Related Experiment Video
Updated: Dec 14, 2025

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
Published on: July 29, 2013
First-passage percolation under extreme disorder: From bond percolation to Kardar-Parisi-Zhang universality
Daniel Villarrubia1, Iván Álvarez Domenech1, Silvia N Santalla2
1Dpto. Física Matemática y de Fluidos, UNED, Spain.
Abstract:
We consider the statistical properties of arrival times and balls on first-passage percolation (FPP) two-dimensional square lattices with strong disorder in the link times. A previous work showed a crossover in the weak disorder regime, between Gaussian and Kardar-Parisi-Zhang (KPZ) universality, with the crossover length decreasing as the noise amplitude grows. On the other hand, this work presents a very different behavior in the strong-disorder regime. An alternative crossover length appears below which the model is described by bond-percolation universality class. This characteristic length scale grows with the noise amplitude and diverges at the infinite-disorder limit. We provide a thorough characterization of the bond-percolation phase, reproducing its associated critical exponents through a careful scaling analysis of the balls, which is carried out through a continuous mapping of the FPP passage time into the occupation probability of the bond-percolation problem. Moreover, the crossover length can be explained merely in terms of properties of the link-time distribution. The interplay between the characteristic length and the correlation length intrinsic to bond percolation determines the crossover between the initial percolation-like growth and the asymptotic KPZ scaling.
More Related Videos
Related Concept Videos
First Law: Particles in One-dimensional Equilibrium
Entropy
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about...
Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
Propagation of Uncertainty from Random Error

