A second eigenvalue bound for the Dirichlet Schroedinger operator

Let $\lambda_i(\Omega,V)$ be the $i$th eigenvalue of the Schr\"odinger operator with Dirichlet boundary conditions on a bounded domain $\Omega \subset \R^n$ and with the positive potential $V$. Following the spirit of the Payne-P\'olya-Weinberger conjecture and under some convexity assumptions on the spherically rearranged potential $V_\star$, we prove that $\lambda_2(\Omega,V) \le \lambda_2(S_1,V_\star)$. Here $S_1$ denotes the ball, centered at the origin, that satisfies the condition $\lambda_1(\Omega,V) = \lambda_1(S_1,V_\star)$. Further we prove under the same convexity assumptions on a spherically symmetric potential $V$, that $\lambda_2(B_R, V) / \lambda_1(B_R, V)$ decreases when the radius $R$ of the ball $B_R$ increases. We conclude with several results about the first two eigenvalues of the Laplace operator with respect to a measure of Gaussian or inverted Gaussian density

Dislocation constriction and cross-slip in Al and Ag: an ab initio study

A novel model based on the Peierls framework of dislocations is developed. The new theory can deal with a dislocation spreading at more than one slip planes. As an example, we study dislocation cross-slip and constriction process of two fcc metals, Al and Ag. The energetic parameters entering the model are determined from ab initio calculations. We find that the screw dislocation in Al can cross-slip spontaneously in contrast with that in Ag, which splits into partials and cannot cross-slip without first being constricted. The dislocation response to an external stress is examined in detail. We determine dislocation constriction energy and critical stress for cross-slip, and from the latter, we estimate the cross-slip energy barrier for the straight screw dislocations

An Isoperimetric Inequality for Fundamental Tones of Free Plates

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given $\tau>0$, the free plate eigenvalues $\omega$ and eigenfunctions $u$ are determined by the equation $\Delta\Delta u-\tau\Delta u = \omega u$ together with certain natural boundary conditions. The boundary conditions are complicated but arise naturally from the plate Rayleigh quotient, which contains a Hessian squared term $|D^2u|^2$. We adapt Weinberger's method from the corresponding free membrane problem, taking the fundamental modes of the unit ball as trial functions. These solutions are a linear combination of Bessel and modified Bessel functions.Comment: PhD thesis. Papers are in preparatio

Exo-hydrogenated Single Wall Carbon Nanotubes

An extensive first-principles study of fully exo-hydrogenated zigzag (n,0) and armchair (n,n) single wall carbon nanotubes (C$_n$H$_n$), polyhedral molecules including cubane, dodecahedrane, and C$_{60}$H$_{60}$ points to crucial differences in the electronic and atomic structures relevant to hydrogen storage and device applications. C$_n$H$_n$'s are estimated to be stable up to the radius of a (8,8) nanotube, with binding energies proportional to 1/R. Attaching a single hydrogen to any nanotube is always exothermic. Hydrogenation of zigzag nanotubes is found to be more likely than armchair nanotubes with similar radius. Our findings may have important implications for selective functionalization and finding a way of separating similar radius nanotubes from each other.Comment: 5 pages, 4 postscript figures, Revtex file, To be appear in Physical Review

Isolation and preliminary characterization of the jaagsiekte retrovirus (JSRV)

Jaagsiekte, or ovine pulmonary adenomatosis, is caused by a recently discovered retrovirus. The virus cannot be cultivated in vitro at present, but a procedure is described for the isolation and purification of small amounts in the form of immune complexes with IgA from affected lungs. The virion was shown to possess a 70S RNA genome which can be transcribed by an endogenous reverse transcriptase. Nine polypeptides, ranging in size from 94 000 to 25 000 daltons, were found in purified preparations. Using neutralization of the viral reverse transcriptase and an enzyme immunoassay as criteria, no serological relationship could be demonstrated to representatives of type B, C and C oncoviruses, or to bovine leukemia virus, maedi-visna virus of sheep or caprine arthritis-encephalitis virus.The articles have been scanned in colour with a HP Scanjet 5590; 600dpi. Adobe Acrobat XI Pro was used to OCR the text and also for the merging and conversion to the final presentation PDF-format

Ab initio and finite-temperature molecular dynamics studies of lattice resistance in tantalum

This manuscript explores the apparent discrepancy between experimental data and theoretical calculations of the lattice resistance of bcc tantalum. We present the first results for the temperature dependence of the Peierls stress in this system and the first ab initio calculation of the zero-temperature Peierls stress to employ periodic boundary conditions, which are those best suited to the study of metallic systems at the electron-structure level. Our ab initio value for the Peierls stress is over five times larger than current extrapolations of experimental lattice resistance to zero-temperature. Although we do find that the common techniques for such extrapolation indeed tend to underestimate the zero-temperature limit, the amount of the underestimation which we observe is only 10-20%, leaving open the possibility that mechanisms other than the simple Peierls stress are important in controlling the process of low temperature slip.Comment: 12 pages and 9 figure

A retrospective evaluation of the impact of a dedicated obstetric and neonatal transport service on transport times within an urban setting

OBJECTIVE:To determine whether the establishment of a dedicated obstetric and neonatal flying squad resulted in improved performance within the setting of a major metropolitan area.DESIGN AND SETTING:The Cape Town metropolitan service of the Emergency Medical Services was selected for a retrospective review of the transit times for the newly implemented Flying Squad programme. Data were imported from the Computer Aided Dispatch programme. Dispatch, Response, Mean Transit and Total Pre-hospital times relating to the obstetric and neonatal incidents was analysed for 2005 and 2008. RESULTS: There was a significant improvement between 2005 and 2008 in all incidents evaluated. Flying Squad dispatch performance improved from 11.7% to 46.6% of all incidents dispatched within 4 min (p < 0.0001). Response time performance at the 15-min threshold did not demonstrate a statistically significant improvement (p = 0.4), although the improvement in the 30-min performance category was statistically significant in both maternity and neonatal incidents. Maternity incidents displayed the greatest improvement with the 30-min performance increasing from 30.3% to 72.9%. The analysis of the mean transit times demonstrated that neonatal transfers displayed the longest status time in all but one of the categories. Even so, the introduction of the Flying Squad programme resulted in a reduction in a total pre-hospital time from 177 to 128 min. CONCLUSION: The introduction of the Flying Squad programme has resulted in significant improvement in the transit times of both neonatal and obstetric patients. In spite of the severe resource constraints facing developing nations, the model employed offers significant gains

Efficient Recursion Method for Inverting Overlap Matrix

A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations with the the non-orthogonal localized basis set. This efficient inverting method can be incorporated in several O(N) methods for diagonalization of a generalized secular equation. By studying convergence properties of the 1-norm of an error matrix for diamond and fcc Al, this method is compared to three other O(N) methods (the divide method, Taylor expansion method, and Hotelling's method) with regard to computational accuracy and efficiency within the density functional theory. The test calculations show that the new method is about one-hundred times faster than the divide method in computational time to achieve the same convergence for both diamond and fcc Al, while the Taylor expansion method and Hotelling's method suffer from numerical instabilities in most cases.Comment: 17 pages and 4 figure

Reversible Band Gap Engineering in Carbon Nanotubes by Radial Deformation

We present a systematic analysis of the effect of radial deformation on the atomic and electronic structure of zigzag and armchair single wall carbon nanotubes using the first principle plane wave method. The nanotubes were deformed by applying a radial strain, which distorts the circular cross section to an elliptical one. The atomic structure of the nanotubes under this strain are fully optimized, and the electronic structure is calculated self-consistently to determine the response of individual bands to the radial deformation. The band gap of the insulating tube is closed and eventually an insulator-metal transition sets in by the radial strain which is in the elastic range. Using this property a multiple quantum well structure with tunable and reversible electronic structure is formed on an individual nanotube and its band-lineup is determined from first-principles. The elastic energy due to the radial deformation and elastic constants are calculated and compared with classical theories.Comment: To be appear in Phys. Rev. B, Apr 15, 200