176 research outputs found
Dissipation-induced instabilities in an optical cavity laser: A mechanical analog near the 1:1 resonance
The 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms has been studied. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities. This mechanism allows one to show that an optical cavity with small pumping is unstable when one takes into account the dissipative effects. The Maxwell-Bloch equations are the asymptotic normal form that describe this instability when energy is injected through forcing at zero frequency. A simple mechanical system close to the 1:1 resonance has been displayed, which is a mechanical analog of the laser
Spin-transfer-driven nano-oscillators are equivalent to parametric resonators
The equivalence between different physical systems permits us to transfer
knowledge between them and to characterize the universal nature of their
dynamics. We demonstrate that a nanopillar driven by a spin-transfer torque is
equivalent to a rotating magnetic plate, which permits us to consider the
nanopillar as a macroscopic system under a time-modulated injection of energy,
that is, a simple parametric resonator. This equivalence allows us to
characterize the phases diagram and to predict magnetic states and dynamical
behaviors, such as solitons, stationary textures, and oscillatory localized
states, among others. Numerical simulations confirm these predictions.Comment: 8 pages, 7 figure
Transversal interface dynamics of a front connecting a stripe pattern to a uniform state
Interfaces in two-dimensional systems exhibit unexpected complex dynamical
behaviors, the dynamics of a border connecting a stripe pattern and a uniform
state is studied. Numerical simulations of a prototype isotropic model, the
subcritical Swift-Hohenberg equation, show that this interface has transversal
spatial periodic structures, zigzag dynamics and complex coarsening process.
Close to a spatial bifurcation, an amended amplitude equation and a
one-dimensional interface model allow us to characterize the dynamics exhibited
by this interface.Comment: 4 pages. To be published in Europhysics Letter
Extended patchy ecosystems may increase their total biomass through self-replication
Patches of vegetation consist of dense clusters of shrubs, grass, or trees,
often found to be circular characteristic size, defined by the properties of
the vegetation and terrain. Therefore, vegetation patches can be interpreted as
localized structures. Previous findings have shown that such localized
structures can self-replicate in a binary fashion, where a single vegetation
patch elongates and divides into two new patches. Here, we extend these
previous results by considering the more general case, where the plants
interact non-locally, this extension adds an extra level of complexity and
shrinks the gap between the model and real ecosystems, where it is known that
the plant-to-plant competition through roots and above-ground facilitating
interactions have non-local effects, i.e. they extend further away than the
nearest neighbor distance. Through numerical simulations, we show that for a
moderate level of aridity, a transition from a single patch to periodic pattern
occurs. Moreover, for large values of the hydric stress, we predict an opposing
route to the formation of periodic patterns, where a homogeneous cover of
vegetation may decay to spot-like patterns. The evolution of the biomass of
vegetation patches can be used as an indicator of the state of an ecosystem,
this allows to distinguish if a system is in a self-replicating or decaying
dynamics. In an attempt to relate the theoretical predictions to real
ecosystems, we analyze landscapes in Zambia and Mozambique, where vegetation
forms patches of tens of meters in diameter. We show that the properties of the
patches together with their spatial distributions are consistent with the
self-organization hypothesis. We argue that the characteristics of the observed
landscapes may be a consequence of patch self-replication, however, detailed
field and temporal data is fundamental to assess the real state of the
ecosystems.Comment: 38 pages, 12 figures, 1 tabl
Spontaneous motion of localized structures induced by parity symmetry transition
We consider a paradigmatic nonvariational scalar Swift-Hohenberg equation
that describes short wavenumber or large wavelength pattern forming systems.
This work unveils evidence of the transition from stable stationary to moving
localized structures in one spatial dimension as a result of a parity breaking
instability. This behavior is attributed to the nonvariational character of the
model. We show that the nature of this transition is supercritical. We
characterize analytically and numerically this bifurcation scenario from which
emerges asymmetric moving localized structures. A generalization for
two-dimensional settings is discussed.Comment: 7 pages, 6 figure
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