Determining the Stability Domain of Perturbed Four-Dimensional Systems in 1:1 Resonance

In an analogy with the problems of non-Hermitian physics, nilpotent 1:1 resonances can originate in the unfolding of the 1:1 semi-simple resonance. This chapter presents a detailed study of this process in the case of general four-dimensional systems. It indicates how the results can be applied to an explicitly given system. The following questions are addressed: Determine the stability domain in parameter space of the original system; Locate the singularities on the boundary of the stability domain; and Identify Hamiltonian and reversible subsystems. The authors find the boundary of the stability domain and list all its singularities including six self-intersections and four “Whitney umbrellas”. They propose an algorithm of approximation of the stability boundary near singularities and apply the results to the study of enhancement of the modulation instability with dissipation as well as to the study of stability of a non-conservative system of rotor dynamics

Kestävä kehitys globaalissa muotiteollisuudessa

Sustainable development is a phenomenon that interest a growing number of consumers. De-spite this, the implementation of its central ideas has been vastly unsuccessful in the field of fashion industry, which remains one of the biggest polluters in the world (Niinimäki et al 2020). This paper takes a look at the central challenges of the implementation of the sustainable development in the fashion industry. The challenges are discussed with the help of a few terms that can be seen as important to the sustainable development ideology of today: circular economy (CE), corporate social responsibility (CSR) and extended producer responsibility (EPR). The modern fashion industry is characterized by a vastly globalized manufacturing supply chain (Boström and Micheletti 2016). This causes multiple challenges in the terms of the environmental and social impact of the industry, from transportation emissions (Filho et al 2019) and pre-consumer waste due to lax design-producer collaboration (Islam et al 2021), to safety violations (Lund-Thomsen and Lindgreen 2014). Besides this, the fast fashion business model, which relies on producing cheap, low-quality clothes that correspond to rapidly changing fashion trends (Ertekin and Atik 2015), contributes to globally growing numbers of fabric waste (Niinimäki et al 2020). Circular economy business model attempts at fighting the negative effects of the fast fashion industry by offering alternative way of designing clothes that takes into account the whole life cycle of the product, from beginning until the end (Levänen et al 2021). The conclusion of the paper is that while some sustainability schemes are already in place around the world, more effort is needed in order to make true change in the fashion industry. Mont and Power (2010) and Niinimäki et al (2020) recommend the focus should be shifted from the actions of individual consumers to wider systems that keep up the growing consumption. Additionally, more research into the economic profitability of sustainability schemes such as business strategies based on CE is needed, in order to motivate companies to initiate them (Levänen et al 2021, Jia et al 2020)

Computation of resonance frequencies for Maxwell equations in non-smooth domains

Summary. We address the computation by finite elements of the non-zero eigenvalues of the (curl, curl) bilinear form with perfect conductor boundary conditions in a polyhedral cavity. One encounters two main difficulties: (i) The infinite dimensional kernel of this bilinear form (the gradient fields), (ii) The unbounded singularities of the eigen-fields near corners and edges of the cavity. We first list possible variational spaces with their functional properties and provide a short description of the edge and corner singularities. Then we address different formulations using a Galerkin approximation by edge elements or nodal elements. After a presentation of edge elements, we concentrate on the functional issues connected with the use of nodal elements. In the framework of conforming methods, nodal elements are mandatory if one regularizes the bilinear form (curl, curl) in order to get rid of the gradient fields. A plain regularization with the (div,div) bilinear form converges to a wrong solution if the domain has reentrant edges or corners. But remedies do exist. We will present the method of addition of singular functions, and the method of regularization with weight, where the (div,div) bilinear form is modified by the introduction of a weight which can be taken as the distance to reentrant edges or corners