New DNLS Equations for Anharmonic Vibrational Impurities

We examine some new DNLS-like equations that arise when considering strongly-coupled electron-vibration systems, where the local oscillator potential is anharmonic. In particular, we focus on a single, rather general nonlinear vibrational impurity and determine its bound state(s) and its dynamical selftrapping properties.Comment: 16 pages, 5 figure

Power Switching in Hybrid Coherent Couplers

We report on a theoretical and numerical investigation of the switching of power in new hybrid models of nonlinear coherent couplers consisting of optical slab waveguides with various orders of nonlinearity. The first model consists of two guides with second-order instead of the usual third-order susceptibilities as typified by the Jensen coupler. This second-order system is shown to have a power self-trapping transition at a critical power greater than the third-order susceptibility coupler. Next, we consider a mixed coupler composed of a second-order guide coupled to a third-order guide and show that, although it does not display a rigorous self-trapping transition, for a particular choice of parameters it does show a fairly abrupt trapping of power at a lower power than in the third-order coupler. By coupling this mixed nonlinear pair to a third, purely linear guide, the power trapping can be brought to even lower levels and in this way a satisfactory switching profile can be achieved at less than one sixth the input power needed in the Jensen coupler.Comment: Latex source,17 pages, 5 figure

Set-based approach to passenger aircraft family design

Presented is a method for the design of passenger aircraft families. Existing point-based methods found in the literature employ sequential approaches in which a single design solution is selected early and is then iteratively modified until all requirements are satisfied. The challenge with such approaches is that the design is driven toward a solution that, although promising to the optimizer, may be infeasible due to factors not considered by the models. The proposed method generates multiple solutions at the outset. Then, the infeasible solutions are discarded gradually through constraint satisfaction and set intersection. The method has been evaluated through a notional example of a three-member aircraft family design. The conclusion is that point-based design is still seen as preferable for incremental (conventional) designs based on a wealth of validated empirical methods, whereas the proposed approach, although resource-intensive, is seen as more suited to innovative designs

Vortex evolution in parametric wave mixing

We investigate the evolution of vortex wave front dislocations in multiple-wave second-harmonic generation processes in quadratic nonlinear media. Vortices nested in finite-size host beams are shown to nucleate and to annihilate in pairs, and to move across the transverse wave front during the beam evolution. A closed-form model that holds under conditions of negligible-depletion of the pump beam is developed to describe the vortex dynamics in order to predict the number of vortices present in the wave fronts of the beams at any instance of the propagation. Results are compared with numerical simulations of the full governing equations and with experimental observations. Limitations of the model are outlined.Peer ReviewedPostprint (published version

From Disordered Crystal to Glass: Exact Theory

We calculate thermodynamic properties of a disordered model insulator, starting from the ideal simple-cubic lattice ($g = 0$) and increasing the disorder parameter $g$ to $\gg 1/2$. As in earlier Einstein- and Debye- approximations, there is a phase transition at $g_{c} = 1/2$. For $g<g_{c}$ the low-T heat-capacity $C \sim T^{3}$ whereas for $g>g_{c}$, $C \sim T$. The van Hove singularities disappear at {\em any finite $g$}. For $g>1/2$ we discover novel {\em fixed points} in the self-energy and spectral density of this model glass.Comment: Submitted to Phys. Rev. Lett., 8 pages, 4 figure