Topological properties of quantum periodic Hamiltonians

We consider periodic quantum Hamiltonians on the torus phase space (Harper-like Hamiltonians). We calculate the topological Chern index which characterizes each spectral band in the generic case. This calculation is made by a semi-classical approach with use of quasi-modes. As a result, the Chern index is equal to the homotopy of the path of these quasi-modes on phase space as the Floquet parameter (\theta) of the band is varied. It is quite interesting that the Chern indices, defined as topological quantum numbers, can be expressed from simple properties of the classical trajectories.Comment: 27 pages, 14 figure

The influence of the synoptic regime on stable water isotopes in precipitation at Dome C, East Antarctica

Abstract. The correct derivation of paleotemperatures from ice cores requires exact knowledge of all processes involved before and after the deposition of snow and the subsequent formation of ice. At the Antarctic deep ice core drilling site Dome C, a unique data set of daily precipitation amount, type, and stable water isotope ratios is available that enables us to study in detail atmospheric processes that influence the stable water isotope ratio of precipitation. Meteorological data from both automatic weather station and a mesoscale atmospheric model were used to investigate how different atmospheric flow patterns determine the precipitation parameters. A classification of synoptic situations that cause precipitation at Dome C was established and, together with back-trajectory calculations, was utilized to estimate moisture source areas. With the resulting source area conditions (wind speed, sea surface temperature, and relative humidity) as input, the precipitation stable isotopic composition was modeled using the so-called Mixed Cloud Isotope Model (MCIM). The model generally underestimates the depletion of 18O in precipitation, which was not improved by using condensation temperature rather than inversion temperature. Contrary to the assumption widely used in ice core studies, a more northern moisture source does not necessarily mean stronger isotopic fractionation. This is due to the fact that snowfall events at Dome C are often associated with warm air advection due to amplification of planetary waves, which considerably increases the site temperature and thus reduces the temperature difference between source area and deposition site. In addition, no correlation was found between relative humidity at the moisture source and the deuterium excess in precipitation. The significant difference in the isotopic signal of hoarfrost and diamond dust was shown to disappear after removal of seasonality. This study confirms the results of an earlier study carried out at Dome Fuji with a shorter data set using the same methods

Semi-classical study of the Quantum Hall conductivity

The semi-classical study of the integer Quantum Hall conductivity is investigated for electrons in a bi-periodic potential $V(x,y)$. The Hall conductivity is due to the tunnelling effect and we concentrate our study to potentials having three wells in a periodic cell. A non-zero topological conductivity requires special conditions for the positions, and shapes of the wells. The results are derived analytically and well confirmed by numerical calculations.Comment: 23 pages, 13 figure

Atmospheric transport and chemistry of trace gases in LMDz5B: evaluation and implications for inverse modelling

Representation of atmospheric transport is a major source of error in the estimation of greenhouse gas sources and sinks by inverse modelling. Here we assess the impact on trace gas mole fractions of the new physical parameterizations recently implemented in the atmospheric global climate model LMDz to improve vertical diffusion, mesoscale mixing by thermal plumes in the planetary boundary layer (PBL), and deep convection in the troposphere. At the same time, the horizontal and vertical resolution of the model used in the inverse system has been increased. The aim of this paper is to evaluate the impact of these developments on the representation of trace gas transport and chemistry, and to anticipate the implications for inversions of greenhouse gas emissions using such an updated model. Comparison of a one-dimensional version of LMDz with large eddy simulations shows that the thermal scheme simulates shallow convective tracer transport in the PBL over land very efficiently, and much better than previous versions of the model. This result is confirmed in three-dimensional simulations, by a much improved reproduction of the radon-222 diurnal cycle. However, the enhanced dynamics of tracer concentrations induces a stronger sensitivity of the new LMDz configuration to external meteorological forcings. At larger scales, the inter-hemispheric exchange is slightly slower when using the new version of the model, bringing them closer to observations. The increase in the vertical resolution (from 19 to 39 layers) significantly improves the representation of stratosphere/troposphere exchange. Furthermore, changes in atmospheric thermodynamic variables, such as temperature, due to changes in the PBL mixing modify chemical reaction rates, which perturb chemical equilibriums of reactive trace gases. One implication of LMDz model developments for future inversions of greenhouse gas emissions is the ability of the updated system to assimilate a larger amount of high-frequency data sampled at high-variability stations. Others implications are discussed at the end of the paper

Summation and transformation formulas for elliptic hypergeometric series

Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.Comment: 21 pages, AMS-LaTe

Population characteristics of Shovelnose Sturgeon during low- and high-water conditions in the lower Platte River, Nebraska

Cycles of low- and high-water periods (i.e., years) in river systems are natural occurrences, but understanding how cyclical climatological patterns affect fishes, especially long-lived species, is unclear. We assessed Shovelnose Sturgeon population dynamics between a period of low- (2001-2004) and high- (2009-2012) water years in the lower Platte River, Nebraska. Low-flow periods in the lower Platte River can cause disconnection(s) between upstream and downstream reaches resulting in isolated pools and elevated water temperatures leading to stressful situations for aquatic life and possible mortality. Our data show no measurable differences between key population indices between flow condition periods which is consistent with current paradigms for long-lived fish species. Shovelnose Sturgeon relative weights were generally \u3e 80 during both low- and high-water periods and the size structure did not differ between the two periods. Shovelnose Sturgeon abundances, however, were greater during high-water conditions compared to low-water conditions (Kruskal-Wallis: χ2 = 6.15, d.f. = 1, P = 0.01). Shovelnose Sturgeon may have migrated to more suitable habitats during low-water periods to seek refuge allowing these individuals to return during more suitable conditions. Shovelnose Sturgeon and other riverine fish have evolved in a variable environment and have been able to endure relatively minor anthropogenic changes within the lower Platte River. Rivers like the lower Platte River that have retained much of their original physical features and flow regimes are likely key components for the resistance and resilience of riverine species. However, as alterations to landscapes continue and uncertainty exists surrounding future climate predictions, it is unknown how these riverine species will be able to adapt to future changes. The reduction in anthropogenic changes that disrupt flow regimes and increasing connectivity among river systems could provide more fish refuge during stressful conditions helping to protect these riverine species