Arnold diffusion for a complete family of perturbations with two independent harmonics

We prove that for any non-trivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete computation of several scattering maps. A complete description of the different kinds of scattering maps taking place as well as the existence of piecewise smooth global scattering maps is also provided.Comment: 23 pages, 14 figure

Arnold diffusion for an a priori unstable Hamiltonian system with 3 ++ 1/2 degrees of freedom

In the present paper we apply the geometrical mechanism of diffusion in an \emph{a priori} unstable Hamiltonian system with 3 $+$ 1/2 degrees of freedom. This mechanism consists of combining iterations of the \emph{inner} and \emph{outer} dynamics associated to a \emph{Normallly Hyperbolic Invariant Manifold} (NHIM), to construct diffusing \emph{pseudo-orbits} and subsequently apply shadowing results to prove the existence of diffusing orbits of the system. In addition to proving the existence of diffusion for a wide range of the parameters of the system, an important part of our study focuses on the search for \emph{Highways}, a particular family of orbits of the outer map (the so-called \emph{scattering} map), whose existence is sufficient to ensure a very large drift of the action variables, with a diffusion time near them that agrees with the optimal estimates in the literature. Moreover, this optimal diffusion time is calculated, with an explicit calculation of the constants involved. All these properties are proved by analytical methods and, where necessary, supplemented by numerical calculations.Comment: 17 pages, 8 figure

N-body dynamics on closed surfaces : the axioms of mechanics

D.G.D. gratefully acknowledges support for this research from CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico ) and FINEP (Inovação e Pesquisa) in Brazil, and from the UK Engineering and Physical Sciences Research Council (grant no. EP/H001794/1)A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfaces M endowed with a metric g. We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid).PostprintPeer reviewe

Glacier expansion in southern Patagonia throughout the Antarctic cold reversal

Resolving debated climate changes in the southern middle latitudes and potential teleconnections between southern temperate and polar latitudes during the last glacial-interglacial transition is required to help understand the cause of the termination of ice ages. Outlet glaciers of the Patagonian Ice Fields are primarily sensitive to atmospheric temperature and also precipitation, thus former ice margins record the extent and timing of past climate changes. 38 10Be exposure ages from moraines show that outlet glaciers in Torres del Paine (51°S, south Patagonia, Chile) advanced during the time of the Antarctic cold reversal (ACR; ca. 14.6–12.8 ka), reaching a maximum extent by ∼14,200 ± 560 yr ago. The evidence here indicates that the South Patagonian Ice Field was responding to late glacial climate change distinctly earlier than the onset of the European Younger Dryas stadial (ca. 12.9 ka). Major glacier recession and deglaciation in the Torres del Paine region occurred by 12.5 ka and thus early in the Younger Dryas. We provide direct evidence for extensive ice in Patagonia at the very start of the ACR that agrees with atmospheric and marine records from the Southern Ocean and Antarctica. Atmospheric conditions responsible for the early late glacial expansion at Torres del Paine resulted from a climate reorganization that prompted a northern migration of the south westerly wind belt to the latitude of Torres del Paine at the onset of the ACR chronozone

Arnold diffusion for a complete family of perturbations

In this work we illustrate the Arnold diffusion in a concrete example — the a priori unstable Hamiltonian system of 2 + 1/2 degrees of freedom H(p, q, I, f, s) = p2/2+ cos q - 1 + I2/2 + h(q, f, s; e) — proving that for any small periodic perturbation of the form h(q, f, s; e) = e cos q (a00 + a10 cosf + a01 cos s) (a10a01 ¿ 0) there is global instability for the action. For the proof we apply a geometrical mechanism based on the so-called scattering map. This work has the following structure: In the first stage, for a more restricted case (I* ~ p/2µ, µ = a10/a01), we use only one scattering map, with a special property: the existence of simple paths of diffusion called highways. Later, in the general case we combine a scattering map with the inner map (inner dynamics) to prove the more general result (the existence of instability for any µ). The bifurcations of the scattering map are also studied as a function of µ. Finally, we give an estimate for the time of diffusion, and we show that this time is primarily the time spent under the scattering map.Peer ReviewedPostprint (published version

Measurement of the Z/gamma* + b-jet cross section in pp collisions at 7 TeV

The production of b jets in association with a Z/gamma* boson is studied using proton-proton collisions delivered by the LHC at a centre-of-mass energy of 7 TeV and recorded by the CMS detector. The inclusive cross section for Z/gamma* + b-jet production is measured in a sample corresponding to an integrated luminosity of 2.2 inverse femtobarns. The Z/gamma* + b-jet cross section with Z/gamma* to ll (where ll = ee or mu mu) for events with the invariant mass 60 < M(ll) < 120 GeV, at least one b jet at the hadron level with pT > 25 GeV and abs(eta) < 2.1, and a separation between the leptons and the jets of Delta R > 0.5 is found to be 5.84 +/- 0.08 (stat.) +/- 0.72 (syst.) +(0.25)/-(0.55) (theory) pb. The kinematic properties of the events are also studied and found to be in agreement with the predictions made by the MadGraph event generator with the parton shower and the hadronisation performed by PYTHIA.Comment: Submitted to the Journal of High Energy Physic

Terrestrial biosphere models need better representation of vegetation phenology: results from the North American Carbon Program Site Synthesis

Phenology, by controlling the seasonal activity of vegetation on the land surface, plays a fundamental role in regulating photosynthesis and other ecosystem processes, as well as competitive interactions and feedbacks to the climate system. We conducted an analysis to evaluate the representation of phenology, and the associated seasonality of ecosystem-scale CO2 exchange, in 14 models participating in the North American Carbon Program Site Synthesis. Model predictions were evaluated using long-term measurements (emphasizing the period 2000-2006) from 10 forested sites within the AmeriFlux and Fluxnet-Canada networks. In deciduous forests, almost all models consistently predicted that the growing season started earlier, and ended later, than was actually observed; biases of 2 weeks or more were typical. For these sites, most models were also unable to explain more than a small fraction of the observed interannual variability in phenological transition dates. Finally, for deciduous forests, misrepresentation of the seasonal cycle resulted in over-prediction of gross ecosystem photosynthesis by +160 ± 145 g C m-2 y-1 during the spring transition period, and +75 ± 130 g C m-2 y-1 during the autumn transition period (13% and 8% annual productivity, respectively) compensating for the tendency of most models to under-predict the magnitude of peak summertime photosynthetic rates. Models did a better job of predicting the seasonality of CO2 exchange for evergreen forests. These results highlight the need for improved understanding of the environmental controls on vegetation phenology, and incorporation of this knowledge into better phenological models. Existing models are unlikely to predict future responses of phenology to climate change accurately, and therefore will misrepresent the seasonality and interannual variability of key biosphere-atmosphere feedbacks and interactions in coupled global climate models.Engineering and Applied SciencesOrganismic and Evolutionary Biolog

Search for supersymmetry in events with b-quark jets and missing transverse energy in pp collisions at 7 TeV

Results are presented from a search for physics beyond the standard model based on events with large missing transverse energy, at least three jets, and at least one, two, or three b-quark jets. The study is performed using a sample of proton-proton collision data collected at sqrt(s) = 7 TeV with the CMS detector at the LHC in 2011. The integrated luminosity of the sample is 4.98 inverse femtobarns. The observed number of events is found to be consistent with the standard model expectation, which is evaluated using control samples in the data. The results are used to constrain cross sections for the production of supersymmetric particles decaying to b-quark-enriched final states in the context of simplified model spectra.Comment: Submitted to Physical Review

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Search for new physics with same-sign isolated dilepton events with jets and missing transverse energy

A search for new physics is performed in events with two same-sign isolated leptons, hadronic jets, and missing transverse energy in the final state. The analysis is based on a data sample corresponding to an integrated luminosity of 4.98 inverse femtobarns produced in pp collisions at a center-of-mass energy of 7 TeV collected by the CMS experiment at the LHC. This constitutes a factor of 140 increase in integrated luminosity over previously published results. The observed yields agree with the standard model predictions and thus no evidence for new physics is found. The observations are used to set upper limits on possible new physics contributions and to constrain supersymmetric models. To facilitate the interpretation of the data in a broader range of new physics scenarios, information on the event selection, detector response, and efficiencies is provided.Comment: Published in Physical Review Letter