12,774 research outputs found
Some Counterexamples in Positive Dependence.
We provide some counterexamples showing that some concepts of positive dependence are strictly stronger than others. In particular we will settle two questions posed by Pemantle (2000) and Pellerey (2002) concerning respectively association versus weak association, weak association versus supermodular dependence, and supermodular dependence versus positive orthant dependence.Association, weak association, supermodular dependence, positive orthant dependence.
Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants
For the first two equations of the Volterra lattice hierarchy and the first
two equations of its non-autonomous (non-isospectral) extension, we present
Riccati systems for functions c_j(t), j=0,1,..., such that an expression in
terms of Hankel determinants built from them solves these equations on the
right half of the lattice. This actually achieves a complete linearization of
these equations of the extended Volterra lattice hierarchy.Comment: 31 pages, 3rd version: introduction extended, part of Section 2 moved
there, Appendix D added, additional references, to appear in Nonlinearit
Using quantum optical sensors for determining the Earth’s gravity field from space
Quantum optical technology provides an opportunity to develop new kinds of gravity sensors and to enable novel measurement concepts for gravimetry. Two candidates are considered in this study: the cold atom interferometry (CAI) gradiometer and optical clocks. Both sensors show a high sensitivity and long-term stability. They are assumed on board of a low-orbit satellite like gravity field and steady-state ocean circulation explorer (GOCE) and gravity recovery and climate experiment (GRACE) to determine the Earth’s gravity field. Their individual contributions were assessed through closed-loop simulations which rigorously mapped the sensors’ sensitivities to the gravity field coefficients. Clocks, which can directly obtain the gravity potential (differences) through frequency comparison, show a high sensitivity to the very long-wavelength gravity field. In the GRACE orbit, clocks with an uncertainty level of 1.0 × 10 - 18 are capable to retrieve temporal gravity signals below degree 12, while 1.0 × 10 - 17 clocks are useful for detecting the signals of degree 2 only. However, it poses challenges for clocks to achieve such uncertainties in a short time. In space, the CAI gradiometer is expected to have its ultimate sensitivity and a remarkable stability over a long time (measurements are precise down to very low frequencies). The three diagonal gravity gradients can properly be measured by CAI gradiometry with a same noise level of 5.0 mE/Hz. They can potentially lead to a 2–5 times better solution of the static gravity field than that of GOCE above degree and order 50, where the GOCE solution is mainly dominated by the gradient measurements. In the lower degree part, benefits from CAI gradiometry are still visible, but there, solutions from GRACE-like missions are superior. © 2020, The Author(s)
Relativistic three-body recombination with the QED vacuum
Electron-positron pair annihilation into a single photon is studied when a
second free electron is present. Focussing on the relativistic regime, we show
that the photon emitted in the three-lepton interaction may exhibit distinct
angular distributions and polarization properties. Moreover, the process can
dominate over two-photon annihilation in relativistic electron-positron plasmas
of few-MeV temperature. An analogy with three-body recombination of electrons
with ions is drawn.Comment: 5 pages, 4 figure
The blue-edge problem of the V1093 Her instability strip revisited using evolutionary models with atomic diffusion
We have computed a new grid of evolutionary subdwarf B star (sdB) models from
the start of central He burning, taking into account atomic diffusion due to
radiative levitation, gravitational settling, concentration diffusion, and
thermal diffusion. We have computed the non-adiabatic pulsation properties of
the models and present the predicted p-mode and g-mode instability strips. In
previous studies of the sdB instability strips, artificial abundance
enhancements of Fe and Ni were introduced in the pulsation driving layers. In
our models, the abundance enhancements of Fe and Ni occur naturally,
eradicating the need to use artificial enhancements. We find that the abundance
increases of Fe and Ni were previously underestimated and show that the
instability strip predicted by our simulations solves the so-called blue edge
problem of the subdwarf B star g-mode instability strip. The hottest known
g-mode pulsator, KIC 10139564, now resides well within the instability strip
{even when only modes with low spherical degrees (l<=2) are considered.Comment: 7 pages, 7 figures. Accepted for publication in Astronomy &
Astrophysic
Photo-production of scalar particles in the field of a circularly polarized laser beam
The photo-production of a pair of scalar particles in the presence of an
intense, circularly polarized laser beam is investigated. Using the optical
theorem within the framework of scalar quantum electrodynamics, explicit
expressions are given for the pair production probability in terms of the
imaginary part of the vacuum polarization tensor. Its leading asymptotic
behavior is determined for various limits of interest. The influence of the
absence of internal spin degrees of freedom is analyzed via a comparison with
the corresponding probabilities for production of spin-1/2 particles; the lack
of spin is shown to suppress the pair creation rate, as compared to the
predictions from Dirac theory. Potential applications of our results for the
search of minicharged particles are indicated.Comment: 6 pages, 2 figure
Shape-dependent universality in percolation
The shape-dependent universality of the excess percolation cluster number and
cross-configuration probability on a torus is discussed. Besides the aspect
ratio of the torus, the universality class depends upon the twist in the
periodic boundary conditions, which for example are generally introduced when
triangular lattices are used in simulations.Comment: 11 pages, 3 figures, to be published in Physica
Excess number of percolation clusters on the surface of a sphere
Monte Carlo simulations were performed in order to determine the excess
number of clusters b and the average density of clusters n_c for the
two-dimensional "Swiss cheese" continuum percolation model on a planar L x L
system and on the surface of a sphere. The excess number of clusters for the L
x L system was confirmed to be a universal quantity with a value b = 0.8841 as
previously predicted and verified only for lattice percolation. The excess
number of clusters on the surface of a sphere was found to have the value b =
1.215(1) for discs with the same coverage as the flat critical system. Finally,
the average critical density of clusters was calculated for continuum systems
n_c = 0.0408(1).Comment: 13 pages, 2 figure
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