Related papers: Diffusion in scale-free networks with annealed dis…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
We study the simple random walk dynamics on an annealed version of a Small-World Network (SWN) consisting of $N$ nodes. This is done by calculating the mean number of distinct sites visited S(n) and the return probability $P_{00}(t)$ as a…
Critical behavior of the contact process is studied in annealed scale-free networks by mapping it on the random walk problem. We obtain the analytic results for the critical scaling, using the event-driven dynamics approach. These results…
An annealed version of the quenched mean-field model for epidemic spread is introduced and investigated analytically and assisted by numerical calculations. The interaction between individuals follows a prescription that is used to generate…
We study diffusion (random walks) on recursive scale-free graphs, and contrast the results to similar studies in other analytically soluble media. This allows us to identify ways in which diffusion in scale-free graphs is special. Most…
We investigate mechanisms of the typically observed recoverable prevalence in epidemic spreading. Assuming the time-independent connectivity correlations, we analyze the dynamics of spreading on linearly growing scale-free (SF) networks,…
We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of four-fold coordinated sites connected via variable length one-dimensional chains.…
Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for…
The problem of random walk is considered in one dimension in the simultaneous presence of a quenched random force field and long-range connections the probability of which decays with the distance algebraically as p_l ~ \beta l^{-s}. The…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We…
A giant cluster emerges discontinuously in bond percolation in various networks when the growth of large clusters is globally suppressed. It was recently revealed that this phenomenon occurs even in a scale-free (SF) network, where hubs…
We study shortest paths and spanning trees of complex networks with random edge weights. Edges which do not belong to the spanning tree are inactive in a transport process within the network. The introduction of quenched disorder modifies…
Above two dimensions, diffusion of a particle in a medium with quenched random traps is believed to be well-described by the annealed continuous time random walk (CTRW). We propose an approximate expression for the first-passage-time (FPT)…
Recent experimental findings on anomalous diffusion have demanded novel models that combine annealed (temporal) and quenched (spatial or static) disorder mechanisms. The comb-model is a simplified description of diffusion on percolation…
We present exact results for the fluctuations in the number of particles crossing the origin up to time $t$ in a collection of non-interacting run and tumble particles in one dimension. In contrast to passive systems, such active particles…
Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently…
Local diffusion coefficients in disordered materials such as living cells are highly heterogeneous. Quenched disorder is utilized substantially to study such complex systems, whereas its analytical treatment is difficult to handle. We…
Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…
We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the…