Skip to Main content Skip to Navigation
Theses

Nonequilibrium critical phenomena : exact Langevin equations, erosion of tilted landscapes.

Abstract : This manuscript is focused on the study of critical phenomena taking place out-of-equilibrium. In the description of such phenomena, Langevin equations are ubiquitous and are usually derived in a phenomenological way by adding a noise term to a deterministic mean-field equation. However, I show that for reaction-diffusion processes it is in fact possible to derive an exact Langevin equation from the microscopic process. A second part of my thesis work has been devoted to the study of specific nonequilibrium critical phenomena using the nonperturbative renormalization group (NPRG), which is a modern implementation of Wilson and Kadanoff's block-spin idea. This tool, very powerful in an equilibrium context, takes care of the growing spatial fluctuations that arise near criticality through the use of a regulator. In a nonequilibrium context, the temporal fluctuations also have to be controlled. I have therefore designed a regulator that tackles both spatial and temporal fluctuations. Finally, I have applied the NPRG techniques to a model of landscape erosion: indeed, the generic scaling behaviour that appear in erosional landscapes suggests the existence of an underlying mechanism naturally fine-tuned to be critical. The Kardar-Parisi-Zhang equation seems to give a correct model for landscape erosion at large length scale (>2 km), but fails to predict the scaling observed at smaller scale. A different model was thus suggested which takes into account the intrinsic anisotropy at smaller length scale (the slope of the mountain). Using NPRG techniques, I show that this model possesses a line of fixed points associated with a continuous range of scaling exponents.
Document type :
Theses
Complete list of metadatas

Cited literature [221 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-01690438
Contributor : Abes Star :  Contact
Submitted on : Tuesday, January 23, 2018 - 9:45:08 AM
Last modification on : Friday, May 29, 2020 - 4:02:03 PM
Long-term archiving on: : Thursday, May 24, 2018 - 11:04:37 AM

File

2017PA066241.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01690438, version 1

Citation

Charlie Duclut. Nonequilibrium critical phenomena : exact Langevin equations, erosion of tilted landscapes.. Physics [physics]. Université Pierre et Marie Curie - Paris VI, 2017. English. ⟨NNT : 2017PA066241⟩. ⟨tel-01690438⟩

Share

Metrics

Record views

405

Files downloads

685