Related papers: Transport Processes on Homogeneous Planar Graphs w…
The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…
We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…
The transport of particles in cells is influenced by the properties of intracellular networks they traverse while searching for localized target regions or reaction partners. Moreover, given the rapid turnover in many intracellular…
We study the urban-scale macroscopic traffic flow in city networks. Star graph is considered as traffic network. Star graphs with controlled traffic flow are transformed to various cell-transmission graphs by using the cell transmission…
Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a…
The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…
We model information traffic on scale-free networks by introducing the node queue length L proportional to the node degree and its delivering ability C proportional to L. The simulation gives the overall capacity of the traffic system,…
To analyze the transport of information or material from a source to every node of a network we use two quantities introduced in the study of river networks: the cost and the flow. For a network with $K$ nodes and $M$ levels, we show that…
We study the dynamics of epidemic spreading processes aimed at spontaneous dissemination of information updates in populations with complex connectivity patterns. The influence of the topological structure of the network in these processes…
In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media…
In this paper a lattice model for diffusional transport of particles in the interphase cell nucleus is proposed. Dense networks of chromatin fibers are created by three different methods: randomly distributed, non-interconnected obstacles,…
We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…
We study the transport properties of model networks such as scale-free and Erd\H{o}s-R\'{e}nyi networks as well as a real network. We consider the conductance $G$ between two arbitrarily chosen nodes where each link has the same unit…
Homogenization method is used to analyse the equivalent behavior of transient flow of a passive solute through highly heterogeneous porous media. The flow is governed by a coupled system which includes an elliptic equation and a linear…
Communication of signals among nodes in a complex network poses fundamental problems of efficiency and cost. Routing of messages along shortest paths requires global information about the topology, while spreading by diffusion, which…
Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is…
We study kinetic transport through modular networks consisting of alternating domains using both analytical and numerical methods. We demonstrate that the mean velocity is insensitive to the local structure of the network, and it indicates…
For realistic scale-free networks, we investigate the traffic properties of stochastic routing inspired by a zero-range process known in statistical physics. By parameters $\alpha$ and $\delta$, this model controls degree-dependent hopping…
We describe how noise propagates through a network by calculating the variance of the outputs. Using stochastic calculus and dynamical systems theory, we study the network topologies that accentuate or alleviate the effect of random…
In this study, we investigate the complexity of two-phase flow (air/water) in a heterogeneous soil sample by using complex network theory, where the supposed porous media is non-deformable media, under the time-dependent gas pressure. Based…