486 research outputs found
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
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