Understanding the complex structure of karst networks is a challenge. In this work, we characterize the fractal properties of some of the largest coastal karst network systems in the world. They are located near the town of Tulum (Quintana Roo, Mexico). Their fractal dimension d f , conductivity exponent μ and walk dimension d w are estimated using real space renormalization and numerical simulations. We obtain the following values for these exponents: d f ≈ 1.5, d w ≈ 2.4, μ ≈ 0.9. We observe that the Einstein relation holds for these structures μ ≈ −d f + d w . These results indicate that coastal karst networks can be considered as critical systems and this provides some foundations to model them within this framework.
Karstic caves, which play a key role in groundwater transport, are often organized as complex connected networks resulting from the dissolution of carbonate rocks. In this work, we propose a new model to describe and study the structures of the two largest submersed karst networks in the world. Both of these networks are located in the area of Tulum (Quintana Roo, Mexico). In a previous work [1] we showed that these networks behave as self-similar structures exhibiting well-defined scaling behaviors. In this paper, we suggest that these networks can be modeled using substructures of percolation clusters (θ -subnetworks) having similar structural behavior (in terms of fractal dimension and conductivity exponent) to those observed in Tulum's karst networks. We show in addition that these θ -subnetworks correspond to structures that minimize a global function, where this global function includes energy dissipation by the viscous forces when water flows through the network, and the cost of network formation itself.
By comparing the evolution of the local and equal load sharing fiber bundle models, we point out the paradoxical result that stresses seem to make the local load sharing model stable when the equal load sharing model is not. We explain this behavior by demonstrating that it is only an apparent stability in the local load sharing model, which originates from a statistical effect due to sample averaging. Even though we use the fiber bundle model to demonstrate the apparent stability, we argue that it is a more general feature of fracture processes.
One aim of the equal load sharing fiber bundle model is to describe the critical behavior of failure events. One way of accomplishing this, is through a discrete recursive dynamics. We introduce a continuous mesoscopic equation catching the critical behavior found through recursive dynamics. It allows us to link the model with the unifying framework of absorbing phase transitions traditionally used in the study of non-equilibrium phase transitions. Moreover, it highlights the analogy between equal load sharing and spinodal nucleation. Consequently, this work is a first step towards the quest of a field theory for fiber bundle models. J els = 0 J els = 10 -8 J els = 10 -6 J els = 10 -4 J meso = 0 J meso = 10 -8 J meso = 10 -6 J meso = 10 -4
<p>Assessing and forecasting avalanche hazard is crucial for the safety of people and infrastructure in mountain areas. Over 20 years of data covering snow precipitation, snowpack properties, weather, on-site observations, and avalanche danger has been collected in the context of operational avalanche forecasting for the Swiss Alps. The quality and breadth of this dataset makes it suitable for machine learning techniques.</p>
<p>Forecasters mainly process a huge and redundant dataset "manually" to produce daily avalanche bulletins during the winter season. The purpose of this work is to provide the forecasters automated tools to support their work.&#160;</p>
<p>By combining clustering and classification algorithms, we are able to reduce the amount of information that needs to be processed and identify relevant weather and snow patterns that characterize a given avalanche situation.</p>
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