Renormalization of oscillator lattices with disorder.
(2009) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 79(5 Pt 1).- Abstract
- A real-space renormalization transformation is constructed for lattices of nonidentical oscillators with dynamics of the general form dvarphi_{k}/dt=omega_{k}+g summation operator_{l}f_{lk}(varphi_{l},varphi_{k}) . The transformation acts on ensembles of such lattices. Critical properties corresponding to a second-order phase transition toward macroscopic synchronization are deduced. The analysis is potentially exact but relies in part on unproven assumptions. Numerically, second-order phase transitions with the predicted properties are observed as g increases in two structurally different two-dimensional oscillator models. One model has smooth coupling f_{lk}(varphi_{l},varphi_{k})=phi(varphi_{l}-varphi_{k}) , where phi(x) is nonodd. The... (More)
- A real-space renormalization transformation is constructed for lattices of nonidentical oscillators with dynamics of the general form dvarphi_{k}/dt=omega_{k}+g summation operator_{l}f_{lk}(varphi_{l},varphi_{k}) . The transformation acts on ensembles of such lattices. Critical properties corresponding to a second-order phase transition toward macroscopic synchronization are deduced. The analysis is potentially exact but relies in part on unproven assumptions. Numerically, second-order phase transitions with the predicted properties are observed as g increases in two structurally different two-dimensional oscillator models. One model has smooth coupling f_{lk}(varphi_{l},varphi_{k})=phi(varphi_{l}-varphi_{k}) , where phi(x) is nonodd. The other model is pulse coupled, with f_{lk}(varphi_{l},varphi_{k})=delta(varphi_{l})phi(varphi_{k}) . Lower bounds for the critical dimensions for different types of coupling are obtained. For nonodd coupling, macroscopic synchronization cannot be ruled out for any dimension D>/=1 , whereas in the case of odd coupling, the well-known result that it can be ruled out for D<3 is regained. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1434321
- author
- Östborn, Per LU
- organization
- publishing date
- 2009
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
- volume
- 79
- issue
- 5 Pt 1
- article number
- 051114
- publisher
- American Physical Society
- external identifiers
-
- wos:000266500700028
- pmid:19518423
- scopus:67149104087
- pmid:19518423
- ISSN
- 1539-3755
- DOI
- 10.1103/PhysRevE.79.051114
- language
- English
- LU publication?
- yes
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Mathematical Physics (Faculty of Technology) (011040002), Classical archaeology and ancient history (015004001)
- id
- 509e07d7-009a-473f-9805-c61b3e92c24b (old id 1434321)
- date added to LUP
- 2016-04-04 07:10:31
- date last changed
- 2022-01-29 01:49:37
@article{509e07d7-009a-473f-9805-c61b3e92c24b,
abstract = {{A real-space renormalization transformation is constructed for lattices of nonidentical oscillators with dynamics of the general form dvarphi_{k}/dt=omega_{k}+g summation operator_{l}f_{lk}(varphi_{l},varphi_{k}) . The transformation acts on ensembles of such lattices. Critical properties corresponding to a second-order phase transition toward macroscopic synchronization are deduced. The analysis is potentially exact but relies in part on unproven assumptions. Numerically, second-order phase transitions with the predicted properties are observed as g increases in two structurally different two-dimensional oscillator models. One model has smooth coupling f_{lk}(varphi_{l},varphi_{k})=phi(varphi_{l}-varphi_{k}) , where phi(x) is nonodd. The other model is pulse coupled, with f_{lk}(varphi_{l},varphi_{k})=delta(varphi_{l})phi(varphi_{k}) . Lower bounds for the critical dimensions for different types of coupling are obtained. For nonodd coupling, macroscopic synchronization cannot be ruled out for any dimension D>/=1 , whereas in the case of odd coupling, the well-known result that it can be ruled out for D<3 is regained.}},
author = {{Östborn, Per}},
issn = {{1539-3755}},
language = {{eng}},
number = {{5 Pt 1}},
publisher = {{American Physical Society}},
series = {{Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)}},
title = {{Renormalization of oscillator lattices with disorder.}},
url = {{http://dx.doi.org/10.1103/PhysRevE.79.051114}},
doi = {{10.1103/PhysRevE.79.051114}},
volume = {{79}},
year = {{2009}},
}