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

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

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

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

Quadrature domains and kernel function zipping

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati

Comments on ISR method in modern experiment and influence of final state radiation

We study the effect of final state radiation in the process $e^++e^- \to \bar p+ p$, in the kinematical conditions of BaBar and BESIII experiment. We show that this effect could be large, in particular in the low $x$ region ($x$ is the photon energy fraction) and should be taken into account.Comment: 8 pages, 5 figure