12,270 research outputs found
High-m Kink/Tearing Modes in Cylindrical Geometry
The global ideal kink equation, for cylindrical geometry and zero beta, is
simplified in the high poloidal mode number limit and used to determine the
tearing stability parameter, . In the presence of a steep
monotonic current gradient, becomes a function of a parameter,
, characterising the ratio of the maximum current gradient to
magnetic shear, and , characterising the separation of the resonant
surface from the maximum of the current gradient. In equilibria containing a
current "spike", so that there is a non-monotonic current profile,
also depends on two parameters: , related to the ratio
of the curvature of the current density at its maximum to the magnetic shear,
and , which now represents the separation of the resonance from the point
of maximum current density. The relation of our results to earlier studies of
tearing modes and to recent gyro-kinetic calculations of current driven
instabilities, is discussed, together with potential implications for the
stability of the tokamak pedestal.Comment: To appear in Plasma Physics and Controlled Fusio
Dynamical Phase Transitions In Driven Integrate-And-Fire Neurons
We explore the dynamics of an integrate-and-fire neuron with an oscillatory
stimulus. The frustration due to the competition between the neuron's natural
firing period and that of the oscillatory rhythm, leads to a rich structure of
asymptotic phase locking patterns and ordering dynamics. The phase transitions
between these states can be classified as either tangent or discontinuous
bifurcations, each with its own characteristic scaling laws. The discontinuous
bifurcations exhibit a new kind of phase transition that may be viewed as
intermediate between continuous and first order, while tangent bifurcations
behave like continuous transitions with a diverging coherence scale.Comment: 4 pages, 5 figure
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