3,964 research outputs found
Trivial Meet and Join within the Lattice of Monotone Triangles
The lattice of monotone triangles ordered by
entry-wise comparisons is studied. Let denote the unique minimal
element in this lattice, and the unique maximum. The number of
-tuples of monotone triangles with minimal infimum
(maximal supremum , resp.) is shown to
asymptotically approach as . Thus, with
high probability this event implies that one of the is
(, resp.). Higher-order error terms are also discussed.Comment: 15 page
On comparability of bigrassmannian permutations
Let Sn and Gn denote the respective sets of ordinary and bigrassmannian (BG) permutations of order n, and let (Gn,≤) denote the Bruhat ordering permutation poset. We study the restricted poset (Bn,≤), first providing a simple criterion for comparability. This criterion is used to show that that the poset is connected, to enumerate the saturated chains between elements, and to enumerate the number of maximal elements below r fixed elements. It also quickly produces formulas for β(ω) (α(ω), respectively), the number of BG permutations weakly below (weakly above, respectively) a fixed ω ∈ Bn, and is used to compute the Mo¨bius function on any interval in Bn.
We then turn to a probabilistic study of β = β(ω) (α = α(ω) respectively) for the uniformly random ω ∈ Bn. We show that α and β are equidistributed, and that β is of the same order as its expectation with high probability, but fails to concentrate about its mean. This latter fact derives from the limiting distribution of β/n3. We also compute the probability that randomly chosen BG permutations form a 2- or 3-element multichain
An alternative approach to field-aligned coordinates for plasma turbulence simulations
Turbulence simulation codes can exploit the flute-like nature of plasma
turbulence to reduce the effective number of degrees of freedom necessary to
represent fluctuations. This can be achieved by employing magnetic coordinates
of which one is aligned along the magnetic field. This work presents an
approach in which the position along the field lines is identified by the
toroidal angle, rather than the most commonly used poloidal angle. It will be
shown that this approach has several advantages. Among these, periodicity in
both angles is retained. This property allows moving to an equivalent
representation in Fourier space with a reduced number of toroidal components.
It will be shown how this duality can be exploited to transform conventional
codes that use a spectral representation on the magnetic surface into codes
with a field-aligned coordinate. It is also shown that the new approach can be
generalised to get rid of magnetic coordinates in the poloidal plane
altogether, for a large class of models. Tests are carried out by comparing the
new approach with the conventional approach employing a uniform grid, for a
basic ion temperature gradient (ITG) turbulence model implemented by the two
corresponding versions of the ETAI3D code. These tests uncover an unexpected
property of the model, that localized large parallel gradients can
intermittently appear in the turbulent regime. This leaves open the question
whether this is a general property of plasma turbulence, which may lead one to
reconsider some of the usual assumptions on micro-turbulence dynamics.Comment: 19 pages (once in pdf format). 1 LaTeX file and 10 eps figures in the
zip folde
NLO Leptoquark Production and Decay: The Narrow-Width Approximation and Beyond
We study the leptoquark model of Buchm\"uller, R\"uckl and Wyler, focusing on
a particular type of scalar () and vector () leptoquark. The primary
aim is to perform the calculations for leptoquark production and decay at
next-to-leading order (NLO) to establish the importance of the NLO
contributions and, in particular, to determine how effective the
narrow-width-approximation (NWA) is at NLO. For both the scalar and vector
leptoquarks it is found that the NLO contributions are large, with the larger
corrections occurring for the case vector leptoquarks. For the scalar
leptoquark it is found that the NWA provides a good approximation for
determining the resonant peak, however the NWA is not as effective for the
vector leptoquark. For both the scalar and vector leptoquarks there are large
contributions away from the resonant peak, which are missing from the NWA
results, and these make a significant difference to the total cross-section.Comment: 22 pages, 17 figure
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