Influence of seeded impurities on the fusion reactor operation

In order to study the influence of seeded impurities on ITER like reactor operation the COREDIV code has been extended to include the transport of several sputtered and/or injected impurities. In the COREDIV code the core plasma is treated in the frame of 1D radial transport model whereas in the edge the 2D multifluid code EPIT is used. The EPIT code solves in the slab geometry the MHD equations for densities and velocities for all ions species as well as for electron and ion temperatures. The iteration scheme in the code leads to steady state solution of coupled core and SOL system. The numerical results for Carbon and Nickel plate and seeded impurities Silicon and Neon are presented.     

Pressure Stabilization Method for Steady Viscous Flows in a System of Pipes

This paper deals with a singular perturbation of the stationary Stokes and Navier-Stokes systems. The term ε²Δp is added to the continuity equation, where ε is a small parameter. For a domain with cylindrical outlets to infinity and exponentially decaying data, existence and uniqueness of solutions under flux conditions at infinity are established for the linear problem and also for the nonlinear problem in the case of small data. Asymptotically exact estimates are proved for ε tending to zero. For sufficiently regular data, these estimates imply the convergence in H _loc ^5/2−δ for the velocity parts and in H _loc ^3/2−δ for the pressure parts, respectively. Bibliography: 17 titles.Dedicated to V. A. Solonnikov on the occasion of his 70th birthday__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 107–133.     

Monotone Nonincreasing Random Fields on Partially Ordered Sets. I

For an arbitrary poset H and measure ρ on H × _R (where _R is the real axis), we construct a monotone decreasing stochastic field η_ρ and compute its finite-dimensional distributions. In the case where H is a Λ-semilattice and the measure ρ satisfies additional conditions, we compute various characteristics of the field η_ρ such as the expectation of the field value at a point, variance of the field value at a point, and correlation function of the field. The described construction of random fields gives a new method for constructing positive definite functions on posets. Bibliography: 6 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 301, 2003, pp. 92–143.     

Reciprocating sliding wear behavior of laser-clad small amplitude Mo2Ni3Si/NiSi metal silicide composite coatings

Mo₂Ni₃Si/NiSi metal silicide composite coatings with a fine microstructure consisting of Mo₂Ni₃Si primary dendrites and the interdendritic Mo₂Ni₃Si/NiSi eutectics were fabricated on austenitic stainless steel AISI 321 by laser cladding process. Small amplitude reciprocating sliding wear resistance of the coatings is evaluated as functions of normal load and slip amplitude and the wear mechanisms were discussed based on worn surface morphology observations. Results showed that the Mo₂Ni₃Si/NiSi coatings have excellent small amplitude reciprocating sliding wear resistance.     

Puzzles in astrophysics in the past and present

About 400 years have passed since the great discoveries by Galileo, Kepler, and Newton, but astronomy still remains an important source of discoveries in physics. They start with puzzles, with phenomena difficult to explain, and phenomena which in fact need new physics for explanation. Do such puzzles exist now? There are at least three candidates: absence of absorption of TeV gamma radiation in extragalactic space (violation of Lorentz invariance?), absence of GZK cutoff in the spectrum of ultrahigh-energy cosmic rays (new particle physics?), tremendous energy (up to 10⁵⁴ erg) released in gamma ray bursts on a time scale of a second (collapsing stars or sources of a new type?). Do these puzzles really exist? A critical review of these phenomena is given.     

Thermal conductivity of crystalline chrysotile asbestos

The thermal conductivity of crystalline chrysotile asbestos made up of hollow tubular Mg₃Si₂O₅(OH)₄ filaments is measured in the range 5–300 K. The paper discusses the possibility of using this material in studies of the thermal conductivity of thin filaments of metals and semiconductors incorporated into the channels of crystalline chrysotile asbestos tubes.     

On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.