Related papers: Degenerate elastic networks
The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity…
We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and regularity of minimizers, and we show some…
This work targets the influence of disorder on the relaxed structure and macroscopic mechanical properties of elastic networks. We construct network classes of different types of disorder (length, topology and stiffness), which are…
We present an edge-based framework for the study of geometric elastic network models to model mechanical interactions in physical systems. We use a formulation in the edge space, instead of the usual node-centric approach, to characterise…
In this note we announce some results that will appear in [6] (joint work with also Matteo Novaga) on the minimization of the functional $F(\Gamma)=\int_\Gamma k^2+1\,\mathrm{d}s$, where $\Gamma$ is a network of three curves with fixed…
A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our $p$-energy is defined through a relaxation process, where a suitable $p$-rotation of inscribed polygonals is adopted.…
Networks of elastic beams can deform either by stretching or bending of their members. The primary mode of deformation (bending or stretching) crucially depends on the specific details of the network architecture. In order to shed light on…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
Analyzing nonlinear conformational relaxation dynamics in elastic networks corresponding to two classical motor proteins, we find that they respond by well-defined internal mechanical motions to various initial deformations and that these…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal…
The two approaches to analyzing the large strain behavior of rubbery networks are phenomenologically, using strain energy functions drawn from continuum mechanics, and molecular models, which apply statistical mechanics to compute the…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
Modeling networks can serve as a means of summarizing high-dimensional complex systems. Adapting an approach devised for dense, weighted networks, we propose a new method for generating and estimating unweighted networks. This approach can…
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…
Athermal models of disordered fibrous networks are highly useful for studying the mechanics of elastic networks composed of stiff biopolymers. The underlying network architecture is a key aspect that can affect the elastic properties of…
Based on Jaynes' maximum entropy principle, exponential random graphs provide a family of principled models that allow the prediction of network properties as constrained by empirical data (observables). However, their use is often hindered…
Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by…
We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…