Bicritical points at wave numbers k(b) larger than the critical wave numbers k(c) are found in parametric surface waves (Faraday waves) using both numerical simulations and nonlinear analysis. Because k(b)-k(c) is small, it is argued that subcritical bifurcations at k>k(b) can be easily observed in experiments. In the second part we present a generic argument predicting the existence of nonline...

In inertial confinement fusion (ICF), where irradiation uniformity is a crucial issue, it is important to understand the process of laser-filamentation instability.' The breakup of laser light into filaments occurs as a result of plasma density depressions that form localized focusing channels. The density depressions may be caused either by ponderomotive forces2 due to laserplasma interactions...

Machine tool chatter causes an instability that can occur in tool-workpiece-machine system. Hence surface roughness and tool wear in metal cutting processes. This instability caused by interaction between current tool positions and surface left by previous tool passes. Many methods have been developed to minimize the effects of regenerative chatter in machine tools and to enhance the damping ca...

Non-linear interactions among the inertial modes of a rotating fluid can be described by a network of coupled oscillators. We use such a description for an incompressible fluid to study the development of the r-mode instability of rotating neutron stars. A previous hydrodynamical simulation of the r-mode reported the catastrophic decay of large amplitude r-modes. We explain the dynamics and tim...

We demonstrate that a weak defocusing Kerr effect in an optical medium with predominantly quadratic [or chi((2))] nonlinear response can eliminate the parametric modulational instability of plane waves, leading to the existence of stable two-wave dark and vortex spatial solitons.

Optical frequency conversion by four-wave mixing (Bragg scattering) in a fiber is considered. If the frequencies and polarizations of the waves are chosen judiciously, Bragg scattering enables the translation of individual and entangled states, without the noise pollution associated with parametric amplification (modulation instability or phase conjugation), and with reduced noise pollution ass...

This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with the actual values computed numerically corroborates the intuition that chaos in such systems can be understood as arising generically from a parametric instab...

The problem of the influence of the structure of forces on the stability of the relative equilibrium of a controlled satellite with a gravitational stabilizer on the circular orbit is studied. In the space of entered parameters, the regions with different degrees of instability by Poincaré are found. Assuming an instability of a potential system, the problem of the possibility of its stabilizat...