Gauge Field Preheating at the End of Inflation

Here we consider the possibility of preheating the Universe via the parametric amplification of a massless, U(1) abelian gauge field. We assume that the gauge field is coupled to the inflaton via a conformal factor with one free parameter. We present the results of high-resolution three-dimensional simulations of this model and show this mechanism efficiently preheats the Universe to a radiation-dominated final state.Comment: 8 pages, 8 figure

Realizability of the Lorentzian (n,1)-Simplex

In a previous article [JHEP 1111 (2011) 072; arXiv:1108.4965] we have developed a Lorentzian version of the Quantum Regge Calculus in which the significant differences between simplices in Lorentzian signature and Euclidean signature are crucial. In this article we extend a central result used in the previous article, regarding the realizability of Lorentzian triangles, to arbitrary dimension. This technical step will be crucial for developing the Lorentzian model in the case of most physical interest: 3+1 dimensions. We first state (and derive in an appendix) the realizability conditions on the edge-lengths of a Lorentzian n-simplex in total dimension n=d+1, where d is the number of space-like dimensions. We then show that in any dimension there is a certain type of simplex which has all of its time-like edge lengths completely unconstrained by any sort of triangle inequality. This result is the d+1 dimensional analogue of the 1+1 dimensional case of the Lorentzian triangle.Comment: V1: 15 pages, 2 figures. V2: Minor clarifications added to Introduction and Discussion sections. 1 reference updated. This version accepted for publication in JHEP. V3: minor updates and clarifications, this version closely corresponds to the version published in JHE

The a-number of hyperelliptic curves

It is known that for a smooth hyperelliptic curve to have a large $a$-number, the genus must be small relative to the characteristic of the field, $p>0$, over which the curve is defined. It was proven by Elkin that for a genus $g$ hyperelliptic curve $C$ to have $a_C=g-1$, the genus is bounded by $g<\frac{3p}{2}$. In this paper, we show that this bound can be lowered to $g <p$. The method of proof is to force the Cartier-Manin matrix to have rank one and examine what restrictions that places on the affine equation defining the hyperelliptic curve. We then use this bound to summarize what is known about the existence of such curves when $p=3,5$ and $7$.Comment: 7 pages. v2: revised and improved the proof of the main theorem based on suggestions from the referee. To appear in the proceedings volume of Women in Numbers Europe-

A Meinardus theorem with multiple singularities

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii) We provided an explanation to the argument for the local limit theorem. The paper is tentatively accepted by "Communications in Mathematical Physics" journa

Plant canopy shape and the influences on UV exposures to the canopy

The solar spectra at selected sites over hemispherical, conical and pinnacle plant canopy models has been evaluated with a dosimetric technique. The irradiance at the sites varies by up to a factor of 0.31 compared to the irradiance on a horizontal plane. The biologically effective (UVBE) exposures evaluated with the dosimetric technique at sites over the plant canopy are up to 19% of that on a horizontal plane. Compared to a spectroradiometer, the technique provides a more practicable method of measuring the UVBE exposures at multiple sites over a plant canopy. Usage of a dosimeter at one site to provide the exposures at that site for different sun angles introduces an error of more than 50%. Knowledge of the spectra allowed the UV and UVBE exposures to be calculated at each site along with the exposures to the entire canopies. These were dependent on the sun angle and the canopy shape. For plant damage, the UVBE was a maximum of about 1.4 mJ cm-2/min. Compared to the hemispherical canopy, the UVBE exposure for generalised plant damage was 45% less for the pinnacle canopy and 23% less for the conical canopy. The canopy exposures could not be determined from measurements of the ambient exposure

Spectral signature of short attosecond pulse trains

We report experimental measurements of high-order harmonic spectra generated in Ar using a carrier-envelope-offset (CEO) stabilized 12 fs, 800nm laser field and a fraction (less than 10%) of its second harmonic. Additional spectral peaks are observed between the harmonic peaks, which are due to interferences between multiple pulses in the train. The position of these peaks varies with the CEO and their number is directly related to the number of pulses in the train. An analytical model, as well as numerical simulations, support our interpretation

Control of sedimentation by active tectonics, glaciation and contourite-depositing currents in Endurance Basin, South Georgia

Endurance Basin is an elongate broadly WNW-ESE trending basin located on the northern margin of the Scotia Sea, adjacent to the southern margin of the South Georgia micro-continent. Bathymetric and TOPAS sub-bottom profile data acquired in 2010 by the British research ship RRS James Clark Ross map this basin and its sedimentology for the first time. Endurance Basin contains a number of sub-basins and a substantial glaciogenic fan. The northern margin of Endurance Basin is formed by a series of steep slopes and intervening troughs. These are interpreted as a left-stepping en echelon array of oblique, strike-slip faults whilst the sub-basins are separated by compressional dip-slip faults. It appears that South Georgia is moving NW with respect to the basin. We interpret five seismic facies from TOPAS data, which are associated with distinct sedimentologies. The most striking units in the basin fill are: substantial contourite drifts located in the NW of the basin and on its southern margin; and two distinct mass transport deposits that pond in the centre of the basin. Combined with the known regional oceanographic setting, the contourites provide evidence of broadly eastward flowing bottom currents, entering the basin from at least two locations. Although landslide scars are present on the steep northern basin margin, the imaged mass transport deposits are interpreted to have been sourced from the glaciogenic fan, located in the SE of the basin, and from a contourite unit located on the basin’s southern margin. Sediments from these events are transported at least 40 km. The contourite drift sequence is at least 100 m thick in the west of the basin and may contain a palaeoenvironmental archive of Antarctic Cirumpolar Current (ACC) flow and the climate of South Georgia extending to the Pliocene. Such an archive would allow reconstruction of ACC flow through the Pleistocene glaciations and provide a means of linking ocean circulation and climate records in the sub-Antarctic Polar Front region

Computations in non-commutative Iwasawa theory

We study special values of L-functions of elliptic curves over Q twisted by Artin representations that factor through a false Tate curve extension $Q(\mu_p^\infty,\sqrt[p^\infty]{m})/Q$. In this setting, we explain how to compute L-functions and the corresponding Iwasawa-theoretic invariants of non-abelian twists of elliptic curves. Our results provide both theoretical and computational evidence for the main conjecture of non-commutative Iwasawa theory.Comment: 60 pages; with appendix by John Coates and Ramdorai Sujath