Hie
Tae Moon
Korea Advance Institute of Science and Technology
Non-equilibrium
process in pattern selection
When the
question
“Is
the solar system stable?
”
was first raised by King Oscar II, Poincar
é
realized that the question
ultimately led us to the fundamental mathematical question
“Is a
periodic orbit stable?
”“How a periodic orbit
or state loses its stability in a
continuous medium?
”
As a play ground, we consider the Stokes wave, an homogeneous
periodic state that appears generically in weakly nonlinear dispersive
media,
and analyze the non-equilibrium process of pattern formation/selection
taking
place beyond the threshold of instability. We consider the situation of
Hamiltonian limit as well as the situation under dissipation. In both
cases we
analyze topologically completely the non-equilibrium process associated
with
patterns, which therefore bears certain generic significance.