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

Perturbations of discrete lattices and almost periodic sets

A discrete set in the $p$-dimensional Euclidian space is {\it almost periodic}, if the measure with the unite masses at points of the set is almost periodic in the weak sense. We propose to construct positive almost periodic discrete sets as an almost periodic perturbation of a full rank discrete lattice. Also we prove that each almost periodic discrete set on the real axes is an almost periodic perturbation of some arithmetic progression. Next, we consider signed almost periodic discrete sets, i.e., when the signed measure with masses $\pm1$ at points of a discrete set is almost periodic. We construct a signed discrete set that is not almost periodic, while the corresponding signed measure is almost periodic in the sense of distributions. Also, we construct a signed almost periodic discrete set such that the measure with masses +1 at all points of the set is not almost periodic.Comment: 6 page

Fractional charges and quantum phase transitions in imbalanced bilayer quantum Hall systems

We extend the Composite Boson theory to study slightly im-balanced bi-layer Quantum Hall systems. In the global $U(1)$ symmetry breaking excitonic superfluid side, as the imbalance increases, the system supports continuously changing fractional charges. In the translational symmetry breaking pseudo-spin density wave (PSDW) side, there are two quantum phase transitions from the commensurate PSDW to an in-commensurate PSDW and then to the excitonic superfluid state. We compare our theory with experimental data and also the previous microscopic calculations.Comment: 4+ pages, 2 figures. 1 table, Final version to appear in Phys. Rev. Let

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

Prospects for application of ultracold Sr2_2 molecules in precision measurements

Precision measurements with ultracold molecules require development of robust and sensitive techniques to produce and interrogate the molecules. With this goal, we theoretically analyze factors that affect frequency measurements between rovibrational levels of the Sr$_2$ molecule in the electronic ground state. This measurement can be used to constrain the possible time variation of the proton-electron mass ratio. Sr$_2$ is expected to be a strong candidate for achieving high precision due to the spinless nature and ease of cooling and perturbation-free trapping of Sr \cite{Zelevinsky2008}. The analysis includes calculations of two-photon transition dipole moments between deeply and weakly bound vibrational levels, lifetimes of intermediate excited states, and Stark shifts of the vibrational levels by the optical lattice field, including possibilities of Stark-cancellation trapping.Comment: 8 pages, 10 figure

Bayesian nonparametric tests via sliced inverse modeling

We study the problem of independence and conditional independence tests between categorical covariates and a continuous response variable, which has an immediate application in genetics. Instead of estimating the conditional distribution of the response given values of covariates, we model the conditional distribution of covariates given the discretized response (aka "slices"). By assigning a prior probability to each possible discretization scheme, we can compute efficiently a Bayes factor (BF)-statistic for the independence (or conditional independence) test using a dynamic programming algorithm. Asymptotic and finite-sample properties such as power and null distribution of the BF statistic are studied, and a stepwise variable selection method based on the BF statistic is further developed. We compare the BF statistic with some existing classical methods and demonstrate its statistical power through extensive simulation studies. We apply the proposed method to a mouse genetics data set aiming to detect quantitative trait loci (QTLs) and obtain promising results.Comment: 32 pages, 7 figure

Comparison of the Efficiency of Budget Financing and the Social Security of a Region

The article deals with theoretical and economic aspects of the “security” category and draws a distinction between philosophical, sociological, and economic approaches to the concept of social security. From the perspective of a system approach, the authors define the place of the region’s social security in ensuring national security. The article describes the theoretical content of the «social security» category and provides the authors’ specification for such terms as «social risks,» «danger,» and «threat.» The authors offer methodological tools to evaluate the region’s social security based on a complex assessment of the region’s socioeconomic and budget-financing indicators to identify the risks (deviations) and factors of inefficient financing. The proposed methodological approach is based on identifying the dependencies between the social and financial security of the region. The following indicators reflecting the social security level in the territory of residence were selected as estimated indicators: the region’s consolidated budget income and expenses, gross domestic product growth rates, natural population growth ratio, unemployment level, the share of the population with income below the subsistence minimum. This approach was tested by the example of the Perm Territory and Sverdlovsk Region revealing the regularities as well as favorable and unfavorable periods for the region’s social security. The obtained estimated indicators are ranked depending on the growth (fall) time lag, resilience, and sensitivity to budget financing. The assessment results show that the Perm Territory has been entering a deep recession in terms of national security since 2012. Similar tendencies are demonstrated by the Sverdlovsk Region; however, in view of the apparent diversity and dominant influence of the Perm Territory and the Sverdlovsk Region on the socioeconomic development of the Privolzhsky and Ural Federal Districts, respectively, the provided comparison is of scientific and practical interest.The research has been supported by the Grant of the Russian Science Foundation (the Project № 14–18–00574 "Anticrisis Information Analysis System: Diagnostics of Regions, Threat Assessment, and Scenario Forecasting to Maintain and Strengthen the Economic Security and Welfare of Russia")