Coherent decay of positronium bose condensate

The rate of self-stimulated emission of photon pairs by pseudoscalar particles from Bose condensate is calculated. Growing with density, this rate exceeds the density-independent rate of spontaneous two-photon decay at plausible density values of positronium gas, thus opening, in principle, the way to the annihilation gamma ray laser realization.     

Integrals of the motion for a nonlinear quantum oscillator

We construct and discusss explicitly time dependent integrals of the motion of non-autonomous quantum systems. Such integrals may exist even when the classical limit of the dynamics is non-integrable.     

On the Pesin set of expansive geodesic flows in manifolds with no conjugate points

In this paper, we show that the Pesin set of an expansive geodesic flow in compact manifold with no conjugate points and bounded asymptote coincides a.e with an open and dense set of the unit tangent bundle. We also show that the set of hyperbolic periodic orbits is dense in the unit tangent bundle.     

On the dynamics of parabolic equations describing diffusion, convection and a chemical reaction

A tubular nonisothermal-nonadiabatic chemical reactor with a consecutive reactions described by a set of three nonlinear parabolic equations, shows a sequence of period-doubling bifurcations of a “limit cycle”. A numerical examination of the model reveals that complex periodic and irregular oscillations are possible. With increasing value of the Peclet number regular and irregular oscillations are suppressed and disappear. From the computed results may be informed that for reacting systems nonlinear parabolic equations may feature similar qualitative properties as the ordinary differential equations. The results of this numerical study may be used to explain turbulization of laminar flames.     

Ranges and standard deviations of implanted ions

This paper presents a theoretical analysis and simple expressions for the calculation of ranges and standard deviations of implanted ions in amorphous targets. Nuclear energy loss models are discussed to introduce an approximation formula for the nuclear stopping cross section appropriate for Thomas-Fermi, Lenz-Jensen and intermediate type potentials. The Firsov electronic stopping model has been used to show its successful application. Algebraical expressions for the total range of ions in monoatomic and biatomic targets as a function of ion energy result from the considerations presented. A quasi-elastic multiscattering model is suggested, which permits an easy estimate of projected ion ranges. The standard range deviation is obtained by determining the total average-square energy loss fluctuations. Finally a comparison of calculated and experimental results is made to show that calculations based on the Firsov electronic stopping model and the nuclear stopping cross section proposed here provide a better agreement with the experimental results than the wellknown Johnson-Gibbons LSS-calculations.