Related papers: Preferential Behaviour and Scaling in Diffusive Dy…
The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
Particles diffusing near interfaces face anisotropic resistance to motion due to hydrodynamic interactions. While this has been extensively studied near \textit{hard} interfaces since the works of Lorentz and Brenner, our understanding of…
We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s)…
Interfaces moving in a disordered medium exhibit stochastic velocity fluctuations obeying universal scaling relations related to the presence or absence of conservation laws. For fluid invasion of porous media, we show that the fluctuations…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…
We consider the role of network geometry in two types of diffusion processes: transport of constant-density information packets with queuing on nodes, and constant voltage-driven tunneling of electrons. The underlying network is a…
The dispersion of a passive scalar by wall turbulence, in the limit of infinite Peclet number, is analyzed using frozen velocity fields from the DNS by our group. The Lagrangian trajectories of fluid particles in those fields are integrated…
We study the dynamics of the Internet topology based on the empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
Traffic fluctuation has so far been studied on unweighted networks. However many real traffic systems are better represented as weighted networks, where nodes and links are assigned a weight value representing their physical properties such…
Isolated complex networks have been studied deeply in the last decades due to the fact that many real systems can be modeled using these types of structures. However, it is well known that the behavior of a system not only depends on…
In the paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing susceptibilities of different networks to changes in external fields. In the…
We study the influence of diffusion on the scaling properties of the first order structure function, S_1, of a two-dimensional chaotically advected passive scalar with finite lifetime, i.e., with a decaying term in its evolution equation.…
Recent studies have shown that in the presence of noise both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper we…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
Growing synthetic networks that follow power law distributions of a node's degree often involves adding one node at a time. Each node is added to the network with a fixed amount of edges and those edges are frozen for all future time steps.…
Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…