237 research outputs found
Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem
We extend our previous analytic existence of a symmetric periodic
simultaneous binary collision orbit in a regularized fully symmetric equal mass
four-body problem to the analytic existence of a symmetric periodic
simultaneous binary collision orbit in a regularized planar pairwise symmetric
equal mass four-body problem. We then use a continuation method to numerically
find symmetric periodic simultaneous binary collision orbits in a regularized
planar pairwise symmetric 1, m, 1, m four-body problem for between 0 and 1.
Numerical estimates of the the characteristic multipliers show that these
periodic orbits are linearly stability when , and are
linearly unstable when .Comment: 6 figure
Is a community still a community? Reviewing definitions of key terms in community ecology
Community ecology is an inherently complicated field, confounded by the conflicting use of fundamental terms. Nearly two decades ago, Fauth etal. (1996) demonstrated that imprecise language led to the virtual synonymy of important terms and so attempted to clearly define four keywords in community ecology; community, assemblage, guild, and ensemble. We revisit Fauth etal.\u27s conclusion and discuss how the use of these terms has changed over time since their review. An updated analysis of term definition from a selection of popular ecological textbooks suggests that definitions have drifted away from those encountered pre-1996, and slightly disagreed with results from a survey of 100 ecology professionals (comprising of academic professors, nonacademic PhDs, graduate and undergraduate biology students). Results suggest that confusion about these terms is still widespread in ecology. We conclude with clear suggestions for definitions of each term to be adopted hereafter to provide greater cohesion among research groups
Cluster density functional theory for lattice models based on the theory of Mobius functions
Rosenfeld's fundamental measure theory for lattice models is given a rigorous
formulation in terms of the theory of Mobius functions of partially ordered
sets. The free-energy density functional is expressed as an expansion in a
finite set of lattice clusters. This set is endowed a partial order, so that
the coefficients of the cluster expansion are connected to its Mobius function.
Because of this, it is rigorously proven that a unique such expansion exists
for any lattice model. The low-density analysis of the free-energy functional
motivates a redefinition of the basic clusters (zero-dimensional cavities)
which guarantees a correct zero-density limit of the pair and triplet direct
correlation functions. This new definition extends Rosenfeld's theory to
lattice model with any kind of short-range interaction (repulsive or
attractive, hard or soft, one- or multi-component...). Finally, a proof is
given that these functionals have a consistent dimensional reduction, i.e. the
functional for dimension d' can be obtained from that for dimension d (d'<d) if
the latter is evaluated at a density profile confined to a d'-dimensional
subset.Comment: 21 pages, 2 figures, uses iopart.cls, as well as diagrams.sty
(included
Density functional formalism in the canonical ensemble
Density functional theory, when applied to systems with , is based
on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to
Mermin (HKSM theorem). While a straightforward canonical ensemble
generalization fails, work in nanopore systems could certainly benefit from
such extension. We show that, if the asymptotic behaviour of the canonical
distribution functions is taken into account, the HKSM theorem can be extended
to the canonical ensemble. We generate -modified correlation and
distribution functions hierarchies and prove that, if they are employed, either
a modified external field or the density profiles can be indistinctly used as
independent variables. We also write down the % -modified free energy
functional and prove that its minimum is reached when the equilibrium values of
the new hierarchy are used. This completes the extension of the HKSM theorem.Comment: revtex, to be submitted to Phys. Rev. Let
Determining the Physical Lens Parameters of the Binary Gravitational Microlensing Event MOA-2009-BLG-016
We report the result of the analysis of the light curve of the microlensing
event MOA-2009-BLG-016. The light curve is characterized by a short-duration
anomaly near the peak and an overall asymmetry. We find that the peak anomaly
is due to a binary companion to the primary lens and the asymmetry of the light
curve is explained by the parallax effect caused by the acceleration of the
observer over the course of the event due to the orbital motion of the Earth
around the Sun. In addition, we detect evidence for the effect of the finite
size of the source near the peak of the event, which allows us to measure the
angular Einstein radius of the lens system. The Einstein radius combined with
the microlens parallax allows us to determine the total mass of the lens and
the distance to the lens. We identify three distinct classes of degenerate
solutions for the binary lens parameters, where two are manifestations of the
previously identified degeneracies of close/wide binaries and positive/negative
impact parameters, while the third class is caused by the symmetric cycloid
shape of the caustic. We find that, for the best-fit solution, the estimated
mass of the lower-mass component of the binary is (0.04 +- 0.01) M_sun,
implying a brown-dwarf companion. However, there exists a solution that is
worse only by \Delta\chi^2 ~ 3 for which the mass of the secondary is above the
hydrogen-burning limit. Unfortunately, resolving these two degenerate solutions
will be difficult as the relative lens-source proper motions for both are
similar and small (~ 1 mas/yr) and thus the lens will remain blended with the
source for the next several decades.Comment: 7 pages, 2 tables, and 5 figure
Microlensing Event MOA-2007-BLG-400: Exhuming the Buried Signature of a Cool, Jovian-Mass Planet
We report the detection of the cool, Jovian-mass planet MOA-2007-BLG-400Lb.
The planet was detected in a high-magnification microlensing event (with peak
magnification A_max = 628) in which the primary lens transited the source,
resulting in a dramatic smoothing of the peak of the event. The angular extent
of the region of perturbation due to the planet is significantly smaller than
the angular size of the source, and as a result the planetary signature is also
smoothed out by the finite source size. Thus the deviation from a single-lens
fit is broad and relatively weak (~ few percent). Nevertheless, we demonstrate
that the planetary nature of the deviation can be unambiguously ascertained
from the gross features of the residuals, and detailed analysis yields a fairly
precise planet/star mass ratio of q = 0.0026+/-0.0004, in accord with the large
significance (\Delta\chi^2=1070) of the detection. The planet/star projected
separation is subject to a strong close/wide degeneracy, leading to two
indistinguishable solutions that differ in separation by a factor of ~8.5.
Upper limits on flux from the lens constrain its mass to be M < 0.75 M_Sun
(assuming it is a main-sequence star). A Bayesian analysis that includes all
available observational constraints indicates a primary in the Galactic bulge
with a mass of ~0.2-0.5 M_Sun and thus a planet mass of ~ 0.5-1.3 M_Jupiter.
The separation and equilibrium temperature are ~0.6-1.1AU (~5.3-9.7AU) and
~103K (~34K) for the close (wide) solution. If the primary is a main-sequence
star, follow-up observations would enable the detection of its light and so a
measurement of its mass and distance.Comment: 30 pages, 6 figures, Submitted to Ap
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