54,685 research outputs found
The # product in combinatorial Hopf algebras
We show that the # product of binary trees introduced by Aval and Viennot
[arXiv:0912.0798] is in fact defined at the level of the free associative
algebra, and can be extended to most of the classical combinatorial Hopf
algebras.Comment: 20 page
Intermittency and transition to chaos in the cubical lid-driven cavity flow
Transition from steady state to intermittent chaos in the cubical lid-driven
flow is investigated numerically. Fully three-dimensional stability analyses
have revealed that the flow experiences an Andronov-Poincar\'e-Hopf bifurcation
at a critical Reynolds number = 1914. As for the 2D-periodic lid-driven
cavity flows, the unstable mode originates from a centrifugal instability of
the primary vortex core. A Reynolds-Orr analysis reveals that the unstable
perturbation relies on a combination of the lift-up and anti lift-up mechanisms
to extract its energy from the base flow. Once linearly unstable, direct
numerical simulations show that the flow is driven toward a primary limit cycle
before eventually exhibiting intermittent chaotic dynamics. Though only one
eigenpair of the linearized Navier-Stokes operator is unstable, the dynamics
during the intermittencies are surprisingly well characterized by one of the
stable eigenpairs.Comment: Accepted for publication in Fluid Dynamics Researc
Quasi-symmetric functions as polynomial functions on Young diagrams
We determine the most general form of a smooth function on Young diagrams,
that is, a polynomial in the interlacing or multirectangular coordinates whose
value depends only on the shape of the diagram. We prove that the algebra of
such functions is isomorphic to quasi-symmetric functions, and give a
noncommutative analog of this result.Comment: 34 pages, 4 figures, version including minor modifications suggested
by referee
Super quasi-symmetric functions via Young diagrams
We consider the multivariate generating series of -partitions in
infinitely many variables . For some family of ranked posets
, it is natural to consider an analog with two infinite alphabets.
When we collapse these two alphabets, we trivially recover . Our main
result is the converse, that is, the explicit construction of a map sending
back onto . We also give a noncommutative analog of the latter. An
application is the construction of a basis of WQSym with a non-negative
multiplication table, which lifts a basis of QSym introduced by K. Luoto.Comment: 12 pages, extended abstract of arXiv:1312.2727, presented at FPSAC
conference. The presentation of the results is quite different from the long
versio
The minimality of the map x/|x| for weighted energy
In this paper, we investigate the minimality of the map
from the euclidean unit ball to its boundary
for weighted energy functionals of the type , where is a non-negative
function. We prove that in each of the two following cases: i) and is
non-decreasing, i)) is an integer, and with
, the map minimizes among the maps
in which coincide with
on . We also study the case where with and prove that
does not minimize for close to and when ,
for close to
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