Memory driven pattern formation

Energy-Driven Pattern Formation

Many physical systems can be modelled by nonconvex variational problems regularized by higher-order terms. Examples include martensitic phase transformation, micromagnetics, and the Ginzburg–Landau model of nucleation. We are interested in the singular limit, when the coefficient of the higher-order term tends to zero. Our attention is on the internal structure of walls, and the character of mi...

Light-driven dynamic pattern formation.

Noise-driven mechanism for pattern formation.

We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation ...

Pattern formation by bacteria-driven flow.

Some marine bacterial species form mucosal layers, called veils, on sulfidic marine sediment. The bacteria attached to this veil actively swim and exert force on the surrounding fluid. The bacteria can break free of the veil and swim, chemotacting back to the veil. Over time the veil forms holes arranged in a hexagonal pattern. Motivated by this system, we present a simplified model to describe...

Localized solutions in parametrically driven pattern formation.

The Mathieu partial differential equation (PDE) is analyzed as a prototypical model for pattern formation due to parametric resonance. After averaging and scaling, it is shown to be a perturbed nonlinear Schrödinger equation (NLS). Adiabatic perturbation theory for solitons is applied to determine which solitons of the NLS survive the perturbation due to damping and parametric forcing. Numerica...