- Access by Xinjiang University
Flow-induced transitions in bistable systems
Phys. Rev. E 86, 056205 – Published 5 November, 2012
DOI: https://doi.org/10.1103/PhysRevE.86.056205
Abstract
We studied transitions between spatiotemporal patterns that can be induced in a spatially extended nonlinear chemical system by a unidirectional flow in combination with constant inflow concentrations. Three different scenarios were investigated. (i) Under conditions where the system exhibited two stable fixed points, the propagation direction of trigger fronts could be reversed, so that domains of the less stable fixed point invaded the system. (ii) For bistability between a stable fixed point and a limit cycle we observed that above a critical flow velocity, the unstable focus at the center of the limit cycle could be stabilized. Increasing the flow speed further, a regime of damped flow-distributed oscillations was found and, depending on the boundary values at the inflow, finally the stable fixed point dominated. Similarly, also in the case of spatiotemporal chaos (iii), the unstable steady state could be stabilized and was replaced by the stable fixed point with increasing flow velocity. We finally outline a linear stability analysis that can explain part of our findings.
Article Text
References (17)
- J. C. Hill, Annu. Rev. Fluid Mech. 8, 135 (1976).
- C. R. Nugent, W. M. Quarles, and T. H. Solomon, Phys. Rev. Lett. 93, 218301 (2004); M. S. Paoletti and T. H. Solomon, Europhys. Lett. 69, 819 (2005).
- P. Andresén, M. Bache, E. Mosekilde, G. Dewel, and P. Borckmanns, Phys. Rev. E 60, 297 (1999); M. Kaern and M. Menzinger, ibid. 60, R3471 (1999); R. Satnoianu and M. Menzinger, ibid. 62, 113 (2000); J. R. Bamforth, J. H. Merkin, S. K. Scott, R. Tóth, and V. Gáspár, PhysChemChemPhys 3, 1435 (2001); J. R. Bamforth, R. Tóth, V. Gáspár, and S. K. Scott, ibid. 4, 1299 (2002).
- G. Fernández-García, D. I. Roncaglia, V. Pérez-Villar, A. P. Muñuzuri, and V. Pérez-Muñuzuri, Phys. Rev. E 77, 026204 (2008).
- L. Rongy, P. M. J. Trevelyan, and A. De Wit, Phys. Rev. Lett. 101, 084503 (2008).
- J. A. Pojman and I. R. Epstein, J. Phys. Chem. 94, 4966 (1990).
- A. Yochelis and M. Steintuch, PhysChemChemPhys 12, 3957 (2010).
- I. Berenstein, Chaos 22, 023112 (2012).
- I. Berenstein and C. Beta, J. Chem. Phys. 135, 164901 (2011).
- K. J. Lee, W. D. McCormick, Q. Ouyang, and H. L. Swinney, Science 261, 192 (1993).
- A. P. Muñuzuri and A. Vázquez-Otero, in Proceedings of the 11th International Workshop on Cellular Neural Networks and Their Applications (IEEE, Piscataway, NJ, 2008), pp. 248–251.
- P. Gray and S. K. Scott, Chem. Eng. Sci. 39, 1087 (1984).
- J. H. Merkin and M. A. Sadiq, IMA J. Appl. Math. 57, 273 (1996).
- R. Wackerbauer and K. Showalter, Phys. Rev. Lett. 91, 174103 (2003).
- W. Van Saarloos, Phys. Rep. 386, 29 (2003).
- P. N. McGraw and M. Menzinger, Phys. Rev. E 72, 027202 (2005).
- P. N. McGraw and M. Menzinger, Phys. Rev. E 72, 026210 (2005).