Related papers: Fracturing the optimal paths
We propose a model for path-planning based on a single performance metric that accurately accounts for the the potential (spatially inhomogeneous) cost of breakdowns and repairs. These random breakdowns (or system faults) happen at a known,…
When a thin film moderately adherent to a substrate is subjected to residual stress, the cooperation between fracture and delamination leads to unusual fracture patterns, such as spirals, alleys of crescents and various types of strips, all…
The roughness of crack interfaces is reported in quasistatic fracture, using an elastic network of beams with random breaking thresholds. For strong disorders we obtain 0.86(3) for the roughness exponent, a result which is very different…
Stress enhancement in the vicinity of brittle cracks makes the macro-scale failure properties extremely sensitive to the micro-scale material disorder. Therefore: (i) Fracturing systems often display a jerky dynamics, so-called crackling…
We consider a scenario where a system experiences a disruption, and the states (representing health values) of its components continue to reduce over time, unless they are acted upon by a controller. Given this dynamical setting, we…
We study the corrections to scaling for the mass of the watershed, the bridge line, and the optimal path crack in two and three dimensions. We disclose that these models have numerically equivalent fractal dimensions and leading…
Disordered spring networks are a well-established model system to study fracture in a wide range of materials, from ceramics to polymer networks and mechanical metamaterials, across length scales from the atomistic to the macroscopic. A…
Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we…
We investigate how the removal of a single bond affects the fracture behavior of triangular spring networks, whereby we systematically vary the position of the removed bond. Our simulations show that removing the bond has two contrasting…
Collagen forms the structural scaffold of connective tissues in all mammals. Tissues are remarkably resistant against mechanical deformations because collagen molecules hierarchically self-assemble in fibrous networks that stiffen with…
The pivotal quality of proximity graphs is connectivity, i.e. all nodes in the graph are connected to one another either directly or via intermediate nodes. These types of graphs are robust, i.e., they are able to function well even if they…
Although spectacular advances in hydraulic fracturing, aka fracking, have taken place and many aspects are well understood by now, the topology, geometry and evolution of the crack system hydraulically produced in the shale still remains an…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
Unstable growth of cracks (rough crack surface and crack branching) in dynamic fracture has long been observed in various materials. Until now, there was no universally agreed upon explanation for these instabilities. Here, we demonstrate…
Fracture toughness is the material property characterizing resistance to failure. Predicting its value from the solid structure at the atomistic scale remains elusive, even in the simplest situations of brittle fracture. We report here…
In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our method is to establish some graph structures on fractal squares to reveal the…
This work joins aspects of reservoir optimization, information-theoretic optimal encoding, and at its center fractal analysis. We build on the observation that, due to the recursive nature of recurrent neural networks, input sequences…
We study the stability and roughness of propagating cracks in heterogeneous brittle two-dimensional elastic materials. We begin by deriving an equation of motion describing the dynamics of such a crack in the framework of Linear Elastic…
We address the velocity fluctuations of fastly moving cracks in stressed materials. One possible mechanism for such fluctuations is the interaction of the main crack with micro cracks (irrespective whether these are existing material…
We investigate dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the…