Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Linear-to-Circular Polarization Reflector With Transmission Band

A new class of polarizing surface is proposed that in a given frequency band can reflect incident linearly polarized waves with circular polarization (CP) while at other frequencies is transparent allowing incident waves to transmit unaffected. The proposed structure consists of two parallel anisotropic frequency selective surfaces (FSSs) that independently interact with TE or TM waves, respectively. The FSSs are designed to, respectively, transmit TE and TM waves within the same transmission frequency range, so that the combined structure is transparent to all polarizations in this band. Likewise, the two arrays are designed to, respectively, reflect TE and TM incident waves in a common reflection band, so that all polarizations are fully reflected in this range; if the separation of the two arrays is such that the TE and TM components of an incident wave polarized at slant 45° experience a 90° phase shift, reflection will occur in CP. The concept and performance limitations are theoretically investigated using transmission line theory as well as full wave results. The predicted performance is validated by means of experimental results on a fabricated prototype. The proposed structure is pertinent for employment as a quasi-optical diplexer in CP dual-band systems such as reflector antennas.

Efficient Non-Linear Idealisations of Aircraft Fuselage Panels in Compression

Aircraft fuselages are complex assemblies of thousands of components and as a result simulation models are highly idealised. In the typical design process, a coarse FE model is used to determine loads within the structure. The size of the model and number of load cases necessitates that only linear static behaviour is considered. This paper reports on the development of a modelling approach to increase the accuracy of the global model, accounting for variations in stiffness due to non-linear structural behaviour. The strategy is based on representing a fuselage sub-section with a single non-linear element. Large portions of fuselage structure are represented by connecting these non-linear elements together to form a framework. The non-linear models are very efficient, reducing computational time significantly

Processing characteristics and mechanical properties of metallocene catalyzed linear low-density polyethylene foams for rotational molding

The object of this work is to assess the suitability of metallocene catalyzed linear low-density polyethylenes for the rotational molding of foams and to link the material and processing conditions to cell morphology and part mechanical properties (flexural and compressive strength). Through adjustments to molding conditions, the significant processing and physical material parameters that optimize metallocene catalyzed linear low-density polyethylene foam structure have been identified. The results obtained from an equivalent conventional grade of Ziegler-Natta catalyzed linear low-density polyethylene are used as a basis for comparison. The key findings of this study are that metallocene catalyzed LLDPE can be used in rotational foam molding to produce a foam that will perform as well as a ZieglerNatta catalyzed foam and that foam density Is by far the most Influential factor over mechanical properties of foam. © 2004 Society of Plastics Engineers.

Integration of shading and texture cues: testing the linear model

One of the first attempts to develop a formal model of depth cue integration is to be found in Maloney and Landy's (1989) "human depth combination rule". They advocate that the combination of depth cues by the visual sysetem is best described by a weighted linear model. The present experiments tested whether the linear combination rule applies to the integration of texture and shading. As would be predicted by a linear combination rule, the weight assigned to the shading cue did vary as a function of its curvature value. However, the weight assigned to the texture cue varied systematically as a function of the curvature value of both cues. Here we descrive a non-linear model which provides a better fit to the data. Redescribing the stimuli in terms of depth rather than curvature reduced the goodness of fit for all models tested. These results support the hypothesis that the locus of cue integration is a curvature map, rather than a depth map. We conclude that the linear comination rule does not generalize to the integration of shading and texture, and that for these cues it is likely that integration occurs after the recovery of surface curvature.