Weak Liouville-Arnold Theorems & Their Implications

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion and obtain two theorems reminiscent of the Liouville-Arnold theorem. Moreover, we also obtain results on the structure of the configuration spaces of such systems that are reminiscent of results on the configuration space of completely integrable Tonelli Hamiltonians.Comment: 24 pages, 1 figure; v2 corrects typo in online abstract; v3 includes new title (was: A Weak Liouville-Arnold Theorem), re-arrangement of introduction, re-numbering of main theorems; v4 updates the authors' email and physical addresses, clarifies notation in section 4. Final versio

Tautness for riemannian foliations on non-compact manifolds

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $\kappa_\mu$ (relatively to a suitable riemannian metric $\mu$) is zero. In the transversally orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group $H^{^{n}}(M/\mathcal{F})$, where n = \codim \mathcal{F}. By the Poincar\'e Duality, this last condition is equivalent to the non-vanishing of the basic twisted cohomology group $H^{^{0}}_{_{\kappa_\mu}}(M/\mathcal{F})$, when $M$ is oriented. When $M$ is not compact, the tautness class is not even defined in general. In this work, we recover the previous study and results for a particular case of riemannian foliations on non compact manifolds: the regular part of a singular riemannian foliation on a compact manifold (CERF).Comment: 18 page

The Greenhouse Gas Climate Change Initiative (GHG-CCI): comparative validation of GHG-CCI SCIAMACHY/ENVISAT and TANSO-FTS/GOSAT CO₂ and CH₄ retrieval algorithm products with measurements from the TCCON

Column-averaged dry-air mole fractions of carbon dioxide and methane have been retrieved from spectra acquired by the TANSO-FTS (Thermal And Near-infrared Sensor for carbon Observations-Fourier Transform Spectrometer) and SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Cartography) instruments on board GOSAT (Greenhouse gases Observing SATellite) and ENVISAT (ENVIronmental SATellite), respectively, using a range of European retrieval algorithms. These retrievals have been compared with data from ground-based high-resolution Fourier transform spectrometers (FTSs) from the Total Carbon Column Observing Network (TCCON). The participating algorithms are the weighting function modified differential optical absorption spectroscopy (DOAS) algorithm (WFMD, University of Bremen), the Bremen optimal estimation DOAS algorithm (BESD, University of Bremen), the iterative maximum a posteriori DOAS (IMAP, Jet Propulsion Laboratory (JPL) and Netherlands Institute for Space Research algorithm (SRON)), the proxy and full-physics versions of SRON's RemoTeC algorithm (SRPR and SRFP, respectively) and the proxy and full-physics versions of the University of Leicester's adaptation of the OCO (Orbiting Carbon Observatory) algorithm (OCPR and OCFP, respectively). The goal of this algorithm inter-comparison was to identify strengths and weaknesses of the various so-called round- robin data sets generated with the various algorithms so as to determine which of the competing algorithms would proceed to the next round of the European Space Agency's (ESA) Greenhouse Gas Climate Change Initiative (GHG-CCI) project, which is the generation of the so-called Climate Research Data Package (CRDP), which is the first version of the Essential Climate Variable (ECV) "greenhouse gases" (GHGs). For XCO₂, all algorithms reach the precision requirements for inverse modelling (< 8 ppm), with only WFMD having a lower precision (4.7 ppm) than the other algorithm products (2.4–2.5 ppm). When looking at the seasonal relative accuracy (SRA, variability of the bias in space and time), none of the algorithms have reached the demanding < 0.5 ppm threshold. For XCH₄, the precision for both SCIAMACHY products (50.2 ppb for IMAP and 76.4 ppb for WFMD) fails to meet the < 34 ppb threshold for inverse modelling, but note that this work focusses on the period after the 2005 SCIAMACHY detector degradation. The GOSAT XCH₄ precision ranges between 18.1 and 14.0 ppb. Looking at the SRA, all GOSAT algorithm products reach the < 10 ppm threshold (values ranging between 5.4 and 6.2 ppb). For SCIAMACHY, IMAP and WFMD have a SRA of 17.2 and 10.5 ppb, respectively

Optimal path planning for nonholonomic robotics systems via parametric optimisation

Abstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping

Simulations of column-averaged CO_2 and CH_4 using the NIES TM with a hybrid sigma-isentropic (σ-θ) vertical coordinate

We have developed an improved version of the National Institute for Environmental Studies (NIES) three-dimensional chemical transport model (TM) designed for accurate tracer transport simulations in the stratosphere, using a hybrid sigma-isentropic (σ-θ) vertical coordinate that employs both terrain-following and isentropic parts switched smoothly around the tropopause. The air-ascending rate was derived from the effective heating rate and was used to simulate vertical motion in the isentropic part of the grid (above level 350 K), which was adjusted to fit to the observed age of the air in the stratosphere. Multi-annual simulations were conducted using the NIES TM to evaluate vertical profiles and dry-air column-averaged mole fractions of CO_2 and CH_4. Comparisons with balloon-borne observations over Sanriku (Japan) in 2000–2007 revealed that the tracer transport simulations in the upper troposphere and lower stratosphere are performed with accuracies of ~5% for CH_4 and SF_6, and ~1% for CO_2 compared with the observed volume-mixing ratios. The simulated column-averaged dry air mole fractions of atmospheric carbon dioxide (XCO_2) and methane (XCH_4) were evaluated against daily ground-based high-resolution Fourier Transform Spectrometer (FTS) observations measured at twelve sites of the Total Carbon Column Observing Network (TCCON) (Bialystok, Bremen, Darwin, Garmisch, Izaña, Lamont, Lauder, Orleans, Park Falls, Sodankylä, Tsukuba, and Wollongong) between January 2009 and January 2011. The comparison shows the model's ability to reproduce the site-dependent seasonal cycles as observed by TCCON, with correlation coefficients typically on the order 0.8–0.9 and 0.4–0.8 for XCO_2 and XCH_4, respectively, and mean model biases of ±0.2% and ±0.5%, excluding Sodankylä, where strong biases are found. The ability of the model to capture the tracer total column mole fractions is strongly dependent on the model's ability to reproduce seasonal variations in tracer concentrations in the planetary boundary layer (PBL). We found a marked difference in the model's ability to reproduce near-surface concentrations at sites located some distance from multiple emission sources and where high emissions play a notable role in the tracer's budget. Comparisons with aircraft observations over Surgut (West Siberia), in an area with high emissions of methane from wetlands, show contrasting model performance in the PBL and in the free troposphere. Thus, the PBL is another critical region for simulating the tracer total column mole fractions

Cohomological tautness for Riemannian foliations

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold

Technical Note: Latitude-time variations of atmospheric column-average dry air mole fractions of CO_2, CH_4 and N_2O

We present a comparison of an atmospheric general circulation model (AGCM)-based chemistry-transport model (ACTM) simulation with total column measurements of CO_2, CH_4 and N_2O from the Total Carbon Column Observing Network (TCCON). The model is able to capture observed trends, seasonal cycles and inter hemispheric gradients at most sampled locations for all three species. The model-observation agreements are best for CO_2, because the simulation uses fossil fuel inventories and an inverse model estimate of non-fossil fuel fluxes. The ACTM captures much of the observed seasonal variability in CO_2 and N_2O total columns (~81 % variance, R>0.9 between ACTM and TCCON for 19 out of 22 cases). These results suggest that the transport processes in troposphere and stratosphere are well represented in ACTM. Thus the poor correlation between simulated and observed CH4 total columns, particularly at tropical and extra-tropical sites, have been attributed to the uncertainties in surface emissions and loss by hydroxyl radicals. While the upward-looking total column measurements of CO_2 contains surface flux signals at various spatial and temporal scales, the N_2O measurements are strongly affected by the concentration variations in the upper troposphere and stratosphere

A geostatistical framework for quantifying the imprint of mesoscale atmospheric transport on satellite trace gas retrievals

National Aeronautics and Space Administration's Orbiting Carbon Observatory‐2 (OCO‐2) satellite provides observations of total column‐averaged CO2 mole fractions (X_(CO₂)) at high spatial resolution that may enable novel constraints on surface‐atmosphere carbon fluxes. Atmospheric inverse modeling provides an approach to optimize surface fluxes at regional scales, but the accuracy of the fluxes from inversion frameworks depends on key inputs, including spatially and temporally dense CO₂ observations and reliable representations of atmospheric transport. Since X_(CO₂) observations are sensitive to both synoptic and mesoscale variations within the free troposphere, horizontal atmospheric transport imparts substantial variations in these data and must be either resolved explicitly by the atmospheric transport model or accounted for within the error covariance budget provided to inverse frameworks. Here, we used geostatistical techniques to quantify the imprint of atmospheric transport in along‐track OCO‐2 soundings. We compare high‐pass‐filtered (<250 km, spatial scales that primarily isolate mesoscale or finer‐scale variations) along‐track spatial variability in X_(CO₂) and X_(H₂O) from OCO‐2 tracks to temporal synoptic and mesoscale variability from ground‐based X_(CO₂) and X_(H₂O) observed by nearby Total Carbon Column Observing Network sites. Mesoscale atmospheric transport is found to be the primary driver of along‐track, high‐frequency variability for OCO‐2 X_(H₂O). For X_(CO₂), both mesoscale transport variability and spatially coherent bias associated with other elements of the OCO‐2 retrieval state vector are important drivers of the along‐track variance budget

Coherent Electronic Wave Packet Motion in C-60 Controlled by the Waveform and Polarization of Few-Cycle Laser Fields

Citation: Li, H., Mignolet, B., Wachter, G., Skruszewicz, S., Zherebtsov, S., Sussmann, F., . . . Kling, M. F. (2015). Coherent Electronic Wave Packet Motion in C-60 Controlled by the Waveform and Polarization of Few-Cycle Laser Fields. Physical Review Letters, 114(12), 6. doi:10.1103/PhysRevLett.114.123004Strong laser fields can be used to trigger an ultrafast molecular response that involves electronic excitation and ionization dynamics. Here, we report on the experimental control of the spatial localization of the electronic excitation in the C-60 fullerene exerted by an intense few-cycle (4 fs) pulse at 720 nm. The control is achieved by tailoring the carrier-envelope phase and the polarization of the laser pulse. We find that the maxima and minima of the photoemission-asymmetry parameter along the laser-polarization axis are synchronized with the localization of the coherent electronic wave packet at around the time of ionization.Additional Authors: Tiggesbaumker, J.;Meiwes-Broer, K. H.;Lemell, C.;Burgdorfer, J.;Levine, R. D.;Remacle, F.;Kling, M. F