The homogenisation of Maxwell's equations with applications to photonic crystals and localised waveforms on metafilms

An asymptotic theory is developed to generate equations that model the global behaviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions; potentially highly-oscillatory short-scale detail is encapsulated through integrated quantities. The theory we develop is then applied to two topical examples, the first being the case of aligned dielectric cylinders, which has great importance in the modelling of photonic crystal fibres. We then consider the propagation of waves in a structured metafilm, here chosen to be a planar array of dielectric spheres. At certain frequencies strongly directional dynamic anisotropy is observed, and the asymptotic theory is shown to capture the effect, giving highly accurate qualitative and quantitative results as well as providing interpretation for the underlying change from elliptic to hyperbolic behaviour

High frequency homogenisation for elastic lattices

A complete methodology, based on a two-scale asymptotic approach, that enables the homogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distinguished from scalar lattices in that two or more types of coupled waves exist, even at low frequencies. Such a theory enables the determination of effective material properties at both low and high frequencies. The theoretical framework is developed for the propagation of waves through lattices of arbitrary geometry and dimension. The asymptotic approach provides a method through which the dispersive properties of lattices at frequencies near standing waves can be described; the theory accurately describes both the dispersion curves and the response of the lattice near the edges of the Brillouin zone. The leading order solution is expressed as a product between the standing wave solution and long-scale envelope functions that are eigensolutions of the homogenised partial differential equation. The general theory is supplemented by a pair of illustrative examples for two archetypal classes of two-dimensional elastic lattices. The efficiency of the asymptotic approach in accurately describing several interesting phenomena is demonstrated, including dynamic anisotropy and Dirac cones.Comment: 24 pages, 7 figure

Parabolic Metamaterials and Dirac Bridges

A new class of multi-scale structures, referred to as `parabolic metamaterials' is introduced and studied in this paper. For an elastic two-dimensional triangular lattice, we identify dynamic regimes, which corresponds to so-called `Dirac Bridges' on the dispersion surfaces. Such regimes lead to a highly localised and focussed unidirectional beam when the lattice is excited. We also show that the flexural rigidities of elastic ligaments are essential in establishing the `parabolic metamaterial' regimes.Comment: 14 pages, 4 figure

Fluid-loaded metasurfaces

We consider wave propagation along fluid-loaded structures which take the form of an elastic plate augmented by an array of resonators forming a metasurface, that is, a surface structured with sub-wavelength resonators. Such surfaces have had considerable recent success for the control of wave propagation in electromagnetism and acoustics, by combining the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. We explore one aspect of recent interest in this field: graded metasurfaces, but within the context of fluid-loaded structures. Graded metasurfaces allow for selective spatial frequency separation and are often referred to as exhibiting rainbow trapping. Experiments, and theory, have been developed for acoustic, electromagnetic, and even elastic, rainbow devices but this has not been approached for fluid-loaded structures that support surface waves coupled with the acoustic field in a bulk fluid. This surface wave, coupled with the fluid, can be used to create an additional effect by designing a metasurface to mode convert from surface to bulk waves. We demonstrate that sub-wavelength control is possible and that one can create both rainbow trapping and mode conversion phenomena for a fluid-loaded elastic plate model.Comment: 13 pages, 10 figure

What’s past (and present) is prologue : interactions between justice levels and trajectories predicting behavioral reciprocity

Much of organizational justice research has tended to take a static approach, linking employees’ contemporaneous justice levels to outcomes of interest. In the present study, we tested a dynamic model emphasizing the interactive influences of both justice levels and trajectories for predicting behavioral social exchange outcomes. Specifically, our model posited both main effects and interactions between present justice levels and past justice changes over time in predicting helping behavior and voluntary turnover behavior. Data over four yearly measurement periods from 4,348 employees of a banking organization generally supported the notion that justice trajectories interact with absolute levels to predict both outcomes. Together, the findings highlight how employees invoke present fairness evaluations within the context of past fairness trends—rather than either in isolation—to inform decisions about behaviorally reciprocating at work

One-way interfacial waves in a flexural plate with chiral double resonators

In this paper, we demonstrate a new approach to control flexural elastic waves in a structured chiral plate. The main focus is on creating one-way interfacial wave propagation at a given frequency by employing double resonators in a doubly periodic flexural system. The resonators consist of two beams attached to gyroscopic spinners, which act to couple flexural and rotational deformations, hence inducing chirality in the system. We show that this elastic structure supports one-way flexural waves, localized at an interface separating two sub-domains with gyroscopes spinning in opposite directions, but with otherwise identical properties. We demonstrate that a special feature of double resonators is in the directional control of wave propagation by varying the value of the gyricity, while keeping the frequency of the external time-harmonic excitation fixed. Conversely, for the same value of gyricity, the direction of wave propagation can be reversed by tuning the frequency of the external excitation. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’

Willing and able: action-state orientation and the relation between procedural justice and employee cooperation

Existing justice theory explains why fair procedures motivate employees to adopt cooperative goals, but it fails to explain how employees strive towards these goals. We study self-regulatory abilities that underlie goal striving; abilities that should thus affect employees’ display of cooperative behavior in response to procedural justice. Building on action control theory, we argue that employees who display effective self-regulatory strategies (action oriented employees) display relatively strong cooperative behavioral responses to fair procedures. A multisource field study and a laboratory experiment support this prediction. A subsequent experiment addresses the process underlying this effect by explicitly showing that action orientation facilitates attainment of the cooperative goals that people adopt in response to fair procedures, thus facilitating the display of actual cooperative behavior. This goal striving approach better integrates research on the relationship between procedural justice and employee cooperation in the self-regulation and the work motivation literature. It also offers organizations a new perspective on making procedural justice effective in stimulating employee cooperation by suggesting factors that help employees reach their adopted goals

Using self-definition to predict the influence of procedural justice on organizational, interpersonal, and job/task-oriented citizenship behaviors

An integrative self-definition model is proposed to improve our understanding of how procedural justice affects different outcome modalities in organizational behavior. Specifically, it is examined whether the strength of different levels of self-definition (collective, relational, and individual) each uniquely interact with procedural justice to predict organizational, interpersonal, and job/task-oriented citizenship behaviors, respectively. Results from experimental and (both single and multisource) field data consistently revealed stronger procedural justice effects (1) on organizational-oriented citizenship behavior among those who define themselves strongly in terms of organizational characteristics, (2) on interpersonal-oriented citizenship behavior among those who define themselves strongly in terms of their interpersonal relationships, and (3) on job/task-oriented citizenship behavior among those who define themselves weakly in terms of their distinctiveness or uniqueness. We discuss the relevance of these results with respect to how employees can be motivated most effectively in organizational settings