Thomas M. Antonsen

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Title of dissertation: SYNCHRONIZATION IN CHAOTIC SYSTEMS: COUPLING OF CHAOTIC MAPS, DATA ASSIMILATION, AND WEATHER FORECASTING Seung-Jong Baek, Doctor of Philosophy, 2007 Dissertation directed by: Distinguished University Professor Edward Ott Department of Electrical and Computer Engineering The theme of this thesis is the synchronization of coupled(More)
It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time(More)
We analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed. The dynamics of this system has been the subject of long-standing interest. In 1984 Kuramoto proposed several conjectures about its behavior; ten years later, Crawford obtained the first analytical results by means of a local center manifold(More)
Title of dissertation: TWO-DIMENSIONAL TURBULENCE WITH DRAG Yue-Kin Tsang, Doctor of Philosophy, 2004 Dissertation directed by: Professor Edward Ott Department of Physics We consider the enstrophy cascade in forced two-dimensional turbulence with a linear drag force. In the presence of linear drag, the energy wavenumber spectrum drops with a power law(More)
A highly efficient, fully parallelized, fully relativistic, three-dimensional particle-in-cell model for simulating plasma and laser wakefield acceleration is described. The model is based on the quasi-static or frozen field approximation, which reduces a fully three-dimensional electromagnetic field solve and particle push to a two-dimensional field solve(More)
Fast time averaged equations are derived for the motion of particles and the generation of electromagnetic wake fields under the action of the ponderomotive potential of an ultraintense laser pulse propagating through a tenuous plasma. Based on these averaged equations, a new particle code is designed which calculates the particle trajectories on the plasma(More)
The time asymptotic decay of the variance of a passive scalar in a chaotic flow is studied. Two mechanisms for this decay, which involve processes at short and long length scales, respectively, are considered. The validity of the short length scale mechanism, which is based on Lagrangian stretching theory, is discussed. We also investigate the regimes of(More)
In a recent paper by Ott and Antonsen [Chaos 19, 023117 (2009)], it was shown for the case of Lorentzian distributions of oscillator frequencies that the dynamics of a very general class of large systems of coupled phase oscillators time-asymptotes to a particular simplified form given by Ott and Antonsen [Chaos 18, 037113 (2008)]. This comment extends this(More)
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We(More)