Coherent structures in reaction-diffusion models for precipitation1

We study a class of models for precipitation from a dynamical systems point of view. The class of models incorporates Cahn-Hilliard-type models for spinodal decomposition and supersaturation theories as natural limiting cases. We analyze existence and stability of coherent structures, and relate our findings to simulations of Liesegang pattern formation.

[1]  P. Bates,et al.  The existence of travelling wave solutions of a generalized phase-field model , 1997 .

[2]  D. Hilhorst,et al.  The Visous Cahn–Hilliard Equation as a Limit of the Phase Field Model: Lower Semicontinuity of the Attractor , 1999 .

[3]  G. Caginalp An analysis of a phase field model of a free boundary , 1986 .

[4]  A. Scheel,et al.  Instability of spikes in the presence of conservation laws , 2010 .

[5]  S. I. Rubinow,et al.  Recurrent precipitation and Liesegang rings , 1981 .

[6]  A. Scheel Robustness of Liesegang patterns , 2009 .

[7]  Traveling Waves in Rapid Solidification , 2000 .

[8]  T. Antal,et al.  Guiding fields for phase separation: controlling Liesegang patterns. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Rapid growth and critical behaviour in phase field models of solidification , 2001, European Journal of Applied Mathematics.

[10]  Gunduz Caginalp,et al.  The existence of travelling waves for phase field equations and convergence to sharp interface models in the singular limit , 1991 .

[11]  Björn Sandstede,et al.  Relative Morse indices, Fredholm indices, and group velocities , 2007 .

[12]  Björn Sandstede,et al.  Defects in Oscillatory Media: Toward a Classification , 2004, SIAM J. Appl. Dyn. Syst..

[13]  D. Hilhorst,et al.  A Mathematical Study of the One-Dimensional Keller and Rubinow Model for Liesegang Bands , 2009 .

[14]  D. Hilhorst,et al.  Fast Reaction Limits and Liesegang Bands , 2006 .

[15]  W. Saarloos Front propagation into unstable states , 2003, cond-mat/0308540.

[16]  Formation of Liesegang patterns: A spinodal decomposition scenario , 1999, cond-mat/9903420.

[17]  M. Droz Recent Theoretical Developments on the Formation of Liesegang Patterns , 2000 .