12 research outputs found
Generalized universal instability: Transient linear amplification and subcritical turbulence
In this work we numerically demonstrate both significant transient (i.e.
non-modal) linear amplification and sustained nonlinear turbulence in a kinetic
plasma system with no unstable eigenmodes. The particular system considered is
an electrostatic plasma slab with magnetic shear, kinetic electrons and ions,
weak collisions, and a density gradient, but with no temperature gradient. In
contrast to hydrodynamic examples of non-modal growth and subcritical
turbulence, here there is no sheared flow in the equilibrium. Significant
transient linear amplification is found when the magnetic shear and
collisionality are weak. It is also demonstrated that nonlinear turbulence can
be sustained if initialized at sufficient amplitude. We prove these two
phenomena are related: when sustained turbulence occurs without unstable
eigenmodes, states that are typical of the turbulence must yield transient
linear amplification of the gyrokinetic free energy
Kuramoto model with coupling through an external medium
Synchronization of coupled oscillators is often described using the Kuramoto
model. Here we study a generalization of the Kuramoto model where oscillators
communicate with each other through an external medium. This generalized model
exhibits interesting new phenomena such as bistability between synchronization
and incoherence and a qualitatively new form of synchronization where the
external medium exhibits small-amplitude oscillations. We conclude by
discussing the relationship of the model to other variations of the Kuramoto
model including the Kuramoto model with a bimodal frequency distribution and
the Millennium Bridge problem.Comment: 9 pages, 3 figure