Related papers: Anomalous biased diffusion in networks
In this paper, we consider a random network such that there could be a link between any two nodes in the network with a certain probability (plink). Diffusion is the phenomenon of spreading information throughout the network, starting from…
A one-dimensional run-and-tumble particle (RTP) switches randomly between a left and right moving state of constant speed $v$. This type of motion arises in a wide range of applications in cell biology, including the unbiased growth and…
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we…
We study a majority based preference diffusion model in which the members of a social network update their preferences based on those of their connections. Consider an undirected graph where each node has a strict linear order over a set of…
In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the…
We propose a model of sub-diffusion in which an external force is acting on a particle at all times not only at the moment of jump. The implication of this assumption is the dependence of the random trapping time on the force with the…
We present analytical results for the distribution of first-passage (FP) times of random walks (RWs) on random regular graphs that consist of $N$ nodes of degree $c \ge 3$. Starting from a random initial node at time $t=0$, at each time…
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…
We study the first-passage time (FPT) problem for widespread recurrent processes in confined though large systems and present a comprehensive framework for characterizing the FPT distribution over many time scales. We find that the FPT…
Diffusion with an incorporated resetting mechanism provides a reference framework for modeling a wide range of natural phenomena. Within this framework, the optimal resetting rate is a key quantity that arises from the optimization of the…
A wide variety of real-life networks share two remarkable generic topological properties: scale-free behavior and modular organization, and it is natural and important to study how these two features affect the dynamical processes taking…
We consider the random walk of a particle in a two-dimensional self-affine random potential of Hurst exponent $H=1/2$ in the presence of an external force $F$. We present numerical results on the statistics of first-passage times that…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
If a piece of information is released from a media site, can it spread, in 1 month, to a million web pages? This influence estimation problem is very challenging since both the time-sensitive nature of the problem and the issue of…
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)…
Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random…
In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto < F_{i} >…
The first passage time (FPT) is a generic measure that quantifies when a random quantity reaches a specific state. We consider the FTP distribution in nonlinear stochastic biochemical networks, where obtaining exact solutions of the…
In this paper, we analyze the effects of random sampling on adaptive diffusion networks. These networks consist in a collection of nodes that can measure and process data, and that can communicate with each other to pursue a common goal of…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…