12,736 research outputs found

    On the exponential transform of lemniscates

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    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

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    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 eNe^{\mp}N scattering, for axial parametrization of two-photon exchange

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    We analyze polarization phenomena for elastic lepton-nucleon scattering, parametrizing the 2γ2\gamma-exchange contribution, as the product of lepton and nucleon axial vector currents, that correspond to C=+1C=+1 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 GE(Q2)/GM(Q2)G_E(Q^2)/G_M(Q^2) of nucleon electromagnetic form factors in model independent way, without any specific assumption about the 2γ2\gamma-exchange mechanism. Both these combinations have a general character and do not depend on the choice of the spin structure for the 2γ2\gamma-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 e+Ae+A-scattering. Part I: Virtual Compton Scattering

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    We calculate polarization phenomena for virtual Compton scattering on protons, at relatively large momentum transfer 1 GeV2^2 q2\le -q^2\le 5 GeV2^2 on the basis of a model for γ+pγ+p\gamma^*+ p\to \gamma+p with two main contributions: π0\pi^0-exchange in tt-channel and Δ\Delta-excitation in ss-channel. This model applies from threshold to Δ\Delta region. The parameters entering in this model, such as coupling constants and electromagnetic form factors are well known. The analyzing powers for γ+pγ+p\gamma^*+\vec p\to \gamma+ p and the components of the final proton polarization in γ+pγ+p\gamma^*+ p\to \gamma+ \vec p are large in absolute value and show strong sensitivity to πΔ\pi\bigotimes\Delta interference. These results can be applied to the calculation of radiative corrections to polarization phenomena in elastic epep-scattering.Comment: 18 pages, 9 figure

    Observation of coherent π0\pi^0 electroproduction on deuterons at large momentum transfer

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    The first experimental results for coherent π0\pi^0-electroproduction on the deuteron, e+de+d+π0e+d\to e+d +\pi^0, 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 1.1<Q2<<Q^2<1.8 GeV2^2, from threshold to 200 MeV excitation energy in the dπ0d\pi^0 system. The Q2Q^2-dependence is compared with theoretical predictions.Comment: 26 page

    Measuring the deviation from the Rutherford formula

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    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

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    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

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    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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