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Nonlinear Chemical Dynamics

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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

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

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

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

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

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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

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

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

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

P. Graae Sørensen, F. Hynne, R. Breiner and (R. Chacón García) truecm

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

K. Nielsen, P. Graae Sørensen and F. Hynne truecm

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. truecm

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

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

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

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. truecm

F. Hynne and P. Graae Sørensen truecm

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

P. Graae Sørensen, F. Hynne and F. Jensen truecm

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. truecm

T. Bohr, (M. Bazhenov, E. Bosch, G. Huber, E. Ott and W. van de Water)

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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

M. Kærn and A. Hunding truecm

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

R. Engelhardt and A. Hunding truecm

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

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

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. truecm

A. Hunding and (T. Lacalli)



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Next: STAFF ACTIVITIES Up: RESEARCH PROJECTS Previous: Biology and physiology



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