The recent findings confirm that bacteria communicate each other through chemical and electrical signals. Bacteria use chemical signaling molecules which are called as quorum sensing molecules( QSMs) or autoinducers. Moreover, the ion channels in bacteria conduct a long-range electrical signaling within biofilm communities through propagated waves of potassium ions and biofilms attracts other b...

We show that a parametrically driven cubic-quintic complex Ginzburg-Landau equation exhibits a hysteretic nonequilibrium Ising-Bloch transition for large enough quintic nonlinearity. These results help to understand the recent experimental observation of this phenomenon [A. Esteban-Martín, Phys. Rev. Lett. 94, 223903 (2005)].

We consider a Ginzburg-Landau type phase-transition model driven by a p-Laplacian type equation. We prove density estimates for absolute minimizers and we deduce the uniform convergence of level sets and the existence of plane-like minimizers in periodic media.