Related papers: Exact solution for mean first-passage time on a ps…
We determine the survival probability and first-passage time (FPT) to capture for a harmonically trapped particle, diffusing outside an absorbing spherical boundary by directly solving the differential equation for the survival probability.…
The global first passage time density of a network is the probability that a random walker released at a random site arrives at an absorbing trap at time T. We find simple expressions for the mean global first passage time <T> for five…
It has been recently reported that the reciprocity of real-life weighted networks is very pronounced, however its impact on dynamical processes is poorly understood. In this paper, we study random walks in a scale-free directed weighted…
We derive a general exact formula for the mean first passage time (MFPT) from a fixed point inside a planar domain to an escape region on its boundary. The underlying mixed Dirichlet-Neumann boundary value problem is conformally mapped onto…
We investigate the multifractals of the normalized first passage time on one-dimensional small-world network with both reflecting and absorbing barriers. The multifractals is estimated from the distribution of the normalized first passage…
We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and…
Average trapping time (ATT) is central in the trapping problem since it is a key indicator characterizing the efficiency of the problem. Previous research has provided the scaling of a lower bound of the ATT for random walks in general…
We present general methods to exactly calculate mean-first passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and…
Graphs are commonly used to model various complex systems, including social networks, power grids, transportation networks, and biological systems. In many applications, the connectivity of these networks can be expressed through the Mean…
Many biological, social, and communication systems can be modeled by ``searchers'' moving through a complex network. For example, intracellular cargo is transported on tubular networks, news and rumors spread through online social networks,…
Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…
Fractal dimension is central to understanding dynamical processes occurring on networks; however, the relation between fractal dimension and random walks on fractal scale-free networks has been rarely addressed, despite the fact that such…
We compute the mean first passage time (MFPT) for a Brownian particle inside a two-dimensional disk with reflective boundaries and a small interior trap that is rotating at a constant angular velocity. The inherent symmetry of the problem…
We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in…
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not…
First passage phenomena arise across physics, biology, and finance when stochastic processes first reach a threshold, triggering downstream events. Examples include the irreversible exit from a domain, a biochemical reaction, a financial…
We develop an analytical approach which provides the dependence of the mean first-passage time (MFPT) for random walks on complex networks both on the target connectivity and on the source-target distance. Our approach puts forward two…
We study the first passage time (FPT) problem for biased continuous time random walks. Using the recently formulated framework of fractional Fokker-Planck equations, we obtain the Laplace transform of the FPT density function when the bias…
We study the problem of searching for a fixed path $\epsilon_0\epsilon_1\cdots\epsilon_l$ on a network through random walks. We analyze the first hitting time of tracking the path, and obtain exact expression of mean first hitting time…
Fractal phenomena may be widely observed in a great number of complex systems. In this paper, we revisit the well-known Vicsek fractal, and study some of its structural properties for purpose of understanding how the underlying topology…