Connection machine simulation of ultrasonic wave propagation in materials III: The three-dimensional case

A formalism for the simulation by parallel processing of the propagation of ultrasonic pulses of arbitrary shape (i.e. not restricted to continuous waves) in complex media is presented. Recursive relationships yielding the time evolution of the displacement field are derived for both homogeneous and heterogeneous materials. In the latter case, formulas for cross-points at the intersection of up to eight different materials are obtained. A few examples of numerical results obtained with the proposed method are shown to demonstrate its applicability and efficiency. The problem of visualization of the results is also briefly discussed.     

New polaron effect in magnetooptic phenomena in a quantum well

It is predicted that resonance coupling between two discrete electron energy levels corresponding to different size-quantization quantum numbers and different Landau quantum numbers can occur in a quantum well in a quantizing magnetic field. The resonance coupling is due to the interaction of an electron with LO phonons and results in the formation of polaron states of a new type. It is shown that for a certain value of the magnetic field, which depends on the splitting of the electron size-quantization levels, the absorption peak and the two-phonon resonance Raman scattering peak split into two components, the separation between which is determined by the electron-phonon coupling constant. The resonance coupling between size-quantization levels with the same Landau quantum numbers is also studied. The splitting of the peaks in this case is virtually independent of the magnetic field and can be observed in much weaker fields. The experimental observation of the effect will make it possible to determine the relative position of the electronic levels and the electron-phonon coupling constant. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 511–515 (10 April 1997)     

Magic neutrino mass matrix and the Bjorken–Harrison–Scott parameterization

Observed neutrino mixing can be described by a tribimaximal MNS matrix. The resulting neutrino mass matrix in the basis of a diagonal charged lepton mass matrix is both 2–3 symmetric and magic. By a magic matrix, I mean one whose row sums and column sums are all identical. I study what happens if 2–3 symmetry is broken but the magic symmetry is kept intact. In that case, the mixing matrix is parameterized by a single complex parameter U_e3, in a form discussed recently by Bjorken, Harrison, and Scott.     

A high-current electron beam ion trap as an on-line charge breeder for the high precision mass measurement TITAN experiment

The precision of atomic mass measurements in a Penning trap is directly proportional to the charge state q of the ion and, hence, can be increased by using highly charged ions (HCI). For this reason, charge breeding with an electron beam ion trap (EBIT) is employed at TRIUMF’s Ion Trap for Atomic and Nuclear science (TITAN) on-line facility in Vancouver, Canada. By bombarding the injected and trapped singly charged ions with an intense beam of electrons, the charge state of the ions is rapidly increased inside the EBIT. To be compatible with the on-line requirements of short-lived isotopes, very high electron beam current densities are needed. The TITAN EBIT includes a 6 Tesla superconducting magnet and is designed to have electron beam currents and energies of up to 5 A and 60 keV, respectively. Once operational at full capacity, most species can be bred into a He-like configuration within tens of ms. Subsequently, the HCI are extracted, pass a Wien filter to reduce isobaric contamination, are cooled, and injected into a precision Penning trap for mass measurement. We will present the first results and current status of the TITAN EBIT, which has recently been moved to TRIUMF after assembly and commissioning at the Max-Planck-Institute (MPI) for Nuclear Physics in Heidelberg, Germany.     

Finite-gap Solutions of the Fuchsian Equations

We find a new class of Fuchsian equations, with algebro-geometric solutions associated to a hyperelliptic curve. A method for calculating its arithmetic genus and branching points is suggested. Numerous examples are given.     

Mössbauer studies on some new magnetic oxides

Three new magnetic oxides have been synthesised, viz., Li₂Fe₃VO₈, YFe₃TiO₈ and CaFe₃VO₈. XRD studies show that the first compound has a cubic symmetry of spinel type while the latter two show orthorhombic symmetry. All the three compounds are magnetic at room temperature, however, the first compound shows a large magnetic moment as compared to the other two. Their Mössbauer spectra at room temperature show distinct hyperfine split spectral lines. The present preliminary investigation indicates that the long range order is ferrimagnetic in Li₂Fe₃VO₈ and CaFe₃VO₈ while in YFe₃TiO₈ it is more likely to be canted antiferromagnetic.     

Blackett Memorial Lecture: the nuclear option—human factors in safety

The UK nuclear industry is currently undergoing a series of dramatic changes. Important, among many is the establishment of the Nuclear Decommissioning Authority (NDA) with an associated impact on service delivery. At the same time, the debate on the future of our energy supply in the UK is increasingly focused on the question of the nuclear option. Issues of safety and reliability are paramount for the nuclear industry given both the nature of the hazard and the associated public perceptions of the associated risks. This paper explores linked developments in human factors and the management of safety in the nuclear industry in the context of unprecedented change.     

Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet

Numerical simulations are carried out to describe the dense zone of a spray where very little information is available, either from experimental or theoretical approaches. Interface tracking is ensured by the level set method and the ghost fluid method (GFM) is used to capture accurately sharp discontinuities for pressure, density and viscosity. The level set method is coupled with the VOF method for mass conservation.     

The mean-value theorem for elliptic operators on stratified sets

In this paper, an analog of the mean-value theorem for harmonic functions is proved for an elliptic operator on the stratified set of “stratified” spheres whose radius is sufficiently small. In contrast to the classical case, the statement of the theorem has the form of a special differential relationship between the mean values over different parts of the sphere. The result is used to prove the strong maximum principle.     

On quasi-conformally flat weakly Ricci symmetric manifolds

The object of the present paper is to study quasi-conformally flat weakly Ricci symmetric manifolds.