Dynamical Systems Seminar: Juan Restrepo
Stabilization of incoherence in the disordered Hamiltonian Mean Field model
Applied Mathematics,Ìý
Date and time:Ìý
Thursday, October 17, 2013 - 2:00pm
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ECCR 257
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We study the Hamiltonian Mean Field model of coupled Hamiltonian rotors with a heterogeneous distribution of moments of inertia and coupling strengths. We show that when the parameters of the rotors are heterogeneous, finite size fluctuations can greatly modify the coupling strength at which the incoherent state loses stability by inducing correlations between the momentum and parameters of the rotors. For unimodal parameter distributions, we find an analytical expression for the modified critical coupling strength in terms of statistical properties of the parameter distributions and confirm our results with numerical simulations. We find numerically that these effects disappear for strongly bimodal parameter distributions.