相关论文: Corrections to Scaling for Watersheds, Optimal Pat…

We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical…

This article is the first in a series of three papers investigating the detailed geometry of river networks. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but…

An analogy between the fractal nature of networks of arteries and that of systems of rivers has been drawn in the previous works. However, the deep structure of the hierarchy of blood vessels has not yet been revealed. This paper is devoted…

In recent decades, much attention has been focused on the topic of optimal paths in weighted networks due to its broad scientific interest and technological applications. In this work we revisit the problem of the optimal path between two…

Rivers exhibit fractal-like properties that are associated with scaling laws linking geometry and size. The optimal channel network (OCN) model, which is a mathematically tractable representation of river networks often used in theoretical…

Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially allocating these elements according to their ranks and…

How local cracks can contribute to the global cracks landscape is a goal of several scientific topics, for example, how bottlenecks can impact the robustness of traffic into a city? In one direction, cracks from cascading failures into…

The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…

Fractures are normally present in the underground and are, for some physical processes, of paramount importance. Their accurate description is fundamental to obtain reliable numerical outcomes useful, e.g., for energy management. Depending…

We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as function of the correlation…

We present an advanced algorithm for the determination of watershed lines on Digital Elevation Models (DEMs), which is based on the iterative application of Invasion Percolation (IIP). The main advantage of our method over previosly…

The optimal path crack model on uncorrelated surfaces, recently introduced by Andrade et al. (Phys. Rev. Lett. 103, 225503, 2009), is studied in detail and its main percolation exponents computed. In addition to beta/nu = 0.46 \pm 0.03 we…

We analyze the Optimal Channel Network model for river networks using both analytical and numerical approaches. This is a lattice model in which a functional describing the dissipated energy is introduced and minimized in order to find the…

We study the complexity of geometric problems on spaces of low fractal dimension. It was recently shown by [Sidiropoulos & Sridhar, SoCG 2017] that several problems admit improved solutions when the input is a pointset in Euclidean space…

By a new type of finite size scaling analysis on the square lattice, and by renormalization group calculations on hierarchical lattices we investigate the effects of dilution on optimal undirected self-avoiding paths in a random…

Optimal paths play a fundamental role in numerous physical applications ranging from random polymers to brittle fracture, from the flow through porous media to information propagation. Here for the first time we explore the path that is…

Using the flow governing equation approach to similarity, Weyburne (D. Weyburne, arXiv:1701.02364, 2016) recently showed that for 2-D turbulent boundary layer flows, the Prandtl Plus scalings are NOT, in general, the proper similarity…

We study symmetry-breaking line defects in the Wilson-Fisher theory with $O(2N+1)$ global symmetry near four dimensions and symmetry-preserving surface defects in a cubic model with $O(2N)$ global symmetry near six dimensions. We introduce…

Even though many objects and phenomena of importance in geophysics have been shown to have fractal character, there are still many of them which show self-similar character and yet to be studied. The objective of the present work is to…

The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…