822 research outputs found
The inverse moment problem for convex polytopes
The goal of this paper is to present a general and novel approach for the
reconstruction of any convex d-dimensional polytope P, from knowledge of its
moments. In particular, we show that the vertices of an N-vertex polytope in
R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to
an unknown polynomial measure od degree D) in d+1 distinct generic directions.
Our approach is based on the collection of moment formulas due to Brion,
Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry
of polytopes, and what variously known as Prony's method, or Vandermonde
factorization of finite rank Hankel matrices.Comment: LaTeX2e, 24 pages including 1 appendi
O(4) texture with a cosmological constant
We investigate O(4) textures in a background with a positive cosmological
constant. We find static solutions which co-move with the expanding background.
There exists a solution in which the scalar field is regular at the horizon.
This solution has a noninteger winding number smaller than one. There also
exist solutions in which scalar-field derivatives are singular at the horizon.
Such solutions can complete one winding within the horizon. If the winding
number is larger than some critical value, static solutions including the
regular one are unstable under perturbations.Comment: 25 pages, revtex, 6 eps figure
A Monitor of Beam Polarization Profiles for the TRIUMF Parity Experiment
TRIUMF experiment E497 is a study of parity violation in pp scattering at an
energy where the leading term in the analyzing power is expected to vanish,
thus measuring a unique combination of weak-interaction flavour conserving
terms. It is desired to reach a level of sensitivity of 2x10^-8 in both
statistical and systematic errors. The leading systematic errors depend on
transverse polarization components and, at least, the first moment of
transverse polarization. A novel polarimeter that measures profiles of both
transverse components of polarization as a function of position is described.Comment: 19 pages LaTeX, 10 PostScript figures. To appear in Nuclear
Instruments and Methods in Physics Research, Section
Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals
High-order derivatives of analytic functions are expressible as Cauchy
integrals over circular contours, which can very effectively be approximated,
e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius
of convergence is equal, numerical stability strongly depends on r. We give a
comprehensive study of this effect; in particular we show that there is a
unique radius that minimizes the loss of accuracy caused by round-off errors.
For large classes of functions, though not for all, this radius actually gives
about full accuracy; a remarkable fact that we explain by the theory of Hardy
spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and
by the saddle-point method of asymptotic analysis. Many examples and
non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature
rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat
The Physics of turbulent and dynamically unstable Herbig-Haro jets
The overall properties of the Herbig-Haro objects such as centerline
velocity, transversal profile of velocity, flow of mass and energy are
explained adopting two models for the turbulent jet. The complex shapes of the
Herbig-Haro objects, such as the arc in HH34 can be explained introducing the
combination of different kinematic effects such as velocity behavior along the
main direction of the jet and the velocity of the star in the interstellar
medium. The behavior of the intensity or brightness of the line of emission is
explored in three different cases : transversal 1D cut, longitudinal 1D cut and
2D map. An analytical explanation for the enhancement in intensity or
brightness such as usually modeled by the bow shock is given by a careful
analysis of the geometrical properties of the torus.Comment: 17 pages, 10 figures. Accepted for publication in Astrophysics &
Spac
(Sub)mm Interferometry Applications in Star Formation Research
This contribution gives an overview about various applications of (sub)mm
interferometry in star formation research. The topics covered are molecular
outflows, accretion disks, fragmentation and chemical properties of low- and
high-mass star-forming regions. A short outlook on the capabilities of ALMA is
given as well.Comment: 20 pages, 7 figures, in proceedings to "2nd European School on Jets
from Young Star: High Angular Resolution Observations". A high-resolution
version of the paper can be found at
http://www.mpia.de/homes/beuther/papers.htm
Population ecology of Psammobates oculifer in a semi-arid environment
We studied the ecology of Psammobates oculifer over 13 months near Kimberley, South Africa, to ascertain if the population’s life history traits conform to chelonian patterns in arid environments. Capture rates were highest in spring and lowest in winter when environmental conditions were respectively most and least favourable for tortoise activity. Body condition did not change from autumn to spring, but reached lower values during the summer drought. Capture effort averaged 5 hours/tortoise, which corresponds closely to that of species with low population densities in arid regions. Population size structure was skewed towards adults, indicative of low recruitment and/or low juvenile survivorship. Females were larger and heavier than males, confirming sexual dimorphism in this species. Body size of cohorts scaled to annuli counts, indicating a close correspondence between body size and age. Telemetered adults deposited one or no growth ring in the year of study; consequently, annuli counts could underestimate adult age. Regression analyses showed that male and female growth rates did not differ, but males matured at a smaller size and younger age than females. The smallest male showing reproductive behaviour had 12 annuli and a shell volume of 157 cm3, while similar measures for females were 14 annuli and 185 cm3. The sex ratio of the population did not differ from 1:1 but the bias towards males in spring, and towards females in autumn, indicates that studies limited to particular seasons can misrepresent life history traits of populations. We concluded that the life history of P. oculifer conforms to chelonian patterns in arid regions.Web of Scienc
Tunneling of quantum rotobreathers
We analyze the quantum properties of a system consisting of two nonlinearly
coupled pendula. This non-integrable system exhibits two different symmetries:
a permutational symmetry (permutation of the pendula) and another one related
to the reversal of the total momentum of the system. Each of these symmetries
is responsible for the existence of two kinds of quasi-degenerated states. At
sufficiently high energy, pairs of symmetry-related states glue together to
form quadruplets. We show that, starting from the anti-continuous limit,
particular quadruplets allow us to construct quantum states whose properties
are very similar to those of classical rotobreathers. By diagonalizing
numerically the quantum Hamiltonian, we investigate their properties and show
that such states are able to store the main part of the total energy on one of
the pendula. Contrary to the classical situation, the coupling between pendula
necessarily introduces a periodic exchange of energy between them with a
frequency which is proportional to the energy splitting between
quasi-degenerated states related to the permutation symmetry. This splitting
may remain very small as the coupling strength increases and is a decreasing
function of the pair energy. The energy may be therefore stored in one pendulum
during a time period very long as compared to the inverse of the internal
rotobreather frequency.Comment: 20 pages, 11 figures, REVTeX4 styl
The Kuiper Belt and Other Debris Disks
We discuss the current knowledge of the Solar system, focusing on bodies in
the outer regions, on the information they provide concerning Solar system
formation, and on the possible relationships that may exist between our system
and the debris disks of other stars. Beyond the domains of the Terrestrial and
giant planets, the comets in the Kuiper belt and the Oort cloud preserve some
of our most pristine materials. The Kuiper belt, in particular, is a
collisional dust source and a scientific bridge to the dusty "debris disks"
observed around many nearby main-sequence stars. Study of the Solar system
provides a level of detail that we cannot discern in the distant disks while
observations of the disks may help to set the Solar system in proper context.Comment: 50 pages, 25 Figures. To appear in conference proceedings book
"Astrophysics in the Next Decade
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