Related papers: Where do rivers grow? Path selection and growth in…

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.…

Natural rivers connect to each other to form networks. The geometric structure of a river network can significantly influence spatial dynamics of populations in the system. We consider a process-oriented model to describe population…

Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acyclic networks (i.e., trees) are optimal structures when…

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…

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…

Inspired by river networks and other structures formed by Laplacian growth, we use the Loewner equation to investigate the growth of a network of thin fingers in a diffusion field. We first review previous contributions to illustrate how…

This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and suggest its compact parameterization. The downstream network…

Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…

Biological transport networks adapt through dynamic interactions between material transport and structural modification during growth and development. In this work, we present a model of transport network growth driven by local material…

Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…

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…

Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…

A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…

Inspired by the structure of technological networks, we discuss network evolution mechanisms which give rise to topological properties found in real spatial networks. Thus, the peculiar structure of transport and distribution networks is…

In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…

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…

Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium in response to the flow, in turn causing flow pathways to evolve. We…

Growth of wormholes in porous media can lead to self-organization of flow networks with an overwhelming geometric complexity. Despite decades of study, the mechanism by which a dominant wormhole develops its path during growth remains…

Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties…

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…