1,410 research outputs found
CR embeddings of CR manifolds
We improve results of Baouendi, Rothschild and Treves and of Hill and Nacinovich by finding a much weaker sufficient condition for a CR manifold of type (n, k) to admit a local CR embedding into a CR manifold of type (n+ ℓ, k- ℓ). While their results require the existence of a finite dimensional solvable transverse Lie algebra of vector fields, we require only a finite dimensional extension
Experimental Identification of the Kink Instability as a Poloidal Flux Amplification Mechanism for Coaxial Gun Spheromak Formation
The magnetohydrodynamic kink instability is observed and identified
experimentally as a poloidal flux amplification mechanism for coaxial gun
spheromak formation. Plasmas in this experiment fall into three distinct
regimes which depend on the peak gun current to magnetic flux ratio, with (I)
low values resulting in a straight plasma column with helical magnetic field,
(II) intermediate values leading to kinking of the column axis, and (III) high
values leading immediately to a detached plasma. Onset of column kinking agrees
quantitatively with the Kruskal-Shafranov limit, and the kink acts as a dynamo
which converts toroidal to poloidal flux. Regime II clearly leads to both
poloidal flux amplification and the development of a spheromak configuration.Comment: accepted for publication in Physical Review Letter
Lp Fourier multipliers on compact Lie groups
In this paper we prove Lp multiplier theorems for invariant and non-invariant
operators on compact Lie groups in the spirit of the well-known
Hormander-Mikhlin theorem on Rn and its variants on tori Tn. We also give
applications to a-priori estimates for non-hypoelliptic operators. Already in
the case of tori we get an interesting refinement of the classical multiplier
theorem.Comment: 22 pages; minor correction
Spectral multipliers for the Kohn Laplacian on forms on the sphere in Cn
The unit sphere S in Cn is equipped with the tangential Cauchy–Riemann complex and the associated Laplacian □ b. We prove a Hörmander spectral multiplier theorem for □ b with critical index n- 1 / 2 , that is, half the topological dimension of S. Our proof is mainly based on representation theory and on a detailed analysis of the spaces of differential forms on S
Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres
A sharp Lp spectral multiplier theorem of Mihlin–Hörmander type is proved for a distinguished sub-Laplacian on quaternionic spheres. This is the first such result on compact sub-Riemannian manifolds where the horizontal space has corank greater than one. The proof hinges on the analysis of the quaternionic spherical harmonic decomposition, of which we present an elementary derivation
Dust-driven Dynamos in Accretion Disks
Magnetically driven astrophysical jets are related to accretion and involve
toroidal magnetic field pressure inflating poloidal magnetic field flux
surfaces. Examination of particle motion in combined gravitational and magnetic
fields shows that these astrophysical jet toroidal and poloidal magnetic fields
can be powered by the gravitational energy liberated by accreting dust grains
that have become positively charged by emitting photo-electrons. Because a dust
grain experiences magnetic forces after becoming charged, but not before,
charging can cause irreversible trapping of the grain so dust accretion is a
consequence of charging. Furthermore, charging causes canonical angular
momentum to replace mechanical angular momentum as the relevant constant of the
motion. The resulting effective potential has three distinct classes of
accreting particles distinguished by canonical angular momentum, namely (i)
"cyclotron-orbit", (ii) "Speiser-orbit", and (iii) "zero canonical angular
momentum" particles. Electrons and ions are of class (i) but depending on mass
and initial orbit inclination, dust grains can be of any class. Light-weight
dust grains develop class (i) orbits such that the grains are confined to
nested poloidal flux surfaces, whereas grains with a critical weight such that
they experience comparable gravitational and magnetic forces can develop class
(ii) or class (iii) orbits, respectively producing poloidal and toroidal field
dynamos.Comment: 70 pages, 16 figure
On a mechanism for enhancing magnetic activity in tidally interacting binaries
We suggest a mechanism for enhancing magnetic activity in tidally interacting
binaries. We suppose that the deviation of the primary star from spherical
symmetry due to the tidal influence of the companion leads to stellar pulsation
in its fundamental mode. It is shown that stellar radial pulsation amplifies
torsional Alfv{\'e}n waves in a dipole-like magnetic field, buried in the
interior, according to the recently proposed swing wave-wave interaction
(Zaqarashvili 2001). Then amplified Alfv{\'e}n waves lead to the onset of
large-scale torsional oscillations, and magnetic flux tubes arising towards the
surface owing to magnetic buoyancy diffuse into the atmosphere producing
enhanced chromospheric and coronal emission.Comment: Accepted in Ap
Growth rate degeneracies in kinematic dynamos
We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary conditions: the magnetic field can be normal (infinite magnetic permeability, also called pseudovacuum) or tangent (perfect electrical conductor) to the boundaries of the domain. These boundary conditions correspond to well-defined physical limits often used in numerical models and relevant to laboratory experiments. The only constraint is for the velocity field u to be reversible, meaning there exists a transformation changing u into −u. We illustrate this surprising property using S2T2 type of flows in spherical geometry inspired by [Dudley and James, Proc. R. Soc. London A 425, 407 (1989)]. Using both types of boundary conditions, it is shown that the growth rates of the dynamos are identical, although the corresponding magnetic eigenmodes are drastically different
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