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Theoretical Nonlinear Science

Spatially extended non-linear systems are typically described by partial differential equations. It permits the study of linear instabilities and different types of pattern formation in such non-linear systems. The combination of non-linear terms with different instabilities together with spatial interactions may produce novel mechanisms of pattern formation. Multi-scale problems where two instabilities appear simultaneously in a co-dimensional point at different scales can be studied and compared with experimental results in non-linear chemical systems, e.g. the Belousov-Zhabotinsky reaction or the catalytic CO oxidation in metal surfaces.

 

Related Publications

 

  • Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations

    D. Schüler, S. Alonso, A. Torcini and M. Bär, Chaos 24, 043142 (2014).

  • Traveling waves and global oscillations triggered by attractive molecular interactions in an excitable system

    K. John, S. Alonso, and M. Bär, Phys. Rev. E 90, 052913 (2014).

  • Control of reaction-diffusion patterns by asymmetric nonlocal coupling

    J. Siebert, S. Alonso, M. Bär, and E. Schöll, Phys. Rev. E 89, 052909 (2014).

  • Twists of opposite handedness on a scroll wave.

    P. Dähmlow, S. Alonso, M. Bär and M. J. B. Hauser, Phys. Rev. Lett. 110, 234102 (2013).

  • Surfactant-induced gradients in the three-dimensional Belousov-Zhabotinsky reaction.

    D. Kupitz, S. Alonso, M. Bär and M. J. B. Hauser, Phys. Rev. E 84, 056210 (2011).

  • Complex wave patterns in an effective reaction-diffusion model for chemical reactions in microemulsions.

    S. Alonso, K. John and M. Bär, J. Chem. Phys. 134, 094117 (2011).

  • Effective medium approach for heterogeneous reaction-diffusion media.

    S. Alonso, M. Bär and R. Kapral, J. Chem. Phys. 131 214102 (2009).

  • Noise-reversed stability of Turing patterns versus Hopf oscillations near codimension-two conditions.

    S. Alonso and F. Sagués, Phys. Rev. E 80, 035203(R) (2009).

  • Effective medium theory for heterogeneous reaction-diffusion systems.

    S. Alonso, R. Kapral and M. Bär. Phys. Rev. Lett. 102, 238302 (2009).

  • Towards active microfluidics: Interface turbulence in thin liquid films with floating molecular machines.

    S. Alonso and A. S. Mikhailov. Phys. Rev. E 79, 061906 (2009).

  • Effects of external global noise on the catalytic CO oxidation on Pt(110).

    P. S. Bodega, S. Alonso and H. H. Rotermund. J. Chem. Phys. 130, 084704 (2009).

  • Negative filament tension at high excitability in a model of cardiac tissue.

    S. Alonso and A. V. Panfilov. Phys. Rev. Lett. 100, 218101 (2008).

  • Differential susceptibity to noise of mixed Turing and Hopf modes in a photosensitive chemical medium.

    S. Alonso, D. G. Míguez and F. Sagués, Europhys. Lett. 81, 30006 (2008).

  • Experimental Evidence of Localized Oscillations in the Photosensitive Chlorine Dioxide-Iodine-Malonic Acid Reaction.

    D. G. Míguez, S. Alonso, A. P. Muñuzuri and F. Sagués. Phys. Rev. Lett. 97, 178301 (2006).