Supersymmetry of FRW Barotropic Cosmologies

Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature of the universe. The K-extended FRW equations in comoving time are presented in explicit form in the low coupling regime. The standard barotropic FRW cosmologies correspond to the dissipationless limit K = 0.     

Improving the Fundamental Theorem of Algebra

Theorems 2 and 3 establish the minimum algebraic conditions necessary for a field to be algebraically closed, and they can therefore be said to “optimize” the Fundamental Theorem of Algebra. But each specific“degree implication” is a first-order consequence of the axioms for fields, and could have been discovered two centuries ago; the existence of these finitary relationships appears to have been unsuspected by practically everyone, with one important exception.     

A TVD Type Wavelet-Galerkin Method for Hamilton-Jacobi Equations

In this paper,we use Daubechies scaling functions as test functions for the Galerkin method,and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations.It can be proved that the schemesare TVD schemes.Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations.Furthermore,they have high-order accuracy in smooth regions and good resolution of singularities.     

200 femtosecond impulse response of a Fabry–Pérot etalon with the spectral ballistic imaging technique

We use the spectral ballistic imaging technique to measure the impulse response of a Fabry–Pérot etalon with less than 0.2 ps temporal resolution. The results show excellent agreement with the theoretical predictions and negligible noise. Comparison to the Kramers–Kronig method along with its limitations is also presented. PACS 42.65.Re; 07.60.Ly; 42.30.Kq     

An improved, free surface, topographic technique

Current techniques of water wave visualization such as shadowgraphy and stereo photography are widely used but are deficient in many aspects. Refraction based visualization observes the bending of light as it traverses across a liquid-air interface. This work describes the continued development of techniques to measure the surface height of a liquid free surface. The method, Reference Image Topography, utilizes refraction of light at the free surface as a function of the local angle of that surface. Particle Image Velocimetry (PIV) software is used to evaluate apparent dislocations of the target image viewed through the free surface, which are approximately proportional to the surface angle. High-resolution images are presented of the dynamic surface topography for a point source and the shallow water flow around a vertical cylinder.     

Black-body radiation of noncommutative gauge fields

The black-body radiation is considered in a theory with noncommutative electromagnetic fields; that is noncommutativity is introduced in field space, rather than in real space. A direct implication of the result on cosmic microwave background map is argued.     

A simple model to extract hyperfine interaction distributions from Mössbauer spectra

The general problem of finding a distribution in hyperfine interaction parameters from experimental Mössbauer spectra is outlined. Existing methods may lack flexibility to be easily applicable to simple problems. A line shape for hyperfine parameter distributions is given, which is based on linear segments in the probability function. This method is applied in the analysis of samples containing iron in a silicate glass.     

Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings

Recently, S. Reich and S. Simons provided a novel proof of the Kirszbraun-Valentine extension theorem using Fenchel duality and Fitzpatrick functions. In the same spirit, we provide a new proof of an extension result for firmly nonexpansive mappings with an optimally localized range.

     

Diffusive motion of iron microcrystals studied by Mössbauer spectroscopy

A new model is presented which explains well the dramatic decrease of the Mössbauer line intensities with raising temperatures for freely dispersed iron microscrystals. In contrast to other theories which consider mainly vibration to be responsible we discuss here the decrease in terms of large amplitude diffusive rotational or translational jumps of the particles. Such diffusive jumps lead — in agreement with the observation — to a strong reduction of the Mössbauer-intensity without broadening the line width in a noticeable way. The typical potential well for a diffusing particle in an equilibrium position is derived quantitatively to be 13 meV. The model might be important also for a new understanding of the dynamics of catalytic clusters either in contact with each other or with larger solid surfaces.Part of this work was supported by the DFG Sonderforschungsbereich 306, Konstanz