Mellin and Green symbols for boundary value problems on manifolds with edges

We introduce the algebra of smoothing Mellin and Green symbols in a pseudodifferential calculus for manifolds with edges. In addition, we define scales of weighted Sobolev spaces with asymptotics based on the Mellin transform and analyze the mapping properties of the operators on these spaces. This will allow us to obtain complete information on the regularity and asymptotics of solutions to elliptic equations on these spaces.     

Measurement and simulations of hollow atom X-ray spectra of solid-density relativistic plasma created by high-contrast PW optical laser pulses

K-shell spectra of solid Al excited by petawatt picosecond laser pulses have been investigated at the Vulcan PW facility. Laser pulses of ultrahigh contrast with an energy of 160 J on the target allow studies of interactions between the laser field and solid state matter at 10²⁰ W/cm². Intense X-ray emission of KK hollow atoms (atoms without n = 1 electrons) from thin aluminum foils is observed from optical laser plasma for the first time. Specifically for 1.5 μm thin foil targets the hollow atom yield dominates the resonance line emission. It is suggested that the hollow atoms are predominantly excited by the impact of X-ray photons generated by radiation friction to fast electron currents in solid-density plasma due to Thomson scattering and bremsstrahlung in the transverse plasma fields. Numerical simulations of Al hollow atom spectra using the ATOMIC code confirm that the impact of keV photons dominates the atom ionization. Our estimates demonstrate that solid-density plasma generated by relativistic optical laser pulses provide the source of a polychromatic keV range X-ray field of 10¹⁸ W/cm² intensity, and allows the study of excited matter in the radiation-dominated regime. High-resolution X-ray spectroscopy of hollow atom radiation is found to be a powerful tool to study the properties of high-energy density plasma created by intense X-ray radiation.     

A theory of pseudo-differential boundary value problems with discontinuous conditions I

Summary The paper deals with mixed boundary value problems and transmission problems for elliptic differential and pseudo-differential operators. These problems are considered as elements of an algebra (where is the considered domain, x=, YX a submanifold of codimension 1, where the conditions have a jump, and x is a certain compactification of X/Y), the elements of which are described on a symbolic level. By means of additional conditions (of trace and potential type, with respect to Y) a given mixed problem is extended to an operator, and the Fredholm property of is established under an ellipticity condition, the parametrix is constructed on symbolic level and ind is expressed. In the second part the authors also study classes of special cases, namely differential operators of second and higher order with mixed boundary conditions for dim 2, where explicit index expressions are derived.     

Influence of higher harmonics of the undulator in X‐ray polarimetry and crystal monochromator design

The spectrum of the undulator radiation of beamline P01 at Petra III has been measured after passing a multiple reflection channel‐cut polarimeter. Odd and even harmonics up to the 15th order, as well as Compton peaks which were produced by the high harmonics in the spectrum, could been measured. These additional contributions can have a tremendous influence on the performance of the polarimeter and have to be taken into account for further polarimeter designs.     

Surface heat transfer from self-heating hotspots

The surface heat transfer coefficient for In, Sn, and Pb films is obtained from the investigation of the hysteresis in the magnetic field-voltage characteristics of these films in He I and He II. This hysteresis is caused by the heating-induced formation of normal hotspots in the resistive state of the films. The experiments demonstrate the influence of the thermal boundary resistance and of the thermal conductivity of the substrate and helium bath on the hysteresis.     

Exponential time integration using Krylov subspaces

The application of exponential integrators based on Krylov techniques to large‐scale simulations of complex fluid flows with multiple time‐scales demonstrates the efficiency of these schemes in reducing the associated time‐step restrictions due to numerical stiffness. Savings of approximately 50% can be achieved for simulations of the three‐dimensional compressible Navier–Stokes equations while still maintaining a truncation error typical of explicit time‐stepping schemes. Exponential time integration techniques of this type are particularly advantageous for fluid flows with a wide range of temporal scales such as low‐Mach number, reactive or acoustically dominated flows. Copyright © 2008 John Wiley & Sons, Ltd.     

Sonochemical treatment of natural ground water at different high frequencies: preliminary results

Naturally occurring ground water polluted by highly volatile chlorinated compounds, with 1,2-dichloroethane as the main contaminant, was sonicated with high frequency ultrasound (361, 620 and 1086 kHz) in order to investigate if results from studies performed with single model compounds in water can be applied to a natural ground water. It was shown that the treated highly volatile halogenated hydrocarbons are almost completely destroyed by ultrasound in natural ground water within 60 min. It also transpired that the naturally occurring inorganic components and gases in the ground water play an important role.     

Die Abreißenergie von Teilchen aus der fluiden Phasengrenze 4. Stabilität oszillierender Blase/Teilchen-Aggregate

Ohne ZusammenfassungMit 2 Abbildungen