On nearly parallel G2-structures

A nearly parallel G₂-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G₂-manifolds with large symmetry group and in particular all homogeneous nearly parallel G₂-structures.     

A combined 14N/27Al nuclear magnetic resonance and powder X-ray diffraction study of impurity phases in beta-sialon ceramics

Beta-sialons are ceramic phases occurring in the SiO(2)-Si(3)N(4)-AlN-Al(2)O(3) system. A series of samples with differing compositions has been investigated by magic-angle spinning nuclear magnetic resonance (NMR) spectroscopy and powder X-ray diffraction (XRD). Although the constituent nitrogen nuclei occupy positions of low symmetry in the beta-sialon structure, 14N NMR spectra could be recorded for the samples examined. The origin of the 14N signal could be traced to the presence of an aluminium nitride (AlN) impurity phase with the help of 27Al NMR and XRD results. Similarly, the existence of Al(2)O(3) grains could be readily detected for a number of samples. Thus, the combination of 14N and 27Al NMR is shown to be an especially effective tool in identifying and characterizing impurity phases in sialon ceramics, complementing the results obtained from standard XRD analysis.     

A Variational Approach to Nonlinear Singularly Perturbed Boundary-Value Problems

Carrier and Pearson introduced a nonlinear singularly perturbed boundary value problem that has served as a paradigm for problems where the method of matched asymptotic expansions (MAE) apparently fails. The “failure” of MAE is its inability to select the location of possible internal layers, though their structure is determined. Thus, a straightforward application of MAE leaves the positions of any internal layers arbitrary, though the asymptotic expansion of the exact solution to the problem exhibits internal layers only at specific locations. For this reason the solutions produced by MAE have been referred to as spurious solutions. We resolve the question of finding the positions of the interior layers by employing the variational approach of Grasman and Matkowsky. In addition, we show that this method tells how solutions bifurcate as the boundary values are varied, and give an alternative motivation for the variational approach via Newton”s method.     

Modal analysis of circular Bragg fibers with arbitrary index profiles

A finite-difference approach based upon the immersed interface method is used to analyze the mode structure of Bragg fibers with arbitrary index profiles. The method allows general propagation constants and eigenmodes to be calculated to a high degree of accuracy, while computation times are kept to a minimum by exploiting sparse matrix algebra. The method is well suited to handle complicated structures comprised of a large number of thin layers with high-index contrast and simultaneously determines multiple eigenmodes without modification.     

Metric Lie algebras with maximal isotropic centre

A metric Lie algebra is a Lie algebra equipped with an invariant non-degenerate symmetric bilinear form. It is called indecomposable if it is not the direct sum of two metric Lie algebras. We are interested in describing the isomorphism classes of indecomposable metric Lie algebras. In the present paper we restrict ourselves to a certain class of solvable metric Lie algebras which includes all indecomposable metric Lie algebras with maximal isotropic centre. We will see that each metric Lie algebra belonging to this class is a twofold extension associated with an orthogonal representation of an abelian Lie algebra. We will describe equivalence classes of such extensions by a certain cohomology set. In particular we obtain a classification scheme for indecomposable metric Lie algebras with maximal isotropic centre and the classification of metric Lie algebras of index 2.     

Timing-jitter reduction in a fiber laser mode locked by an input bit stream

We present analytical and numerical results for the amount of timing-jitter reduction obtained in an all-optical clock-recovery device in which a data stream is used to mode lock a fiber laser through cross-phase modulation. This situation is analyzed when the laser pulses are close to optical solitons, so the effect of the data stream on the laser pulses is predicted from soliton perturbation theory. In our numerical simulations, both periodic input and pseudorandom input data streams are considered. The results show that for both types of data the rms timing jitter in the recovered clock is reduced significantly from that present in the input data.     

Skew Killing spinors in four dimensions

Annals of Global Analysis and Geometry - This paper is devoted to the classification of 4-dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor $$\psi $$ is a...     

Parallel Spinors and Holonomy Groups on Pseudo-Riemannian Spin Manifolds

We describe the possible holonomy groups of simply connected irreducible non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel spinors.     

Pulsed degenerate optical parametric oscillator based on a nonlinear-fiber Sagnac interferometer

We report operation of an all-fiber degenerate optical parametric oscillator that employs a nonlinear-fiber Sagnac interferometer as a parametric amplifier. Synchronous pumping with 3.9-ps pulses at 1544 nm yields 0.83-ps output pulses. The wide bandwidth of the fiber parametric amplifier causes the oscillator to act as a pulse compressor. The output signal pulses exhibit improved spectral symmetry and a reduced time-bandwidth product compared with the pump pulses. Currently, the net group-velocity dispersion in the passive section of the fiber cavity limits the signal-pulse bandwidth and hence the minimum-obtainable pulse width. This experiment suggests the possibility of frequency conversion by operation of a similar pulsed parametric oscillator away from degeneracy.     

Magnetization studies of the nuclear spin ordered phases of solid <Superscript>3</Superscript>He in silver sinters

Solid ³He, in the bcc lattice between 34 and 100 bar, exhibits two nuclear magnetic ordered phases in the sub-mK temperature range, the so called U2D2 low (magnetic) field phase and the “high field phase” above 0.4 T. To determine the exact spin structure of these phases we started a project of neutron scattering from the ordered solid in collaboration with the Hahn-Meitner Institute, Berlin, and other European and US groups. For this experiment it is crucial to grow a single crystal within the sinter needed for cooling the solid to temperatures of the order of 500 μK (or even twenty times lower in the case of the hcp lattice which is formed above 100 bar) and to keep it there long enough to measure a magnetic neutron reflection. We studied the growth of crystals in Ag sinters of different pore size and with different growth speeds to find an optimal way to obtain single crystalline samples. As a first diagnostic step we performed pulsed NMR measurements in the ordered phases of solid ³He in a sinter of 2700 Å particle size down to temperatures of 450 μK at various molar volumes. We could keep the samples in the ordered state for as long as 140 h. The second method we used was SQUID magnetometry. For the low field phase T_N was indicated by a drop of the intensity, both in the NMR signal and in the dc magnetization, whereas in the high field phase an increase of about 30% was observed below the ordering temperature. For the fabrication of the sinters a packing fraction of 50% and subsequent annealing proved to be very favorable to obtain cold ordered solid. Furthermore, we find that a paramagnetic surface contribution from a few monolayers of ³He exists down to 500 μK in addition to the bulk magnetization.