148,986 research outputs found
Heavy tails in last passage percolation
We consider last-passage percolation models in two dimensions, in which the underlying weight distribution has a heavy tail of index . We prove scaling laws and asymptotic distributions, both for the passage times and for the shape of optimal paths; these are expressed in terms of a family (indexed by ) of ``continuous last-passage percolation'' models in the unit square. In the extreme case (corresponding to a distribution with slowly varying tail) the asymptotic distribution of the optimal path can be represented by a random self-similar measure on [0,1], whose multifractal spectrum we compute. By extending the continuous last-passage percolation model to we obtain a heavy-tailed analogue of the Airy process, representing the limit of appropriately scaled vectors of passage times to different points in the plane. We give corresponding results for a directed percolation problem based on -stable Levy processes, and indicate extensions of the results to higher dimensions
Quantum fields, dark matter and non-standard Wigner classes
The Elko field of Ahluwalia and Grumiller is a quantum field for massive
spin-1/2 particles. It has been suggested as a candidate for dark matter. We
discuss our attempts to interpret the Elko field as a quantum field in the
sense of Weinberg. Our work suggests that one should investigate quantum fields
based on representations of the full Poincar\'e group which belong to one of
the non-standard Wigner classes.Comment: 6 pages. Submitted to proceedings of Dark2009, Christchurch, New
Zealand, January 200
On Tits' Centre Conjecture for Fixed Point Subcomplexes
We give a short and uniform proof of a special case of Tits' Centre
Conjecture using a theorem of J-P. Serre and a result from our earlier work. We
consider fixed point subcomplexes of the building of a
connected reductive algebraic group , where is a subgroup of .Comment: 4 pages; minor changes, to appear in C. R. Acad. Sci. Paris Ser. I
Mat
Effective Three-Body Interactions in Jaynes-Cummings-Hubbard Systems
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity
arrays is introduced, where the embedded two-level system in each cavity is
replaced by a -type three-level system. We demonstrate that the resulting
effective polariton-polariton interactions at each site are both two-body and
three-body. By tuning the ratio of the two transition dipole matrix elements,
we show that the strength and sign of the two-body interaction can be
controlled whilst maintaining a three-body repulsion. We then proceed to
demonstrate how different two-body and three-body interactions alter the mean
field superfluid-Mott insulator phase diagram, with the possible emergence of a
pair superfluid phase in the two-body attractive regime.Comment: 10 pages, 4 figures, accepted for publication in Scientific Reports;
v3 - revised manuscrip
Complete Reducibility and Commuting Subgroups
Let G be a reductive linear algebraic group over an algebraically closed
field of characteristic p. We study J.-P. Serre's notion of G-complete
reducibility for subgroups of G. In particular, for a subgroup H and a normal
subgroup N of H, we look at the relationship between G-complete reducibility of
N and of H, and show that these properties are equivalent if H/N is linearly
reductive, generalizing a result of Serre. We also study the case when H = MN
with M a G-completely reducible subgroup of G which normalizes N. We show that
if G is connected, N and M are connected commuting G-completely reducible
subgroups of G, and p is good for G, then H = MN is also G-completely
reducible.Comment: 21 pages; to appear in J. Reine Angew. Math. final for
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Effect of soil waterlogging on below-ground biomass allometric relations in Norway spruce
An increasing importance is assigned to the estimation and verification of carbon stocks in forests. Forestry practice has several long-established and reliable methods for the assessment of aboveground biomass; however we still miss accurate predictors of belowground biomass. A major windthrow event exposing the coarse root systems of Norway spruce trees allowed us to assess the effects of contrasting soil stone and water content on belowground allocation. Increasing stone content decreases root/shoot ratio, while soil waterlogging leads to an increase in this ratio. We constructed allometric relationships for belowground biomass prediction and were able to show that only soil waterlogging significantly impacts model parameters. We showed that diameter at breast height is a reliable predictor of belowground biomass and, once site-specific parameters have been developed, it is possible to accurately estimate belowground biomass in Norway spruce
Wind-tunnel acoustic results of two rotor models with several tip designs
A three-phase research program has been undertaken to study the acoustic signals due to the aerodynamic interaction of rotorcraft main rotors and tail rotors. During the first phase, two different rotor models with several interchangeable tips were tested in the Langley 4- by 7-Meter Tunnel on the U.S. Army rotor model system. An extensive acoustic data base was acquired, with special emphasis on blade-vortex interaction (BVI) noise. The details of the experimental procedure, acoustic data acquisition, and reduction are documented. The overall sound pressure level (OASPL) of the high-twist rotor systems is relatively insensitive to flight speed but generally increases with rotor tip-path-plane angle. The OASPL of the high-twist rotors is dominated by acoustic energy in the low-frequency harmonics. The OASPL of the low-twist rotor systems shows more dependence on flight speed than the high-twist rotors, in addition to being quite sensitive to tip-path-plane angle. An integrated band-limited sound pressure level, limited by 500 to 3000 Hz, is a useful metric to quantify the occurrence of BVI noise. The OASPL of the low-twist rotors is strongly influenced by the band-limited sound levels, indicating that the blade-vortex impulsive noise is a dominant noise source for this rotor design. The midfrequency acoustic levels for both rotors show a very strong dependence on rotor tip-path-plane angle. The tip-path-plane angle at which the maximum midfrequency sound level occurs consistently decreases with increasing flight speed. The maximum midfrequency sound level measured at a given location is constant regardless of the flight speed
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