A single oscillating bubble in liquids with high Mach number

The oscillation characteristics of a single bubble and its induced radiation pressure and the dissipated power are essential for a wide range of applications. For bubble oscillations with high Mach number, the influence of the liquid compressibility is significantly strong and should be fully considered. In the present paper, the bubble wall motion equation with the second-order Mach number is employed for investigating a free oscillating bubble in the liquid with numerical and experimental verifications. For the purpose of comparisons, the revised Keller-Miksis equation up to the first-order Mach number is solved with the same conditions (e.g. the initial conditions and the ambient pressure). Through our simulations, comparing with the predictions by the first-order equation, we find that: (1) The bubble radius, the bubble wall radial velocity and the bubble wall radial acceleration predicted by the second-order equation with high Mach number are significantly different respectively, and the dimensionless differences increase with the increase of the Mach number. (2) The valid prediction range of the second-order equation is much larger. (3) The dissipated power predicted by the second-order equation with high Mach number is smaller.     

Bestimmung der Empfindlichkeit bei Tc-99-NMR-Messungen an einem 250-MHz-Spektrometer

By means of different concentrations the signal-to-noise ratios of Tc-99-NMR spectra were determined applying well measurable Tc-samples [tetrabutylammoniwn pertechnetate, TBA (TcO₄)J and a 250 MHz-spectrometer. The signal-to-noise ratios of the spectra were determined by using the integrated routines of the firm's software and accumulating different number of scans. By fittings of data of the signal-to-noise ratio dependence and by extrapolation the minimum Tc-concentralion could be empirically found out. Applying a duration of measurements of 12 hours about 10^?7 molar concentrations can be determined.     

Some variant of Newton’s method with third-order convergence

We present a new modification of the Newton’s method which produces iterative methods with order of convergence three. A general error analysis providing the higher order of convergence is given, and the best efficiency, in term of function evaluations, of two of this new methods is provided.     

Bulk viscosity of hot dense Quark matter in the PNJL model

Starting from the Kubo formula and the QCD low energy theorem, we study the the bulk viscosity of hot dense quark matter in the PNJL model from the equation of state. We show that the bulk viscosity has a sharp peak near the chiral phase transition, and that the ratio of bulk viscosity over entropy rises dramatically in the vicinity of the phase transition. These results agree with those from the lattice and other model calculations. In addition, we show that the increase of chemical potential raises the bulk viscosity.     

基于能量分布的红外像点定位分析方法

在红外探测器的应用中,常用统计分析、算例验证等方法研究目标成像精确定位问题。鉴于上述方法难以充分阐释物理意义与揭示普遍规律,提出基于能量分布及成像特征的分析方法,针对红外探测目标成像精确定位问题,利用能量分布和数字图像中成像规律,研究像点定位及精度分析。研究了红外目标成像和数字图像特点,建立了定位模型和方法流程;分析了定位误差影响因素,实现了定位结果精度评定;最后结合典型应用实例,进行了计算验证。该方法与已有方法相比,分析过程更直观,获取了红外像点定位分析的理论依据,并给出了定位结果的精度水平:通常红外成像应用中,精度优于1/6像元;在成像较大时,精度可达1/10像元以上。该研究结论对红外探测应用中目标准确定位具有重要意义。     

Poincaré series of semi-invariants of 2×2 matrices

The Poincaré series of the algebra of -invariants of m-tuples of 2×2 matrices is presented both as a rational function and as a series of Schur functions. We show that this algebra of invariants is generated by the determinants, the mixed discriminants and the discriminants of 2×2 matrices. Consequences on invariants of three-dimensional matrices of the shape 2×2×m are discussed. For arbitrary n2, we prove an explicit functional equation for the Poincaré series of the -invariants of m-tuples of n×n matrices.     

Heat and mass transfer in annular liquid jets: I. Formulation

Heat and mass transfer phenomena in annular liquid jets are analyzed at high Reynolds numbers by means of a model derived from the governing equations that takes into account the effects of surface tension and boundary conditions at the gas–liquid interfaces and the large differences between the thermal and mass diffusivities, densities, dynamic viscosities, and thermal conductivities between gases and liquids. The model clearly illustrates the stiffness in both space and time associated with the concentration, linear momentum and energy boundary layers, and the initial cooling of the gases enclosed by the jet when, starting from a steady state where gases are injected into the volume enclosed by the jet at a rate equal to the heat and mass absorption rates by the liquid, gas injection is stopped. It is shown that, owing to the non-linear integrodifferential coupling between the fluid dynamics and heat and mass transfer processes, the pressure of the gases enclosed by the jet may vary in either a monotonic or an oscillatory manner depending on the large number of non-dimensional parameters that govern the heat and mass transfer phenomena. For the underpressurized jets considered here, it is shown that thermal equilibrium is achieved at a much faster rate than that associated with mass transfer, double diffusive phenomena in the liquid may occur, and the mass and volume of the gases enclosed by the jet may increase or decrease as functions of time until a steady equilibrium condition is reached.     

On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

Peculiarities of phase transitions when synthesizing diamond in high pressure apparatus of various types

Abstract

The influence of P, T-parmeters and duration of heat when synthesizing diamond in high pressure apparatus both of recessed anvil-type and cylindrical type (belt-type) on properties of diamond powders was studied. The dependence of pressure in reaction cells on temperature of force elements of apparatus in initial state and on efficiency of high pressure production in a reaction cell before heating was shown.     

Symmetric Powers of Galois Modules on Dedekind Schemes

We prove a certain Riemann–Roch-type formula for symmetric powers of Galois modules on Dedekind schemes which, in the number field or function field case, specializes to a formula of Burns and Chinburg for Cassou–Noguès–Taylor operations.