7,357 research outputs found
Lagrangian turbulence in the Adriatic Sea as computed from drifter data: effects of inhomogeneity and nonstationarity
The properties of mesoscale Lagrangian turbulence in the Adriatic Sea are
studied from a drifter data set spanning 1990-1999, focusing on the role of
inhomogeneity and nonstationarity. A preliminary study is performed on the
dependence of the turbulent velocity statistics on bin averaging, and a
preferential bin scale of 0.25 is chosen. Comparison with independent estimates
obtained using an optimized spline technique confirms this choice. Three main
regions are identified where the velocity statistics are approximately
homogeneous: the two boundary currents, West (East) Adriatic Current, WAC
(EAC), and the southern central gyre, CG. The CG region is found to be
characterized by symmetric probability density function of velocity,
approximately exponential autocorrelations and well defined integral quantities
such as di usivity and time scale. The boundary regions, instead, are
significantly asymmetric with skewness indicating preferential events in the
direction of the mean flow. The autocorrelation in the along mean flow
direction is characterized by two time scales, with a secondary exponential
with slow decay time of 11-12 days particularly evident in the EAC region.
Seasonal partitioning of the data shows that this secondary scale is especially
prominent in the summer-fall season. Possible physical explanations for the
secondary scale are discussed in terms of low frequency fluctuations of
forcings and in terms of mean flow curvature inducing fluctuations in the
particle trajectories. Consequences of the results for transport modelling in
the Adriatic Sea are discussed.Comment: 45 pages, 18 figure
Affine Hecke algebras of type D and generalisations of quiver Hecke algebras
We define and study cyclotomic quotients of affine Hecke algebras of type D.
We establish an isomorphism between (direct sums of blocks of) these cyclotomic
quotients and a generalisation of cyclotomic quiver Hecke algebras which are a
family of Z-graded algebras closely related to algebras introduced by Shan,
Varagnolo and Vasserot. To achieve this, we first complete the study of
cyclotomic quotients of affine Hecke algebras of type B by considering the
situation when a deformation parameter p squares to 1. We then relate the two
generalisations of quiver Hecke algebras showing that the one for type D can be
seen as fixed point subalgebras of their analogues for type B, and we carefully
study how far this relation remains valid for cyclotomic quotients. This allows
us to obtain the desired isomorphism. This isomorphism completes the family of
isomorphisms relating affine Hecke algebras of classical types to
(generalisations of) quiver Hecke algebras, originating in the famous result of
Brundan and Kleshchev for the type A.Comment: 26 page
Affine Hecke algebras and generalisations of quiver Hecke algebras for type B
We define and study cyclotomic quotients of affine Hecke algebras of type B.
We establish an isomorphism between direct sums of blocks of these algebras and
a generalisation, for type B, of cyclotomic quiver Hecke algebras which are a
family of graded algebras closely related to algebras introduced by Varagnolo
and Vasserot. Inspired by the work of Brundan and Kleshchev we first give a
family of isomorphisms for the corresponding result in type A which includes
their original isomorphism. We then select a particular isomorphism from this
family and use it to prove our result.Comment: 37 page
Markov traces on affine and cyclotomic Yokonuma-Hecke algebras
In this article, we define and study the affine and cyclotomic Yokonuma-Hecke
algebras. These algebras generalise at the same time the Ariki-Koike and affine
Hecke algebras and the Yokonuma-Hecke algebras. We study the representation
theory of these algebras and construct several bases for them. We then show how
we can define Markov traces on them, which we in turn use to construct
invariants for framed and classical knots in the solid torus. Finally, we study
the Markov trace with zero parameters on the cyclotomic Yokonuma-Hecke algebras
and determine the Schur elements with respect to that trace.Comment: 37 page
Representation theory of the Yokonuma-Hecke algebra
We develop an inductive approach to the representation theory of the
Yokonuma-Hecke algebra , based on the study of the spectrum
of its Jucys-Murphy elements which are defined here. We give explicit formulas
for the irreducible representations of in terms of standard
-tableaux; we then use them to obtain a semisimplicity criterion. Finally,
we prove the existence of a canonical symmetrising form on
and calculate the Schur elements with respect to that form.Comment: 28 page
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