Layer entanglement in multiplex, temporal multiplex, and coupled multilayer networks

Complex networks, such as transportation networks, social networks, or biological networks, capture the complex system they model by often representing only one type of interactions. In real world systems, there may be many different aspects that connect entities together. These can be captured using multilayer networks, which combine different modalities of interactions in a single model. Coupling in multilayer networks may exhibit different properties which can be related to the very nature of the data they model (or to events in time-dependent data). We hypothesise that such properties may be reflected in the way layers are intertwined. In this paper, we investigated these through the prism of layer entanglement in coupled multilayer networks. We test over 30 real-life networks in 6 different disciplines (social, genetic, transport, co-authorship, trade, and neuronal networks). We further propose a random generator, displaying comparable patterns of elementary layer entanglement and transition coupling entanglement across 1,329,696 synthetic coupled multilayer networks. Our experiments demonstrate difference of layer entanglement across disciplines, and even suggest a link between entanglement intensity and homophily. We additionally study entanglement in 3 real world temporal datasets displaying a potential rise in entanglement activity prior to other network activity.

Complete In-plane Elastic Characterisation under Tensile Tests of Angle-Ply Laminates Composed of Polymer-Matrix Layers

In this paper we present a new strategy to completely characterise the in-plane elastic properties of a large range of angle-ply laminates using only unidirectional tests. We consider laminates having the same number of identical plies in the α and – α directions. This new method uses some preceding results found by Verchery for orthotropic laminates, namely the conditions of existence of a specific direction ω, in which the shear-extension coupling is null. The characterisation of the laminate is then made using the results of three tensile tests: two in the orthotropy axes, and the third one in the ω direction, in order to have always a pure one-dimensional state of stress. We show that for the most common unidirectional fibre-reinforced materials, the angle ω is, in most cases, close to the α direction of the fibres. This result permits a complete experimental characterisation of the laminate, which then does not need any a priori knowledge of the elastic properties of the elementary layer. In addition, it provides a simple method to verify the predictions of the laminate behaviour obtained by the Classical Laminated Plate Theory (CLPT) when the elementary layer is completely known. The paper ends with numerical examples and with the results of some experimental tests.