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Vertical oscillation of a fluid interface above a critical amplitude excites the Faraday instability, typically manifesting itself as a standing wave pattern. Fundamentally, the phenomenon is an example of parametric resonance. At high…
We present theoretical and experimental studies of the size and thickness dependencies of the optical emission spectra from microcavities with hexagonal shape in films of two-dimensional photonic crystal. A semiclassical plane-wave model,…
We develop a statistical description of chaotic wavefunctions in closed systems obeying arbitrary boundary conditions by combining a semiclassical expression for the spatial two-point correlation function with a treatment of eigenfunctions…
The observation of anomalously large polarization rotations in pump-probe experiments with circularly polarized light has recently challenged the conventional understanding of the inverse Faraday effect. The striking magnitude of these…
The statistical evolution of ensembles of random, weakly-interacting waves is governed by wave kinetic equations. To simplify the analysis, one frequently works with reduced differential models of the wave kinetics. However, the conditions…
In this third of a series of four articles, we continue the study of the representations of the hamiltonian dynamical transformations of systems of correlated quantized oscillators. By our use of generalized wave function solutions to…
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in…
For real symmetric positive definite matrices $A$ and $B$, we characterize when a function $f \in L^2(\mathbb{R}^d)$ satisfies \[ |f(x)| \lesssim e^{-(\frac12 - \lambda) \langle Ax, x\rangle} \quad \text{and} \quad |\widehat{f}(\xi)|…
We study the properties of wave functions and the wave-packet dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds…
Turbulence is a dominant feature operating in gaseous flows across nearly all scales in astrophysical environments. Accordingly, accurately estimating the statistical properties of such flows is necessary for developing a comprehensive…
We study the generation of 2D turbulence in Faraday waves by investigating the creation of spatially periodic vortices in this system. Measurements which couple a diffusing light imaging technique and particle tracking algorithms allow the…
Similarities between quantum systems and analogous systems for classical waves have been used to great effect in the physics community, be it to gain an intuition for quantum systems or to anticipate novel phenomena in classical waves. This…
We study the propagation of low frequency shallow water waves on a one dimensional flow of varying depth. When taking into account dispersive effects, the linear propagation of long wavelength modes on uneven bottoms excites new solutions…
We determine the statistical properties of wave functions in disordered quantum systems by exact diagonalization of one-, two- and quasi-one dimensional tight-binding Hamiltonians. In the quasi-one dimensional case we find that the tails of…
We study parametric resonance of interacting waves having the same wave vector and frequency. In addition to the well-known period-doubling instability we show that under certain conditions the instability is caused by a Hopf bifurcation…
We examine the hydrodynamics of systems with spontaneously broken multipolar symmetries using a systematic effective field theory. We focus on the simplest non-trivial setting: a system with charge and dipole symmetry, but without momentum…
We study the possibility of complex tensor ($d$-wave) superconducting order in three-dimensional semimetals with chiral spin-1/2 triple-point fermions, which have an effective orbital angular momentum of $L=1$ arising from a crossing of…
Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…
We investigate the broadband turbulent dynamics of attached and separated flows over a Gaussian bump, focusing on the origin of low-frequency coherent structures. The analysis combines time-resolved experimental measurements with…
In the study of weakly turbulent wave systems possessing incomplete self-similarity it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave…