Related papers: Percolation Framework of the Earth's Topography
We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting…
Many papers and monographs were written about the modeling the Earth climate and its variability. However there is still an obvious need for a module that presents the fundamentals of climate modeling to students at the undergraduate level.…
We study surfaces with a constant ratio of principal curvatures in Euclidean and simply isotropic geometries and characterize rotational, channel, ruled, helical, and translational surfaces of this kind under some technical restrictions…
Dune fields are commonly associated with periodic patterns that are among the most recognizable landscapes on Earth and other planetary bodies. However, in zones of limited sediment supply, where periodic dunes elongate and align in the…
We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a…
The study of the properties and structure of a city's road network has for many years been the focus of much work, as has the mathematical modelling of the location of its retail activity and of the emergence of clustering in retail…
Complex network theory provides a powerful toolbox for studying the structure of statistical interrelationships between multiple time series in various scientific disciplines. In this work, we apply the recently proposed climate network…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only…
The Earth's surface is composed of a staggering diversity of particulate-fluid mixtures: dry to wet, dilute to dense, colloidal to granular, and attractive to repulsive particles. This material variety is matched by the range of relevant…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of non-interacting line segments and disks in two spatial dimensions. These examples serve as models for…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
Global warming is affecting our Earth's environment. For example, sea level is rising with thermal expansion of water and fresh water input from the melting of continental ice sheets due to human-induced global warming. However, observing…
We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $\sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For…
Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network…
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…
Understanding the resilience of infrastructures such as transportation network has significant importance for our daily life. Recently, a homogeneous spatial network model was developed for studying spatial embedded networks with…
Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…
Infrastructure systems, such as power, transportation, telecommunication, and water systems, are composed of multiple components which are interconnected and interdependent to produce and distribute essential goods and services. So, the…