Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

Recent studies have raised doubts about the occurrence of r modes in Newtonian stars with a large degree of differential rotation. To assess the validity of this conjecture we have solved the eigenvalue problem for Rossby-Haurwitz waves (the analogues of r waves on a thin-shell) in the presence of differential rotation. The results obtained indicate that the eigenvalue problem is never singular and that, at least for the case of a thin-shell, the analogues of r modes can be found for arbitrarily large degrees of differential rotation. This work clarifies the puzzling results obtained in calculations of differentially rotating axi-symmetric Newtonian stars.Comment: 8pages, 3figures. Submitted to CQ

General Relativistic Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

We show that, at first order in the angular velocity, the general relativistic description of Rossby-Haurwitz waves (the analogues of r-waves on a thin shell) can be obtained from the corresponding Newtonian one after a coordinate transformation. As an application, we show that the results recently obtained by Rezzolla and Yoshida (2001) in the analysis of Newtonian Rossby-Haurwitz waves of a slowly and differentially rotating, fluid shell apply also in General Relativity, at first order in the angular velocity.Comment: 4 pages. Comment to Class. Quantum Grav. 18(2001)L8

Evolution equations for slowly rotating stars

We present a hyperbolic formulation of the evolution equations describing non-radial perturbations of slowly rotating relativistic stars in the Regge--Wheeler gauge. We demonstrate the stability preperties of the new evolution set of equations and compute the polar w-modes for slowly rotating stars.Comment: 27 pages, 2 figure

Design concepts for broadband high-efficiency DOEs

Several design-concepts are presented for so-called efficiency achromatized diffractive optical elements (EA-DOEs) possessing diffraction efficiency larger than 97% over a broad spectral range. We start with tracing two different methods for surface relief profiles well known from the literature: common depth and multilayer EA-DOEs. Successively we present the following new approaches together with design parameters and performance properties: 1) gradient-index EA DOEs, 2) sub-wavelength EA-DOEs, and 3) a so-called cut-and-paste strategy. All designs are based on scalar assumptions and certain necessary dispersion relations of two different materials. The scalar assumption is no real limitation as the minimum zone width of our main application, the correction of chromatic aberrations, is 50 -100 times the wavelength. From aforementioned relations, design parameters as profile heights are derived and the resulting diffraction efficiency can be deduced. Additionally it turns out that the necessary dispersion relation concerning the sub-wavelength EA-DOE is the same as for the common depth EA-DOE. Moreover, for the multilayer EA-DOE we were able to show that if the dispersion relations of the materials can be accurately described by a second order Cauchy series, the efficiency becomes generic and will be the same regardless of which materials are chosen. By proper choice of the materials, all types of EA-DOEs yield thicknesses of 10 - 30 µm which is more than ten times larger than for conventional DOEs. Due to the small refractive index difference of GRIN materials, such EA-DOEs exhibit thicknesses of 90 µm and more. Therefore, it is advisable to look for material combinations which yield thicknesses as small as possible

Nanoscale Weibull Statistics

In this paper a modification of the classical Weibull Statistics is developed for nanoscale applications. It is called Nanoscale Weibull Statistics. A comparison between Nanoscale and classical Weibull Statistics applied to experimental results on fracture strength of carbon nanotubes clearly shows the effectiveness of the proposed modification. A Weibull's modulus around 3 is, for the first time, deduced for nanotubes. The approach can treat (also) a small number of structural defects, as required for nearly defect free structures (e.g., nanotubes) as well as a quantized crack propagation (e.g., as a consequence of the discrete nature of matter), allowing to remove the paradoxes caused by the presence of stress-intensifications

Enhancement of Friction between Carbon Nanotubes: An Efficient Strategy to Strengthen Fibers

Interfacial friction plays a crucial role in the mechanical properties of carbon nanotube based fibers, composites, and devices. Here we use molecular dynamics simulation to investigate the pressure effect on the friction within carbon nanotube bundles. It reveals that the intertube frictional force can be increased by a factor of 1.5 ~ 4, depending on tube chirality and radius, when all tubes collapse above a critical pressure and when the bundle remains collapsed with unloading down to atmospheric pressure. Furthermore, the overall cross-sectional area also decreases significantly for the collapsed structure, making the bundle stronger. Our study suggests a new and efficient way to reinforce nanotube fibers, possibly stronger than carbon fibers, for usage at ambient conditions.Comment: revtex, 5 pages, accepted by ACS Nano 10 Dec 200

Accurate strain measurements in highly strained Ge microbridges

Ge under high strain is predicted to become a direct bandgap semiconductor. Very large deformations can be introduced using microbridge devices. However, at the microscale, strain values are commonly deduced from Raman spectroscopy using empirical linear models only established up to 1.2% for uniaxial stress. In this work, we calibrate the Raman-strain relation at higher strain using synchrotron based microdiffraction. The Ge microbridges show unprecedented high tensile strain up to 4.9 % corresponding to an unexpected 9.9 cm-1 Raman shift. We demonstrate experimentally and theoretically that the Raman strain relation is not linear and we provide a more accurate expression.Comment: 10 pages, 4 figure

Scalar field induced oscillations of neutron stars and gravitational collapse

We study the interaction of massless scalar fields with self-gravitating neutron stars by means of fully dynamic numerical simulations of the Einstein-Klein-Gordon perfect fluid system. Our investigation is restricted to spherical symmetry and the neutron stars are approximated by relativistic polytropes. Studying the nonlinear dynamics of isolated neutron stars is very effectively performed within the characteristic formulation of general relativity, in which the spacetime is foliated by a family of outgoing light cones. We are able to compactify the entire spacetime on a computational grid and simultaneously impose natural radiative boundary conditions and extract accurate radiative signals. We study the transfer of energy from the scalar field to the fluid star. We find, in particular, that depending on the compactness of the neutron star model, the scalar wave forces the neutron star either to oscillate in its radial modes of pulsation or to undergo gravitational collapse to a black hole on a dynamical timescale. The radiative signal, read off at future null infinity, shows quasi-normal oscillations before the setting of a late time power-law tail.Comment: 12 pages, 13 figures, submitted to Phys. Rev.

Phase behavior and material properties of hollow nanoparticles

Effective pair potentials for hollow nanoparticles like the ones made from carbon (fullerenes) or metal dichalcogenides (inorganic fullerenes) consist of a hard core repulsion and a deep, but short-ranged, van der Waals attraction. We investigate them for single- and multi-walled nanoparticles and show that in both cases, in the limit of large radii the interaction range scales inversely with the radius, $R$, while the well depth scales linearly with $R$. We predict the values of the radius $R$ and the wall thickness $h$ at which the gas-liquid coexistence disappears from the phase diagram. We also discuss unusual material properties of the solid, which include a large heat of sublimation and a small surface energy.Comment: Revtex, 13 pages with 8 Postscript files included, submitted to Phys. Rev.

In-Situ Nuclear Magnetic Resonance Investigation of Strain, Temperature, and Strain-Rate Variations of Deformation-Induced Vacancy Concentration in Aluminum

Critical strain to serrated flow in solid solution alloys exhibiting dynamic strain aging (DSA) or Portevin–LeChatelier effect is due to the strain-induced vacancy production. Nuclear magnetic resonance (NMR) techniques can be used to monitor in situ the dynamical behavior of point and line defects in materials during deformation, and these techniques are nondestructive and noninvasive. The new CUT-sequence pulse method allowed an accurate evaluation of the strain-enhanced vacancy diffusion and, thus, the excess vacancy concentration during deformation as a function of strain, strain rate, and temperature. Due to skin effect problems in metals at high frequencies, thin foils of Al were used and experimental results correlated with models based on vacancy production through mechanical work (vs thermal jogs), while in situ annealing of excess vacancies is noted at high temperatures. These correlations made it feasible to obtain explicit dependencies of the strain-induced vacancy concentration on test variables such as the strain, strain rate, and temperature. These studies clearly reveal the power and utility of these NMR techniques in the determination of deformation-induced vacancies in situ in a noninvasive fashion.