• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

Ballistic and superdiffusive scales in the macroscopic evolution of a chain of oscillators

Komorowski, Tomasz; Olla, Stefano (2016), Ballistic and superdiffusive scales in the macroscopic evolution of a chain of oscillators, Nonlinearity, 29, 3. 10.1088/0951-7715/29/3/962

View/Open
ko-euler-scaling-revision-submitted.pdf (482.0Kb)
Type
Article accepté pour publication ou publié
Date
2016
Journal name
Nonlinearity
Volume
29
Number
3
Publisher
IOP Publishing
Publication identifier
10.1088/0951-7715/29/3/962
Metadata
Show full item record
Author(s)
Komorowski, Tomasz
Institut of Mathematics - Polish Academy of Sciences [PAN]
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider a one dimensional infinite acoustic chain of harmonic oscillators whose dynamics is perturbed by a random exchange of velocities, such that the energy and momentum of the chain are conserved. Consequently, the evolution of the system has only three conserved quantities: volume, momentum and energy. We show the existence of two space–time scales on which the en- ergy of the system evolves. On the hyperbolic scale (tε−1,xε−1) the limits of the conserved quantities satisfy a Euler system of equa- tions, while the thermal part of the energy macroscopic profile re- mains stationary. Thermal energy starts evolving at a longer time scale, corresponding to the superdiffusive scaling (tε−3/2, xε−1) and follows a fractional heat equation. We also prove the diffusive scal- ing limit of the Riemann invariants - the so called normal modes, corresponding to the linear hyperbolic propagation.
Subjects / Keywords
chain of oscillators; diffusive scaling limit of the Riemann invariants

Related items

Showing items related by title and author.

  • Thumbnail
    Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities 
    Olla, Stefano; Simon, Marielle; Komorowski, Tomasz (2018) Article accepté pour publication ou publié
  • Thumbnail
    Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise 
    Jara, Milton; Komorowski, Tomasz; Olla, Stefano (2015) Article accepté pour publication ou publié
  • Thumbnail
    On the Conversion of Work into Heat: Microscopic Models and Macroscopic Equations 
    Komorowski, Tomasz; Lebowitz, Joel L.; Olla, Stefano; Simon, Marielle (2022) Document de travail / Working paper
  • Thumbnail
    High frequency limit for a chain of harmonic oscillators with a point Langevin thermostat 
    Komorowski, Tomasz; Olla, Stefano; Ryzhik, Lenya; Spohn, Herbert (2020) Article accepté pour publication ou publié
  • Thumbnail
    Kinetic limit for a chain of harmonic oscillators with a point Langevin thermostat 
    Komorowski, Tomasz; Olla, Stefano (2020) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo