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.
Spatio-temporal phenomena in complex systems with time delays
Serhiy Yanchuk and Giovanni Giacomelli
J. Phys. A: Math. Theor. 50 103001 (2017) [PDF]
Propagation delays in the loop arms of feedback cannot always be neglected in the study of dynamical systems. Complex phenomena have shown to occur in such a case, when the delay is comparable with the internal timescale of the solitary system. A regime of particular interest is represented by the so-called long-delayed systems, where the delay time is much longer that any other timescale. The complicated temporal series resulting from the dynamics can be organized by means of a specific method, named spatio-temporal reconstruction. It allows to map the data on an equivalent pattern which can be thus analyzed in the framework of the spatially extended systems. Several phenomena in different systems have been studied in such an approach, ranging from phase and defect turbulence, chaos, bistable and excitable front dynamics to coarsening and nucleation to directed percolation.