Chemo-capillary instabilities of a contact line

Equilibrium and motion of a contact line are viewed as analogs of phase equilibrium and motion of an interphase boundary. This point of view makes evident the tendency to minimization of the length of the contact line at equilibrium. The concept of line tension is, however, of limited applicability, in view of a qualitatively different relaxation response of the contact line, compared to a two-dimensional curve. Both the analogy and qualitative distinction extend to a non-equilibrium situation arising due to coupling with reversible substrate modification. Under these conditions, the contact line may suffer a variety of chemo-capillary instabilities (fingering, traveling and oscillatory), similar to those of dissipative structures in nonlinear non-equilibrium systems. The preference order of the various instabilities changes, however, significantly due to a different way the interfacial curvature is relaxed.Comment: 8 pages, 4 figures; corrected version of the published pape

Turing patterns and solitary structures under global control

Striped Turing patterns and solitary band and disk structures are constructed using a three-variable multiscale model with cubic nonlinearity and global control. The existence and stability conditions of regular structures are analysed using the equation of motion of curved boundaries between alternative states of the short-range component. The combined picture of transitions between striped and spotted patterns with changing level of global control is in qualitative agreement with the results of the computer experiment by Middya and LussComment: RevTeX 30 pages, 10 PS-figure

The biological frontier of pattern formation

Morphogenetic patterns are highly sophisticated dissipative structures. Are they governed by the same general mechanisms as chemical and hydrodynamic patterns? Turing's symmetry breaking and Wolpert's signalling provide alternative mechanisms. The current evidence points out that the latter is more relevant but reality is still far more complicated.Comment: 9 pages, 0 figure