39,252 research outputs found
Castelnuovo-Mumford Regularity in Biprojective Spaces
We define the concept of regularity for bigraded modules and bigraded
polynomial ring. In this setting we prove analogs of some of the classical
results on -regularity for graded modules over polynomial algebras.Comment: 17 Pages, 2 figure
Curvilinear Base Points, Local Complete Intersection and Kozsul Syzygies in Biprojective Spaces
We prove analogs of results of Cox/Schenck on the structure of certain ideals
in the bigraded polynomial ring k[s,u;t,v].Comment: 12 page
Edge States and Broken Symmetry Phases of Laterally Confined He Films
Broken symmetries in topological condensed matter systems have implications
for the spectrum of Fermionic excitations confined on surfaces or topological
defects. The Fermionic spectrum of confined (quasi-2D) He-A consists of
branches of chiral edge states. The negative energy states are related to the
ground-state angular momentum, , for Cooper pairs. The
power law suppression of the angular momentum, for , in the fully gapped 2D
chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We
discuss the effects of wave function overlap, and hybridization between edge
states confined near opposing surfaces on the edge currents, ground-state
angular momentum and ground-state order parameter. Under strong lateral
confinement, the chiral A phase undergoes a sequence of phase transitions,
first to a pair density wave (PDW) phase with broken translational symmetry at
. The PDW phase is described by a periodic array of
chiral domains with alternating chirality, separated by domain walls. The
period of PDW phase diverges as the confinement length .
The PDW phase breaks time-reversal symmetry, translation invariance, but is
invariant under the combination of time-reversal and translation by a one-half
period of the PDW. The mass current distribution of the PDW phase reflects this
combined symmetry, and orignates from the spectra of edge Fermions and the
chiral branches bound to the domain walls. Under sufficiently strong
confinement a second-order transition occurs to the non-chiral "polar phase" at
, in which a single p-wave orbital state of Cooper pairs
is aligned along the channel.Comment: 16 pages, 16 figure
Zonal Flow Magnetic Field Interaction in the Semi-Conducting Region of Giant Planets
All four giant planets in the Solar System feature zonal flows on the order
of 100 m/s in the cloud deck, and large-scale intrinsic magnetic fields on the
order of 1 Gauss near the surface. The vertical structure of the zonal flows
remains obscure. The end-member scenarios are shallow flows confined in the
radiative atmosphere and deep flows throughout the entire planet. The
electrical conductivity increases rapidly yet smoothly as a function of depth
inside Jupiter and Saturn. Deep zonal flows will inevitably interact with the
magnetic field, at depth with even modest electrical conductivity. Here we
investigate the interaction between zonal flows and magnetic fields in the
semi-conducting region of giant planets. Employing mean-field electrodynamics,
we show that the interaction will generate detectable poloidal magnetic field
perturbations spatially correlated with the deep zonal flows. Assuming the peak
amplitude of the dynamo alpha-effect to be 0.1 mm/s, deep zonal flows on the
order of 0.1 - 1 m/s in the semi-conducting region of Jupiter and Saturn would
generate poloidal magnetic perturbations on the order of 0.01% - 1% of the
background dipole field. These poloidal perturbations should be detectable with
the in-situ magnetic field measurements from the Juno mission and the Cassini
Grand Finale. This implies that magnetic field measurements can be employed to
constrain the properties of deep zonal flows in the semi-conducting region of
giant planets.Comment: 38 pages, 12 figures, revised submission to Icaru
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