Title: Renormalization Group approach to Oscillator Synchronization Speaker: Dr. Oleg Kogan, Physics Dept., CalTech and Michigan State Date/Time: Thursday, February 5, 2009, 9:00am – 10:00am Location: CSRI Building/Room 95 Brief Abstract: Nonlinear oscillators serve as a good test-bed for exploring various frontier topics in nonequilibrium statistical mechanics. One example of collective phenomena in nonequilibrium systems is spontaneous synchronization in networks of self-driven nonlinear oscillators with randomly distributed frequencies. These model a variety of natural and man-made systems, ranging from neural networks to integrated arrays of nanomechanical oscillators. If the coupling between the oscillators is weak, they will evolve in an uncoordinated fashion. In contrast, with proper connectivity and coupling strength, the population can display the same frequency as order forms. In this talk, I will begin with an overview of some known facts about synchronization, including the paradigm known as the Kuramoto model and circumstances under which it may exhibit a transition to a state of global frequency entrainment. It is known that such transition does not occur in a 1-dimensional chain of self-sustaining phase oscillators coupled via nearest-neighbor interaction. However, the system does develop interesting collective structures such as clusters of common frequency. In the second part of the talk I will describe our effort to predict properties of such clusters by means of a renormalization group (RG) method. We apply the RG to the case of Lorentzian distributions of intrinsic frequencies and couplings and investigate the statistics of the resultant cluster sizes and cluster frequencies. The distributions of cluster sizes are exponential. The characteristic cluster length develops an asymptotic power law versus the width of the coupling distribution. The RG predictions are in very good agreement with the results based numerical solution of the chain's equation of motion. At the end of the talk, I will also mention potential ways to extract information about quenched disorder by introduction of temporal noise. CSRI POC: Randall LaViolette, (505) 284-1325 |