Robust Phenomena

Life develops on scales where matter is macroscopic (made up of many microscopic constituents) and is in a constant exchange of energy, momentum, and matter, out-of-equilibrium systems. The understanding of physics on these scales has adopted two main strategies: understanding behavior from its microscopic constituents (equilibrium and non-equilibrium statistical physics) and understanding it as a whole, recognizing the relevant variables and their models, Nonlinear physics.

The phenomena that more have captivated me, in my contact with the science, are Robust phenomena, that is, phenomena that do not depend on underlying Physics, hence appear in several physical systems, for instance, pattern formation. The patterns are self-organized structures which exist under non-equilibrium conditions. Surprisingly ordered non-equilibrium patterns are found in many different places in nature, including convection cells in fluids, the transverse section in a semiconductor laser, spiral in oscillatory chemical reactions, ripples on the blown sand, and in many biological and geological processes. The understanding of these phenomena is associated with the study of the qualitative behavior of differential equations, that is, a geometrical understanding of differential equations. H. Poincaré iniciated this study.

The main goal of Nonlinear Physics is the understanding and application of robust phenomena to different the branch of natural sciences.

Henri Poincare (Pioneer of chaos phenomenon):"De très petites différences initiales entre leurs distances au soleil, ou ce qui revient au même entre leurs mouvements moyens, on fini par donner d'énormes différences entre leurs longitudes actuelles; une excès d'un millième de seconde dans le moyen mouvement diurne, donnera en effet une seconde en trois ans, un degré en dix mille ans, une circonférence entière en trois ou quatre millions d'années, et qu`est-ce que cela auprès du temps qui s'est écoulé depuis que les petites planètes se sont détachées de la nébuleuse de Laplace? Voici donc une fois de plus une petite cause et un grand effet ; ou mieux, de petites différences dans la cause et de grandes différences dans l'effet." (Science et Méthode, 1914).

Nonlinear Physics: Mechanics, Nonlinear Optic, Liquid Crystals, Fluid dynamics, Magnetic Systems, Statistical mechanics, Stochastic process, Granular media, Non equilibrium systems, Bifurcation and Dynamical Systems Theory.
  Physics, Chemistry, Biology, and Mathematics.  
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