From modular invariants to graphs: the modular splitting method

We start with a given modular invariant M of a two dimensional su(n)_k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; 2) the quantum symmetries of the higher ADE graph G associated to the initial modular invariant M. Notice that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyze several su(3)_k exceptional cases at levels 5 and 9.Comment: 28 pages, 7 figures. Version 2: updated references. Typos corrected. su(2) example has been removed to shorten the paper. Dual annular matrices for the rejected exceptional su(3) diagram are determine

Long-term variability of CO2 and O in the Mars upper atmosphere from MRO radio science data

We estimate the annual variability of CO2 and O partial density using approximately 6years of Mars Reconnaissance Orbiter (MRO) radio science data from August 2006 to January 2012, which cover three full Martian years (from the northern hemisphere summer of 28 to the northern hemisphere summer of 31). These two elements are the dominant species at the MRO periapsis altitude, constituting about 70-80% of the total density. We report the recovered annual cycle of CO2 and the annual and seasonal cycle of O in the upper atmosphere. Although no other observations are available at those altitudes, our results are in good agreement with the density measurements of the Mars Express Spectroscopy for Investigation of Characteristics of the Atmosphere of Mars, which uses stellar occultations between 60 and 130km to determine the CO2 variability, and with the Mars Global Reference Atmospheric Model 2010 for the O annual and seasonal variabilities. Furthermore, the updated model provides more reasonable MRO drag coefficients (CD), which are estimated to absorb mismodeling in the atmospheric density prediction. The higher content of dust in the atmosphere due to dust storms increases the density, so the CDs should compensate for this effect. The correlation between the drag coefficient and the dust optical depth, measured by the Mars Odyssey Thermal Emission Imaging System (THEMIS) instrument, increases from 0.4 to 0.8 with the a priori and adjusted models, respectively. The trend of CDs not only confirms a substantial improvement in the prediction of the atmospheric density with the updated model but also provides useful information for local dust storms, near MRO periapsis, that cannot be measured by the opacity level since THEMIS does not always sample the southern hemisphere evenly

Lorentz and CPT Invariance Violation In High-Energy Neutrinos

High-energy neutrino astronomy will be capable of observing particles at both extremely high energies and over extremely long baselines. These features make such experiments highly sensitive to the effects of CPT and Lorentz violation. In this article, we review the theoretical foundation and motivation for CPT and Lorentz violating effects, and then go on to discuss the related phenomenology within the neutrino sector. We describe several signatures which might be used to identify the presence of CPT or Lorentz violation in next generation neutrino telescopes and cosmic ray experiments. In many cases, high-energy neutrino experiments can test for CPT and Lorentz violation effects with much greater precision than other techniques.Comment: 27 pages, 8 figure

A search for double beta decays of tin isotopes with enhanced sensitivity

A search for the various double beta decay modes of 124Sn and 112Sn has been performed on 75 kg.days of data. New half-life limits for excited states in 124Sn have been obtained including a lower limit for the decay into the first excited 2+ state of 124Te of T_half > 0.87e20 yrs (90% CL) and into the first excited 0+ state of T_half > 1.08e20 yrs (90% CL). Ground state and excited state transitions of 112Sn have also been experimentally explored. A limit for the 2 neutrino double electron capture of T_half > 1.8e19 yrs (90% CL) is obtained. The non-observation of de-excitation gammas from the 0+ at 1888.5keV results in a lower half-life limit on the 0 neutrino double electron capture decay of 112Sn of T_half > 0.8e19 yrs (90% CL), despite a possible resonant enhancement of the decay rate due to degenerated states.Comment: 6 pages, 7 figures, updated analysis and tex

Kaon physics with a high-intensity proton driver

We study opportunities for future high-precision experiments in kaon physics using a high-intensity proton driver, which could be part of the front-end of a muon storage ring complex. We discuss in particular the rare decays $K_L\to\pi^0\nu\bar\nu$, $K^+\to\pi^+\nu\bar\nu$, $K_L\to\pi^0e^+e^-$, and lepton-flavour violating modes such as $K_L\to\mu e$ and $K\to\pi\mu e$. The outstanding physics potential and long-term interest of these modes is emphasized. We review status and prospects of current and planned experiments for the processes under consideration, and indicate possible improvements and strategies towards achieving the necessary higher sensitivity. Finally, we outline the machine requirements needed to perform these high-precision kaon experiments in the context of a muon storage ring facility.Comment: 26 pages, 12 figures; report of the kaon physics working group for the ECFA studies on neutrino factory and muon storage rings at CERN, G. Buchalla (convener); references update

A 40th deg and order gravitational field model for Mars

Understanding the origin and evolution of major photographic features on Mars, such as the hemispheric dichotomy and Tharsis rise, will require improved resolution of that planet's gravitational and topographic fields. The highest resolution gravity model for Mars published to date was derived from Doppler tracking data from the Mariner 9 and Viking 1 and 2 spacecraft, and is of 18th degree and order. That field has a maximum spatial resolution of approx. 600 km, which is comparable to that of the best topographic model. The resolution of previous gravity models was limited not by data density, but rather by the computational resources available at the time. Because this restriction is no longer a limitation, the Viking and Mariner data sets were reanalyzed and a gravitational field was derived complete to the 40th degree and order with a corresponding maximum spatial resolution of 300 km where the data permit

Global surface slopes and roughness of the Moon from the Lunar Orbiter Laser Altimeter

The acquisition of new global elevation data from the Lunar Orbiter Laser Altimeter, carried on the Lunar Reconnaissance Orbiter, permits quantification of the surface roughness properties of the Moon at unprecedented scales and resolution. We map lunar surface roughness using a range of parameters: median absolute slope, both directional (along-track) and bidirectional (in two dimensions); median differential slope; and Hurst exponent, over baselines ranging from ~17 m to ~2.7 km. We find that the lunar highlands and the mare plains show vastly different roughness properties, with subtler variations within mare and highlands. Most of the surface exhibits fractal-like behavior, with a single or two different Hurst exponents over the given baseline range; when a transition exists, it typically occurs near the 1 km baseline, indicating a significant characteristic spatial scale for competing surface processes. The Hurst exponent is high within the lunar highlands, with a median value of 0.95, and lower in the maria (with a median value of 0.76). The median differential slope is a powerful tool for discriminating between roughness units and is useful in characterizing, among other things, the ejecta surrounding large basins, particularly Orientale, as well as the ray systems surrounding young, Copernican-age craters. In addition, it allows a quantitative exploration on mare surfaces of the evolution of surface roughness with age

Formation of fold and thrust belts on Venus due to horizontal shortening of a laterally heterogeneous lithosphere

An outstanding question relevant to understanding the tectonics of Venus is the mechanism of formation of fold and thrust belts, such as the mountain belts that surround Lakshmi Planum in western Ishtar Terra. These structures are typically long (hundreds of km) and narrow (many tens of km), and are often located at the margins of relatively high (km-scale) topographic rises. Previous studies have attempted to explain fold and thrust belts in various areas of Venus in the context of viscous and brittle wedge theory. However, while wedge theory can explain the change in elevation from the rise to the adjacent lowland, it fails to account for a fundamental aspect of the deformation, i.e., the topographic high at the edge of the rise. In this study we quantitatively explore the hypothesis that fold and thrust belt morphology on Venus can alternatively be explained by horizontal shortening of a lithosphere that is laterally heterogeneous, due either to a change in thickness of the lithosphere or the crust. Lateral heterogeneities in lithosphere structure may arise in response to thermal thinning or extensive faulting, while variations in crustal thickness may arise due to either spatially variable melting of mantle material or by horizontal shortening of the crust. In a variable thickness lithosphere or crust that is horizontally shortened, deformation will tend to localize in the vicinity of thickness heterogeneity, resulting in a higher component of dynamic topography there as compared to elsewhere in the shortening lithosphere. This mechanism may thus provide a simple explanation for the topographic high at the edge of the rise

Incidence of Arrhythmias and Myocardial Ischaemia During Haemodialysis and Haemofiltration

Thirty-two patients (10 male, 22 female; age 37-82 years) undergoing maintenance haemodialysis or haemofiltration were studied by means of Holter device capable of simultaneously analysing rhythm and ST changes in three leads. Twenty-five patients were on haemodialysis, seven on haemofiltration, mean duration of haemodialysis/haemofiltration being 3.4±3 years. Incidence of ventricular tachycardia was low, being detected only in 1 of 32 patients. Ventricular premature beats in excess of 10/h during a period of 2 h were found in 8 of 32 patients and 100 supraventricular premature beats for 2 h or more in 4 of 32 patients. Both ventricular premature beats and supraventricular premature beats were most frequently recorded during the last hour of haemodialysis/haemofiltration. ECG signs of ischaemia were detected in eight patients, four of whom were asymptomatic. Ischaemia also occurred predominantly during the last hour of haemodialysis/haemofiltration. Two symptomatic patients displayed neither arrhythmias nor ST-changes while being monitored. The study shows that silent ischaemia and arrhythmias in patients under going chronic haemodialysis/haemofiltration may not be infrequent. Recognition of these events could be of importance in the management of these patient

Invariant expansion for the trigonal band structure of graphene

We present a symmetry analysis of the trigonal band structure in graphene, elucidating the transformational properties of the underlying basis functions and the crucial role of time-reversal invariance. Group theory is used to derive an invariant expansion of the Hamiltonian for electron states near the K points of the graphene Brillouin zone. Besides yielding the characteristic k-linear dispersion and higher-order corrections to it, this approach enables the systematic incorporation of all terms arising from external electric and magnetic fields, strain, and spin-orbit coupling up to any desired order. Several new contributions are found, in addition to reproducing results obtained previously within tight-binding calculations. Physical ramifications of these new terms are discussed.Comment: 10 pages, 1 figure; expanded version with more details and additional result