Characterization and modeling of aperiodic pressure oscillations in combustion chambers

Classification of the long-term dynamical behavior of pressure oscillations in a laboratory combustion chamber has been performed using methods of modern dynamical systems theory. The method involves the construction of a phase-space representation from a single pressure record or time series using the time-delay embedding method. The pointwise correlation dimension of the resulting attractor in phase-space provides a lower bound on the number of modes that participate in the oscillations. The results show that the oscillations are quasiperiodic with a dimension near two over an order of magnitude of amplitudes. Quasiperiodicity is a result of the incommensurate frequencies of the system acoustic modes. A model for the dynamics is constructed by converting the governing equations to a kicked-oscillator model. When compared with the experimental data, the model results have similar pressure and velocity spectra and the attractor dimension verifies that quasiperiodic oscillations are present

Self-generated and externally driven current oscillations in n-GaAs

Experimental investigations of self-generated and externally driven non-linear current oscillations due to impact ionization of shallow impurities in n-type GaAs at low temperatures are presented. The regular relaxation oscillations which appear at the onset of breakdown are destabilized by a magnetic field normal to the epitaxial layer and multifrequency oscillations and chaotic fluctuations following the Ruelle-Takens-Newhouse scenario can be found. Driving the self-generated oscillations with an external periodic bias voltage quasiperiodicity, mode locking, interaction and overlap of mode locked resonances and period doubling can be observed depending on frequency and amplitude of the external force. The reconstructed return maps, recorded phase diagrams and Devil's staircase agree with theoretical predictions based on the circle map and give new evidence of the universality of the transition from quasiperiodicity to chaos

Bose-Einstein Condensates in Optical Quasicrystal Lattices

We analyze the physics of Bose-Einstein condensates confined in 2D quasi-periodic optical lattices, which offer an intermediate situation between ordered and disordered systems. First, we analyze the time-of-flight interference pattern that reveals quasi-periodic long-range order. Second, we demonstrate localization effects associated with quasi-disorder as well as quasiperiodic Bloch oscillations associated with the extended nature of the wavefunction of a Bose-Einstein condensate in an optical quasicrystal. In addition, we discuss in detail the crossover between diffusive and localized regimes when the quasi-periodic potential is switched on, as well as the effects of interactions

Quasiperiodic Envelope Solitons

We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally.Comment: Submitted to PRL. 4 pages with 5 figure