On the hierarchy of partially invariant submodels of differential equations

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given

Imaging Molecules from Within: Ultra-fast, {\AA}ngstr\"om Scale Structure Determination of Molecules via Photoelectron Holography using Free Electron Lasers

A new scheme based on (i) upcoming brilliant X-ray Free Electron Laser (FEL) sources, (ii) novel energy and angular dispersive, large-area electron imagers and (iii) the well-known photoelectron holography is elaborated that provides time-dependent three-dimensional structure determination of small to medium sized molecules with {\AA}ngstr\"om spatial and femtosecond time resolution. Inducing molecular dynamics, wave-packet motion, dissociation, passage through conical intersections or isomerization by a pump pulse this motion is visualized by the X-ray FEL probe pulse launching keV photoelectrons within few femtoseconds from specific and well-defined sites, deep core levels of individual atoms, inside the molecule. On their way out the photoelectrons are diffracted generating a hologram on the detector that encodes the molecular structure at the instant of photoionization, thus providing 'femtosecond snapshot images of the molecule from within'. Detailed calculations in various approximations of increasing sophistication are presented and three-dimensional retrieval of the spatial structure of the molecule with {\AA}ngstr\"om spatial resolution is demonstrated. Due to the large photo-absorption cross sections the method extends X-ray diffraction based, time-dependent structure investigations envisioned at FELs to new classes of samples that are not accessible by any other method. Among them are dilute samples in the gas phase such as aligned, oriented or conformer selected molecules, ultra-cold ensembles and/or molecular or cluster objects containing mainly light atoms that do not scatter X-rays efficiently.Comment: 18 pages, 11 figure

Sub-nanosecond Pulse Generation from a Two-section Laser-thyristor: Theoretical Analysis

We have developed a theoretical model of a two-section laser-thyristor. It is shown that using a 4 µm weakly doped p-base can increase blocking voltage up to 50 V, which makes it possible to generate 2 ns 10 A current pulses. It is demonstrated that the proposed device utilizes passive Q switching to generate high-power short optical pulses that account for up to 80% of output power. By picking the optimal passive section length, we have achieved optical pulses of ∼30 ps full width at half maximum (FWHM) and ∼100 W peak power.     Keywords: pulsed laser, semiconductor N-p-N-i-P heterostructure, laser-thyristor, dynamic model of pulsed lase

Long-term operation of a multi-channel cosmic muon system based on scintillation counters with MRS APD light readout

A Cosmic Ray Test Facility (CRTF) is the first large-scale implementation of a scintillation triggering system based on a new scintillation technique known as START. In START, the scintillation light is collected and transported by WLS optical fibers, while light detection is performed by pairs of avalanche photodiodes with the Metal-Resistor-Semiconductor structure operated in the Geiger mode (MRS APD). START delivers 100% efficiency of cosmic muon detection, while its intrinsic noise level is less than 10^{-2} Hz. CRTF, consisting of 160 START channels, has been continuously operated by the ALICE TOF collaboration for more than 25 000 hours, and has demonstrated a high level of stability. Fewer than 10% of MRS APDs had to be replaced during this period.Comment: Proceedings of NDIP-2008. 8 pages, 8 figures, 6 reference