Global existence for a translating near-circular Hele-Shaw bubble with surface tension

This paper concerns global existence for arbitrary nonzero surface tension of bubbles in a Hele-Shaw cell that translate in the presence of a pressure gradient. When the cell width to bubble size is sufficiently large, we show that a unique steady translating near-circular bubble symmetric about the channel centerline exists, where the bubble translation speed in the laboratory frame is found as part of the solution. We prove global existence for symmetric sufficiently smooth initial conditions close to this shape and show that the steady translating bubble solution is an attractor within this class of disturbances. In the absence of side walls, we prove stability of the steady translating circular bubble without restriction on symmetry of initial conditions. These results hold for any nonzero surface tension despite the fact that a local planar approximation near the front of the bubble would suggest Saffman Taylor instability. We exploit a boundary integral approach that is particularly suitable for analysis of nonzero viscosity ratio between fluid inside and outside the bubble. An important element of the proof was the introduction of a weighted Sobolev norm that accounts for stabilization due to advection of disturbances from the front to the back of the bubble

Diplomacy of the project "Economic belt of the Great Silk Road" in modern foreign policy of China

The authors consider the Chinese policies of promoting the Silk Road Economic Belt project as a means of expansion of China’s influence on the global scale in general and as a means to find new markets for its goods. China’s strategies to implement its project are viewed

Entanglement and spin-squeezing in a network of distant optical lattice clocks

We propose an approach for collective enhancement of precision for remotely located optical lattice clocks and a way of generation of the Einstein-Podolsky-Rosen state of remote clocks. Close to Heisenberg scaling of the clock precision with the number of clocks M can be achieved even for an optical channel connecting clocks with substantial losses. This scenario utilizes a collective quantum nondemolition measurement on clocks with parallel Bloch vectors for enhanced measurement precision. We provide an optimal network solution for distant clocks as well as for clocks positioned in close proximity of each other. In the second scenario, we employ collective dissipation to drive two clocks with oppositely oriented Bloch vectors into a steady state entanglement. The corresponding EPR entanglement provides enhanced time sharing beyond the projection noise limit between the two quantum synchronized clocks protected from eavesdropping, as well as allows better characterization of systematic effects

Acoustic Attenuation by Two-dimensional Arrays of Rigid Cylinders

In this Letter, we present a theoretical analysis of the acoustic transmission through two-dimensional arrays of straight rigid cylinders placed parallelly in the air. Both periodic and completely random arrangements of the cylinders are considered. The results for the sound attenuation through the periodic arrays are shown to be in a remarkable agreement with the reported experimental data. As the arrangement of the cylinders is randomized, the transmission is significantly reduced for a wider range of frequencies. For the periodic arrays, the acoustic band structures are computed by the plane-wave expansion method and are also shown to agree with previous results.Comment: 4 pages, 3 figure

Probing the interactions of charmed mesons with nuclei in pˉ\bar p induced reactions

We study the perspectives of resonant and nonresonant charmed meson production in $\bar{p} + A$ reactions within the Multiple Scattering Monte Carlo (MSMC) approach. We calculate the production of the resonances $\Psi(3770), \Psi(4040)$ and $\Psi(4160)$ on various nuclei, their propagation and decay to $D, \bar{D}, D^*, \bar{D}^*, D_s, \bar{D}_s$ in the medium and vacuum, respectively. The modifications of the open charm vector mesons in the nuclear medium are found to be rather moderate or even small such that dilepton spectroscopy will require an invariant mass resolution of a few MeV. Furthermore, the elastic and inelastic interactions of the open charm mesons in the medium are taken into account, which can be related to $(u,d)$-, $s$- or $c$-quark exchange with nucleons. It is found that by studying the $D/\bar{D}$ ratio for low momenta in the laboratory ($\leq 2-2.2$ GeV/c) as a function of target mass $A$ stringent constraints on the $c$-quark exchange cross section can be obtained. On the other hand, the ratios $D^-_s/D^+_s$ as well as $D/D^-_s$ and $D/D^+_s$ at low momenta as a function of $A$ will permit to fix independently the strength of the $s$-quark exchange reaction in $D^-_s N$ scattering.Comment: 9 pages, LaTeX, including 9 postscript figures, submitted to Eur. Phys. J.

Nuclear transparency in quasielastic A(e,e'p): intranuclear cascade versus eikonal approximation

The problem of nuclear propagation through the nuclear medium in quasielastic A(e,e'p) reactions is discussed in the kinematic range 1<Q^2<7 (GeV/c)^2. The coefficient of nuclear transparency is calculated for each Q^2 in the framework of the intranuclear cascade model (INC) and of the eikonal approximation (EA). The predictions of both models are in good agreement with each other and with experimental data recently obtained at SLAC, BATES and TJNAF. The EA gives an explanation of the Q^2 behaviour of the transparency coefficient as a kinematic effect related to the superposition of contributions from each target shell.Comment: RevTeX, 23 pages, 11 figures separately, submitted to Phys. Rev.