Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain

We consider the equations of a viscous polytropic ideal gas in the domain exterior to a ball in ⁿ (n=2 or 3) and prove the global existence of spherically symmetric smooth solutions for (large) initial data with spherical symmetry. The large-time behavior of the solutions is also discussed. To prove the existence we first study an approximate problem in a bounded annular domain and then obtain a priori estimates independent of the boundedness of the annular domain. Letting the diameter of the annular domain tend to infinity, we get a global spherically symmetric solution as the limit.Dedicated to Professor Rolf Leis on the occasion of his 65th birthdaySupported by the SFB 256 of the Deutsche Forschungsgemeinschaft at the University of Boon.     

A lightweight symmetric image encryption cryptosystem in wavelet domain based on an improved sine map

In the era of big data, the number of images transmitted over the public channel increases exponentially. As a result,it is crucial to devise the efficient and highly secure encryption method to safeguard the sensitive image. In this paper, an improved sine map(ISM) possessing a larger chaotic region, more complex chaotic behavior and greater unpredictability is proposed and extensively tested. Drawing upon the strengths of ISM, we introduce a lightweight symmetric image encryption cryptosystem ...     

Condensate splitting in an asymmetric double well for atom chip based sensors

We report on the adiabatic splitting of a Bose-Einstein condensate of 87Rb atoms by an asymmetric double-well potential located above the edge of a perpendicularly magnetized TbGdFeCo film atom chip. By controlling the barrier height and double-well asymmetry, the sensitivity of the axial splitting process is investigated through observation of the fractional atom distribution between the left and right wells. This process constitutes a novel sensor for which we infer a single shot sensitivity to gravity fields of deltag/g approximately 2 x 10(-4). From a simple analytic model, we propose improvements to chip-based gravity detectors using this demonstrated methodology.     

Intertwining operators for solving differential equations,with applications to symmetric spaces

The use of intertwining operators to solve both ordinary and partial differential equations is developed. Classes of intertwining operators are constructed which transform between Laplacians which are self-adjoint with respect to different non-trivial measures. In the two-dimensional case, the intertwining operator transforms a non-separable partial differential operator to a separable one. As an application, the heat kernels on the rank 1 and rank 2 symmetric spaces are constructed.     

A hierarchy of high-order theories for symmetric modes in an elastic layer

A hierarchy of high-order theories for symmetric modes in an infinitely long elastic layer of the constant thickness is derived by means of the inertia-corrected polynomial approximations. For each member of the hierarchy, boundary conditions for layers of the finite length are formulated. The forcing problems at several approximation levels are solved with the use of the bi-orthogonality conditions. Accuracy of these approximations is assessed by comparison of results with the exact solution of the Rayleigh–Lamb problem. Special attention is paid to the power flow analysis in alternative modal excitation cases and to the applicability of the Saint-Venant?s principle in stationary elasto-dynamics.     

Relations,analogous to Snoek's one,for domain wall processes

The suitability of relations having a formal similarity with the known Snoek's law is analysed for polycrystalline ferrites (PF) in their typical domain wall process frequency range. The parameters used in these relations are the saturation magnetization and those taken from the complex permeability spectrum and from microstructure of PF sample.     

Spherically symmetric equations in gauge theories for an arbitrary semisimple compact lie group

An explicit construction of spherically symmetric equations (not only static and/or self-dual) in gauge theories for the minimal embedding of SU(2) in an arbitrary semisimple compact Lie group G is given. The final equations are written in a form containing only gauge invariant quantities in R₂. The whole group structure is concentrated in the only matrix, which is directly related to the Cartan matrix of G. In particular, the developed technique allows to generalize the Witten duality equation [1] and to obtain the spectrum of pointlike solutions in G.     

Thermally stimulated acoustic splitting of an elastic wave in polycrystalline niobium subjected to electron-beam remelting

The effect of temperature on the Young’s modulus of electron-beam-remelted polycrystalline niobium is studied in the temperature range 20–1000°C. The impurity content in the material is Ta<0.5 wt% and O₂<0.1 wt%. The acoustic split of the resonant frequency is found in the temperature range 60–180°C, which makes the determination of the Young’s modulus uncertain. Mechanisms behind the thermally stimulated splitting of an elastic wave and the behavior of the Young’s modulus over a wide temperature interval are discussed.     

A new measurement method for electrode gain in an orthogonally symmetric beam position monitor

The new beam position monitor (BPM) system of the injector at the upgrade project of the Hefei Light Source (HLS Ⅱ) has 19 stripline beam position monitors. Most consist of four orthogonally symmetric stripline electrodes. Differences in electronic gain and mismachining tolerance can cause changes in the beam response of the BPM electrodes. This variation will couple the two measured horizontal positions, resulting in measuring error. To alleviate this effect, a new technique to measure the relative response of the four electrodes has been developed. It is independent of the beam charge, and the related coefficient can be calculated theoretically. The effect of electrode coupling on this technique is analyzed. The calibration data is used to fit the gain for all 19 injector beam position monitors. The results show the standard deviation of the distribution of measured gains is about 5%.     

Power of spontaneous emission for a nonrelativistic particle in an axially symmetric magnetic field

Using the quasiclassical trajectory-coherent states method for a nonrelativistic particle moving in an axially symmetric magnetic field, we have determined the characteristics of spontaneous emission, taking into account the first quantum correction. In the special case of a constant homogeneous magnetic field, the result agrees well with previously known characteristics.Tomsk Polytechnical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 79–82, October, 1992.     

Vortex splitting in the interference effect for a quantized vortex released from an optical lattice

For a quantized vortex in a harmonic trap and an optical lattice, we study the interference effect after the combined potentials are switched off. Both numerical and analytical calculations show that there is a vortex splitting in the interference effect of this freely expanding quantum gas, i.e. every interference peak is also a quantized vortex. The experimental scheme to verify this interference effect is discussed.     

Anomalous, quasilinear, and percolative regimes for magnetic-field-line transport in axially symmetric turbulence

We studied a magnetic turbulence axisymmetric around the unperturbed magnetic field for cases having different ratios l( ||)/l( perpendicular). We find, in addition to the fact that a higher fluctuation level deltaB/B(0) makes the system more stochastic, that by increasing the ratio l( ||)/l( perpendicular) at fixed deltaB/B(0), the stochasticity increases. It appears that the different transport regimes can be organized in terms of the Kubo number R=(deltaB/B(0))(l( ||)/l( perpendicular)). The simulation results are compared with the two analytical limits, that is the percolative limit and the quasilinear limit. When R<1 weak chaos, closed magnetic surfaces, and anomalous transport regimes are found. When R approximately 1 the diffusion regime is Gaussian, and the quasilinear scaling of the diffusion coefficient D( perpendicular) approximately (deltaB/B(0))(2) is recovered. Finally, for R>1 the percolation scaling of the diffusion coefficient D( perpendicular) approximately (deltaB/B(0))(0.7) is obtained.     

Angular splitting of the Bragg diffraction order in an acoustooptical modulator due to a frequency-modulated acoustic wave

Effects of angular splitting of the Bragg diffraction order arising in light acoustooptical diffraction by a frequency-modulated acoustic wave are considered. These effects occur when the size of the light spot in the acoustooptical interaction zone exceeds the characteristic spatial period of the modulating function. The Bragg diffraction order is found to be split into several beams. The directions of the additional beams, their number, and intensities are determined by the modulation parameters. In particular, there occurs a situation where the diffracted field consists of three beams of equal intensity spaced at a distance approximately equal to the diffraction divergence of the incident beam and the diffraction total efficiency is of the order of 100%. Therein lies the difference between this diffraction regime and the case where several independent acoustic waves are generated in the interaction domain and the diffraction total efficiency is limited to the intermodulation arisen. The effect is used in design of modulators for systems of image plotting with the help of high-power lasers.     

Experimental evidence for dendrite tip splitting in deeply undercooled,ultrahigh purity Cu

In a recent paper we used a phase-field model of solidification in deeply undercooled pure melts to show that a kinetic instability could result in dendrite tip splitting, and we speculated that such tip splitting could give rise to the phenomenon of spontaneous grain refinement. Here we present evidence, from the as-solidified microstructure of deeply undercooled ultrahigh purity Cu, of what appears to be dendrite tip splitting during recalescence. The significance of this finding in a nongrain refined sample is discussed in terms of the current theories for spontaneous grain refinement.     

Emergence of unstable modes in an expanding domain for energy-conserving wave equations

Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schrödinger equation in a finite domain and show how the expansion or contraction of the domain, under appropriate conditions, can destabilize its originally stable solutions through the modulational instability mechanism. Using both real and Fourier space diagnostics, we monitor and control the crossing of the instability threshold and, hence, the activation of the instability. We also consider how the manifestation of this mechanism is modified in a spatially inhomogeneous setting, namely in the presence of an external parabolic potential, which is relevant to trapped Bose-Einstein condensates.     

轴对称谐振势阱中玻色凝聚气体基态和单涡旋态解

对囚禁在轴对称谐振势阱中的玻色凝聚气体，提出一种新的试探波函数，运用Gross-Pitaevskii(G-P)平均场能量泛函和变分的方法，得到玻色凝聚气体基态和单涡旋态波函数的解析表达式，并计算出凝聚原子的平均能量、原子云轴向和径向尺度比，以及产生单涡旋态的临界角速度等重要物理量与凝聚原子数N之间的关系.其结果与Dalfovo等人直接数值求解G-P方程所得到的结果相一致. 关键词： 玻色凝聚气体 G-P泛函 波函数 谐振势阱