Cooling nonlinear lattices toward energy localization
TLDR
The energy relaxation process produced by surface damping on lattices of classical anharmonic oscillators is described and a statistical analysis of the resulting quasistationary state through the distribution of breathers' energies yield information on their effective interactions.Abstract:
We describe the energy relaxation process produced by surface damping on lattices of classical anharmonic oscillators. Spontaneous emergence of localized vibrations dramatically slows down dissipation and gives rise to quasistationary states where energy is trapped in the form of a gas of weakly interacting discrete breathers. In one dimension, strong enough on-site coupling may yield stretched-exponential relaxation which is reminiscent of glassy dynamics. We illustrate the mechanism generating localized structures and discuss the crucial role of the boundary conditions. For two-dimensional lattices, the existence of a gap in the breather spectrum causes the localization process to become activated. A statistical analysis of the resulting quasistationary state through the distribution of breathers’ energies yield information on their effective interactions.read more
Citations
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Discrete breathers — Advances in theory and applications
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Discrete Breathers: Localization and transfer of energy in discrete Hamiltonian nonlinear systems
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Discrete breathers in protein structures
TL;DR: In this paper, a numerical surface cooling approach was used to show that highly energetic discrete breathers (DBs) can form in the stiffest parts of nonlinear network models of large protein structures.
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Long-range energy transfer in proteins
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Discrete breathers in protein structures
TL;DR: The regions of protein structures where DBs form easily are unfailingly the most highly connected ones, also characterized by weak local clustering, which reinforces the idea that localized modes of nonlinear origin may play an important biological role, e.g., by providing a ready channel for energy storage and/or contributing to lower energy barriers of chemical reactions.
References
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Discrete Breathers
Sergej Flach,C. R. Willis +1 more
TL;DR: In this article, the existence of discrete breathers in nonlinear classical Hamiltonian lattices has been studied and existence proofs, necessary existence conditions, and structural stability of such breathers have been discussed, as well as potential applications in lattice dynamics of solids.
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Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
Robert S. MacKay,Serge Aubry +1 more
TL;DR: In this paper, the existence of time-periodic, spatially localized solutions for weakly coupled oscillators is proved for a broad range of time reversible or Hamiltonian networks.
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Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices
TL;DR: In this paper, the authors studied the energy properties of discrete breathers in one-, two-, and three-dimensional lattices and showed that they have a positive lower bound if the lattice dimension of a given nonlinear lattice is greater than or equal to a certain critical value.
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Localization and equipartition of energy in the b-FPU chain: chaotic breathers
Thierry Cretegny,Thierry Cretegny,Thierry Dauxois,Thierry Dauxois,Stefano Ruffo,Alessandro Torcini +5 more
TL;DR: In this article, the evolution of the β-FPU chain is studied considering as initial condition the highest frequency mode, and the lifetime of the chaotic breather is related to the time necessary for the system to reach equipartition.
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Modulational instability: first step towards energy localization in nonlinear lattices
TL;DR: In this paper, the authors studied the modulational instability in discrete lattices and showed how the discreteness drastically modifies the stability condition and predicted the evolution of a linear wave in the presence of noise.