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Chemical reaction-diffusion systems

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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

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

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

Normal Form Analysis of the BZ Reaction near a Hopf Bifurcation truecm

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. truecm

P. Graae Sørensen, F. Hynne, (J. Kosek) and (M. Marek) 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

Spontaneous Pattern Formation in Cells and Embryos truecm

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. truecm

A. Hunding, (T. Lacalli) and (J. Boissonade) truecm

Turing Structures and Turbulence in Chemical Reaction-Diffusion Systems truecm

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. truecm

(P. Borckmans), (G. Dewel), O. Jensen, E. Mosekilde and V.O. Pannbacker



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



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