Nonlinear interfaces: intrinsically nonparaxial regimes and effects

The behaviour of optical solitons at planar nonlinear boundaries is a problem rich in intrinsically nonparaxial regimes that cannot be fully addressed by theories based on the nonlinear Schrödinger equation. For instance, large propagation angles are typically involved in external refraction at interfaces. Using a recently proposed generalized Snell's law for Helmholtz solitons, we analyse two such effects: nonlinear external refraction and total internal reflection at interfaces where internal and external refraction, respectively, would be found in the absence of nonlinearity. The solutions obtained from the full numerical integration of the nonlinear Helmholtz equation show excellent agreement with the theoretical predictions

Helmholtz solitons in optical materials with a dual power-law refractive index

A nonlinear Helmholtz equation is proposed for modelling scalar optical beams in uniform planar waveguides whose refractive index exhibits a purely-focusing dual powerlaw dependence on the electric field amplitude. Two families of exact analytical solitons, describing forward- and backward-propagating beams, are derived. These solutions are physically and mathematically distinct from those recently discovered for related nonlinearities. The geometry of the new solitons is examined, conservation laws are reported, and classic paraxial predictions are recovered in a simultaneous multiple limit. Conventional semi-analytical techniques assist in studying the stability of these nonparaxial solitons, whose propagation properties are investigated through extensive simulations

Wave envelopes with second-order spatiotemporal dispersion : I. Bright Kerr solitons and cnoidal waves

We propose a simple scalar model for describing pulse phenomena beyond the conventional slowly-varying envelope approximation. The generic governing equation has a cubic nonlinearity and we focus here mainly on contexts involving anomalous group-velocity dispersion. Pulse propagation turns out to be a problem firmly rooted in frames-of-reference considerations. The transformation properties of the new model and its space-time structure are explored in detail. Two distinct representations of exact analytical solitons and their associated conservation laws (in both integral and algebraic forms) are presented, and a range of new predictions is made. We also report cnoidal waves of the governing nonlinear equation. Crucially, conventional pulse theory is shown to emerge as a limit of the more general formulation. Extensive simulations examine the role of the new solitons as robust attractors

Helmholtz bright and boundary solitons

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic Non-Linear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently-reported Helmholtz bright solitons, for this type of polynomial non-linearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterpart

Korteweg-de Vries description of Helmholtz-Kerr dark solitons

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schrödinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equations. Here, a novel analytical approach reveals that the evolution of small-amplitude Helmholtz–Kerr dark solitons is also governed by a KdV equation. This broadens the class of nonlinear systems that are known to possess KdV soliton solutions, and provides a framework for perturbative analyses when propagation angles are not negligibly small. The derivation of this KdV equation involves an element that appears new to weakly nonlinear analyses, since transformations are required to preserve the rotational symmetry inherent to Helmholtz-type equations

Wave envelopes with second-order spatiotemporal dispersion: II. Modulational instabilities and dark Kerr solitons

A simple scalar model for describing spatiotemporal dispersion of pulses, beyond the classic “slowly-varying envelopes + Galilean boost” approach, is studied. The governing equation has a cubic nonlinearity and we focus here mainly on contexts with normal group-velocity dispersion. A complete analysis of continuous waves is reported, including their dispersion relations and modulational instability characteristics. We also present a detailed derivation of exact analytical dark solitons, obtained by combining direct-integration methods with geometrical transformations. Classic results from conventional pulse theory are recovered as-ymptotically from the spatiotemporal formulation. Numerical simulations test new theoretical predictions for modulational instability, and examine the robustness of spatiotemporal dark solitons against perturbations to their local pulse shape

When and why entrepreneurial employees want to quit their job: Exploring two conflicting mechanisms

Past turnover research has posited personality traits as important antecedents to quit intentions. Nevertheless, previous literature has not investigated the relationship between employees’ entrepreneurial tendencies—a constellation of domain specific traits—and turnover. Drawing on dispositional trait theory and attraction‐selection‐attrition theory, we propose engagement and intentions to start a business as mediators of the relationship between entrepreneurial tendencies and quit intentions. We test our predictions in a sample of full‐time employees from the United Kingdom (N = 224). In line with our hypotheses, an inconsistent mediation is found, where both positive and negative links between entrepreneurial tendencies and turnover intentions were mediated by engagement and intentions to start a business respectively. Thus, entrepreneurial employees were more likely to be engaged, but at the same time also more likely to be considering starting their own business, leading to a conflicting relationship to turnover intentions. The current study informs the human resource management literature concerning the motivational mechanisms explaining turnover intentions among entrepreneurial employees. It also provides practical insights with regards to the effective management of this workforce

Towards a sustainable optimization of pavement maintenance programs under budgetary restrictions

Transport sector constitutes the second largest source of global greenhouse gas (GHG) emissions, being the road transportation the main contributor of these emissions. Efforts in the road sector have traditionally focused on vehicle emissions and infrastructure is typically not included in the emissions account. Road environmental impact is estimated to increase by 10% if the stages of road design, construction, and operation were considered. Previous literature has widely study sustainable practices in pavement design and construction, with little attention paid to maintenance. Current state of practice reveals that pavement managers barely consider environmental performance and their evaluations solely rely on technical and economic criteria. This situation creates the need to incorporate, in an integrated manner, technical, economic, and environmental aspects in the design of maintenance programs. The main objective of this research is to develop a tool for the optimal design of sustainable maintenance programs. Given a maintenance budget, the tool aims to maximize the long-term effectiveness of the network while minimizing GHG emissions derived from the application of maintenance treatments. The capability of the proposed tool is analyzed in a case study dealing with an urban pavement network. In comparison to the traditional maintenance policy, the proposed tool designs maintenance programs that increase the average network condition by up to 22% and reduces GHG emissions by 12%. This application also analyzes the effect of different budgetary scenarios in the technical and environmental performance of the network. This application helps pavement managers in the trade-off between budget and network performance.The authors gratefully acknowledge members of the research group at the Pontificia Universidad Catolica de Chile for providing information concerning the case study analyzed in this paper. The research team acknowledges Fondef/Conicyt 2009 for funding the project "Research and Development of Solutions for Urban Pavement Management in Chile" (D0911018) and the National Research Center for Integrated Natural Disaster Management CONICYT/FONDAP/15110017. Funding from CONICYT (CONICYT-PCHA/Doctorado Nacional/2013-63130138) to support this work is sincerely appreciated.Torres Machí, C.; Pellicer Armiñana, E.; Yepes, V.; Chamorro, A. (2017). Towards a sustainable optimization of pavement maintenance programs under budgetary restrictions. Journal of Cleaner Production. 148:90-102. https://doi.org/10.1016/j.jclepro.2017.01.100S9010214