Related papers: Transport Processes on Homogeneous Planar Graphs w…
While ubiquitous, energy redistribution remains a poorly understood facet of the nonequilibrium thermodynamics of biomolecules. At the molecular level, finite-size effects, pronounced nonlinearities, and ballistic processes produce behavior…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as…
We present a comparative network theoretic analysis of the two largest global transportation networks: The worldwide air-transportation network (WAN) and the global cargoship network (GCSN). We show that both networks exhibit striking…
This paper introduces a new macroscopic perspective for simulating transportation networks. The idea is to look at the network as connected nodes. Each node sends an information package to its neighbors. Basically, the information package…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
We consider the effects of network topology on the optimality of packet routing quantified by $\gamma_c$, the rate of packet insertion beyond which congestion and queue growth occurs. The key result of this paper is to show that for any…
The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in $\R^n$. Our primary contribution is a stochastic homogenization result that characterizes the effective…
We study the transport properties of a long non-uniform quantum wire where the electron-electron interactions and the density vary smoothly at large length scales. We show that these inhomogeneities lead to a finite resistivity of the wire,…
We have generalized the semi-analytic approach of special flow to the description of flows of passive particles taking into account internal noise. The model is represented by a series of recurrence relations. The recurrence relations are…
The study of complex networks sheds light on the relation between the structure and function of complex systems. One remarkable result is the absence of an epidemic threshold in infinite-size scale-free networks, which implies that any…
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
Understanding the dynamics of traffic clusters is crucial for enhancing urban transportation systems, particularly in managing congestion and free-flow states. This study applies computational percolation theory to analyze the formation and…
In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric…
Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free…
Using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations.…
The recently introduced hierarchical regular networks HN3 and HN4 are analyzed in detail. We use renormalization group arguments to show that HN3, a 3-regular planar graph, has a diameter growing as \sqrt{N} with the system size, and random…
Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…
The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns of activity…