We consider a non-acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the curvature (or bending) of the chain satisfy a system of evolution equations. We prove that, in a diffusive space-time scaling, the curvature and momentum evolve following a linear system that corresponds to a damped EULER–BERNOULLI beam equation. The macroscopic energy density evolves following a non linear diffusive equation. In particular, the energy transfer is diffusive in this dynamics. This provides a first rigorous example of a normal diffusion of energy in a one dimensional dynamics that conserves the momentum.

Diffusive Propagation of Energy in a Non-acoustic Chain

Olla, Stefano
2017-01-01

Abstract

We consider a non-acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the curvature (or bending) of the chain satisfy a system of evolution equations. We prove that, in a diffusive space-time scaling, the curvature and momentum evolve following a linear system that corresponds to a damped EULER–BERNOULLI beam equation. The macroscopic energy density evolves following a non linear diffusive equation. In particular, the energy transfer is diffusive in this dynamics. This provides a first rigorous example of a normal diffusion of energy in a one dimensional dynamics that conserves the momentum.
2017
OSCILLATORS; CONDUCTION
File in questo prodotto:
File Dimensione Formato  
2017_ArchRationalMechAnal_223_Komorowski.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Accesso gratuito
Dimensione 751.15 kB
Formato Adobe PDF
751.15 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12571/16074
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
social impact