Harmonic maps with torsion

In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion. Such connections have already been classified in the work of Cartan(1924).The maps under consideration do not arise as critical points of an energy functional leading to interesting mathematical challenges. We will perform a first mathematical analysis of these maps which we will call harmonic maps with torsion.     

A class of stationary charged dust solutions of Einstein's field equations

We consider a special class of stationary rotating charged dust solutions of Einstein's field equations without cosmological constant. In these space-times, the motion of freely falling particles and of light rays can be visualized by the motion of charged particles in an appropriate model magnetic field. Any curl-free magnetostatic field, given on an open subset of Euclidean 3-space, can serve as a model magnetic field for a charged dust solution in this sense. The simplest example, corresponding to a homogeneous model magnetic field, is given by Som-Raychaudhuri space-time. Some other examples are worked out.     

A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

     

Precise Coupling Terms in Adiabatic Quantum Evolution

It is known that for multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. For a family of two-state systems with real-symmetric Hamiltonian we construct such a superadiabatic representation and explicitly determine the asymptotic behavior of the exponentially small coupling term. First order perturbation theory in the superadiabatic representation then allows us to describe the time-development of exponentially small adiabatic transitions. The latter result rigorously confirms the predictions of Sir Michael Berry for our family of Hamiltonians and slightly generalizes a recent mathematical result of George Hagedorn and Alain Joye.submitted 29/06/04, accepted 14/08/04     

Magnetic poly(N‐isopropylacrylamide) microspheres by dispersion and inverse emulsion polymerization

The aim of this study was to develop novel thermally responsive polymer microspheres with magnetic properties. Dispersion and inverse emulsion copolymerization of N‐isopropylacrylamide (NIPAAm) and N,N′‐methylenebisacrylamide (MBAAm) was investigated in the presence of γ‐Fe₂O₃ nanoparticles. The resulting microspheres were characterized in terms of morphology, size, polydispersity, iron content, and temperature‐dependent swelling using optical microscopy, transmission electron microscopy, scanning electron microscopy, QELS, and AAS. The effects of several variables, such as the concentration of γ‐Fe₂O₃, MBAAm crosslinking agent, Span 80 surfactant, 2,2′‐azobis(2‐methyloctanenitrile) (AMON) initiator, and polymerization temperature on the properties of the microspheres were studied. Swelling and thermoresponsive behavior of the microspheres containing γ‐Fe₂O₃ nanoparticles were also investigated. The microspheres contained about 8 wt % of iron. The presence of magnetic nanoparticles and their concentration changes did not have any significant effect on the temperature sensitivity of the composites. The particles gradually shrink into an increasingly collapsed state when the temperature is raised to 40 °C since the increase in temperature weakens the hydration and PNIPAAm chains gradually become more hydrophobic, which leads to the collapse of the particles. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5884–5898, 2007     

Time structure of iodine laser pulse in the free running mode of operation

Time structure of iodine laser pulse in the free running mode of operation was studied using the power amplifier of laser system PERUN as the laser oscillator. Two characteristic shapes of laser pulse correspond to different regimes of laser operation, the existence of which is ascribed to the critical concentration of I₂ molecules. Simultaneously an additional chemical pumping was proved at least in the initial phase of photodissociation and in a late-time lasing after the end of flashlamps pumping light.     

Reference values for drag and lift of a two‐dimensional time‐dependent flow around a cylinder

This paper presents a numerical study of a two‐dimensional time‐dependent flow around a cylinder. Its main objective is to provide accurate reference values for the maximal drag and lift coefficient at the cylinder and for the pressure difference between the front and the back of the cylinder at the final time. In addition, the accuracy of these values obtained with different time stepping schemes and different finite element methods is studied. Copyright © 2004 John Wiley & Sons, Ltd.     

Electronic structure and topography of annealed SrTiO3(1 1 1) surfaces studied with MIES and STM

Perovskites of ABO₃ type like strontium titanate (SrTiO₃) are of great practical concern as materials for oxygen sensors operating at high temperatures. It is well known that the surface layer shows different properties compared to the bulk. Numerous studies exist for the SrTiO₃(1 0 0) and (1 1 0) surfaces which have investigated the changes in the electronic structure and topography as a function of the preparation conditions. They have indicated a rather complex behaviour of the surface and the near surface region of SrTiO₃ at elevated temperatures. Up to now, the behaviour of the SrTiO₃(1 1 1) surfaces under thermal treatment is not sufficiently known. This contribution is intended to work out the relation between alteration of the surface topography with respect to the preparation conditions and the simultaneous changes of the electronic structure. We applied scanning tunneling microscopy (STM) to investigate the surface topography and, additionally, metastable impact electron spectroscopy (MIES) to study the surface electronic structure of reconstructed SrTiO₃(1 1 1) surfaces. The crystals were heated up to 1000 °C under reducing and oxidizing conditions. Both preparation conditions cause strong changes of the surface topography and electronic structure. A microfaceting of the topmost layers is found.