Related papers: Strength Reduction in Electrical and Elastic Netwo…
We study the failure properties of fiber bundles with a finite lower cutoff of the strength disorder varying the range of interaction between the limiting cases of completely global and completely local load sharing. Computer simulations…
We consider the worst-case load-shedding problem in electric power networks where a number of transmission lines are to be taken out of service. The objective is to identify a pre-specified number of line outage that leads to the maximum…
We introduce a mathematical model, based on networks, for the elasticity and plasticity of materials. We define the tension tensor for a periodic graph in a Euclidean space, and we show that the tension tensor expresses elasticity under…
Feature selection is important in data representation and intelligent diagnosis. Elastic net is one of the most widely used feature selectors. However, the features selected are dependant on the training data, and their weights dedicated…
We employ a mathematical model to analyze stress chains in thermoplastic elastomers (TPEs) with a microphase-separated spherical structure composed of triblock copolymers. The model represents stress chains during uniaxial and biaxial…
Networks of genetic expression can be modelled by hypergraphs with the additional structure that real coefficients are given to each vertex-edge incidence. The spectra, i.e. the multiset of the eigenvalues, of such hypergraphs, are known to…
The fracture strength distribution of materials is often described in terms of the Weibull law which can be derived by using extreme value statistics if elastic interactions are ignored. Here, we consider explicitly the interplay between…
Elastomers that can sustain large reversible strain are essential components for stretchable electronics. The stretchability and mechanical robustness of unfilled elastomers can be enhanced by introducing easier-to-break cross-links, e.g.…
Many systems, ranging from engineering to medical to societal, can only be properly characterized by multiple interdependent networks whose normal functioning depends on one another. Failure of a fraction of nodes in one network may lead to…
In the electrical grid, the distribution system is themost vulnerable to severe weather events. Well-placed and coordinatedupgrades, such as the combination of microgrids, systemhardening and additional line redundancy, can greatly reduce…
Resonance is a well-known phenomenon that happens in systems with second order dynamics. In this paper we address the fundamental question of making a network robust to signal being periodically pumped into it at or near a resonant…
Complex systems are ubiquitous in nature and engineering, but their analysis and control are hampered by their high dimensionality and the influence of various factors on their dynamics. Dimensionality reduction aims to find a…
The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that…
We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity,…
Real-world complex systems exhibit intricate interconnections and dependencies, especially social networks, technological infrastructures, and communication networks. These networks are prone to disconnection due to random failures or…
Experiments have long shown that a polymer network of covalent bonds commonly ruptures at a stress that is orders of magnitude lower than the strength of the covalent bonds. Here we investigate this large reduction in strength by…
The power grid defines one of the most important technological networks of our times and sustains our complex society. It has evolved for more than a century into an extremely huge and seemingly robust and well understood system. But it…
Double network (DN) materials exhibit anomalous strength and toughness that far exceed the sum of their constituents. While widely exploited, the fundamental physical mechanisms underlying this synergy remain elusive. Here, we show that a…
As a consequence of elasticity, mechanical deformations of crystals occur on a length scale comparable to their thickness. This is exemplified by applying a homogeneous electric field to a multi-domain ferroelectric crystal: as one domain…
The recently introduced dropout training criterion for neural networks has been the subject of much attention due to its simplicity and remarkable effectiveness as a regularizer, as well as its interpretation as a training procedure for an…