Quantum Gravity signatures in the Unruh effect

We study quantum gravity signatures emerging from phenomenologically motivated multiscale models, spectral actions, and Causal Set Theory within the detector approach to the Unruh effect. We show that while the Unruh temperature is unaffected, Lorentz-invariant corrections to the two-point function leave a characteristic fingerprint in the induced emission rate of the accelerated detector. Generically, quantum gravity models exhibiting dynamical dimensional reduction exhibit a suppression of the Unruh rate at high energy while the rate is enhanced in Kaluza-Klein theories with compact extra dimensions. We quantify this behavior by introducing the "Unruh dimension" as the effective spacetime dimension seen by the Unruh effect and show that it is related, though not identical, to the spectral dimension used to characterize spacetime in quantum gravity. We comment on the physical origins of these effects and their relevance for black hole evaporation.Comment: 38 pages, 7 figures; v3: section 2 rewritten, references adde

A simple reactive-transport model of calcite precipitation in soils and other porous media

Calcite formation in soils and other porous media generally occurs around a localised source of reactants, such as a plant root or soil macro-pore, and the rate depends on the transport of reactants to and from the precipitation zone as well as the kinetics of the precipitation reaction itself. However most studies are made in well mixed systems, in which such transport limitations are largely removed. We developed a mathematical model of calcite precipitation near a source of base in soil, allowing for transport limitations and precipitation kinetics. We tested the model against experimentally-determined rates of calcite precipitation and reactant concentration–distance profiles in columns of soil in contact with a layer of HCO3−-saturated exchange resin. The model parameter values were determined independently. The agreement between observed and predicted results was satisfactory given experimental limitations, indicating that the model correctly describes the important processes. A sensitivity analysis showed that all model parameters are important, indicating a simpler treatment would be inadequate. The sensitivity analysis showed that the amount of calcite precipitated and the spread of the precipitation zone were sensitive to parameters controlling rates of reactant transport (soil moisture content, salt content, pH, pH buffer power and CO2 pressure), as well as to the precipitation rate constant. We illustrate practical applications of the model with two examples: pH changes and CaCO3 precipitation in the soil around a plant root, and around a soil macro-pore containing a source of base such as urea

Collective learning in schools described: building collective learning capacity

Processes of collective learning are expected to increase the professionalism of teachers and school leaders. Little is known about the processes of collective learning which take place in schools and about the way in which those processes may be improved. This paper describes a research into processes of collective learning at three primary schools. Processes of collective learning are described which took place in small teams in these schools. It is also pointed out which attempts can be made in order to reinforce these processes in the schools mentioned

Upper bounds for linear graph codes

A linear graph code is a family $\mathcal{C}$ of graphs on $n$ vertices with the property that the symmetric difference of the edge sets of any two graphs in $\mathcal{C}$ is also the edge set of a graph in $\mathcal{C}$. In this article, we investigate the maximal size of a linear graph code that does not contain a copy of a fixed graph $H$. In particular, we show that if $H$ has an even number of edges, the size of the code is $O(2^{\binom{n}{2}}/\log n)$, making progress on a question of Alon. Furthermore, we show that for almost all graphs $H$ with an even number of edges, there exists $\varepsilon_H>0$ such that the size of a linear graph code without a copy of $H$ is at most $2^{\binom{n}{2}}/n^{\varepsilon_H}$.Comment: 12 pages, fixed typos and changed formulations to match thesi

A proof of the 3/5-conjecture in the domination game

The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph $G$. A vertex is said to be dominated if it has been selected or is adjacent to a selected vertex. Each selected vertex must strictly increase the number of dominated vertices at the time of its selection, and the game ends once every vertex in $G$ is dominated. Dominator aims to keep the game as short as possible, while Staller tries to achieve the opposite. In this article, we prove that for any graph $G$ on $n$ vertices, Dominator has a strategy to end the game in at most $3n/5$ moves, which was conjectured by Kinnersley, West and Zamani.Comment: 30 pages, 6 figure