Nonlinear Physical Chemistry Unit
Service de Chimie Physique et Biologie
Théorique
Physico-chemical systems driven far from equilibrium by mass or energy fluxes may develop space or time symmetry breaking bifurcations that lead to time dependent oscillations or space periodic dissipative structures. We investigate theoretically the conditions of appearance of such symmetry breaking instabilities as well as the resulting nonlinear spatio-temporal dynamics. Our results encompass pattern selection theories of 2D and 3D Turing patterns and an analysis of the dynamics resulting from the coupling between Turing and Hopf instabilities. Our current interest lies in the analysis of spatial bistability and reaction-diffusion fronts in confined geometries as well as in the study of chemo-mechanical coupling.
References:
- P.M.J. Trevelyan, D.E. Strier and A. De Wit, Analytical asymptotic solutions of nA+mB—>C reaction-diffusion equations in two-layer systems : A general study, Phys. Rev. E., 78, 026122 (2008).
G. Nicolis and A. De Wit, Reaction-Diffusion Systems, Scholarpedia, 2(9) : 1475 (2007).
- K. Benyaich, T. Erneux, S. Métens, S. Villain, P. Borckmans, Spatio-temporal behaviors of a clock reaction in an open gel reactor, Chaos 16, 037109 (2006).
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P. Borckmans and G. Dewel, Turing Patterns, Encyclopedia of Nonlinear Science (Ed. Alwyn Scott, Taylor & Francis, New York), p.957-959 (2005).
- P. Borckmans, K. Benyaich and G. Dewel, Spatial Bistability : A Chemical Idiosyncracy?, Int. Journ. Quantum Chem. 98, p.239-247 (2004).
P. Borckmans, K. Benyaich, A. De Wit and G. Dewel, A model for self-oscillating miniaturized gels, chapter of the book Nonlinear Dynamics in Polymeric Systems, ACS Symposium Series No. 869; (J.A. Pojman and Q. Tran-Cong-Miyata Eds.; American Chemical Society: Washington, DC), p.58-70 (2003).
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P. Borckmans, G. Dewel, A. De Wit, E. Dulos, J. Boissonade, F. Gauffre and P. De Kepper, Diffusive instabilities and chemical reactions, Int. J. Bif. and Chaos, 12, 2307-2332 (2002).
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P. De Kepper, E. Dulos, J. Boissonade, A. De Wit, G. Dewel and P. Borckmans, Reaction-Diffusion Patterns in Confined Chemical Systems, J. Stat. Phys., 101, p.495-508 (2000).
- A. De Wit, Spatial Patterns and Spatiotemporal Dynamics in Chemical Systems, Adv. Chem. Phys., 109, p.435-513 (1999).
- P. De Kepper, E. Dulos, A. De Wit, G. Dewel and P. Borckmans, ``Taches, rayures and labyrinthes''}, La Recherche, 305, p.84-89 (1998).
- M. Meixner, A. De Wit, S. Bose and E. Schoell, Generic Spatiotemporal Dynamics near Codimension-Two Turing-Hopf Bifurcations, Phys. Rev. E, 55, p.6690-6697 (1997).
- A.
De Wit, P. Borckmans and G. Dewel, Twist Grain Boundaries in
Three-Dimensional Lamellar Turing Structures, Proc. Nat. Acad. Sciences
(USA), 94, p.12765-12768 (1997).
- A. De Wit, D. Lima, G. Dewel and P. Borckmans, Spatiotemporal Dynamics near a Codimension-Two Point, Phys. Rev. E, 54, p.261-271 (1996).
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G. Dewel, A. De Wit, S. Metens, J. Verdasca and P. Borckmans, Pattern
Selection in Reaction-Diffusion Systems with Competing Bifurcation, Phys. Scripta, T67, p.51-57 (1996).
- D. Lima, A. De Wit, G. Dewel and P. Borckmans, Chaotic Spatially Subharmonic Oscillations, Phys. Rev. E, 53, p.R1305-R1308 (1996).
- P. Borckmans, G. Dewel, A. De Wit and D. Walgraef, Turing Bifurcations and Pattern Selection', chapter of the book Chemical Waves and Patterns, (R. Kapral and K. Showalter Eds, Kluwer, 1995) p.323-363.
- G.
Dewel, P. Borckmans, A. De Wit, B. Rudovics, J.-J. Perraud, E. Dulos,
J. Boissonade and P. De Kepper, Pattern Selection and Localized
Structures in Reaction-Diffusion System, Physica A, 213, p.181-198 (1995).
- J.-J.
Perraud, A. De Wit, E. Dulos, P. De Kepper, G. Dewel and P. Borckmans,
``One-dimensional Spirals: Novel Asynchronous Chemical Wave Sources", Phys. Rev. Lett., 71, p.1272-1275 (1993).
- A. De Wit, G. Dewel and P. Borckmans, ``Chaotic Turing-Hopf Mixed Mode", Phys. Rev. E, 48, p.R4191-R4194 (1993).
- J. Verdasca, A. De Wit, G. Dewel and P. Borckmans, ``Reentrant Hexagonal Turing Structures", Phys. Lett. A, 168, p.194-198 (1992).
- P. Borckmans, A. De Wit and G. Dewel, ``Competition in Ramped Turing Structures", Physica A, 188, p.137-157 (1992).
- A. De Wit, G. Dewel, P. Borckmans and D. Walgraef, Three-Dimensional Dissipative Structures in Reaction Diffusion Systems,
Physica D, 61, p.289-296 (1992).