The instability of a viscous sheet floating on an air cushion

The dynamics of a thin sheet of viscous liquid levitating on an air cushion is studied. Experimentally, it is observed that, after an initial settling stage, a local disturbance grows, eventually leading to the sheet blowing up like a viscous balloon. We derive a dynamical model for the levitating sheet and propose a mechanism for the onset of the instability. This instability is driven by the local drainage of the sheet due to a growing disturbance on its lower surface and is moderated by surface tension, the bending stiffness of the sheet and advection in the air layer. The balance between these effects determines the most unstable wavelength and this is illustrated by some numerical simulations

Asymptotics of large bound states of localized structures

We analyze stationary fronts connecting uniform and periodic states emerging from a pattern-forming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale expansion. We apply the method to the Swift-Hohenberg equation and derive analytically a snaking bifurcation curve. At each fold of this bifurcation curve, a new pair of peaks is added to the periodic domain, which can thus be seen as a bound state of localized structures. Such scenarios have been reported with optical localized structures in nonlinear cavities and localized buckling

Inertial levitation

We consider the steady levitation of a rigid plate on a thin air cushion with prescribed injection velocity. This injection velocity is assumed to be much larger than that in a conventional Prandtl boundary layer, so that inertial effects dominate. After applying the classical ‘blowhard’ theory of Cole & Aroesty (1968) to the two-dimensional version of the problem, it is shown that in three dimensions the flow may be foliated into streamline surfaces using Lagrangian variables. An example is given of how this may be exploited to solve the three-dimensional problem when the injection pressure distribution is known

Bouncing localized structures in a liquid-crystal light-valve experiment

Experimental evidence of bouncing localized structures in a nonlinear optical system is reported.Comment: 4 page

A new model for passive mode-looking in a semiconductor laser

We propose a new model for passive mode-locking that is a set of ordinary delay differential equations. We assume the ring cavity geometry and a Lorentzian spectral filtering of the pulses, but do not use small gain and loss and weak saturation approximations. By means of a continuation method we study mode-locking solutions and their stability. We found that stable mode-locking can exist even when the non-lasing state between pulses becomes unstable

Nonvariational real Swift-Hohenberg equation for biological, chemical, and optical systems

We derive asymptotically an order parameter equation in the limit where nascent bistability and long-wavelength modulation instabilities coalesce. This equation is a variant of the Swift-Hohenberg equation that generally contains nonvariational terms of the form ψ ∇2 ψ and ∫∇ψ ∫2. We briefly review some of the properties already derived for this equation and derive it on three examples taken from chemical, biological, and optical contexts. Finally, we derive the equation on a general class of partial differential systems. © 2007 American Institute of Physics.info:eu-repo/semantics/publishe

Bragg localized structures in a passive cavity with transverse refractive index modulation

We consider a passive nonlinear optical cavity containing a photonic crystal inside it. The cavity is driven by a superposition of the two coherent beams forming a periodically modulated pump. Using a coupled mode reduction and direct numerical modeling of the full system we demonstrate existence of resting and moving transversely localized structures of light in this system

Control and removing of modulational instabilities in low dispersion photonic crystal fiber cavities

Taking up to fourth order dispersion effects into account, we show that fiber resonators become stable for large intensity regime. The range of pump intensities leading to modulational instability becomes finite and controllable. Moreover, by computing analytically the thresholds and frequencies of these instabilities, we demonstrate the existence of a new unstable frequency at the primary threshold. This frequency exists for arbitrary small but nonzero fourth order dispersion coefficient. Numerical simulations for a low and flattened dispersion photonic crystal fiber resonator confirm analytical predictions and opens the way to experimental implementation

A model for the break-up of a tuft of fibers

A simple model for the forces acting on a single fiber as it is withdrawn from a tangled fiber assembly is proposed. Particular emphasis is placed on understanding the dynamics of the reptating fiber with respect to the entanglement of fibers within the tuft. The resulting two-parameter model captures the qualitative features of experimental simulation. The model is extended to describe the break-up of a tuft. The results show good agreement with experiment and indicate where a fiber is most likely to fracture based on the density of fiber end-points