3+1 Approach to the Long Wavelength Iteration Scheme

Large-scale inhomogeneities and anisotropies are modeled using the Long Wavelength Iteration Scheme. In this scheme solutions are obtained as expansions in spatial gradients, which are taken to be small. It is shown that the choice of foliation for spacetime can make the iteration scheme more effective in two respects: (i) the shift vector can be chosen so as to dilute the effect of anisotropy on the late-time value of the extrinsic curvature of the spacelike hypersurfaces of the foliation; and (ii) pure gauge solutions present in a similar calculation using the synchronous gauge vanish when the spacelike hypersurfaces have extrinsic curvature with constant trace. We furthermore verify the main conclusion of the synchronous gauge calculation which is large-scale inhomogeneity decays if the matter--considered to be that of a perfect-fluid with a barotropic equation of state--violates the strong-energy condition. Finally, we obtain the solution for the lapse function and discuss its late-time behaviour. It is found that the lapse function is well-behaved when the matter violates the strong energy condition.Comment: 21 pages, TeX file, already publishe

pH electrode performance under automated management conditions

pH is frequently measured in laboratories, but to have confidence in the results it is necessary to know that it was measured properly. For an electrode to give accurate results it must be treated well and calibrated correctly. In this paper, an automated system for pH measurement is described; the system uses the operational pH scale and calibrates using two or three buffer solutions, taking proper account of the effects of temperature on the system. The system can be programmed with standard methods and procedures to ensure that the electrode gives the best possible performance. Calibrations and measurements within the system are reproducible, and the automated system is more robust than the manual pH meter, and requires less operator time

Unconstrained Hamiltonian formulation of General Relativity with thermo-elastic sources

A new formulation of the Hamiltonian dynamics of the gravitational field interacting with(non-dissipative) thermo-elastic matter is discussed. It is based on a gauge condition which allows us to encode the six degrees of freedom of the ``gravity + matter''-system (two gravitational and four thermo-mechanical ones), together with their conjugate momenta, in the Riemannian metric q_{ij} and its conjugate ADM momentum P^{ij}. These variables are not subject to constraints. We prove that the Hamiltonian of this system is equal to the total matter entropy. It generates uniquely the dynamics once expressed as a function of the canonical variables. Any function U obtained in this way must fulfil a system of three, first order, partial differential equations of the Hamilton-Jacobi type in the variables (q_{ij},P^{ij}). These equations are universal and do not depend upon the properties of the material: its equation of state enters only as a boundary condition. The well posedness of this problem is proved. Finally, we prove that for vanishing matter density, the value of U goes to infinity almost everywhere and remains bounded only on the vacuum constraints. Therefore the constrained, vacuum Hamiltonian (zero on constraints and infinity elsewhere) can be obtained as the limit of a ``deep potential well'' corresponding to non-vanishing matter. This unconstrained description of Hamiltonian General Relativity can be useful in numerical calculations as well as in the canonical approach to Quantum Gravity.Comment: 29 pages, TeX forma

Tensor mass and particle number peak at the same location in the scalar-tensor gravity boson star models - an analytical proof

Recently in boson star models in framework of Brans-Dicke theory, three possible definitions of mass have been identified, all identical in general relativity, but different in scalar-tensor theories of gravity.It has been conjectured that it's the tensor mass which peaks, as a function of the central density, at the same location where the particle number takes its maximum.This is a very important property which is crucial for stability analysis via catastrophe theory. This conjecture has received some numerical support. Here we give an analytical proof of the conjecture in framework of the generalized scalar-tensor theory of gravity, confirming in this way the numerical calculations.Comment: 9 pages, latex, no figers, some typos corrected, reference adde

Spm Oxidation and Parallel Writing on Zirconium Nitride Thin Films

Systematic investigation of the SPM oxidation process of sputter-deposited ZrN thin films is reported. During the intrinsic part of the oxidation, the density of the oxide increases until the total oxide thickness is approximately twice the feature height. Further oxide growth is sustainable as the system undergoes plastic flow followed by delamination from the ZrN-silicon interface keeping the oxide density constant. ZrN exhibits superdiffusive oxidation kinetics in these single tip SPM studies. We extend this work to the fabrication of parallel oxide patterns 70 nm in height covering areas in the square centimeter range. This simple, quick, and well-controlled parallel nanolithographic technique has great potential for biomedical template fabrication. (c) 2005 American Vacuum Society

Anisotropic stresses in inhomogeneous universes

Anisotropic stress contributions to the gravitational field can arise from magnetic fields, collisionless relativistic particles, hydrodynamic shear viscosity, gravitational waves, skew axion fields in low-energy string cosmologies, or topological defects. We investigate the effects of such stresses on cosmological evolution, and in particular on the dissipation of shear anisotropy. We generalize some previous results that were given for homogeneous anisotropic universes, by including small inhomogeneity in the universe. This generalization is facilitated by a covariant approach. We find that anisotropic stress dominates the evolution of shear, slowing its decay. The effect is strongest in radiation-dominated universes, where there is slow logarithmic decay of shear.Comment: 7 pages Revte

Long-wavelength iteration scheme and scalar-tensor gravity

Inhomogeneous and anisotropic cosmologies are modeled withing the framework of scalar-tensor gravity theories. The inhomogeneities are calculated to third-order in the so-called long-wavelength iteration scheme. We write the solutions for general scalar coupling and discuss what happens to the third-order terms when the scalar-tensor solution approaches at first-order the general relativistic one. We work out in some detail the case of Brans-Dicke coupling and determine the conditions for which the anisotropy and inhomogeneity decay as time increases. The matter is taken to be that of perfect fluid with a barotropic equation of state.Comment: 13 pages, requires REVTeX, submitted to Phys. Rev.

Oscillations of General Relativistic Multi-fluid/Multi-layer Compact Stars

We develop the formalism for determining the quasinormal modes of general relativistic multi-fluid compact stars in such a way that the impact of superfluid gap data can be assessed. Our results represent the first attempt to study true multi-layer dynamics, an important step towards considering realistic superfluid/superconducting compact stars. We combine a relativistic model for entrainment with model equations of state that explicity incorporate the symmetry energy. Our analysis emphasises the many different parameters that are required for this kind of modelling, and the fact that standard tabulated equations of state are grossly incomplete in this respect. To make progress, future equations of state need to provide the energy density as a function of the various nucleon number densities, the temperature (i.e. entropy), and the entrainment among the various components

Parallel Writing on Zirconium Nitride Thin Films by Local Oxidation Nanolithography

Parallel pattern transfer of submicrometer-scale oxide features onto zirconium nitride thin films is reported. The oxidation reaction was verified by Auger microprobe analysis and secondary ion mass spectrometry. Oxide features of similar to70 nm in height can be formed and selectively etched in a dilute aqueous hydrogen fluoride solution. This provides an interesting route to potential new applications for high-melting point, biocompatible surfaces that possess small feature sizes with controlled geometries. (C) 2004 American Institute of Physics

Neutron Stars in a Varying Speed of Light Theory

We study neutron stars in a varying speed of light (VSL) theory of gravity in which the local speed of light depends upon the value of a scalar field $\phi$. We find that the masses and radii of the stars are strongly dependent on the strength of the coupling between $\phi$ and the matter field and that for certain choices of coupling parameters, the maximum neutron star mass can be arbitrarily small. We also discuss the phenomenon of cosmological evolution of VSL stars (analogous to the gravitational evolution in scalar-tensor theories) and we derive a relation showing how the fractional change in the energy of a star is related to the change in the cosmological value of the scalar field.Comment: 15 pages, 2 figures. Added solutions with a more realistic equation of state. To be published in PR