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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).
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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.
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