Clustering behaviors in networks of integrate-and-fire oscillators

Clustering behavior is studied in a model of integrate-and-fire oscillators with excitatory pulse coupling. When considering a population of identical oscillators, the main result is a proof of global convergence to a phase-locked clustered behavior. The robustness of this clustering behavior is then investigated in a population of nonidentical oscillators by studying the transition from total clustering to the absence of clustering as the group coherence decreases. A robust intermediate situation of partial clustering, characterized by few oscillators traveling among nearly phase-locked clusters, is of particular interest. The analysis complements earlier studies of synchronization in a closely related model. © 2008 American Institute of Physics.

First-principles energetics of water clusters and ice: a many-body analysis.

Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.