Localised structures and pattern formation in heterogenous nonlinear systems
Instituto de Física, Pontificia Universidad Católica de Valparaíso (2018)
Characterization of Faraday pattern bifurcation subject to a heterogenous localized injection
Instituto de Física, Pontificia Universidad Católica de Valparaíso (2019)
Ondas de Faraday con inyección localizada en una celda cuasi-unidimensional
Instituto de Física, Pontificia Universidad Católica de Valparaíso (2016)
Estudio numérico de estabilidad de solitones en un sistema paramétrico inhomogéneo
For many nonlinear dissipative systems, theoretical methods have been developed under ideal considerations as, uniform and homogeneous injection, non-boundary conditions, infinite systems, to mention a few. In the nonlinear regime, away from the bifurcation, numerical simulations allow grasping the dynamics under real conditions as boundaries effects, the presence of defects, and heterogeneous media. Propagation failure of fronts, oscillations, dissipation-driven behavior in finite systems, nucleation of stable structures, and chaotic behavior are examples of effects in systems under non-ideal conditions. The main goal of the present work is to study theoretically, numerically, and experimentally the dynamical behavior of nonlinear out-of-equilibrium systems in heterogeneous media. In particular, aim to explore two main questions, robust Rabi oscillations in dissipative out-of equilibrium systems and Faraday waves dynamics on a periodic localized substrate.
The theoretical and numerical studies focus on a well known but yet not fully explored amplitude equation model under heterogeneous spatial conditions (PDNLS). We expect to broaden the knowledge on out-of-equilibrium systems through the theoretical description on the onset of new instabilities caused by spatial heterogeneities. This is combined with a low-cost, versatile experiment where dynamical exploration on pattern formation and localized structures under non-uniform conditions can be studied. We propose modifications and technical improvements on the setup, which will bring us the opportunity to mimics physical conditions on a controlled but still out-of-equilibrium environment.