3,201 research outputs found
Orbit Determination with the two-body Integrals
We investigate a method to compute a finite set of preliminary orbits for
solar system bodies using the first integrals of the Kepler problem. This
method is thought for the applications to the modern sets of astrometric
observations, where often the information contained in the observations allows
only to compute, by interpolation, two angular positions of the observed body
and their time derivatives at a given epoch; we call this set of data
attributable. Given two attributables of the same body at two different epochs
we can use the energy and angular momentum integrals of the two-body problem to
write a system of polynomial equations for the topocentric distance and the
radial velocity at the two epochs. We define two different algorithms for the
computation of the solutions, based on different ways to perform elimination of
variables and obtain a univariate polynomial. Moreover we use the redundancy of
the data to test the hypothesis that two attributables belong to the same body
(linkage problem). It is also possible to compute a covariance matrix,
describing the uncertainty of the preliminary orbits which results from the
observation error statistics. The performance of this method has been
investigated by using a large set of simulated observations of the Pan-STARRS
project.Comment: 23 pages, 1 figur
Symmetric Periodic Solutions of the Anisotropic Manev Problem
We consider the Manev Potential in an anisotropic space, i.e., such that the
force acts differently in each direction. Using a generalization of the
Poincare' continuation method we study the existence of periodic solutions
for weak anisotropy. In particular we find that the symmetric periodic orbits
of the Manev system are perturbed to periodic orbits in the anisotropic
problem.Comment: Late
Hierarchical Self-Assembly of Halogen-Bonded Block Copolymer Complexes into Upright Cylindrical Domains
Self-assembly of block copolymers into well-defined, ordered arrangements of chemically distinct domains is a reliable strategy for preparing tailored nanostructures. Microphase separation results from the system, minimizing repulsive interactions between dissimilar blocks and maximizing attractive interactions between similar blocks. Supramolecular methods have also achieved this separation by introducing small-molecule additives binding specifically to one block by noncovalent interactions. Here, we use halogen bonding as a supramolecular tool that directs the hierarchical self-assembly of low-molecular-weight perfluorinated molecules and diblock copolymers. Microphase separation results in a lamellar-within-cylindrical arrangement and promotes upright cylindrical alignment in films upon rapid casting and without further annealing. Such cylindrical domains with internal lamellar self-assemblies can be cleaved by solvent treatment of bulk films, resulting in separated and segmented cylindrical micelles stabilized by halogen-bond-based supramolecular crosslinks. These features, alongside the reversible nature of halogen bonding, provide a robust modular approach for nanofabricatio
Non-minimally Coupled Quintom Model Inspired by String Theory
In this paper we consider a quintom model of dark energy with a single scalar
field given by a Lagrangian which inspired by tachyonic Lagrangian in
string theory. We consider non-minimal coupling of tachyon field to the scalar
curvature, then we obtain the equation of state (EoS), and the condition
required for the model parameters when crosses over -1.Comment: 8 pages, 2 figure
Chirikov Diffusion in the Asteroidal Three-Body Resonance (5,-2,-2)
The theory of diffusion in many-dimensional Hamiltonian system is applied to
asteroidal dynamics. The general formulations developed by Chirikov is applied
to the Nesvorn\'{y}-Morbidelli analytic model of three-body (three-orbit)
mean-motion resonances (Jupiter-Saturn-asteroid system). In particular, we
investigate the diffusion \emph{along} and \emph{across} the separatrices of
the (5,-2,-2) resonance of the (490) Veritas asteroidal family and their
relationship to diffusion in semi-major axis and eccentricity. The estimations
of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type
sympletic map and numerical integrations for times up to years.Comment: 27 pages, 6 figure
Compartmentalization of corticotropin-dependent steroidogenic factors in adrenal cortex: evidence for a post-translational cascade in stimulation of the cholesterol side-chain split.
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