From noise on the sites to noise on the links: Discretizing the conserved Kardar-Parisi-Zhang equation in real space.
Phys Rev E
; 109(6-1): 064136, 2024 Jun.
Article
de En
| MEDLINE
| ID: mdl-39020940
ABSTRACT
Numerical analysis of conserved field dynamics has been generally performed with pseudospectral methods. Finite differences integration, the common procedure for nonconserved field dynamics, indeed struggles to implement a conservative noise in the discrete spatial domain. In this work we present a method to generate a conservative noise in the finite differences framework, which works for any discrete topology and boundary conditions. We apply it to numerically solve the conserved Kardar-Parisi-Zhang (cKPZ) equation, widely used to describe surface roughening when the number of particles is conserved. Our numerical simulations recover the correct scaling exponents α, ß, and z in d=1 and in d=2. To illustrate the potentiality of the method, we further consider the cKPZ equation on different kinds of nonstandard lattices and on the random Euclidean graph. This is a unique numerical study of conserved field dynamics on an irregular topology, paving the way for a broad spectrum of possible applications.
Texte intégral:
1
Collection:
01-internacional
Base de données:
MEDLINE
Langue:
En
Journal:
Phys Rev E
/
Phys. rev., E (Online)
/
Physical review. E (Online)
Année:
2024
Type de document:
Article
Pays d'affiliation:
Italie
Pays de publication:
États-Unis d'Amérique