Related papers: Robust network formation with biological applicati…
We study hierarchical properties of optimal transportation networks with biological background. The networks are obtained as minimizers of an energy functional which involves a metabolic cost term of a power-law form with exponent…
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…
The branching geometry of biological transport networks is characterized by a diameter scaling exponent $\alpha$. Two structural attractors compete: impedance matching ($\alpha \sim 2$) for pulsatile flow and viscous-metabolic minimization…
We introduce a mesoscopic model for natural network formation processes, acting as a bridge between the discrete and continuous network approach proposed by Hu and Cai. The models are based on a common approach where the dynamics of the…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
Biological transport networks are highly optimized structures that ensure power-efficient distribution of fluids across various domains, including animal vasculature and plant venation. Theoretically, these networks can be described as…
Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
Units of complex systems -- such as neurons in the brain or individuals in societies -- must communicate efficiently to function properly: e.g., allowing electrochemical signals to travel quickly among functionally connected neuronal areas…
Why does the mammalian vascular tree maintain a conserved branching exponent $\alpha^* \approx 2.72$ across a $10^7$-fold range in body mass, despite a fundamental shift from viscous to wave-dominated transport? We prove this universality…
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…
This paper deals with the large-scale behaviour of dynamical optimal transport on $\mathbb{Z}^d$-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes…
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…
Numerous networks, such as transportation, distribution and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods,…
Understanding the structure of minor-free metrics, namely shortest path metrics obtained over a weighted graph excluding a fixed minor, has been an important research direction since the fundamental work of Robertson and Seymour. A…
Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral…
The congestion formation on a urban road network is one of the key issue for the development of a sustainable mobility in the future smart cities. In this work we propose a reductionist approach studying the stationary states of a simple…
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. Given a flow (traffic path)…
Coherent transport of an excitation through a network corresponds to continuous-time quantum walk on a graph, and the transport properties of the system may be radically different depending on the graph and on the initial state. The…
Motivated by recent physics papers describing the formation of biological transport networks we study a discrete model proposed by Hu and Cai consisting of an energy consumption function constrained by a linear system on a graph. For the…