A Lorentzian Gromov-Hausdoff notion of distance

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quantum gravity and - for the mathematicians - global Lorentzian geometry.Comment: 20 pages, 0 figures, submitted to Classical and quantum gravity, seriously improved presentatio

FRW cosmologies between chaos and integrability

A recent paper by Castagnino, Giacomini and Lara concludes that there is no chaos in a conformally coupled closed Friedmann-Robertson-Walker universe, which is in apparent contradiction with previous works. We point out that although nonchaotic the quoted system is nonintegrable.Comment: Revtex, 2 pages, no figure

The Big Bang as a Phase Transition

We study a five-dimensional cosmological model, which suggests that the universe bagan as a discontinuity in a (Higgs-type) scalar field, or alternatively as a conventional four-dimensional phase transition.Comment: 10 pages, 2 figures; typo corrected in equation (18); 1 reference added; version to appear in International Journal of Modern Physics

Tinted Semi-Transparent Solar Panels Allow Concurrent Production of Crops and Electricity on the Same Cropland

Agrivoltaics describes concurrent agricultural production of crops and photovoltaic generation of electricity on the same cropland. By using tinted semi-transparent solar panels, this study introduces a novel element to transform the concept of agrivoltaics from just solar-sharing to selective utilisation of different light wavelengths. Agrivoltaic growth of basil and spinach was tested. When compared with classical agriculture, and based on the feed-in-tariff of the experimental location, agrivoltaic co-generation of biomass and electricity is calculated to result in an estimated financial gross gain up to +2.5% for basil and +35% for spinach. Marketable biomass yields did not change significantly for basil, while a statistically significant loss was observed for spinach. This was accompanied by a relative increase in the protein content for both plants grown under agrivoltaic conditions. Agrivoltaics implemented with tinted solar panels improved the biomass production per unit amount of solar radiation up to 68%, with up to 63% increase in the ratio of leaf and stem biomass to root. Agrivoltaics can enrich the portfolio of farmers, mitigate risks associated with climate, and vastly enhance global photovoltaics capacity without compromising agricultural production.Leverhulme Trust RPG-2015-393 Italian Ministry of University and Research (to co-author A Schievano

Evidence for a continuum limit in causal set dynamics

We find evidence for a continuum limit of a particular causal set dynamics which depends on only a single ``coupling constant'' $p$ and is easy to simulate on a computer. The model in question is a stochastic process that can also be interpreted as 1-dimensional directed percolation, or in terms of random graphs.Comment: 24 pages, 19 figures, LaTeX, adjusted terminolog

The moduli space of isometry classes of globally hyperbolic spacetimes

This is the last article in a series of three initiated by the second author. We elaborate on the concepts and theorems constructed in the previous articles. In particular, we prove that the GH and the GGH uniformities previously introduced on the moduli space of isometry classes of globally hyperbolic spacetimes are different, but the Cauchy sequences which give rise to well-defined limit spaces coincide. We then examine properties of the strong metric introduced earlier on each spacetime, and answer some questions concerning causality of limit spaces. Progress is made towards a general definition of causality, and it is proven that the GGH limit of a Cauchy sequence of $\mathcal{C}^{\pm}_{\alpha}$, path metric Lorentz spaces is again a $\mathcal{C}^{\pm}_{\alpha}$, path metric Lorentz space. Finally, we give a necessary and sufficient condition, similar to the one of Gromov for the Riemannian case, for a class of Lorentz spaces to be precompact.Comment: 29 pages, 9 figures, submitted to Class. Quant. Gra

On the "renormalization" transformations induced by cycles of expansion and contraction in causal set cosmology

We study the ``renormalization group action'' induced by cycles of cosmic expansion and contraction, within the context of a family of stochastic dynamical laws for causal sets derived earlier. We find a line of fixed points corresponding to the dynamics of transitive percolation, and we prove that there exist no other fixed points and no cycles of length two or more. We also identify an extensive ``basin of attraction'' of the fixed points but find that it does not exhaust the full parameter space. Nevertheless, we conjecture that every trajectory is drawn toward the fixed point set in a suitably weakened sense.Comment: 22 pages, 1 firgure, submitted to Phys. Rev.

On alternative approaches to Lorentz violation in loop quantum gravity inspired models

Recent claims point out that possible violations of Lorentz symmetry appearing in some semiclassical models of extended matter dynamics motivated by loop quantum gravity can be removed by a different choice of canonically conjugated variables. In this note we show that such alternative is inconsistent with the choice of variables in the underlying quantum theory together with the semiclassical approximation, as long as the correspondence principle is maintained. A consistent choice will violate standard Lorentz invariance. Thus, to preserve a relativity principle in this framework, the linear realization of Lorentz symmetry should be extended or superseded.Comment: 4 pages, revtex4, no figures, references adde

Fractal Scales in a Schwarzschild Atmosphere

Recently, Glass and Krisch have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid [1999 Class. Quantum Grav. vol 16, 1175]. Mass diffusion in the extended Schwarzschild atmosphere was studied. The continuous solutions of classical diffusive transport are believed to describe the envelope of underlying fractal behavior. In this work we examine the classical picture at scales on which fractal behavior might be evident.Comment: to appear in Class. Quantum Gra

Enhancing plasma membrane NADPH oxidase activity increases current output by diatoms in biophotovoltaic devices

Biophotovoltaic (BPV) devices employ the photosynthetic activity of microalgae or cyanobacteria to harvest light energy and generate electrical current directly as a result of the release of electrons from the algal cells. NADPH oxidases (NOX) are plasma-membrane enzymes that transport electrons from the cytosol to generate extracellular superoxide anions, and have been implicated in BPV output. In this study, we investigated NOX activity in the diatoms, Phaeodactylum tricornutum and Thalassiosira pseudonana in an attempt to understand and enhance NOX and BPV function. We found that NOX activity was linked to defined growth regimes and growth phases, and was light dependent. Crucially, current output in a BPV device correlated with NOX activity, and levels of up to 14 μA per 106 cells (approximately 500 mA.m-2) were obtained. Expression of two putative P. tricornutum NOX genes (PtNOX1 and PtNOX2) was found to correspond with the observed growth patterns of superoxide anion production and power output, suggesting these are responsible for the observed patterns of NOX activity. Crucially, we demonstrate that NOX activity levels could be enhanced via semi-continuous culturing, pointing to the possibility of maintaining long-term power output in BPV devices.This work was supported by the United Kingdom Engineering and Physical Sciences Research Council (EPSRC), grant reference EP/F047940/1.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.algal.2015.08.00