17,185 research outputs found
Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions
The -Young lattice is a partial order on partitions with no part
larger than . This weak subposet of the Young lattice originated from the
study of the -Schur functions(atoms) , symmetric functions
that form a natural basis of the space spanned by homogeneous functions indexed
by -bounded partitions. The chains in the -Young lattice are induced by a
Pieri-type rule experimentally satisfied by the -Schur functions. Here,
using a natural bijection between -bounded partitions and -cores, we
establish an algorithm for identifying chains in the -Young lattice with
certain tableaux on cores. This algorithm reveals that the -Young
lattice is isomorphic to the weak order on the quotient of the affine symmetric
group by a maximal parabolic subgroup. From this, the
conjectured -Pieri rule implies that the -Kostka matrix connecting the
homogeneous basis \{h_\la\}_{\la\in\CY^k} to \{s_\la^{(k)}\}_{\la\in\CY^k}
may now be obtained by counting appropriate classes of tableaux on -cores.
This suggests that the conjecturally positive -Schur expansion coefficients
for Macdonald polynomials (reducing to -Kostka polynomials for large )
could be described by a -statistic on these tableaux, or equivalently on
reduced words for affine permutations.Comment: 30 pages, 1 figur
Faraday patterns in dipolar Bose-Einstein condensates
Faraday patterns can be induced in Bose-Einstein condensates by a periodic
modulation of the system nonlinearity. We show that these patterns are
remarkably different in dipolar gases with a roton-maxon excitation spectrum.
Whereas for non-dipolar gases the pattern size decreases monotonously with the
driving frequency, patterns in dipolar gases present, even for shallow roton
minima, a highly non trivial frequency dependence characterized by abrupt
pattern size transitions, which are especially pronounced when the dipolar
interaction is modulated. Faraday patterns constitute hence an optimal tool for
revealing the onset of the roton minimum, a major key feature of dipolar gases.Comment: 4 pages, 10 figure
Interim user's manual for boundary layer integral matrix procedure, version J
A computer program for analyzing two dimensional and axisymmetric nozzle performance with a variety of wall boundary conditions is described. The program has been developed for application to rocket nozzle problems. Several aids to usage of the program and two auxiliary subroutines are provided. Some features of the output are described and three sample cases are included
Boundary layer integral matrix procedure code modifications and verifications
A summary of modifications to Aerotherm's Boundary Layer Integral Matrix Procedure (BLIMP) code is presented. These modifications represent a preliminary effort to make BLIMP compatible with other JANNAF codes and to adjust the code for specific application to rocket nozzle flows. Results of the initial verification of the code for prediction of rocket nozzle type flows are discussed. For those cases in which measured free stream flow conditions were used as input to the code, the boundary layer predictions and measurements are in excellent agreement. In two cases, with free stream flow conditions calculated by another JANNAF code (TDK) for use as input to BLIMP, the predictions and the data were in fair agreement for one case and in poor agreement for the other case. The poor agreement is believed to result from failure of the turbulent model in BLIMP to account for laminarization of a turbulent flow. Recommendations for further code modifications and improvements are also presented
A Hybrid Observer for a Distributed Linear System with a Changing Neighbor Graph
A hybrid observer is described for estimating the state of an channel,
-dimensional, continuous-time, distributed linear system of the form
. The system's state is
simultaneously estimated by agents assuming each agent senses and
receives appropriately defined data from each of its current neighbors.
Neighbor relations are characterized by a time-varying directed graph
whose vertices correspond to agents and whose arcs depict
neighbor relations. Agent updates its estimate of at "event
times" using a local observer and a local parameter
estimator. The local observer is a continuous time linear system whose input is
and whose output is an asymptotically correct estimate of
where a matrix with kernel equaling the unobservable space of .
The local parameter estimator is a recursive algorithm designed to estimate,
prior to each event time , a constant parameter which satisfies the
linear equations , where is a small
positive constant and is the state estimation error of local observer
. Agent accomplishes this by iterating its parameter estimator state
, times within the interval , and by making use of
the state of each of its neighbors' parameter estimators at each iteration. The
updated value of at event time is then . Subject to the assumptions that (i) the neighbor graph
is strongly connected for all time, (ii) the system whose state
is to be estimated is jointly observable, (iii) is sufficiently large, it
is shown that each estimate converges to exponentially fast as
at a rate which can be controlled.Comment: 7 pages, the 56th IEEE Conference on Decision and Contro
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