A statistical approach to the solution of ill-posed problems in geophysics

The article surveys the main results of the statistical approach to the solution of ill-posed problems of mathematical physics, in application to specific ill-posed inverse problems in geophysics.Invited paper presented at the International Seminar on Mathematical Foundations of the Interpretation of Geophysical Fields, Moscow, May–June 1972.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 79, pp. 67–81, 1978.     

Isotopic families of contact manifolds for elliptic PDE

A test for a function to be a solution of an elliptic PDE is given in terms of extensions, as solutions, from the boundaries inside the domains belonging to an isotopic family. It generalizes a result of Ehrenpreis for spheres moved along a straight line.

     

CONCEPTUAL DESIGN STUDIES OF AN 84 GHz, 500 kW, CW GYROTRON

The feasibility of an 84 GHz, 500 kW, CW gyrotron for ECRH on an experimental tokamak will be presented in this paper. Mode competition and mode selection procedures are carefully investigated by considering various candidate modes and the TE_10,4 mode is chosen as the operating mode. A conventional cylindrical cavity resonator with weak input and output tapers and parabolic roundings is considered for interaction studies. Self-consistent, both single mode and time-dependent, calculations are carried out and power and efficiencies are computed for a typical set of beam parameters. The results show that an output power of well over 500 kW, CW and efficiency around 40% can be reached without a depressed collector.     

Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

An unstructured mesh finite volume method for modelling saltwater intrusion into coastal aquifers

In this paper, a two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular background interpolation mesh is developed for analysing the evolution of the saltwater intrusion into single and multiple coastal aquifer systems. The model formulation consists of a ground-water flow equation and a salt transport equation. These coupled and non-linear partial differential equations are transformed by FVUM into a system of differential/algebraic equations, which is solved using backward differentiation formulas of order one through five. Simulation results are compared with previously published solutions where good agreement is observed.     

The energy conservation law for optical two-port devices

Optics and Spectroscopy - The relationship between the parameters of quadripoles (mirrors, for example) ensuring the fulfillment of the energy conservation law are considered. Apart from the...     

Temperature dependence of corundum roentgenoluminescence and thermoluminescence

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 3, pp. 438–444, March, 1991.