Investigation of the problem of singularities in general relativity

Recently Addy and Datta have obtained a linearized solution for isentropic motions of a perfect fluid by assigning Cauchy data on the hypersurfacex ⁴=0 and by imposing a restriction on the equation of state. In the present paper we pursue this study and discuss the problem of singularities from the standpoint of a local observer for which a singularity is defined as a state with an infinite proper rest mass density. It is shown that for a closed universe with any distribution of matter whatsoever there occurred a singularity in the past in the nonrotating parts of the universe and it must recur in the future. Furthermore, the collapse of a rotating fluid to a singularity seems inevitable when the relativistic equation of state is considered.     

Curvature Computations of 2-Manifolds in $\mathbb{R}^k$

In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IR^k with k ≥ 3.     

NURBS approximation of surface/surface intersection curves

We use a combination of both symbolic and numerical techniques to construct degree boundedC ^k -continuous, rational B-spline ε-approximations of real algebraic surface-surface intersection curves. The algebraic surfaces could be either in implicit or rational parametric form. At singular points, we use the classical Newton power series factorizations to determine the distinct branches of the space intersection curve. In addition to singular points, we obtain an adaptive selection of regular points about which the curve approximation yields a small number of curve segments yet achievesC ^k continuity between segments. Details of the implementation of these algorithms and approximation error bounds are also provided. Supported in part by NSF Grants CCR 92.22467, DMS 91-01424, AFOSR Grant F49620-10138 and NASA Grant NAG-1-1473. Supported in part by K.C. Wong Education Foundation, Hong Kong.     

Molecular beam study of photoionization of uranium and uranium oxide

Crossed laser molecular beam configuration was used to study the photoionization of U and UO by the UV-lines of an argon ion laser. Photoionization efficiencies of both U and UO were found to be line sensitive. Photoionization by the 3638 Å line was observed for the first time. Uranium atom ionization efficiency being higher for the 3345 Å and 3511 Å groups of lines, while UO ionization efficiency being maximum for the 3638 Å line. Dependence of photoion signal on laser power and relative photoionization efficiencies of the two isotopic species of uranium are also investigated.     

Effect of free carrier screening on the binding energy of D− centers in polar semiconductors

A calculation of the binding energy of a D^? center, defined as the energy required to remove one of the two electrons from the D^? center to infinity, in the presence of other free carriers is reported in polar crystals. It is assumed that the effective interaction between each of the two electrons and the positive ion is described by Thomas-Fermi potential. The effective interaction between the two electrons in polar crystals is, however, described by two recently proposed potentials. The binding energy of a D^? ion is calculated variationally in several polar crystals as a function of the screening parameter δ and the value of δ at which the binding energy goes to zero (D^? Mott transition) is determined. A possible experimental situations where this system may be studied is discussed.     

Dynamic nuclear polarization at 9T using a novel 250 GHz gyrotron microwave source. 2003

In this communication, we report enhancements of nuclear spin polarization by dynamic nuclear polarization (DNP) in static and spinning solids at a magnetic field strength of 9 T (250 GHz for g = 2 electrons, 380 MHz for ¹H). In these experiments, ¹H enhancements of up to 170 ± 50 have been observed in 1-¹³C-glycine dispersed in a 60:40 glycerol/water matrix at temperatures of 20 K; in addition, we have observed significant enhancements in ¹⁵N spectra of unoriented pf1-bacteriophage. Finally, enhancements of ∼17 have been obtained in two-dimensional ¹³C–¹³C chemical shift correlation spectra of the amino acid U–¹³C, ¹⁵N-proline during magic angle spinning (MAS), demonstrating the stability of the DNP experiment for sustained acquisition and for quantitative experiments incorporating dipolar recoupling. In all cases, we have exploited the thermal mixing DNP mechanism with the nitroxide radical 4-amino-TEMPO as the paramagnetic dopant. These are the highest frequency DNP experiments performed to date and indicate that significant signal enhancements can be realized using the thermal mixing mechanism even at elevated magnetic fields. In large measure, this is due to the high microwave power output of the 250 GHz gyrotron oscillator used in these experiments.     

Continuous-Wave Operation of a 460-GHz Second Harmonic Gyrotron Oscillator

We report the regulated continuous-wave (CW) operation of a second harmonic gyrotron oscillator at output power levels of over 8 W (12.4 kV and 135 mA beam voltage and current) in the TE(0,6,1) mode near 460 GHz. The gyrotron also operates in the second harmonic TE(2,6,1) mode at 456 GHz and in the TE(2,3,1) fundamental mode at 233 GHz. CW operation was demonstrated for a one-hour period in the TE(0,6,1) mode with better than 1% power stability, where the power was regulated using feedback control. Nonlinear simulations of the gyrotron operation agree with the experimentally measured output power and radio-frequency (RF) efficiency when cavity ohmic losses are included in the analysis. The output radiation pattern was measured using a pyroelectric camera and is highly Gaussian, with an ellipticity of 4%. The 460-GHz gyrotron will serve as a millimeter-wave source for sensitivity-enhanced nuclear magnetic resonance (dynamic nuclear polarization) experiments at a magnetic field of 16.4 T.     

Decays of the mesons and the singlet photon

In an attempt to explain the recent measurements on the radiative decays of the vector-mesons (V→Pγ), we study the consequences of introducing a small admixture of SU (3) singlet piece in the electromagnetic current. We find that this leads to an excellent fit of the theory with the new measurements on theV→Pγ decays. However, this addition adversely affects the fit of the leptonic decays of the vector mesons (V→e ⁺ e ⁻) and of the radiative decay of the pion (π→2γ). We conclude that the overall fit to the available data does not favour a large (>10%) admixture of the SU(3) singlet. The decay rates have been calculated in the vectormeson dominance model. At the hadronic vertex (VVP), we assume asymptotic nonet symmetry. The electromagnetic couplings (V−γ) are the ones appropriate to vector-mixing.