Renormalization of oscillator lattices with disorder.
(2009) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)20010101+01:0020160101+01:00 79(5 Pt 1). Abstract
 A realspace 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 secondorder phase transition toward macroscopic synchronization are deduced. The analysis is potentially exact but relies in part on unproven assumptions. Numerically, secondorder phase transitions with the predicted properties are observed as g increases in two structurally different twodimensional 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 realspace 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 secondorder phase transition toward macroscopic synchronization are deduced. The analysis is potentially exact but relies in part on unproven assumptions. Numerically, secondorder phase transitions with the predicted properties are observed as g increases in two structurally different twodimensional 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 wellknown result that it can be ruled out for D<3 is regained. (Less)
Please use this url to cite or link to this publication:
http://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)20010101+01:0020160101+01:00
 volume
 79
 issue
 5 Pt 1
 publisher
 American Physical Society
 external identifiers

 wos:000266500700028
 pmid:19518423
 scopus:67149104087
 ISSN
 15393755
 DOI
 10.1103/PhysRevE.79.051114
 language
 English
 LU publication?
 yes
 id
 509e07d7009a473f9805c61b3e92c24b (old id 1434321)
 date added to LUP
 20090702 14:44:53
 date last changed
 20171210 04:41:05
@article{509e07d7009a473f9805c61b3e92c24b, abstract = {A realspace 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 secondorder phase transition toward macroscopic synchronization are deduced. The analysis is potentially exact but relies in part on unproven assumptions. Numerically, secondorder phase transitions with the predicted properties are observed as g increases in two structurally different twodimensional 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 wellknown result that it can be ruled out for D<3 is regained.}, articleno = {051114}, author = {Östborn, Per}, issn = {15393755}, language = {eng}, number = {5 Pt 1}, publisher = {American Physical Society}, series = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)20010101+01:0020160101+01:00}, title = {Renormalization of oscillator lattices with disorder.}, url = {http://dx.doi.org/10.1103/PhysRevE.79.051114}, volume = {79}, year = {2009}, }