Related papers: Spatiotemporal patterns in a DC semiconductor-gas-…
A semiclassical model of charge transport in a semiconductor superlattice is solved, using moments in the wavenumber direction and finite elements in the spatial direction (first order). The selection of numerical methods guarantees the…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced…
The spurious states found in numerical implementations of envelope function models for semiconductor heterostructures and nanostructures have been shown to be readily removed by employing a first-order difference scheme. This approach is…
A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class…
A space-time crystal has recently been observed in a superfluid Bose gas. Here we construct a variational model that allows us to describe from first principles the coupling between the radial breathing mode and the higher-order axial modes…
A suspension of swimming microorganisms often generates a large-scale convective pattern known as bioconvection. In contrast to the thermal Rayleigh-Benard system, recent experimental studies report an emergence of steady localized…
It has been recently observed that synthetic materials subjected to an external elastic stress give rise to scaling phenomena in the acoustic emission signal. Motivated by this experimental finding we develop a mesoscopic model in order to…
We study the stability of a vector field associated to a nearly-integrable Hamiltonian dynamical system to which a dissipation is added. Such a system is governed by two parameters, named the perturbing and dissipative parameters, and it…
A distributed Kerr-lens mode locking regime can be realized in a waveguide laser by spatial profiling of the pump beam, thus creating a spatio-temporal soliton. Additional slow temporal modulation of the pump source stabilizes the…
We study the Swift-Hohenberg equation - a paradigm model for pattern formation - with "large" spatially periodic coefficients and find a Turing bifurcation that generates patterns whose leading order form is a Bloch wave modulated by…
The study and characterization of the diversity of spatiotemporal patterns generated when a rectangular layer of fluid is locally heated beneath its free surface is presented. We focus on the instability of a stationary cellular pattern of…
Without our ability to model and manipulate the band structure of semiconducting materials, the modern digital computer would be impractically large, hot, and expensive. In the undergraduate QM curriculum, we studied the effect of spatially…
In this paper, we study the dynamic formation of transients when plane waves impinge on a dispersive slab that abruptly changes its electrical properties in time. The time-varying slab alternates between air and metal-like states, whose…
The most common method to characterize the electrical response of a nanofluidic system is through its steady-state current-voltage response. In Part I, we demonstrated that this current-voltage response depends on the geometry, the layout…
Semiconductor microcavities, in which strong coupling of excitons to confined photon modes leads to the formation of exciton-polariton modes, have increasingly become a focus for the study of spontaneous coherence, lasing, and condensation…
Crystals spontaneously break the continuous translation symmetry in space, despite the invariance of the underlying energy function. This has triggered suggestions of time crystals analogously lifting translational invariance in time.…
Patterns are quotidian in nature. Distinct multiscale patterns are generally a consequence of nonequilibrium dynamical processes associated with mechanical or hydrodynamic instabilities. In this thesis, I report experimental investigations…
Interference patterns associated with soliton-soliton interaction are investigated in detail. We find that the temporal and spatial interference patterns exhibit quite different characteristics. The period of the spatial interference…
We report the first experimental observation of multi-stable states in a single-longitudinal mode semiconductor ring laser. We show how the operation of the device can be steered to either monostable, bistable or multi-stable dynamical…