Related Experiment Video
Updated: Jun 28, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Shape effects in the fluctuations of random isochrones on a square lattice
Iván Álvarez Domenech1, Javier Rodríguez-Laguna2, Rodolfo Cuerno3
1Dto. Física Matemática y de Fluidos, Universidad Nacional de Educación a Distancia, Las Rozas 28232, Spain.
Abstract:
We consider the isochrone curves in first-passage percolation on a 2D square lattice, i.e., the boundary of the set of points which can be reached in less than a given time from a certain origin. The occurrence of an instantaneous average shape is described in terms of its Fourier components, highlighting a crossover between a diamond and a circular geometry as the noise level is increased. Generally, these isochrones can be understood as fluctuating interfaces with an inhomogeneous local width which reveals the underlying lattice structure. We show that once these inhomogeneities have been taken into account, the fluctuations fall into the Kardar-Parisi-Zhang universality class with very good accuracy, where they reproduce the Family-Vicsek Ansatz with the expected exponents and the Tracy-Widom histogram for the local radial fluctuations.
More Related Videos
11:03An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
10:35Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
Related Concept Videos
Trends in Lattice Energy: Ion Size and Charge
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about...
Fermi Level Dynamics
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Atomic Nuclei: Larmor Precession Frequency
Atomic Nuclei: Nuclear Spin State Population Distribution