Related papers: Networks of geometrically exact beams: well-posedn…

In this work, we consider networks of so-called geometrically exact beams, namely, shearable beams that may undergo large motions. The corresponding mathematical model, commonly written in terms of displacements and rotations expressed in a…

In this work we address the problem of boundary feedback stabilization for a geometrically exact shearable beam, allowing for large deflections and rotations and small strains. The corresponding mathematical model may be written in terms of…

We study well-posedness, stabilization and control problems involving freely vibrating beams that may undergo motions of large magnitude -- i.e. large displacements of the reference line and large rotations of the cross sections. Such…

In this paper we study the stability of a tree-shaped network of elastic strings and beams with some feedbacks at the ends. The whole system is asymptotically stable. Moreover, the energy of the solution decay exponentially to zero if there…

A systematic approach to maximise estimates on the region of attraction in the exponential stabilisation of geometrically exact (nonlinear) beam models via boundary feedback is presented. Starting from recently established stability results…

We present neural network-based constitutive models for hyperelastic geometrically exact beams. The proposed models are physics-augmented, i.e., formulated to fulfill important mechanical conditions by construction, which improves accuracy…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…

This work is devoted to the construction of explicit feedback control laws for the robust, global, exponential stabilization of general, uncertain, discrete-time, acyclic traffic networks. We consider discrete-time, uncertain network models…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on…

In domains with interdependent data, such as graphs, quantifying the epistemic uncertainty of a Graph Neural Network (GNN) is challenging as uncertainty can arise at different structural scales. Existing techniques neglect this issue or…

Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves. Natural structures are often highly…

This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this…

We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…

We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…

In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and…

The rigidity of a network of elastic beams crucially depends on the specific details of its structure. We show both numerically and theoretically that there is a class of isotropic networks which are stiffer than any other isotropic network…

The stability of complex networks, from power grids to biological systems, is crucial for their proper functioning. It is thus important to control such systems to maintain or restore their stability. Traditional approaches rely on…

Deformation due to embedded fluidic networks is currently studied in the context of soft-actuators and soft-robotics. Expanding on this concept, beams can be designed so that the pressure in the channel-network is created directly from…