11,999 research outputs found
Scale-factor duality in string Bianchi cosmologies
We apply the scale factor duality transformations introduced in the context
of the effective string theory to the anisotropic Bianchi-type models. We find
dual models for all the Bianchi-types [except for types and ] and
construct for each of them its explicit form starting from the exact original
solution of the field equations. It is emphasized that the dual Bianchi class
models require the loss of the initial homogeneity symmetry of the
dilatonic scalar field.Comment: 18 pages, no figure
Ripples in Tapped or Blown Powder
We observe ripples forming on the surface of a granular powder in a container
submitted from below to a series of brief and distinct shocks. After a few
taps, the pattern turns out to be stable against any further shock of the same
amplitude. We find experimentally that the characteristic wavelength of the
pattern is proportional to the amplitude of the shocks. Starting from
consideration involving Darcy's law for air flow through the porous granulate
and avalanche properties, we build up a semi-quantitative model which fits
satisfactorily the set of experimental observations as well as a couple of
additional experiments.Comment: 7 pages, four postscript figures, submitted PRL 11/19/9
Quantization of Fayet-Iliopoulos Parameters in Supergravity
In this short note we discuss quantization of the Fayet-Iliopoulos parameter
in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos
parameter determines a lift of the group action to a line bundle, and such
lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted
in terms of moment maps and symplectic reductions, we argue that in
supergravity the quantization of the Fayet-Iliopoulos parameter has a natural
understanding in terms of linearizations in geometric invariant theory (GIT)
quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe
Resampling technique applied to statistics of microsegregation characterization
Characterization of chemical heterogeneities at the dendrite scale is of practical importance for understanding phase transformation either during solidification or during subsequent solid-state treatment. Spot analysis with electron probe is definitely well-suited to investigate such heterogeneities at the micron scale that is relevant for most solidified products. However, very few has been done about the statistics of experimental solute distributions gained from such analyses when they are now more and more used for validating simulation data. There are two main sources generating discrepancies between estimated and actual solute distributions in an alloy: i) data sampling with a limited number of measurements to keep analysis within a reasonable time length; and ii) uncertainty linked to the measurement process, namely the physical noise that accompanies X-ray emission. Focusing on the first of these sources, a few 2-D composition images have been generated by phase field modelling of a Mg-Al alloy. These images were then used to obtain "true" solute distributions to which to compare coarse grid analyses as generally performed with a microanalyser. Resampling, i.e. generating several distributions by grid analyses with limited number of picked-up values, was then used to get statistics of estimates of solute distribution. The discussion of the present results deals first with estimating the average solute content and then focuses on the distribution in the primary phase
Multi-Hamiltonian structures for r-matrix systems
For the rational, elliptic and trigonometric r-matrices, we exhibit the links
between three "levels" of Poisson spaces: (a) Some finite-dimensional spaces of
matrix-valued holomorphic functions on the complex line; (b) Spaces of spectral
curves and sheaves supported on them; (c) Symmetric products of a surface. We
have, at each level, a linear space of compatible Poisson structures, and the
maps relating the levels are Poisson. This leads in a natural way to Nijenhuis
coordinates for these spaces. At level (b), there are Hamiltonian systems on
these spaces which are integrable for each Poisson structure in the family, and
which are such that the Lagrangian leaves are the intersections of the
symplective leaves over the Poisson structures in the family. Specific examples
include many of the well-known integrable systems.Comment: 26 pages, Plain Te
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