21,449 research outputs found
Breaking scale invariance from a singular inflaton potential
In this paper we break the scale invariance of the primordial power spectrum
of curvature perturbations of inflation. Introducing a singular behaviour due
to spontaneous symmetry breaking in the inflaton potential, we obtain fully
analytic expressions of scale dependent oscillation and a modulation in power
on small scale in the primordial spectrum. And we give the associated cosmic
microwave background and matter power spectra which we can observe now and
discuss the signature of the scale dependence. We also address the possibility
of whether some inflationary model with featured potential might mimic the
predictions of the scale invariant power spectrum. We present some examples
which illustrate such degeneracies.Comment: 20 pages, 9 figures; Discussion expanded and references added;
Miscellaneous typos correcte
The Sorting Index and Permutation Codes
In the combinatorial study of the coefficients of a bivariate polynomial that
generalizes both the length and the reflection length generating functions for
finite Coxeter groups, Petersen introduced a new Mahonian statistic ,
called the sorting index. Petersen proved that the pairs of statistics
and have the same joint distribution over
the symmetric group, and asked for a combinatorial proof of this fact. In
answer to the question of Petersen, we observe a connection between the sorting
index and the B-code of a permutation defined by Foata and Han, and we show
that the bijection of Foata and Han serves the purpose of mapping
to . We also give a type analogue of the
Foata-Han bijection, and we derive the quidistribution of and over signed
permutations. So we get a combinatorial interpretation of Petersen's
equidistribution of and . Moreover, we show that
the six pairs of set-valued statistics ,
, , ,
and are equidistributed over signed
permutations. For Coxeter groups of type , Petersen showed that the two
statistics and are equidistributed. We introduce two statistics
and for elements of and we prove that the two
pairs of statistics and are
equidistributed.Comment: 25 page
A Simple Three-Parameter Model Potential For Diatomic Systems: From Weakly and Strongly Bound Molecules to Metastable Molecular Ions
Based on a simplest molecular orbital theory of H, a
three-parameter model potential function is proposed to describe ground-state
diatomic systems with closed-shell and/or S-type valence-shell constituents
over a significantly wide range of internuclear distances. More than 200 weakly
and strongly bound diatomics have been studied, including neutral and
singly-charged diatomics (e.g., H, Li, LiH, Cd, Na,
and RbH), long-range bound diatomics (e.g., NaAr, CdNe, He, CaHe,
SrHe, and BaHe), metastable molecular dications (e.g., BeH, AlH,
Mg, and LiBa), and molecular trications (e.g., YHe
and ScHe).Comment: 5 pages, 4 figures, accepted by Physical Review Letter
Compensation of compliance errors in parallel manipulators composed of non-perfect kinematic chains
The paper is devoted to the compliance errors compensation for parallel
manipulators under external loading. Proposed approach is based on the
non-linear stiffness modeling and reduces to a proper adjusting of a target
trajectory. In contrast to previous works, in addition to compliance errors
caused by machining forces, the problem of assembling errors caused by
inaccuracy in the kinematic chains is considered. The advantages and practical
significance of the proposed approach are illustrated by examples that deal
with groove milling with Orthoglide manipulator.Comment: Advances in Robot Kinematics, France (2012
Inflationary Hubble Parameter from the Gravitational Wave Spectrum in the General Slow-roll Approximation
Improved general slow-roll formulae giving the primordial gravitational wave
spectrum are derived in the present work. Also the first and second order
general slow-roll inverse formulae giving the Hubble parameter in terms of
the gravitational wave spectrum are derived. Moreover, the general slow-roll
consistency condition relating the scalar and tensor spectra is obtained
Quantum enhancement of N-photon phase sensitivity by interferometric addition of down-converted photon pairs to weak coherent light
It is shown that the addition of down-converted photon pairs to coherent
laser light enhances the N-photon phase sensitivity due to the quantum
interference between components of the same total photon number. Since most of
the photons originate from the coherent laser light, this method of obtaining
non-classical N-photon states is much more efficient than methods based
entirely on parametrically down-converted photons. Specifically, it is possible
to achieve an optimal phase sensitivity of about delta phi^2=1/N^(3/2), equal
to the geometric mean of the standard quantum limit and the Heisenberg limit,
when the average number of down-converted photons contributing to the N-photon
state approaches (N/2)^(1/2).Comment: 21 pages, including 6 figures. Extended version gives more details on
down-conversion efficiencies and clarifies the relation between phase
sensitivity and squeezing. The title has been changed in order to avoid
misunderstandings regarding these concept
Extracting particle freeze-out phase-space densities and entropies from sources imaged in heavy-ion reactions
The space-averaged phase-space density and entropy per particle are both
fundamental observables which can be extracted from the two-particle
correlation functions measured in heavy-ion collisions. Two techniques have
been proposed to extract the densities from correlation data: either by using
the radius parameters from Gaussian fits to meson correlations or by using
source imaging, which may be applied to any like pair correlation. We show that
the imaging and Gaussian fits give the same result in the case of meson
interferometry. We discuss the concept of an equivalent instantaneous source on
which both techniques rely. We also discuss the phase-space occupancy and
entropy per particle. Finally, we propose an improved formula for the
phase-space occupancy that has a more controlled dependence on the uncertainty
of the experimentally measured source functions.Comment: 14 pages, final version, to appear PRC. Fixed typos, added refs. for
last section, added discussions of imaging and d/p ratio
Climate change and changing landscape - a coparativ evaluation on chinese and hungarian sample areas
The effects of globalisation are becoming obvious not only in the world economy but in natural processes as well. Increase of deterioration of natural conditions result in more and more decrease of land and water resources. Some experts even suggest that the changing climate of the next several decades can result in the transformation of the natural landscape. Human activities, global and regional changes of climate and land use destroy the ecological environment, which also make the service function of the local ecosystem damaged constantly. We can improve ecological security of an area through regional land use pattern opti-mizing. The physical geographical consequences of aridification might be described through the decrease of ground water level, the change of the biomass quantity and quality. Their spatial and temporal variation may reflect the intensity and strength of degradation. Remote sensing is one of the best tools to follow these processes, applying different databases. Spatial analysis of the gained information may help us to delineate the areas potentially endangered by even a minor climate change
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