Neicu et al. observed experimentally spontaneous formation of the long-range orientational order and large-scale vortices in a system of vibrated macroscopic rods. We propose a phenomenological theory of this phenomenon based on a coupled system of equations for local rods density and tilt. The density evolution is described by the modified Cahn-Hilliard equation, while the tilt is described by...

We study in this article the bifurcation and stability of the solutions of the Ginzburg–Landau equation, using a notion of bifurcation called attractor bifurcation. We obtain in particular a full classification of the bifurcated attractor and the global attractor as λ crosses the first critical value of the linear problem. Bifurcations from the rest of the eigenvalues of the linear problem are ...

We address the striking coexistence of localized waves (‘pulses’) of different lengths which was observed in recent experiments and full numerical simulations of binary-mixture convection. Using a set of extended Ginzburg-Landau equations, we show that this multiplicity finds a natural explanation in terms of the competition of two distinct, physical localization mechanisms; one arises from dis...

Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons. We study the stability of the oscillating hexagons using three coupled Ginzburg-Landau equations. Close to the bifurcation point we derive reduced equations for the amplitude of the oscillation, coupled to the phase of the underlying hexagons...

Part 3: (H, PB) Interacting systems, phase transitions and critical phenomena (11 lectures) Interacting spin systems, Ising model. Interacting classical gas, cluster expansion, van der Waals equation of state, Virial Expansion, phase equilibrium, chemical equilibrium. Interacting quantum gases in atom traps. BCS theory of Superconductivity, Landau and Ginzburg Landau theory. Topological excitat...

Part I Near-equilibrium critical dynamics 1 Introduction 3 1 Equilibrium critical phenomena 5 1.1 Mean-field theory 6 1.1.1 Van-der-Waals equation of state 6 1.1.2 Mean-field theory for the ferromagnetic Ising model 9 1.1.3 Ornstein–Zernicke correlation function 14 1.2 Landau–Ginzburg theory 17 1.2.1 Mean-field theory revisited: Landau expansion 17 1.2.

Several systems discussed at this workshop on Spatio-Temporal Patterns in Nonequilibrium Complex Systems have been related to or analyzed in the context of the so-called Complex Ginzburg-Landau equation (CGL). What is the difference between the physics underlying the usual amplitude description for stationary patterns and the one underlying the CGL? Why are there many more stable coherent struc...