On the Stability of Bifurcation Diagrams of Vanishing Flattening Points

On a smooth surface in Euclidean 3-space, we consider vanishing curves whose projections on a given plane are small circles centered at the origin. The bifurcations diagram of a parameter-dependent surface is the set of parameters and radii of the circles corresponding to curves with degenerate flattening points. Solving a problem due to Arnold, we find a normal form of the first nontrivial example of a flattening bifurcation diagram, which contains one continuous invariant.     

Homogenization of the periodic magnetic Schrödinger operator with degenerate lower edge of the spectrum

Homogenization of the periodic magnetic Schrödinger operator with degenerate lower edge of the spectrum is considered. The standard problem of homogenization leads to a degenerate limiting operator. To obtain more precise information, one needs a certain modification of the problem considered. Bibliography: 10 titles.     

Discovery of a new long-lived isomeric state in 125Ce

A new long-lived isomeric state in the near proton dripline nucleus ¹²⁵Ce has been identified with Schottky mass spectrometry at GSI. The excitation energy E ^* = 103(12)keV and the decay time of 193(1)s have been obtained from a single stored fully ionized ^125m Ce⁵⁸⁺ ion. The data implies an E3 transition and a 1/2⁺ assignment for the spin of the isomer.     

A method for automatic correction of drift-distorted SPM images

A method for automatic correction of drift-distorted surface images obtained using a scanning probe microscope is developed. For the case of slowly varying drifts, simple linear transformations describing the observed distortions are constructed. One or two pairs of counter-scanned images (CSIs) are used as initial data. A system of linear equations is solved by finding the coordinate of the same surface feature in each CSI. The solutions obtained, i.e., linear transformation coefficients, are used to correct drift-induced distortions in horizontal and vertical planes. Two nonlinear drift correction methods are proposed, which provide a better accuracy in comparison with the linear correction method. The developed method can be used in feature-oriented scanning of the surface.     

Charge density fluctuation of low frequency in a dusty plasma

The charge density fluctuation of low frequency in a dusty plasma, which is derived from the longitudinal dielectric permittivity of the dusty plasma, has been studied by kinetic theory. The results show that theP value, which describes the relative charge density on the dust in the plasma, and the charging frequency of a dust particle Ω _c , which describes the ratio of charge changing of the dust particles, determine the character of the charge density fluctuation of low frequency. For a dusty plasma ofP≪1, when the charging frequency Ω _c , is much smaller than the dusty plasma frequency ω_d, there is a strong charge density fluctuation which is of character of dust acoustic eigenwave. For a dusty plasma ofP≫1, when the frequency Ω _c , is much larger than ω _d there are weaker fluctuations with a wide spectrum. The results have been applied to the ionosphere and the range of radius and density of dust particles is found, where a strong charge density fluctuation of low frequency should exist.     

A high-speed high-sensitivity acoustic cell for in-line continuous monitoring of MOCVD precursor gases

We describe a continuous wave resonant acoustic sensor that has been optimized as a very sensitive in-line monitor for measuring the composition of precursor gases used in MOCVD processes. The precursor/carrier gas mixtures flow through a compact stainless steel acoustic chamber that is isolated from the acoustic transducers by a set of metallic diaphragms. The sensor has been successfully operated at supply line pressures from atmosphere down to 50 Torr with gas flow rates of up to 1600 sccm. The accuracy of the speed of sound measurement for hydrogen gas is better than 0.005%, even in a high noise and low pressure environment. Hydrogen, as well as nitrogen or argon carrier gases, are accommodated within the instrument's 1–5 kHz working frequency range. The instrument's sensitivity and stability are demonstrated with the laboratory data. Measurements of the dynamic response characteristics of the metalorganic bubbler lines at low pressure are also be presented. Application of the cell is general, encompassing any of the metalorganic and hydride materials typically used in MOCVD processes.     

X-ray induced fluorescence spectrometry at grazing incidence for quantitative surface and layer analysis

Summary Single layers and layer systems on diverse substrates were measured by Total Reflection X-Ray Fluorescence (TXRF) spectrometry. The angular dependence of the fluorescence intensities at grazing incidence allows the elemental composition, density and thickness of the layers to be evaluated using model calculations.