Pattern Selection in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing

We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe or hexagon patterns are linearly stable, whereas square patterns and patterns involving more than three modes are unstable. In the case of hexagon patterns up- and down-hexagons can be simultaneously stable. The third-order, weakly nonlinear analysis predicts stable square patterns and super-hexagons for larger amplitudes. Direct simulations show, however, that in this regime the third-order weakly nonlinear analysis is insufficient, and these patterns are, in fact unstable

High-Frequency-Induced Cathodic Breakdown during Plasma Electrolytic Oxidation

The present communication shows the possibility of observing microdischarges under cathodic polarization during plasma electrolytic oxidation at high frequency. Cathodic microdischarges can ignite beyond a threshold frequency found close to 2 kHz. The presence (respectively, absence) of an electrical double layer is put forward to explain how the applied voltage can be screened, which therefore prevents (respectively, promotes) the ignition of a discharge. Interestingly, in the conditions of the present study, the electrical double layer requires between 175 and 260 μs to form. This situates the expected threshold frequency between 1.92 and 2.86 kHz, which is in good agreement with the value obtained experimentally

Solitons in combined linear and nonlinear lattice potentials

We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons. Under the direct commensurability (equal periods of the lattices, the family of ordinary solitons is similar to its counterpart in the free space. The situation is different in the case of the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or incommensurability. In those cases, there is an existence threshold for the solitons, and the scaling relation between their amplitude and width is different from that in the free space. GS families demonstrate a bistability, unless the direct commensurability takes place. Specific scaling relations are found for them too. Ordinary solitons can be readily set in motion by kicking. GSs are mobile too, featuring inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion, while the stability of GS families follows an inverted ("anti-VK") criterion, which is explained by means of the averaging approximation.Comment: 9 pages, 6 figure

Beam Wandering in the Atmosphere: The Effect of Partial Coherence

The effect of a random phase screen on laser beam wander in a turbulent atmosphere is studied theoretically. The method of photon distribution function is used to describe the photon kinetics of both weak and strong turbulence. By bringing together analytical and numerical calculations, we have obtained the variance of beam centroid deflections caused by scattering on turbulent eddies. It is shown that an artificial distortion of the initial coherence of the radiation can be used to decrease the wandering effect. The physical mechanism responsible for this reduction and applicability of our approach are discussed.Comment: 16 pages, 5 figure

The religious dimension of lay leadership in Catholic schools: Preserving Catholic culture in an era of change

This article is a qualitative study of the practice of leadership in Catholic schools in Australia. Within an interpretivist framework, a multiple case study of six lay principals was employed. Findings suggest that successful leadership in Catholic schools is highly influenced by the cultural and spiritual capital that a principal brings to a school, signifying a fundamental importance of appointing principals who are not only professionally competent, but who are spiritually competent as well. The relationship between the lay Catholic principal in the parish and the parish priest emerged as a challenging issue in many contexts. Indeed, it was highly problematic for some principals