2,205 research outputs found
Universality of multi-field -attractors
We study a particular version of the theory of cosmological
-attractors with , in which both the dilaton (inflaton)
field and the axion field are light during inflation. The kinetic terms in this
theory originate from maximal superconformal symmetry and from
maximal supergravity. We show that because of the underlying
hyperbolic geometry of the moduli space in this theory, it exhibits double
attractor behavior: their cosmological predictions are stable not only with
respect to significant modifications of the dilaton potential, but also with
respect to significant modifications of the axion potential: , . We also show that the universality of
predictions extends to other values of with
general two-field potentials that may or may not have an embedding in
supergravity. Our results support the idea that inflation involving multiple,
not stabilized, light fields on a hyperbolic manifold may be compatible with
current observational constraints for a broad class of potentials.Comment: 26 pages, 9 figures; v2: published version with references added and
discussion extende
Ramification estimates for the hyperbolic Gauss map
We give the best possible upper bound on the number of exceptional values and
the totally ramified value number of the hyperbolic Gauss map for
pseudo-algebraic constant mean curvature one surfaces in the hyperbolic
three-space and some partial results on the Osserman problem for algebraic
case. Moreover, we study the value distribution of the hyperbolic Gauss map for
complete constant mean curvature one faces in de Sitter three-space.Comment: 16 pages, corrected some typos. OCAMI Preprint Series 08-1, to appear
in Osaka Journal of Mathematic
Dynamic evolution of current sheets, ideal tearing, plasmoid formation and generalized fractal reconnection scaling relations
Magnetic reconnection may be the fundamental process allowing energy stored
in magnetic fields to be released abruptly, solar flares and coronal mass
ejection (CME) being archetypal natural plasma examples. Magnetic reconnection
is much too slow a process to be efficient on the large scales, but accelerates
once small enough scales are formed in the system. For this reason, the fractal
reconnection scenario was introduced (Shibata and Tanuma 2001) to explain
explosive events in the solar atmosphere: it was based on the recursive
triggering and collapse via tearing instability of a current sheet originally
thinned during the rise of a filament in the solar corona. Here we compare the
different fractal reconnection scenarios that have been proposed, and derive
generalized scaling relations for the recursive triggering of fast, `ideal' -
i.e. Lundquist number independent - tearing in collapsing current sheet
configurations with arbitrary current profile shapes. An important result is
that the Sweet-Parker scaling with Lundquist number, if interpreted as the
aspect ratio of the singular layer in an ideally unstable sheet, is universal
and does not depend on the details of the current profile in the sheet. Such a
scaling however must not be interpreted in terms of stationary reconnection,
rather it defines a step in the accelerating sequence of events of the ideal
tearing mediated fractal cascade. We calculate scalings for the expected number
of plasmoids for such generic profiles and realistic Lundquist numbers.Comment: 11 pages, 2 figure
Experimental and numerical study of error fields in the CNT stellarator
Sources of error fields were indirectly inferred in a stellarator by
reconciling computed and numerical flux surfaces. Sources considered so far
include the displacements and tilts (but not the deformations, yet) of the four
circular coils featured in the simple CNT stellarator. The flux surfaces were
measured by means of an electron beam and phosphor rod, and were computed by
means of a Biot-Savart field-line tracing code. If the ideal coil locations and
orientations are used in the computation, agreement with measurements is poor.
Discrepancies are ascribed to errors in the positioning and orientation of the
in-vessel interlocked coils. To that end, an iterative numerical method was
developed. A Newton-Raphson algorithm searches for the coils' displacements and
tilts that minimize the discrepancy between the measured and computed flux
surfaces. This method was verified by misplacing and tilting the coils in a
numerical model of CNT, calculating the flux surfaces that they generated, and
testing the algorithm's ability to deduce the coils' displacements and tilts.
Subsequently, the numerical method was applied to the experimental data,
arriving at a set of coil displacements whose resulting field errors exhibited
significantly improved quantitative and qualitative agreement with experimental
results.Comment: Special Issue on the 20th International Stellarator-Heliotron
Worksho
A uniform approach to soliton cellular automata using rigged configurations
For soliton cellular automata, we give a uniform description and proofs of
the solitons, the scattering rule of two solitons, and the phase shift using
rigged configurations in a number of special cases. In particular, we prove
these properties for the soliton cellular automata using when is
adjacent to in the Dynkin diagram or there is a Dynkin diagram automorphism
sending to .Comment: 37 pages, 3 figures, 4 table
- …