12,736 research outputs found
On the exponential transform of lemniscates
It is known that the exponential transform of a quadrature domain is a
rational function for which the denominator has a certain separable form. In
the present paper we show that the exponential transform of lemniscate domains
in general are not rational functions, of any form. Several examples are given
to illustrate the general picture. The main tool used is that of polynomial and
meromorphic resultants.Comment: 19 pages, to appear in the Julius Borcea Memorial Volume, (eds.
Petter Branden, Mikael Passare and Mihai Putinar), Trends in Mathematics,
Birkhauser Verla
Perturbation theorems for Hele-Shaw flows and their applications
In this work, we give a perturbation theorem for strong polynomial solutions
to the zero surface tension Hele-Shaw equation driven by injection or suction,
so called the Polubarinova-Galin equation. This theorem enables us to explore
properties of solutions with initial functions close to but are not polynomial.
Applications of this theorem are given in the suction or injection case. In the
former case, we show that if the initial domain is close to a disk, most of
fluid will be sucked before the strong solution blows up. In the later case, we
obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows
in terms of invariant Richardson complex moments. This rescaling behavior
result generalizes a recent result regarding large-time rescaling behavior for
small data in terms of moments. As a byproduct of a theorem in this paper, a
short proof of existence and uniqueness of strong solutions to the
Polubarinova-Galin equation is given.Comment: 25 page
Polarization phenomena in elastic scattering, for axial parametrization of two-photon exchange
We analyze polarization phenomena for elastic lepton-nucleon scattering,
parametrizing the -exchange contribution, as the product of lepton and
nucleon axial vector currents, that correspond to exchange in the
annihilation channel. We found two combinations of polarization observables
(one for three T-odd observables and another one - for five T-even
observables), which allow to measure the ratio of nucleon
electromagnetic form factors in model independent way, without any specific
assumption about the -exchange mechanism. Both these combinations have
a general character and do not depend on the choice of the spin structure for
the -exchange. We show the inconsistency of other approximations
recently used in the literature.Comment: Eight pages, no figure
Radiative corrections to polarization observables for elastic -scattering. Part I: Virtual Compton Scattering
We calculate polarization phenomena for virtual Compton scattering on
protons, at relatively large momentum transfer 1 GeV 5
GeV on the basis of a model for with two main
contributions: -exchange in channel and -excitation in
-channel. This model applies from threshold to region. The
parameters entering in this model, such as coupling constants and
electromagnetic form factors are well known. The analyzing powers for
and the components of the final proton
polarization in are large in absolute value and
show strong sensitivity to interference. These results
can be applied to the calculation of radiative corrections to polarization
phenomena in elastic -scattering.Comment: 18 pages, 9 figure
Observation of coherent electroproduction on deuterons at large momentum transfer
The first experimental results for coherent -electroproduction on the
deuteron, , at large momentum transfer, are reported. The
experiment was performed at Jefferson Laboratory at an incident electron energy
of 4.05 GeV. A large pion production yield has been observed in a kinematical
region for 1.11.8 GeV, from threshold to 200 MeV excitation energy
in the system. The -dependence is compared with theoretical
predictions.Comment: 26 page
Measuring the deviation from the Rutherford formula
Modern experiments with heavy ion-leptons collisions open the possibility to
measure the deviation of cross section of small angles electron(positron)-ion
elastic scattering from the Rutherford formula due to multiple virtual photons
exchange. The charge asymmetry and the polarization of the scattered leptons
are calculated and numerical predictions are given. A generalization to elastic
proton-nucleus scattering is discussed.Comment: 4 pages, 4 figures, Brief Repor
Disentangling the Hercules stream
Using high-resolution spectra of nearby F and G dwarf stars, we have
investigated the detailed abundance and age structure of the Hercules stream.
We find that the stars in the stream have a wide range of stellar ages,
metallicities, and element abundances. By comparing to existing samples of
stars in the solar neighbourhood with kinematics typical of the Galactic thin
and thick disks we find that the properties of the Hercules stream distinctly
separate into the abundance and age trends of the two disks. Hence, we find it
unlikely that the Hercules stream is a unique Galactic stellar population, but
rather a mixture of thin and thick disk stars. This points toward a dynamical
origin for the Hercules stream, probably caused by the Galactic bar.Comment: Accepted for publication in ApJ Letter
The nature of turbulence in OMC1 at the star forming scale: observations and simulations
Aim: To study turbulence in the Orion Molecular Cloud (OMC1) by comparing
observed and simulated characteristics of the gas motions.
Method: Using a dataset of vibrationally excited H2 emission in OMC1
containing radial velocity and brightness which covers scales from 70AU to
30000AU, we present the transversal structure functions and the scaling of the
structure functions with their order. These are compared with the predictions
of two-dimensional projections of simulations of supersonic hydrodynamic
turbulence.
Results: The structure functions of OMC1 are not well represented by power
laws, but show clear deviations below 2000AU. However, using the technique of
extended self-similarity, power laws are recovered at scales down to 160AU. The
scaling of the higher order structure functions with order deviates from the
standard scaling for supersonic turbulence. This is explained as a selection
effect of preferentially observing the shocked part of the gas and the scaling
can be reproduced using line-of-sight integrated velocity data from subsets of
supersonic turbulence simulations. These subsets select regions of strong flow
convergence and high density associated with shock structure. Deviations of the
structure functions in OMC1 from power laws cannot however be reproduced in
simulations and remains an outstanding issue.Comment: 12 pages, 8 figures, accepted A&A. Revised in response to referee.
For higher resolution, see http://www.astro.phys.au.dk/~maikeng/sim_paper
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