A mixed directed-undirected data structure for a parallel implementation of a domain decomposition algorithm

The choice of data structures influences the parallelization, efficiency and the manageability of a mesh refinement program. We introduce a mixed directed-undirected graph that combines both communication and scheduling needs. An inverted index is maintained for the directed graph to improve code performance and readability.This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.     

Classes of regular and singular boundary problems

Translated from Matematicheskie Zametki, Vol. 51, No. 2, pp. 149–151, February, 1992.     

Quasiparticle and Cooper pair tenneling in small capacitance Josephson junctions

The tunneling of single electrons in small capacitance tunnel junctions is influenced by charging effects and by the fluctuations of the elecromagnetic environment. We study the effect of an external circuit with arbitrary impedance on the tunneling of quasiparticles and Cooper pairs in voltage driven Josephson junctions. We present results at finite temperatures and also consider an acdriven system.     

Optical waveguide analysis using modified Airy functions

We review a little-used but powerful method of solving the scalar wave equation. It uses a modification of the well-known Airy functions, which are easily calculated on desktop computers. The techniques are reminiscent of the WKBJ methodology, but the solution, although approximate, is much more useful than the traditional WKBJ solution and can be used with almost as much ease. Re method is extremely powerful but, to our knowledge, is not used in the optics community. It is useful in analyzing integrated optical waveguide components.     

Vacuum discharge effects in the diodes of high-current electronaccelerators

The processes occurring in the diodes of high-current electron accelerators which affect the electron beam structure are discussed. Two types of diodes are analyzed: planar diodes producing large cross-section beams, and magnetically insulated diodes producing cylindrical beams. The effects considered are: the screening effect, the effect of touches, the relay effect, the ring effect, etc. They are entirely associated with the explosive electron emission occurring on the cathode of a high-current diode. Methods which can be employed to eliminate or control some of these effects are described-namely, the application of an additional magnetic field, artificial initiation of emission centers, and employment of metal-dielectric cathodes. Examples of several types of cathode are given     

The 3-D FEL pulse propagation equation: An analytical treatment in the low-gain and small-signal regime

Summary In this paper we show that the transverse mode evolution of a FEL operating with short pulses can be treated, in the small-signal and low-gain regime, using a relatively simple mathematical technique leading to a potentially fast numerical algorithm. We also point out that analytical solutions can be obtained for the cases where the slippage length is small compared to the longitudinal bunch length.     

Rectangular oscillation of the sequence of partial sums of a multiple Fourier series and absence of the BMO property

Translated from Matematicheskie Zametki, Vol. 52, No. 2, pp. 152–154, August, 1992.