Robust effects of noise.
Nondiabatic effect and pinning.
Inertial effects for thin viscous fluid layers near a solid wal.
Noise induced transition is an unexpected phenomena leading to
the appearance of equilibrium states. Localized patterns are the most studied
localized structures. When noise is added the patterns propagate or shrink over
the homogeneous state, that is, noise induces the propagation of fronts giving
rise to the appearance of patterns. Close to spatial bifurcation, below the
threshold, noise induces the appearance of localized structures.
This current project proposes to understand the mechanism behind the
propagation induced by noise and noise sustain localized structures close to a
spatial bifurcation. We shall study experimentally this robust phenomenon,
in particular, in a valve of liquid crystal with optical feedback and in a Newtonian
fluid forced with two resonant frequencies (Faraday instability).
People involved
Marcel G Clerc (University of Chile)
Nicolas Mujica (University of Chile)
Stefania Residori (Institut non lineaire de Nice)
Enrique Tirapegui (University of Chile)
We are interested in the defects dynamics, in particular, the front
solution which connect a homogeneous state with a pattern state. In
1986 Y. Pomeau pointed out that these fronts showed a zero speed in a
finite region around the Maxwell point. It was conjectured that this
could be due to nonadiabatic effect produced by nonresonant terms. Two
years after D. Bensimon, B.I. Shraiman, and V. Croquette showed this in
a particular case. Our aim is clarify in general the origin of this
phenomenon and extend the results of the nonadiabatic effect to other
problems.
People involved
Pierre Coullet (Institut non lineaire de Nice)
René Rojas Cortés (University of Chile)
Enrique Tirapegui (University of Chile)
Charles Tresser (IBM)
References
Y. Pomeau, Physica D 23 (1986), 3.
D. Bensimon, B.I. Shraiman, and V. Croquette, Phys.
Rev. A 38 (1988), 5461.
Although a fluid layer can be very thin or viscosity strong, if energy is pumped into the system inertial modes will be excited. Some examples include the viscous hydraulic jump and Faraday instability. We have been sucessful to obtain the minimal linear equations that describe those phenomena, but now our aim is to find the set of equations which contain the full nonlinear behavior.
People involved
Enrique Cerda (Universidad de Santiago)
Nicolas Rojas (Universidad de Chile)
Enrique Tirapegui (Universidad de Chile)
References
“Universal Pinching of 3D Axisymmetric Free Surface Flow”,Eggers, J. 1993.
Physical Review Letters, 71, 3458.
“Faraday Instability for Viscous Fluids”, Cerda, E. and Tirapegui E.,1997.
Physical Review Letters, 78, 859.
“Averaging theory for the structure of hydraulic jumps and separation
in laminar free-surface”, Bohr, T., Putkaradze, V. and
Watanabe, S. 1997. Physical Review Letters, 79,1038-1041.
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