8,327 research outputs found
Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths
The problem of counting plane trees with edges and an even or an odd
number of leaves was studied by Eu, Liu and Yeh, in connection with an identity
on coloring nets due to Stanley. This identity was also obtained by Bonin,
Shapiro and Simion in their study of Schr\"oder paths, and it was recently
derived by Coker using the Lagrange inversion formula. An equivalent problem
for partitions was independently studied by Klazar. We present three parity
reversing involutions, one for unlabelled plane trees, the other for labelled
plane trees and one for 2-Motzkin paths which are in one-to-one correspondence
with Dyck paths.Comment: 8 pages, 4 figure
An Investigation of the Large-scale Variability of the Apparently Single Wolf-Rayet Star WR 1
In recent years, much studies have focused on determining the origin of the
large-scale line-profile and/or photometric patterns of variability displayed
by some apparently single Wolf-Rayet stars, with the existence of an unseen
(collapsed?) companion or of spatially extended wind structures as potential
candidates. We present observations of WR 1 which highlight the unusual
character of the variations in this object. Our narrowband photometric
observations reveal a gradual increase of the stellar continuum flux amounting
to Delta v = 0.09 mag followed by a decline on about the same timescale (3-4
days). Only marginal evidence for variability is found during the 11 following
nights.
Strong, daily line-profile variations are also observed but they cannot be
easily linked to the photometric variations.
Similarly to the continuum flux variations, coherent time-dependent changes
are observed in 1996 in the centroid, equivalent width, and skewness of He II
4686. Despite the generally coherent nature of the variations, we do not find
evidence in our data for the periods claimed in previous studies. While the
issue of a cyclical pattern of variability in WR 1 is still controversial, it
is clear that this object might constitute in the future a cornerstone for our
understanding of the mechanisms leading to the formation of largely anisotropic
outflows in Wolf-Rayet stars.Comment: 11 pages, 9 figures, accepted for publication in Astronomy &
Astrophysic
Ballistic magnon transport and phonon scattering in the antiferromagnet NdCuO
The thermal conductivity of the antiferromagnet NdCuO was measured
down to 50 mK. Using the spin-flop transition to switch on and off the acoustic
Nd magnons, we can reliably separate the magnon and phonon contributions to
heat transport. We find that magnons travel ballistically below 0.5 K, with a
thermal conductivity growing as , from which we extract their velocity. We
show that the rate of scattering of acoustic magnons by phonons grows as ,
and the scattering of phonons by magnons peaks at twice the average Nd magnon
frequency.Comment: 4 pages, 3 figures, one figure modifie
Giant electron-electron scattering in the Fermi-liquid state of Na_0.7CoO_2
The in-plane resistivity, rho, and thermal conductivity, kappa, of a single
crystal of Na_0.7CoO_2 were measured down to 40 mK. Verification of the
Wiedemann-Franz law, kappa/T = L_0/rho as T -> 0, and observation of a T^2
dependence of rho at low temperature, rho = rho_0 + AT^2, establish the
existence of a well-defined Fermi-liquid state. The measured value of
coefficient A reveals enormous electron-electron scattering, characterized by
the largest Kadowaki-Woods ratio, A/gamma^2, encountered in any material. The
rapid suppression of A with magnetic field suggests a possible proximity to a
magnetic quantum critical point. We also speculate on the possible role of
magnetic frustration and proximity to a Mott insulator.Comment: 4 pages, 4 figures; replaced with published version; added references
and supporting dat
Theory of asymmetric non-additive binary hard-sphere mixtures
We show that the formal procedure of integrating out the degrees of freedom
of the small spheres in a binary hard-sphere mixture works equally well for
non-additive as it does for additive mixtures. For highly asymmetric mixtures
(small size ratios) the resulting effective Hamiltonian of the one-component
fluid of big spheres, which consists of an infinite number of many-body
interactions, should be accurately approximated by truncating after the term
describing the effective pair interaction. Using a density functional treatment
developed originally for additive hard-sphere mixtures we determine the zero,
one, and two-body contribution to the effective Hamiltonian. We demonstrate
that even small degrees of positive or negative non-additivity have significant
effect on the shape of the depletion potential. The second virial coefficient
, corresponding to the effective pair interaction between two big spheres,
is found to be a sensitive measure of the effects of non-additivity. The
variation of with the density of the small spheres shows significantly
different behavior for additive, slightly positive and slightly negative
non-additive mixtures. We discuss the possible repercussions of these results
for the phase behavior of binary hard-sphere mixtures and suggest that
measurements of might provide a means of determining the degree of
non-additivity in real colloidal mixtures
Rosenfeld functional for non-additive hard spheres
The fundamental measure density functional theory for hard spheres is
generalized to binary mixtures of arbitrary positive and moderate negative
non-additivity between unlike components. In bulk the theory predicts
fluid-fluid phase separation into phases with different chemical compositions.
The location of the accompanying critical point agrees well with previous
results from simulations over a broad range of non-additivities and both for
symmetric and highly asymmetric size ratios. Results for partial pair
correlation functions show good agreement with simulation data.Comment: 8 pages with 4 figure
Stability of benthic coral reef communities: top-down herbivory control versus bottom-up eutrophication
Geometrodynamical Formulation of Two-Dimensional Dilaton Gravity
Two-dimensional matterless dilaton gravity with arbitrary dilatonic potential
can be discussed in a unitary way, both in the Lagrangian and canonical
frameworks, by introducing suitable field redefinitions. The new fields are
directly related to the original spacetime geometry and in the canonical
picture they generalize the well-known geometrodynamical variables used in the
discussion of the Schwarzschild black hole. So the model can be quantized using
the techniques developed for the latter case. The resulting quantum theory
exhibits the Birkhoff theorem at the quantum level.Comment: 15 pages, LATE
Thermal conductivity in the vicinity of the quantum critical endpoint in Sr3Ru2O7
Thermal conductivity of Sr3Ru2O7 was measured down to 40 mK and at magnetic
fields through the quantum critical endpoint at H_c = 7.85 T. A peak in the
electrical resistivity as a function of field was mimicked by the thermal
resistivity. In the limit as T -> 0 K we find that the Wiedemann-Franz law is
satisfied to within 5% at all fields, implying that there is no breakdown of
the electron despite the destruction of the Fermi liquid state at quantum
criticality. A significant change in disorder (from (H=0T) = 2.1
cm to 0.5 cm) does not influence our conclusions. At
finite temperatures, the temperature dependence of the Lorenz number is
consistent with ferromagnetic fluctuations causing the non-Fermi liquid
behavior as one would expect at a metamagnetic quantum critical endpoint.Comment: 4 figures, published in PR
Potential effect of mangrove regression for fish species of commercial interest in Guadeloupe
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