Related papers: An Analytical and Numerical Study of Optimal Chann…
The existence and stability of the universality class associated to local minimal energy landscapes is investigated. Using extensive numerical simulations, we first study the dependence on a parameter $\gamma$ of a partial differential…
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…
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…
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…
Power minimisation in branched fluidic networks has gained significant attention in biology and engineering. The optimal network is defined by channel radii that minimise the sum of viscous dissipation and the volumetric energetic cost of…
Metabolic allometry, a common pattern in nature, is a close-to-3/4-power scaling law between metabolic rate and body mass in organisms, across and within species. An analogous relationship between metabolic rate and water volume in river…
We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape…
River networks serve as a paradigmatic example of all branching networks. Essential to understanding the overall structure of river networks is a knowledge of their detailed architecture. Here we show that sub-branches are distributed…
We analyze the microscopic dynamics of vortex motion through channels that form river-like fractal networks in a variety of superconducting samples, and relate it to macroscopic measurable quantities such as the power spectrum. As a…
The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method.…
We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamics and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A…
Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland…
A cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed.…
Landscapes evolve toward surfaces with complex networks of channels and ridges in response to climatic and tectonic forcing. Here we analyze variational principles giving rise to minimalist models of landscape evolution as a system of…
The hierarchy of channel networks in landscapes displays features that are characteristic of non-equilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial…
We consider two variational models for transport networks, an urban planning and a branched transport model, in which the degree of network complexity and ramification is governed by a small parameter $\varepsilon>0$. Smaller $\varepsilon$…
Both natural and engineered supply networks exhibit universal structural patterns, such as the formation of loops, yet the principles governing optimal structures remain unclear. These patterns can be interpreted as solutions of…
The structure of pipe networks minimizing the total energy dissipation rate is studied analytically. Among all the possible pipe networks that can be built with a given total pipe volume (or pipe lateral surface area), the network which…
In this paper we study the problem of learning a shallow artificial neural network that best fits a training data set. We study this problem in the over-parameterized regime where the number of observations are fewer than the number of…
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of…