Three-wave Nonlinear Scattering by Quasiperiodic Dielectric Structure

The combinatorial frequency generation by a Fibonacci type quasi-periodic dielectric multilayered structure illuminated by two plane waves has been analysed. The effects of the layer parameters and Fibonacci sequence order on the properties of the combinatorial frequency waves emitted from the stacked nonlinear layers are discussed.

Asset allocation, cross-class correlation and the structure of property returns

Practical applications of portfolio optimisation tend to proceed on a “top down” basis where funds are allocated first at asset class level (between, say, bonds, cash, equities and real estate) and then, progressively, at sub-class level (within property to sectors, office, retail, industrial for example). While there are organisational benefits from such an approach, it can potentially lead to sub-optimal allocations when compared to a “global” or “side-by-side” optimisation. This will occur where there are correlations between sub-classes across the asset divide that are masked in aggregation – between, for instance, City offices and the performance of financial services stocks. This paper explores such sub-class linkages using UK monthly stock and property data. Exploratory analysis using clustering procedures and factor analysis suggests that property performance and equity performance are distinctive: there is little persuasive evidence of contemporaneous or lagged sub-class linkages. Formal tests of the equivalence of optimised portfolios using top-down and global approaches failed to demonstrate significant differences, whether or not allocations were constrained. While the results may be a function of measurement of market returns, it is those returns that are used to assess fund performance. Accordingly, the treatment of real estate as a distinct asset class with diversification potential seems justified.

Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = cgA where cg is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum. The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ0(z) so long as the variation in θ0(z) over the depth of the fluid is small compared with θ0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., dθ0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow. The counterparts to results for the two-dimensional Boussinesq equations are also noted.

Consumption-wealth ratio and expected stock returns: evidence from panel data

This paper investigates the role of consumption-wealth ratio on predicting future stock returns through a panel approach. We follow the theoretical framework proposed by Lettau and Ludvigson (2001), in which a model derived from a nonlinear consumer’s budget constraint is used to settle the link between consumption-wealth ratio and stock returns. Using G7’s quarterly aggregate and financial data ranging from the first quarter of 1981 to the first quarter of 2014, we set an unbalanced panel that we use for both estimating the parameters of the cointegrating residual from the shared trend among consumption, asset wealth and labor income, cay, and performing in and out-of-sample forecasting regressions. Due to the panel structure, we propose different methodologies of estimating cay and making forecasts from the one applied by Lettau and Ludvigson (2001). The results indicate that cay is in fact a strong and robust predictor of future stock return at intermediate and long horizons, but presents a poor performance on predicting one or two-quarter-ahead stock returns.

Investigation of the two-photon absorption cross-section in perylene tetracarboxylic derivatives: Nonlinear spectra and molecular structure

We investigated the 2PA absorption spectrum of a family of perylene tetracarboxylic derivatives ( PTCDs): bis( benzimidazo) perylene ( AzoPTCD), bis( benzimidazo) thioperylene ( Monothio BZP), n-pentylimidobenzimidazoperylene ( PazoPTCD), and bis( n-butylimido) perylene ( BuPTCD). These compounds present extremely high two-photon absorption, which makes them attractive for applications in photonics devices. The two-photon absorption cross-section spectra of perylene derivatives obtained via Z-scan technique were fitted by means of a sum-over-states ( SOS) model, which described with accuracy the different regions of the 2PA cross-section spectra. Frontier molecular orbital calculations show that all molecules present similar features, indicating that nonlinear optical properties in PTCDs are mainly determined by the central portion of the molecule, with minimal effect from the lateral side groups. In general, our results pointed out that the differences in the 2PA cross-sections among the compounds are mainly due to the nonlinearity resonance enhancement.

Remarks on an Optimal Linear Control Design Applied to a Nonideal and an Ideal Structure Coupled to an Essentially Nonlinear Oscillator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On energy pumping, synchronization and beat phenomenon in a nonideal structure coupled to an essentially nonlinear oscillator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A nonlinear and non-ideal wind generator supporting structure

We present a simple mathematical model of a wind turbine supporting tower. Here, the wind excitation is considered to be a non-ideal power source. In such a consideration, there is interaction between the energy supply and the motion of the supporting structure. If power is not enough, the rotation of the generator may get stuck at a resonance frequency of the structure. This is a manifestation of the so-called Sommerfeld Effect. In this model, at first, only two degrees of freedom are considered, the horizontal motion of the upper tip of the tower, in the transverse direction to the wind, and the generator rotation. Next, we add another degree of freedom, the motion of a free rolling mass inside a chamber. Its impact with the walls of the chamber provides control of both the amplitude of the tower vibration and the width of the band of frequencies in which the Sommerfeld effect occur. Some numerical simulations are performed using the equations of motion of the models obtained via a Lagrangian approach.

The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.

Causal structure and birefringence in nonlinear electrodynamics

We investigate the causal structure of general nonlinear electrodynamics and determine which Lagrangians generate an effective metric conformal to Minkowski. We also prove that there is only one analytic nonlinear electrodynamics not presenting birefringence.