The present work reports thermo-acoustic instability in a mesoscale tube of diameter 8 mm (> quenching diameter) and length 702 mm. Mixtures with Lewis number, Le~ 0.8 (rich C2H4/O2/CO2), 1.05 (lean C2H4/O2/CO2) 1.34 C2H4/O2/N2) are used. Several new flame responses observed. For lower burning velocity mixtures, extinction is observed due to heat loss when primary transforms secondary for all L...

A shear Alfvén wave parametric instability is observed for the first time in the laboratory. When a single finite ω/Ω_{i} kinetic Alfvén wave (KAW) is launched in the Large Plasma Device above a threshold amplitude, three daughter modes are produced. These daughter modes have frequencies and parallel wave numbers that are consistent with copropagating KAW sidebands and a low frequency nonresona...

We theoretically investigate the generation of spatial patterns in intracavity second-harmonic generation. We consider a cavity with planar mirrors that is resonant at the fundamental frequency, but not at the secondharmonic frequency. A mean-field model is derived that describes the resonant fundamental field, and its coupling to a pair of nondegenerate parametric fields. The parametric fields...

Abstract. We study the effects of periodically time varying mass on the stability of the Helmholtz oscillator, which, when linearised, takes the form of Ince’s equation and exhibits parametric resonance. The resonance regions in the parameter space are mapped and we use the Melnikov function to demonstrate that the parametric instability does not affect the qualitative dynamics of the nonlinear...

We discuss the parametric instabilities of large-amplitude parallel propagating Alfvén waves using the 2-D PIC simulation code. First, we confirmed the results in the past study [Sakai et al., 2005] that the electrons are heated due to the modified two stream instability and that the ions are heated by the parallel propagating ion acoustic waves. However, although the past study argued that suc...

Coexistence The special case when all the independent solutions of a linear, T -periodic ODE are T -periodic. Hill’s equation A second order ODE of the form ẍ + p(t)x = 0, with p(t) T -periodic. Instability pockets Finite domains, usually intersections of instability tongues, where the trivial solution of linear, T -periodic ODEs is unstable. Instability tongues Domains in parameter space where...

Using an example of cavity solitons in optical parametric oscillators it is demonstrated that Hopf instability of these dissipative structures can be directly associated with internal modes of their conservative counterparts. The latter ones are free propagating quadratic solitons in this case. Linear stability analysis and numerical simulation also reveal multistability and complex instability...