The Persistence of Pancakes and the Revival of Self-gravity in Tidal Disruption Events
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Disclosed herein are representative embodiments of methods, apparatus, and systems for facilitating operation and control of a resource distribution system (such as a power grid). Among the disclosed embodiments is a distributed hierarchical control architecture (DHCA) that enables smart grid assets to effectively contribute to grid operations in a controllable manner, while helping to ensure system stability and equitably rewarding their contribution. Embodiments of the disclosed architecture can help unify the dispatch of these resources to provide both market-based and balancing services.
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We study the stability of current filaments produced by the Weibel, or current filamentation, instability in weakly magnetized counter-streaming plasmas. It is shown that a resonance exists between the current-carrying ions and a longitudinal drift-kink mode that strongly deforms and eventually breaks the current filaments. Analytical estimates of the wavelength, growth rate and saturation level of the resonant mode are derived and validated by three-dimensional particle-in-cell simulations. Furthermore, self-consistent simulations of counter-streaming plasmas indicate that this drift-kink mode is dominant in the slow down of the flows and in the isotropization of the magnetic field, playing an important role in the formation of collision less shocks.
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