How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

High-power photonic-bandgap fiber laser

An original architecture of an active fiber allowing a nearly diffraction-limited beam to be produced is demonstrated. The active medium is a double-clad large-mode-area photonic-bandgap fiber consisting of a 10,000 ppm by weight Yb(3+)-doped core surrounded by an alternation of high- and low-index layers constituting a cylindrical photonic crystal. The periodic cladding allows the robust propagation of a approximately 200 microm(2) fundamental mode and efficiently discriminates against the high-order modes. The M(2) parameter was measured to be 1.17. A high-power cw laser was built exhibiting 80% slope efficiency above threshold. The robust propagation allows the fiber to be tightly bent. Weak incidence on the slope efficiency was observed with wounding radii as small as 6 cm.     

Investigation of the effect of heavy gas injection into a supersonic boundary layer on laminar-turbulent transition

The effect of distributed tangential injection of heavy SF₆ gas into the wall zone of a boundary layer on the supersonic flow stability and laminar-turbulent transition is experimentally and theoretically investigated at the freestream Mach number M_∞ = 2. For the first time it is experimentally shown that in the case of this injection laminar-turbulent transition is downstream displaced.     

Possible contribution of an intermediate-leptoquark-boson mechanism to free-neutron beta decay

A possible mechanism of the virtual intermediate-scalar-leptoquark-boson exchange associated with the contribution of right-handed nucleon currents to free-neutron beta decay is demonstrated. The hypothesis can be extended by considering the realization of the same mechanism in beta decay via the emission of right-handed neutrinos (left-handed antineutrinos). It is shown that a hypothesis of this kind leads to the appearance of scalar and tensor terms in the effective Hamiltonian of weak interaction and that these terms include the right-handed neutrinos. Relevant experimental data are discussed.     

Numerical study of the laminar thermocapillary flow in a square cavity

The hydrodynamic and heat-transfer processes in the problem of a laminar thermocapillary flow of a viscous incompressible fluid in a square cavity with isothermal vertical and isentropic horizontal surfaces are investigated numerically under the assumption that the gravity is absent, the free surface is flat, and the surface tension depends linearly on the temperature. Calculations were performed by a compact-difference method on irregular grids with a fifth-order accuracy for four Prandtl numbers (Pr=1, 16, 200, and 3000) as the Marangoni (Ma) number varies from 10² to 10⁴. The maximum local heat transfer versus theMa number is obtained. It is shown that, for thePr values considered, the maxima of the distribution of the horizontal velocity component on the surface is displaced to the cold boundary according to a law inversely proportional to theMa number. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 81–89, July–August, 1999.