A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

Influence of Fermi surface topology on the quasiparticle spectrum in the vortex state

We study the influence of Fermi surface topology on the quasiparticle density of states in the vortex state of type II superconductors. We observe that the field dependence and the shape of the momentum and spatially averaged density of states is affected significantly by the topology of the Fermi surface. We show that this behavior can be understood in terms of characteristic Fermi surface functions and that an important role is played by the number of points on the Fermi surface at which the Fermi velocity is directed parallel to the magnetic field. A critical comparison is made with a broadened BCS type density of states, that has been used frequently in analysis of tunneling data. We suggest a new formula as a replacement for the broadened BCS model for the special case of a cylindrical Fermi surface. We apply our results to the two gap superconductor MgB$_2$ and show that in this particular case the field dependence of the partial densities of states of the two gaps behaves very differently due to the different topologies of the corresponding Fermi surfaces, in qualitative agreement with recent tunneling experiments.Comment: 12 pages 12 figure

ff-minimal surface and manifold with positive mm-Bakry-\'{E}mery Ricci curvature

In this paper, we first prove a compactness theorem for the space of closed embedded $f$-minimal surfaces of fixed topology in a closed three-manifold with positive Bakry-\'{E}mery Ricci curvature. Then we give a Lichnerowicz type lower bound of the first eigenvalue of the $f$-Laplacian on compact manifold with positive $m$-Bakry-\'{E}mery Ricci curvature, and prove that the lower bound is achieved only if the manifold is isometric to the $n$-shpere, or the $n$-dimensional hemisphere. Finally, for compact manifold with positive $m$-Bakry-\'{E}mery Ricci curvature and $f$-mean convex boundary, we prove an upper bound for the distance function to the boundary, and the upper bound is achieved if only if the manifold is isometric to an Euclidean ball.Comment: 15 page

Old Inflation in String Theory

We propose a stringy version of the old inflation scenario which does not require any slow-roll inflaton potential and is based on a specific example of string compatification with warped metric. Our set-up admits the presence of anti-D3-branes in the deep infrared region of the metric and a false vacuum state with positive vacuum energy density. The latter is responsible for the accelerated period of inflation. The false vacuum exists only if the number of anti-D3-branes is smaller than a critical number and the graceful exit from inflation is attained if a number of anti-D3-branes travels from the ultraviolet towards the infrared region. The cosmological curvature perturbation is generated through the curvaton mechanism.Comment: 31 pages, 3 figures; typos corrected and reference adde

A Naturally Small Cosmological Constant on the Brane?

There appears to be no natural explanation for the cosmological constant's small size within the framework of local relativistic field theories. We argue that the recently-discussed framework for which the observable universe is identified with a p-brane embedded within a higher-dimensional `bulk' spacetime, has special properties that may help circumvent the obstacles to this understanding. This possibility arises partly due to several unique features of the brane proposal. These are: (1) the potential such models introduce for partially breaking supersymmetry, (2) the possibility of having low-energy degrees of freedom which are not observable to us because they are physically located on a different brane, (3) the fundamental scale may be much smaller than the Planck scale. Furthermore, although the resulting cosmological constant in the scenarios we outline is naturally suppressed by weak coupling constants of gravitational strength, it need not be exactly zero, raising the possibility it could be in the range favoured by recent cosmological observations.Comment: 7 pages. Powercounting arguments clarified, and comparison between the induced cosmological constant and supersymmetric mass splittings made more explici

Magnetothemopower study of quasi two-dimensional organic conductor α\alpha-(BEDT-TTF)2_2KHg(SCN)4_4

We have used a low-frequency magneto-thermopower (MTEP) method to probe the high magnetic field ground state behavior of $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$ along all three principal crystallographic axes at low temperatures. The thermopower tensor coefficients ($S_{xx}, S_{yx}$ and $S_{zz}$) have been measured to 30 T, beyond the anomalous low temperature, field-induced transition at 22.5 T. We find a significant anisotropy in the MTEP signal, and also observe large quantum oscillations associated with the de Haas - van Alphen effect. The anisotropy indicates that the ground state properties are clearly driven by mechanisms that occur along specific directions for the in-plane electronic structure. Both transverse and longitudinal magnetothermopower show asymptotic behavior in field, which can be explained in terms of magnetic breakdown of compensated closed orbits.Comment: 9 pages, 10 figure

Universal scaling of the Hall resistivity in MgB2 superconductors

The mixed-state Hall resistivity and the longitudinal resistivity in superconducting MgB2 thin films have been investigated as a function of the magnetic field over a wide range of current densities from 100 to 10000 A/cm^2. We observe a universal Hall scaling behavior with a constant exponent of 2.0, which is independent of the magnetic field, the temperature, and the current density. This result can be interpreted well within the context of recent theories.Comment: 4 page

A mutli-technique search for the most primitive CO chondrites

As part of a study to identify the most primitive COs and to look for weakly altered CMs amongst the COs, we have conducted a multi-technique study of 16 Antarctic meteorites that had been classified as primitive COs. For this study, we have determined: (1) the bulk H, C and N abundances and isotopes, (2) bulk O isotopic compositions, (3) bulk modal mineralogies, and (4) for some selected samples the abundances and compositions of their insoluble organic matter (IOM). Two of the 16 meteorites do appear to be CMs – BUC 10943 seems to be a fairly typical CM, while MIL 090073 has probably been heated. Of the COs, DOM 08006 appears to be the most primitive CO identified to date and is quite distinct from the other members of its pairing group. The other COs fall into two groups that are less primitive than DOM 08006 and ALH 77307, the previously most primitive CO. The first group is composed of members of the DOM 08004 pairing group, except DOM 08006. The second group is composed of meteorites belonging to the MIL 03377 and MIL 07099 pairing groups. These two pairing groups should probably be combined. There is a dichotomy in the bulk O isotopes between the primitive (all Antarctic finds) and the more metamorphosed COs (mostly falls). This dichotomy can only partly be explained by the terrestrial weathering experienced by the primitive Antarctic samples. It seems that the more equilibrated samples interacted to a greater extent with 16O-poor material, probably water, than the more primitive meteorites

Optical application and measurement of torque on microparticles of isotropic nonabsorbing material

We show how it is possible to controllably rotate or align microscopic particles of isotropic nonabsorbing material in a TEM00 Gaussian beam trap, with simultaneous measurement of the applied torque using purely optical means. This is a simple and general method of rotation, requiring only that the particle is elongated along one direction. Thus, this method can be used to rotate or align a wide range of naturally occurring particles. The ability to measure the applied torque enables the use of this method as a quantitative tool--the rotational equivalent of optical tweezers based force measurement. As well as being of particular value for the rotation of biological specimens, this method is also suitable for the development of optically-driven micromachines.Comment: 8 pages, 6 figure

A system for investigating oesophageal photoplethysmographic signals in anaesthetised patients

The monitoring of arterial blood oxygen saturation in patients with compromised peripheral perfusion is often difficult, because conventional non-invasive techniques such as pulse oximetry (SpO2) can fail. Poor peripheral circulation commonly occurs after major surgery including cardiopulmonary bypass. The difficulties in these clinical situations might be overcome if the sensor were to monitor a better perfused central part of the body such as the oesophagus. A new oesophageal photoplethysmographic (PPG) probe and an isolated processing system have been developed to investigate the pulsatile signals of anaesthetised adult patients undergoing routine surgery. Measurements were made in the middle third of the oesophagus, 25 cm to 30 cm from the upper incisors. The AC PPG signals are sampled by a data acquisition system connected to a laptop computer. The signals recorded correspond to infrared and red AC PPGs from the middle third oesophagus and the finger. Preliminary results from 20 patients show that good quality AC PPG signals can be measured in the human oesophagus. The ratio of the oesophageal to finger AC PPG amplitudes was calculated for the infrared and red wavelengths for each patient. The mean (+/- standard deviation) of this ratio was 2.9 +/- 2.1 (n = 19) for the infrared wavelength and 3.1 +/- 2.4 (n = 16) for the red wavelength. The red and infrared wavelengths used are appropriate for pulse oximetry and this investigation indicates that the mid-oesophagus may be a suitable site for the reliable monitoring of SpO2 in patients with poor peripheral perfusion