1,979 research outputs found
Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I: General presentation and periodic solutions
We present experimental results on hydrothermal traveling-waves dynamics in
long and narrow 1D channels. The onset of primary traveling-wave patterns is
briefly presented for different fluid heights and for annular or bounded
channels, i.e., within periodic or non-periodic boundary conditions. For
periodic boundary conditions, by increasing the control parameter or changing
the discrete mean-wavenumber of the waves, we produce modulated waves patterns.
These patterns range from stable periodic phase-solutions, due to supercritical
Eckhaus instability, to spatio-temporal defect-chaos involving traveling holes
and/or counter-propagating-waves competition, i.e., traveling sources and
sinks. The transition from non-linearly saturated Eckhaus modulations to
transient pattern-breaks by traveling holes and spatio-temporal defects is
documented. Our observations are presented in the framework of coupled complex
Ginzburg-Landau equations with additional fourth and fifth order terms which
account for the reflection symmetry breaking at high wave-amplitude far from
onset. The second part of this paper (nlin.PS/0208030) extends this study to
spatially non-periodic patterns observed in both annular and bounded channel.Comment: 45 pages, 21 figures (elsart.cls + AMS extensions). Accepted in
Physica D. See also companion paper "Nonlinear dynamics of waves and
modulated waves in 1D thermocapillary flows. II: Convective/absolute
transitions" (nlin.PS/0208030). A version with high resolution figures is
available on N.G. web pag
Interaction of Ising-Bloch fronts with Dirichlet Boundaries
We study the Ising-Bloch bifurcation in two systems, the Complex Ginzburg
Landau equation (CGLE) and a FitzHugh Nagumo (FN) model in the presence of
spatial inhomogeneity introduced by Dirichlet boundary conditions. It is seen
that the interaction of fronts with boundaries is similar in both systems,
establishing the generality of the Ising-Bloch bifurcation. We derive reduced
dynamical equations for the FN model that explain front dynamics close to the
boundary. We find that front dynamics in a highly non-adiabatic (slow front)
limit is controlled by fixed points of the reduced dynamical equations, that
occur close to the boundary.Comment: 10 pages, 8 figures, submitted to Phys. Rev.
Transitions between dissipative localized structures in the simplified Gilad-Meron model for dryland plant ecology
Spatially extended patterns and multistability of possible different states
is common in many ecosystems, and their combination has an important impact on
their dynamical behaviours. One potential combination involves tristability
between a patterned state and two different uniform states. Using a simplified
version of the Gilad-Meron model for dryland ecosystems, we study the
organization, in bifurcation terms, of the localized structures arising in
tristable regimes. These states are generally related with the concept of wave
front locking, and appear in the form of spots and gaps of vegetation. We find
that the coexistence of localized spots and gaps, within tristable
configurations, yield the appearance of hybrid states. We also study the
emergence of spatiotemporal localized states consisting in a portion of a
periodic pattern embedded in a uniform Hopf-like oscillatory background in a
subcritical Turing-Hopf dynamical regime
Dissipative solitons in pattern-forming nonlinear optical systems : cavity solitons and feedback solitons
Many dissipative optical systems support patterns. Dissipative solitons are generally found where a pattern coexists with a stable unpatterned state. We consider such phenomena in driven optical cavities containing a nonlinear medium (cavity solitons) and rather similar phenomena (feedback solitons) where a driven nonlinear optical medium is in front of a single feedback mirror. The history, theory, experimental status, and potential application of such solitons is reviewed
Bifurcations and chaos in semiconductor superlattices with a tilted magnetic field
We study the effects of dissipation on electron transport in a semiconductor
superlattice with an applied bias voltage and a magnetic field that is tilted
relative to the superlattice axis.In previous work, we showed that although the
applied fields are stationary,they act like a THz plane wave, which strongly
couples the Bloch and cyclotron motion of electrons within the lowest miniband.
As a consequence,the electrons exhibit a unique type of Hamiltonian chaos,
which creates an intricate mesh of conduction channels (a stochastic web) in
phase space, leading to a large resonant increase in the current flow at
critical values of the applied voltage. This phase-space patterning provides a
sensitive mechanism for controlling electrical resistance. In this paper, we
investigate the effects of dissipation on the electron dynamics by modifying
the semiclassical equations of motion to include a linear damping term. We
demonstrate that even in the presence of dissipation,deterministic chaos plays
an important role in the electron transport process. We identify mechanisms for
the onset of chaos and explore the associated sequence of bifurcations in the
electron trajectories. When the Bloch and cyclotron frequencies are
commensurate, complex multistability phenomena occur in the system. In
particular, for fixed values of the control parameters several distinct stable
regimes can coexist, each corresponding to different initial conditions. We
show that this multistability has clear, experimentally-observable, signatures
in the electron transport characteristics.Comment: 14 pages 11 figure
Dynamics of Coupled Maps with a Conservation Law
A particularly simple model belonging to a wide class of coupled maps which
obey a local conservation law is studied. The phase structure of the system and
the types of the phase transitions are determined. It is argued that the
structure of the phase diagram is robust with respect to mild violations of the
conservation law. Critical exponents possibly determining a new universality
class are calculated for a set of independent order parameters. Numerical
evidence is produced suggesting that the singularity in the density of Lyapunov
exponents at is a reflection of the singularity in the density of
Fourier modes (a ``Van Hove'' singularity) and disappears if the conservation
law is broken. Applicability of the Lyapunov dimension to the description of
spatiotemporal chaos in a system with a conservation law is discussed.Comment: To be published in CHAOS #7 (31 page, 16 figures
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