A Solution to the Graceful Exit Problem in Pre-Big Bang Cosmology

We examine the string cosmology equations with a dilaton potential in the context of the Pre-Big Bang Scenario with the desired scale factor duality, and give a generic algorithm for obtaining solutions with appropriate evolutionary properties. This enables us to find pre-big bang type solutions with suitable dilaton behaviour that are regular at $t=0$, thereby solving the graceful exit problem. However to avoid fine tuning of initial data, an `exotic' equation of state is needed that relates the fluid properties to the dilaton field. We discuss why such an equation of state should be required for reliable dilaton behaviour at late times.Comment: 16 pages LaTeX, 5 figures. To appear in Physical Review

Bounce behaviour in Kantowski-Sachs and Bianchi Cosmologies

Many cosmological scenarios envisage either a bounce of the universe at early times, or collapse of matter locally to form a black hole which re-expands into a new expanding universe region. Energy conditions preclude this happening for ordinary matter in general relativistic universes, but scalar or dilatonic fields can violate some of these conditions, and so could possibly provide bounce behaviour. In this paper we show that such bounces cannot occur in Kantowski-Sachs models without violating the {\it reality condition} $\dot{\phi}^2\geq 0$. This also holds true for other isotropic spatially homogenous Bianchi models, with the exception of closed Friedmann-Robertson-Walker and Bianchi IX models; bounce behaviour violates the {\em weak energy condition} $\rho\geq 0$ and $\rho+p\geq 0$. We turn to the Randall-Sundrum type braneworld scenario for a possible resolution of this problem.Comment: Matches published versio

Local electronic density of states of a semiconducting carbon nanotube interface

The local electronic structure of semiconducting single-wall carbon nanotubes was studied with scanning tunneling microscopy. We performed scanning tunneling spectroscopy measurement at selected locations on the center axis of carbon nanotubes, acquiring a map of the electronic density of states. Spatial oscillation was observed in the electronic density of states with the period of atomic lattice. Defect induced interface states were found at the junctions of the two semiconducting nanotubes, which are well-understood in analogy with the interface states of bulk semiconductor heterostructures. The electronic leak of the van Hove singularity peaks was observed across the junction, due to inefficient charge screening in a one-dimensional structure.open111

Caustics of Compensated Spherical Lens Models

We consider compensated spherical lens models and the caustic surfaces they create in the past light cone. Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. `Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical lens, on the scale of the cusp caused by the lens; summing over many lenses will still leave a residual effect.Comment: 21 pages, 5 ps figures, eps

Observational signatures of a non-singular bouncing cosmology

We study a cosmological scenario in which inflation is preceded by a bounce. In this scenario, the primordial singularity, one of the major shortcomings of inflation, is replaced by a non-singular bounce, prior to which the universe undergoes a phase of contraction. Our starting point is the bouncing cosmology investigated in Falciano et al. (2008), which we complete by a detailed study of the transfer of cosmological perturbations through the bounce and a discussion of possible observational effects of bouncing cosmologies. We focus on a symmetric bounce and compute the evolution of cosmological perturbations during the contracting, bouncing and inflationary phases. We derive an expression for the Mukhanov-Sasaki perturbation variable at the onset of the inflationary phase that follows the bounce. Rather than being in the Bunch-Davies vacuum, it is found to be in an excited state that depends on the time scale of the bounce. We then show that this induces oscillations superimposed on the nearly scale-invariant primordial spectra for scalar and tensor perturbations. We discuss the effects of these oscillations in the cosmic microwave background and in the matter power spectrum. We propose a new way to indirectly measure the spatial curvature energy density parameter in the context of this model.Comment: 40 pages, 5 figures, typos corrected and reference adde

Density growth in Kantowski-Sachs cosmologies with cosmological constant

In this work the growth of density perturbations in Kantowski-Sachs cosmologies with a positive cosmological constant is studied, using the 1+3 and 1+1+2 covariant formalisms. For each wave number we obtain a closed system for scalars formed from quantities that are zero on the background and hence are gauge-invariant. The solutions to this system are then analyzed both analytically and numerically. In particular the effects of anisotropy and the behaviour close to a bounce in the cosmic scale factor are considered. We find that typically the density gradient in the bouncing directions experiences a local maximum at or slightly after the bounce.Comment: 33 pages, 17 picture

A finite-difference solution of solute transport through a membrane bioreactor

The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR), immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod) rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM). An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i) the radial and axial convective velocity, (ii) the convective mass transfer rates, (iii) the reaction rates, (iv) the fraction retentate, and (v) the aspect ratio

Intracellular zinc depletion induces caspase activation and p21Waf1/Cip1 cleavage in human epithelial cell lines

To better understand the mechanisms by which zinc deficiency induces epithelial cell death, studies were done of the effects of intracellular zinc depletion induced by the zinc chelator TPEN on apoptosis-related events in human malignant epithelial cell lines LIM1215 (colonic), NCI-H292 (bronchial), and A549 (alveolar type II). In TPEN-treated cells, depletion of zinc was followed by activation of caspase-3 (as demonstrated by enzymatic assay and Western blotting), DNA fragmentation, and morphologic changes. Increase in caspase-3 activity began 1–2 h after addition of TPEN, suggesting that zinc may suppress a step just before the activation of this caspase. Caspase-6, a mediator of caspase-3 processing, also increased, but later than caspase-3. Effects of TPEN on apoptosis were completely prevented by exogenous ZnSO4 and partially prevented by peptide caspase inhibitors. A critical substrate of caspase-3 may be the cell cycle regulator p21Waf1/Cip1, which was rapidly cleaved in TPEN-treated cells to a 15-kDa fragment before further degradation.F. Chai, A. Q. Truong-Tran, A. Evdokiou, G. P. Young and P. D. Zalewsk