Ordering and patterns
Pattern formation is related to a system which is kept out-of-equilibrium and a heat, mass, momentum macroscopic current is imposed via boundary conditions. Because of that the homogeneous state of the system (typical of its equilibrium condition) is made unstable. Instead, Phase ordering appears when the initial and final state of a relaxing system are separated by a critical point.
Research ranges over different lines: from extended interactions in phase separtion processes to the relevance of conservation laws in strongly out-of-equilibrium systems, from noise tto feedback effects in pattern forming systems.
F. Di Patti, L. Lavacchi, R. Arbel-Goren, L. Schein-Lubomirsky, D. Fanelli, J. Stavans:
PLoS Biology 16(5): e2004877 (2018)
A mathematical model is proposed that explains the formation mechanism of the cellular pattern in Anabaena, a bacterium that carries out photosynthesis. Anabaena is a one dimensional filament, made of adjacent cells. In normal environmental conditions (in the presence of nitrogen) the bacterium is mostly formed by vegetative cells. In the absence of nitrogen, however, is able to differentiate some vegetative cells in others specialized in nitrogen fixation. This differentiation occurs following a certain regularity: every 10–15 vegetative cells, a heterocyst one is formed. This ingenious biological process guarantees the necessary nitrogen supply to all the cells that make up the Anabaena filament. The process of pattern formation is triggered by endogenous noise: microscopic disturbances yields therefore regular macroscopic motifs.
Iubini S, Chirondojan L, Oppo G, Politi A, Politi P:
arXiv (2018) [PDF]
Several examples of slow relaxation exist, the most famous one is due to quenched disorder which determines a very irregular free energy profile. Here we discuss an example where slow relaxation is a purely dynamic effect induced by conserved and quasi conserved quantities. Mass and energy conservation can induce the formation of localized excitations whose relaxation dynamics is almost frozen, if an adiabatico invariant (a quasi conserved quantity) exists.
In the figure we show that relaxation time increases exponentially with breather size and that such process is accompanied by the hopping of the breather.