing structures.
Pattern formation based on all these phenomena may account for the
lack of an ancient `proto pattern gene'. It appears that pattern formation
has arisen by widely different mechanisms throughout evolution,
but highly nonlinear control is suggested to be an essential part for the
majority of these mechanisms, rather than specific genes or gene clusters.
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A. Hunding, (T. Lacalli) and (J. Boissonade)
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Turing Structures and Turbulence in Chemical Reaction-Diffusion
Systems
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We have performed a numerical analysis of pattern selection,
localized structure formation, front propagation and turbulence
for the Lengyel-Epstein model. This model is distinguished from
previously studied simple reaction-diffusion models by producing
a strongly subcritical transition to stripes. The speed of
propagation for a front between the homogeneous steady state and
a one-dimensional Turing structure has been obtained. This
velocity shows a characteristic behavior at the crossover
between the subcritical and supercritical regimes for the Turing
bifurcation. In the subcritical regime there is an interval
where the front velocity vanishes as a result of pinning of the
front to the underlying structure. This makes it possible for a
wide variety of localized structures to arise and be stable. In
two dimensions different nucleation mechanisms for hexagonal
structures have been illustrated for the Lengyel-Epstein and the
Brusselator models. One and two dimensional spirals with Turing
induced cores have been observed. We have also obtained
preliminary results on the dynamics of phase singularities and
the emergence of chemical turbulence.
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(P. Borckmans), (G. Dewel), O. Jensen, E. Mosekilde and V.O.
Pannbacker
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Mon Mar 6 19:42:06 MET 1995