Related papers: Why is topography fractal?
The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to…
We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of…
To describe the energy transport in the seismic coda, we introduce a system of radiative transfer equations for coupled surface and body waves in a scalar approximation. Our model is based on the Helmholtz equation in a half-space geometry…
The size of large cliff failures may be described in several ways, for instance considering the horizontal eroded area at the cliff top and the maximum local retreat of the coastline. Field studies suggest that, for large failures, the…
The concept of derivative coordinate functions proved useful in the formulation of analytic fractal functions to represent smooth symmetric binary fractal trees [1]. In this paper we introduce a new geometry that defines the fractal space…
In the present article, topological, metric, and fractal properties of certain sets are investigated. These sets are images of sets whose elements have restrictions on using digits or combinations of digits in own s-adic representations,…
Protein dynamics is a fundamental element to comprehend their biological functions. However, a theoretical picture providing microscopic-detail explanation of its relevant features is still missing. One of the outmost relevant properties…
The distribution of fracture network is crucial to characterize the behaviors of flow field and solute transport, especially for enhanced geothermal systems, as fractures provide preferential flow paths. However, estimating the parameters…
The impact of inhomogeneous arrangement of nodes in space on network organization cannot be neglected in most of real-world scale-free networks. Here, we wish to suggest a model for a geographical network with nodes embedded in a fractal…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the…
Land reclamation methods, indispensable for the proper development of modern coastal cities, are ecologically destructive. We present a fractal structure, similar to a Sierpinski triangle, which solves this problem by resting directly on…
In this work we present a model reduction procedure to derive a hybrid-dimensional framework for the mathematical modeling of reactive transport in fractured porous media. Fractures are essential pathways in the underground which allow fast…
In this paper, we'll answer several abstract, formal questions about the nature of crack growth and nucleation. Bringing a field theory point of view to fracture illuminates things in what I hope will be an entertaining way. Formally, what…
What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by…
The process of frictional rupture, i.e. the failure of frictional systems, abounds in the technological and natural world around us, ranging from squealing car brake pads to earthquakes along geological faults. A general framework for…
Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that…
The two-fractal overlap model of earthquake shows that the contact area distribution of two fractal surfaces follows power law decay in many cases and this agrees with the Guttenberg-Richter power law. Here, we attempt to predict the large…
In this paper we consider the multiscale modelling of water transport in vegetated soil. In the microscopic model we distinguish between subdomains of soil and plant tissue, and use the Richards equation to model the water transport through…
The universal fractality of river networks is very well known, however understanding of the underlying mechanisms for them is still lacking in terms of stochastic processes. By introducing probability changing dynamically, we have described…