We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601-1 (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 approximatio...

The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on the basis of spatio-temporal pattern formation by local contraction-oscillators. This biological system can be regarded as a reaction-diffusion system which has spatial interaction by active flow of protoplasmic sol in the cell. Paying attention to the physiological evidence that the flow is determined by contraction pat...

A quasi-potential approximation to the Navier-Stokes equation for low viscosity uids is developed to study pattern formation in parametric surface waves driven by a force that has two frequency components. A bicritical line separating regions of instability to either one of the driving frequencies is explicitly obtained, and compared with experiments involving a frequency ratio of 1/2. The proc...

– A novel pattern forming instability in a mixture of a granular material and water in a horizontal rotating drum is experimentally investigated. The particles accumulate in radial symmetric rings separated by pure water. The transition between the homogeneous state and the structured state is hysteretic. The transition point is extrapolated from the growth rates of the chain of rings. The traj...

We present a system for pattern formation in networks that is inspired by biological development. The system hierarchically forms a specific pattern in a rough-to-detail manner as seen in biological development. We apply the system to generating gray-scaled images. In this application, a network topology is first generated from a given original image in which pixels correspond to network nodes ...

We present the first of two articles on the small volume fraction limit of a nonlocal Cahn–Hilliard functional introduced to model microphase separation of diblock copolymers. Here we focus attention on the sharp-interface version of the functional and consider a limit in which the volume fraction tends to zero but the number of minority phases (called particles) remains O(1). Using the languag...