Special features of the radiative capture of ultracold neutrons by thin and thick layers of matter

The radiative capture of ultracold neutrons traversing thin and thick homogeneous layers of matter is analyzed. The applicability range of the formulas for the probabilities of reflection, transmission, and capture in thick layers (under certain conditions, they admit a simple interpretation—it is often quoted in the literature—that is based on the effective capture cross section, which is in inverse proportion to the velocity of a neutron in matter) is investigated, along with the conditions under which there arises the effective capture cross section.     

Stability of translating solutions to mean curvature flow

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates. The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions of Non-linear Evolution Equations”.     

A broadband excimer source of visible radiation with barrier discharge pumping

We investigate the characteristics of a broadband cylindrical excimer source of visible radiation with a surface area of 230 cm² excited by a pulse-periodic barrier discharge based on multicomponent mixtures (mercury diiodide and dibromide with helium and admixtures of molecular nitrogen and xenon). The working mixture components were excited by a pulse-periodic (pulse repetition rate 500–5000 Hz, pulse duration ～150 ns) barrier discharge. We detected radiation from excimer HgI* and HgBr* molecules, the second positive system of molecular nitrogen, and mercury and xenon atoms. The amplitude, duration, and trailing edge of the radiation pulses in the HgI₂:HgBr₂:Xe:He and HgI₂: HgBr₂:N₂:He mixtures with admixtures of xenon and molecular nitrogen were found to change compared to the HgI₂:HgBr₂:He mixture. The optimal partial pressure of helium lies within the range 162–195 kPa. The most intense radiation from HgI* and HgBr* molecules (in a ratio of more than 3: 1) is observed in the HgI₂:HgBr₂: Xe:He mixture. The mean and pulse radiation powers are 45 W and 93 kW, respectively, at a pumping pulse repetition rate of 5000 Hz and an efficiency of 30%. We discuss the spectral and temporal characteristics of the radiation source and the dependence of the radiation intensity of excimer molecules of mercury monoiodide and monobromide on the partial pressures of xenon and nitrogen. We point out that the radiation source is of considerable interest for applications in biotechnology and medicine.     

Third harmonics of cosmic ray intensity on quiet days at Deep River Neutron Monitoring Station

The cosmic ray (CR) intensity data recorded in Deep River Neutron Monitoring Station have been investigated on quietest days (QD) for third harmonics of daily variation during solar cycles 21 and 22. It has been observed that in spite of abrupt change in the amplitude and phase of tri-diurnal anisotropy in CR intensity, the amplitude is quite significant throughout the period of investigation with larger amplitude during the years 1980 and 1985. Thus, tri-diurnal anisotropy clearly shows 11-year variation at the mid latitude neutron monitoring station.      

Improved scales of spaces and elliptic boundary-value problems. III

We study elliptic boundary-value problems in improved scales of functional Hilbert spaces on smooth manifolds with boundary. The isotropic Hörmander-Volevich-Paneyakh spaces are elements of these scales. The local smoothness of a solution of an elliptic problem in an improved scale is investigated. We establish a sufficient condition under which this solution is classical. Elliptic boundary-value problems with parameter are also studied.     

Some results of the local theory of smooth functions

We present results of the investigation of the local behavior of smooth functions in neighborhoods of their regular and critical points and prove theorems on the mean values of the functions considered similar to the Lagrange finite-increments theorem. We also study the symmetry of the derivative of an analytic function in the neighborhood of its multiple zero, prove new statements of the Weierstrass preparation theorem related to the critical point of a smooth function with finite smoothness, determine a nongradient vector field of a function in the neighborhood of its critical point, and consider one critical case of stability of an equilibrium position of a nonlinear system. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 2, pp. 231–267, February, 2007.     

Orbifold fibrations of Eschenburg spaces

Most of the few known examples of compact Riemannian manifolds with positive sectional curvature are the total space of a Riemannian submersion. In this article we show that this is true for all known examples, if we enlarge the category to orbifold fibrations. For this purpose we study all almost free isometric circle actions on positively curved Eschenburg spaces, which give rise to principle orbifold bundle structures, and we examine in detail their geometric properties. In particular, we obtain a new family of 6-dimensional orbifolds with positive sectional curvature whose singular locus consists of just two points.      

Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnets

We study the dynamics of magnetic bubble solitons in a two-dimensional isotropic antiferromagnetic spin lattice in the case where the exchange integral J(x, y) is position dependent. In the near-continuum regime, this system is described by the relativistic O(3) sigma model on a space-time with a spatially inhomogeneous metric determined by J. We use the geodesic approximation to describe the low-energy soliton dynamics in this system: the n-soliton motion is approximated by geodesic motion in the moduli space M _n of static n-solitons equipped with the L ² metric γ. We obtain explicit formulas for γ for various natural choices of J(x, y). Based on these, we show that single soliton trajectories are refracted with J⁻¹ being analogous to the refractive index and that this refraction effect allows constructing simple bubble lenses and bubble guides. We consider the case where J has a disk inhomogeneity (with the value J ₊ outside a disk and J ₋ < J ₊ inside) in detail. We argue that for sufficiently large J ₊/J ₋, this type of antiferromagnet supports approximate quasibreathers: two or more coincident bubbles confined within the disk spin internally while their shape oscillates with a generically incommensurate period. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 191–208, July, 2007.