Three-dimensional blow-up solutions of the Navier-Stokes equations

In this paper we extend the plane blow-up results of Grundy& McLaughlin (1997) to the three-dimensional Navier-Stokes equations.Using a solution structure originally due to Lin we first providenumerical evidence for the existence of blow-up solutions on- < x, z < , 0 y 1 with boundary conditions on y = 0and y = 1 involving derivatives of the velocity components.The formulation enables us to consider plane and radial flowas special cases. Various features of the computations are isolatedand are used to construct a formal asymptotic solution closeto blow-up. We show that the numerical and asymptotic analysesprovide a mutually consistent global picture which supportsthe conclusion that, for the family of problems we considerhere, blow-up in fact can take place in three dimensions butat an inverse linear rate rather than the faster inverse squareof the plane case.     

Molecular-orbital X-rays from 1 GeV 208Pb + 208Pb and 209Bi + 209Bi collisions

We have measured the spectra of continuum X-rays above the characteristic K lines for 4.5 to 4.8 MeV/N ²⁰⁸₈₂Pb → ²⁰⁸₈₂Pb, Pb → Bi, Bi → Pb and Bi → Bi collisions. Above ≈400 keV X-ray energy the spectral shape and intensity agree roughly with calculations of Kirsch et al. for the 1sσ molecular-orbital (MO) X-ray spectrum from Pb-Pb. Deviations from the theory below ≈400 keV suggest transitions to other MO's.     

Evidence for a molecular REC-effect in heavy ion collisions

Anisotropy spectra of the MOK X-ray transitions have been measured in F-Al, Al-Al and Cl-Al collisions as a function of the projectile energy. The measurements at higher energies indicate a new molecular effect due to transitions from quasicontinuum states to the MO 1s _σ-orbitals.     

Long-term retention of ice-nucleating active Pseudomonas fluorescens by overwintering colorado potato beetles

Ice nucleating-active Pseudomonas fluorescens F264C was fed to Colorado potato beetles to determine bacterial retentioin in the beetle gut and its effect on the cold hardiness of this insect pest. The bacrterium was present in beetles recovered after overwintering in the field, seven months after their exposure to P. fluorescens. Retention was evident not only in the detection of the P. fluorescens ice nucleating gene, inaW, in bacterial cultures from beetle guts but also in the elevated supercooling points of some treated beetles.     

Kinematical problem in Spin-wave theory

A spin-1/2, nearest neighbor Heisenberg Hamiltonian acting on a periodic,d-dimensional lattice is considered. Multi-spin-wave solutions to the Schrödinger equation for a Heisenberg ferromagnet involve an unlimited superposition of spin-reversal operators at sites. This violates the physical restriction that no more than one excitation reside on any one site. This exclusion rule affects spin-wave interaction—the determination of these effects is called the kinematical problem. A general nonperturbative treatment that includes kinematical effects in spin-wave theory is developed along the following lines. Using the property of the Heisenberg Hamiltonian that it does not couple states obeying the single occupation condition at all sites with states that violate the single-occupancy condition at some sites, the unphysical multiply occupied states can be eliminated by a nonunitary transformation of the eigenvalue equation. An overcomplete Hamiltonian matrix is obtained that contains all the physical eigenvalues as a subset of its spectrum. Overcompleteness is shown to be a large part of the kinematical problem and several schemes to handle it are discussed. The remainder of the kinematical problem lies in the nonorthogonality of spin waves. It is shown that a new type of distribution, one that is neither Bose nor Fermi, correctly describes free spin-wave statistics at all temperatures. This formal but nonetheless complete solution to the overcompleteness aspect of the kinematical problem is then carried over,in toto, to the boson formulation of the spin Hamiltonian. Application to the calculation of the partition function and to thermal Green's functions is noted.     

Branching ratios between correlated and uncorrelated two electron transitions into the K-shell of Al,Ca, Fe and Ni ions

The branching ratios between the radiative single and double electron transitions into the doubly ionized K-shell were measured as a function of the atomic number. The results are compared with various theoretical predictions.