A Robust Numerical Method to Study Oscillatory Instability of Gap Solitary Waves *

Abstract. The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to eigenvalues. These problems may exhibit oscillatory instabilities where eigenvalues detach from the edges of the continuous spectrum-socalled edge bifurcations. A numerical framework, based on a fast robust shooting algorithm using exterior algebra, is described. The complete algorithm is robust in the sense that it does not produce spurious unstable eigenvalues. The algorithm allows us to locate exactly where the unstable discrete eigenvalues detach from the continuous spectrum. Moreover, the algorithm allows for stable shooting along multidimensional stable and unstable manifolds. The method is illustrated by computing the stability and instability of gap solitary waves of a coupled mode model

Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice *

Abstract. We study homoclinic snaking of one-dimensional, localized states on two-dimensional, bistable lattices via the method of exponential asymptotics. Within a narrow region of parameter space, fronts connecting the two stable states are pinned to the underlying lattice. Localized solutions are formed by matching two such stationary fronts back-to-back; depending on the orientation relative to the lattice, the solution branch may "snake" back and forth within the pinning region via successive saddle-node bifurcations. Standard continuum approximations in the weakly nonlinear limit (equivalently, the limit of small mesh size) do not exhibit this behavior, due to the resultant leading-order reaction-diffusion equation lacking a periodic spatial structure. By including exponentially small effects hidden beyond all algebraic orders in the asymptotic expansion, we find that exponentially small but exponentially growing terms are switched on via error function smoothing near Stokes lines. Eliminating these otherwise unbounded beyond-all-orders terms selects the origin (modulo the mesh size) of the front, and matching two fronts together yields a set of equations describing the snaking bifurcation diagram. This is possible only within an exponentially small region of parameter space-the pinning region. Moreover, by considering fronts orientated at an arbitrary angle ψ to the x-axis, we show that the width of the pinning region is nonzero only if tan ψ is rational or infinite. The asymptotic results are compared with numerical calculations, with good agreement. Key words. homoclinic snaking, direction-dependent pinning, exponential asymptotics, square lattice AMS subject classifications. 34A33, 34E05, 34K18 DOI. 10.1137/140966897 1. Introduction. The phenomenon known as homoclinic snaking, referring to the existence of a multiplicity of localized solutions within a narrow region of parameter space, has been observed in a wide variety of experimental and theoretical context

Mozambique : administrative districts of Niassa, Cabo Delgado, Nampula and Zambezia Province (SER A)

This is a map of the administrative districts of Niassa, Cabo Delgado, Nampula and Zambezia Province

John Beishon Memorial Lectures: Summary Overview

John Beishon (1930-2001) was the first Professor of Systems at the Open University (UK). His life and contribution to systems thinking and practice, in particular the founding of the Systems Group at the OU, are celebrated in ASTiP’s sponsoring an occasional lecture series called the John Beishon Memorial Lecture. This document provides an account of the lectures held thus far

Ordinary petri net matrices

This work presents some ideas and theory on representing ordinary Petri nets using matrices and builds on previous work in [11],[12]. The three main types of matrices used for Petri net representation are the input, output and incidence matrices. The motivation for this work is that matrices can provide an alternative way to describe Petri nets from the conventional graphical representation. As is indicated several properties can be inferred, observed and derived from the matrices. Some definitions and examples are used.peer-reviewe

Continuous Open Access Special Issue "Aircraft Design": Number 2/2020

Following the successful initial Special Issue on “Aircraft Design (SI-1/2017)”, this is already the second SI “Aircraft Design (SI-2/2020)”. Activities in the past showed that aircraft design may be a field too small to justify its own (subscription-based) journal. A continuous open access special issue may fill the gap. As such, the Special Issue “Aircraft Design” can be a home for all those working in the field who regret the absence of an aircraft design journal. SI-2/2020 contains seven papers; an Editorial: 1.) "Publishing in 'Aircraft Design' with a Continuous Open Access Special Issue" and six Original Research Articles about 2.) Amphibious Aircraft Developments, 3.) Design Space Exploration of Jet Engine Components, 4.) Study of Subsonic Wing Flutter, 5.) Design Optimization of a Blended Wing Body Aircraft, 6.) Discrete Mobile Control Surfaces, 7.) Electro-Impulse De-Icing Systems

Continuous Open Access Special Issue "Aircraft Design": Number 3/2021

Following the successful initial Special Issue on "Aircraft Design (SI-1/2017)" and the relaunch with "Aircraft Design (SI-2/2020)", this is already the third SI in sequence named "Aircraft Design (SI 3/2021)". Activities in the past showed that aircraft design may be a field too small to justify its own (subscription-based) journal. A continuous open access special issue may fill the gap. As such, the Special Issue "Aircraft Design" can be a home for all those working in the field who regret the absence of an aircraft design journal. SI-3/2021 contains six papers (original research articles) about 1.) Oil Fumes in the Cabin and Flight Safety, 2.) Closed-Loop Flying Quality Requirements, 3.) Preliminary Design of a Medium Range Box Wing Aircraft, 4.) Influence of Novel Airframe Technologies on the Feasibility of Fully-Electric Regional Aviation, 5.) Design and Optimization of a Large Turboprop Aircraft, 6.) Sources of Onboard Fumes and Smoke

Who Drives Climate-Relevant Policies in the Rising Powers?

The future of human life on our planet is influenced increasingly by what goes on in the rising powers. This paper provides a political economy analysis of the climate-relevant policies of China, India, Brazil and South Africa. It shows that alliances play a key role in driving such policies. However, most actors who support such policies have priorities other than climate change mitigation. Their support for such policies comes from concerns with securing energy, building competitive green industries, creating jobs or providing a basis for future public revenue. This insight is not just of analytical but also of political importance. It means that climate-relevant policies can draw on support from a wide constituency – not just those with green convictions. Such analysis provides the stepping-stone for understanding the political feasibility of low-carbon transformations. PLEASE NOTE: this article supersedes IDS Evidence Report: Who Drives Climate-relevant Policies in the Rising Powers? http://opendocs.ids.ac.uk/opendocs/handle/123456789/993

When enough should be enough: Improving the use of current agricultural lands could meet production demands and spare natural habitats in Brazil

Providing food and other products to a growing human population while safeguarding natural ecosystems and the provision of their services is a significant scientific, social and political challenge. With food demand likely to double over the next four decades, anthropization is already driving climate change and is the principal force behind species extinction, among other environmental impacts. The sustainable intensification of production on current agricultural lands has been suggested as a key solution to the competition for land between agriculture and natural ecosystems. However, few investigations have shown the extent to which these lands can meet projected demands while considering biophysical constraints. Here we investigate the improved use of existing agricultural lands and present insights into avoiding future competition for land. We focus on Brazil, a country projected to experience the largest increase in agricultural production over the next four decades and the richest nation in terrestrial carbon and biodiversity. Using various models and climatic datasets, we produced the first estimate of the carrying capacity of Brazil's 115 million hectares of cultivated pasturelands. We then investigated if the improved use of cultivated pasturelands would free enough land for the expansion of meat, crops, wood and biofuel, respecting biophysical constraints (i.e., terrain, climate) and including climate change impacts. We found that the current productivity of Brazilian cultivated pasturelands is 32–34% of its potential and that increasing productivity to 49–52% of the potential would suffice to meet demands for meat, crops, wood products and biofuels until at least 2040, without further conversion of natural ecosystems. As a result up to 14.3 Gt CO2 Eq could be mitigated. The fact that the country poised to undergo the largest expansion of agricultural production over the coming decades can do so without further conversion of natural habitats provokes the question whether the same can be true in other regional contexts and, ultimately, at the global scale