A Note on Segre Types of Second Order Symmetric Tensors in 5-D Brane-world Cosmology

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of most brane cosmological models is that in which the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we reexamine the classification of the second order symmetric tensors in 5--D, and prove two theorems which collect together some basic results on the algebraic structure of these tensors in 5-dimensional space-times. We also briefly indicate how one can obtain, by induction, the classification of symmetric two-tensors (and the corresponding canonical forms) on n-dimensional spaces from the classification on 4-dimensional spaces. This is important in the context of 11--D supergravity and 10--D superstrings.Comment: 12 pages, to appear in Mod. Phys. Lett. A (2003) in the present for

Star formation in clusters: a survey of compact mm-wave sources in the Serpens core

We report the results of a millimeter interferometric survey of compact 3 mm continuum sources in the inner 5.5'x5.5' region of the Serpens core. We detect 32 discrete sources above 4.0 mJy/beam, 21 of which are new detections at millimeter wavelengths. By comparing our data with published infrared surveys, we estimate that 26 sources are probably protostellar condensations and derive their mass assuming optically thin thermal emission from dust grains. The mass spectrum of the clumps, dN/dM~M^(-2.1), is consistent with the stellar initial mass function, supporting the idea that the stellar masses in young clusters are determined by the fragmentation of turbulent cloud cores.Comment: To be published on The Astrophysical Journal Letters, 11 pages, 4 figures, aastex macros neede

High Mass Star Formation. II. The Mass Function of Submillimeter Clumps in M17

We have mapped an approximately 5.5 by 5.5 pc portion of the M17 massive star-forming region in both 850 and 450 micron dust continuum emission using the Submillimeter Common-User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope (JCMT). The maps reveal more than 100 dusty clumps with deconvolved linear sizes of 0.05--0.2 pc and masses of 0.8--120 solar masses, most of which are not associated with known mid-infrared point sources. Fitting the clump mass function with a double power law gives a mean power law exponent of alpha_high = -2.4 +/- 0.3 for the high-mass power law, consistent with the exponent of the Salpeter stellar mass function. We show that a lognormal clump mass distribution with a peak at about 4 solar masses produces as good a fit to the clump mass function as does a double power law. This 4 solar mass peak mass is well above the peak masses of both the stellar initial mass function and the mass function of clumps in low-mass star-forming regions. Despite the difference in intrinsic mass scale, the shape of the M17 clump mass function appears to be consistent with the shape of the core mass function in low-mass star-forming regions. Thus, we suggest that the clump mass function in high-mass star-forming regions may be a scaled-up version of that in low-mass regions, instead of its extension to higher masses.Comment: 33 pages, 6 figures, 3 tables. Accepted for publication in the Astrophysical Journa

Giant oscillations of the current in a dirty 2D electron system flowing perpendicular to a lateral barrier under magnetic field

The charge transport in a dirty 2-dimensional electron system biased in the presence of a lateral potential barrier under magnetic field is theoretically studied. The quantum tunneling across the barrier provides the quantum interference of the edge states localized on its both sides that results in giant oscillations of the charge current flowing perpendicular to the lateral junction. Our theoretical analysis is in a good agreement with the experimental observations presented in Ref.8. In particular, positions of the conductance maxima coincide with the Landau levels while the conductance itself is essentially suppressed even at the energies at which the resonant tunneling occurs and hence these puzzling observations can be resolved without taking into account the electron-electron interaction.Comment: 6 pages, 4 figure

Vortex mediated microwave absorption in superclean layered superconductors

In the superclean case the spectrum of vortex core excitations in the presence of disorder is not random but consists of two series of equally-spaced levels. The I-V characteristics of such superconductors displays many interesting phenomena. A series of resonances is predicted at frequencies commensurate with the spacing of the vortex excitations. These resonances reveal an even-odd anomaly. In the presence of one weak impurity the excitation levels can approach each other and almost cross. Absorption at very low frequencies is identified with the resonances arising in this case. The results of such microscopic theory coincide up to the order of magnitude with both the theory employing kinetic equation and the experiment. The non-linear effects associated with Zener transitions in such crossings are studied. These phenomena can be used as a probe of vortex core excitations.Comment: 11 pages, 2 Postscript figure