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Spiral wave patterns observed in models of cardiac arrhythmias and chemical oscillations develop alternans and stationary line defects, which can both be thought of as period-doubling instabilities. These instabilities are observed on…
Leakage channel fibers, designed to suppress higher-order modes, demonstrate resonant power loss at certain critical radii of curvature. Outside the resonance, the power recovers to the levels offset by the usual mechanism of bend-induced…
We study bond-order parameters for generalized $t$-$J$ models on a square lattice. Using the plane-wave limit the considered order parameters form basis functions for irreducible representations of the symmetry transformations of the point…
For some synchrotron light source beamline applications, a round beam is preferable to a flat one. A conventional method of obtaining round beam in an electron storage ring is to shift its tune close to a linear difference resonance. The…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem…
We study collective processes for an electron beam propagating through a background plasma using simulations and analytical theory. A new regime where the instability of a Langmuir wave packet can grow locally much faster than ion frequency…
We describe spontaneous symmetry breaking in the powers of two optical modes coupled into a ring resonator, using a pair of coupled Lorentzian equations, featuring tunable self- and cross-phase modulation terms. We investigate a wide…
Rotational superradiance was predicted theoretically decades ago, and is chiefly responsible for a number of important effects and phenomenology in black-hole physics. However, rotational superradiance has never been observed…
A novel regime of atom-cavity physics is explored, arising when large atom samples dispersively interact with high-finesse optical cavities. A stable far detuned optical lattice of several million rubidium atoms is formed inside an optical…
We describe the emergence and interactions of breather modes and resonant wave modes within a two-dimensional ring-like oscillator chain in a microcanonical situation. Our analytical results identify different dynamical regimes…
A blowup of vertical emittance has been observed in particle tracking simulations with beam-beam and lattice misalignments. It was somewhat unexpected, since estimation without lattice errors did not predict such a blowup unless a residual…
The stability of a rotating fluid disk to the formation of spiral arms is studied in the tightwinding approximation in the linear regime. The dispersion relation for spirals that was derived by Bertin et al. is shown to contain a new,…
PT-symmetric optical resonators combine absorbing regions with active, amplifying regions. The latter are the source of radiation generated via spontaneous and stimulated emission, which embodies quantum noise and can result in lasing. We…
Flows forced by a precessional motion can exhibit instabilities of crucial importance, whether they concern the fuel of a flying object or the liquid core of a telluric planet. So far, stability analyses of these flows have focused on the…
Resonances usually result from wave superpositions in cavities where they are due to the wave spatio-temporal folding imposed by the boundaries. These energy accumulations are the signature of the cavity eigenmodes. Here we study a…
Three-mode parametric interactions occur in triply-resonant optomechanical systems: photons from an optical pump mode are coherently scattered to a high-order mode by mechanical motion of the cavity mirrors, and these modes resonantly…
Dynamics of an array of line defects interacting with a background elastic medium is studied in the linear regime. It is shown that the inertial coupling between the defects and the ambient phonons leads to an anomalous response behavior…
We studied the transverse beam dynamics including aberration effects of sextupole and octupole perturbations in a thermal wave model. A functional integration method was used to calculate the first-order perturbation effects. We found that…
Extensive studies have investigated the transition mechanism of boundary layers initiated by a single primary instability. In a real-world scenario, however, multiple primary instabilities of different physical nature would coexist and…