Lagrangian submanifolds and dynamics on Lie affgebroids

We introduce the notion of a symplectic Lie affgebroid and their Lagrangian submanifolds in order to describe the Lagrangian (Hamiltonian) dynamics on a Lie affgebroid in terms of this type of structures. Several examples are discussed.Comment: 50 pages. Several sections update

Reduction of Symplectic Lie Algebroids by a Lie Subalgebroid and a Symmetry Lie Group

We describe the reduction procedure for a symplectic Lie algebroid by a Lie subalgebroid and a symmetry Lie group. Moreover, given an invariant Hamiltonian function we obtain the corresponding reduced Hamiltonian dynamics. Several examples illustrate the generality of the theory

Scale of time-averaging in archaeological shell middens from the Canary Islands

Characterizing the degree of disturbance in archaeological deposits is critically important for archaeologists assessing foraging strategies, environmental conditions, or behavior patterns of ancient human groups. Qualitative techniques (e.g. micromorphology analysis) have previously been applied to assess the degree of disturbance (age-mixing) in archaeological sites; however, quantitative dating of material in the sites provides a more robust assessment of potential age-mixing. Unfortunately, because of budget constraints, archaeologists are frequently forced to rely on few quantitative age dates for an assemblage, thus obfuscating the signal of age-mixing of the deposit. The development of an affordable and rapid carbonate-target accelerator mass spectrometry (AMS) radiocarbon (14C) dating method provides a cost-effective way to retrieve more quantitative dates from carbonate material in archaeological assemblages to assess the degree of age-mixing in the deposit. This study tests this new technique and dates numerous harvested marine limpet shells from archaeological sites in the Canary Islands to determine whether there is multidecadal to multicentennial age-mixing. A total of 58 shells retrieved from six sites and three islands yielded uncalibrated radiocarbon ages ranging from 2265 ± 40 to 765 ± 35 BP, coinciding with the time of prehistoric human occupation in these islands. While most shells from the same stratum showed statistically equivalent ages, in some cases we detected age ranges that exceeded the imprecisions from analytical errors. This investigation is one of the first to quantitatively illustrate that shells retrieved from depth intervals without evident stratigraphic disturbance do not always contain contemporaneous remains and, therefore, dating each specimen is valuable for developing further paleoclimatic and paleoanthropological inferences. This study presents the first report of carbonate-target 14C ages from archaeological shell middens, and suggests that this novel radiocarbon methodology can be applied to these sites, thus allowing the generation of a more comprehensive chronology

Discrete Variational Optimal Control

This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher-dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical and a practical examples, e.g. the control of an underwater vehicle, will illustrate the application of the proposed approach.Comment: 30 pages, 6 figure

Discrete Nonholonomic Lagrangian Systems on Lie Groupoids

This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot).Comment: 45 page

Shellfish Exploitation in the Western Canary Islands Over the Last Two Millennia

The residents of the Canary Archipelago consumed limpets since the arrival of humans ∼2500 yrs. ago, and these harvested gastropods were deposited in large coastal shell middens. This work preliminarily explores shell margin oxygen isotope composition (δ18O) and body size of the black limpet (Patella candei d’Orbigny, 1840) from archaeological sites in the Canary Islands to assess possible seasonal variability and intensity of shellfish collection throughout the late Holocene. The shell margin δ18O values of 100 shells (radiocarbon dated between ∼500 and ∼1800 cal. yr BP) were analysed to estimate sea surface temperature (SST) at time of death. Paleotemperature estimates suggest shellfish harvesting was not year-round, and was avoided in the cooler months (when SST < 20°C). This pattern differs from most higher latitude Mesolithic and Neolithic human groups, which gathered shellfish year-round, targeting winter more heavily. Preliminary body-size measurements suggest shell sizes have experienced a decline from aboriginal times to the present, which possibly resulted from increasing anthropogenic pressures. During aboriginal inhabitation, maximum adult shell size remained stable, suggesting that present-day harvesting practices are more intense than harvesting from aboriginal human groups. This intensive collection has likely diminished the average adult size of limpet populations in the islands by ∼27%

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters

Measurement of the Lambda(b) cross section and the anti-Lambda(b) to Lambda(b) ratio with Lambda(b) to J/Psi Lambda decays in pp collisions at sqrt(s) = 7 TeV

The Lambda(b) differential production cross section and the cross section ratio anti-Lambda(b)/Lambda(b) are measured as functions of transverse momentum pt(Lambda(b)) and rapidity abs(y(Lambda(b))) in pp collisions at sqrt(s) = 7 TeV using data collected by the CMS experiment at the LHC. The measurements are based on Lambda(b) decays reconstructed in the exclusive final state J/Psi Lambda, with the subsequent decays J/Psi to an opposite-sign muon pair and Lambda to proton pion, using a data sample corresponding to an integrated luminosity of 1.9 inverse femtobarns. The product of the cross section times the branching ratio for Lambda(b) to J/Psi Lambda versus pt(Lambda(b)) falls faster than that of b mesons. The measured value of the cross section times the branching ratio for pt(Lambda(b)) > 10 GeV and abs(y(Lambda(b))) < 2.0 is 1.06 +/- 0.06 +/- 0.12 nb, and the integrated cross section ratio for anti-Lambda(b)/Lambda(b) is 1.02 +/- 0.07 +/- 0.09, where the uncertainties are statistical and systematic, respectively.Comment: Submitted to Physics Letters

Search for new physics in events with opposite-sign leptons, jets, and missing transverse energy in pp collisions at sqrt(s) = 7 TeV

A search is presented for physics beyond the standard model (BSM) in final states with a pair of opposite-sign isolated leptons accompanied by jets and missing transverse energy. The search uses LHC data recorded at a center-of-mass energy sqrt(s) = 7 TeV with the CMS detector, corresponding to an integrated luminosity of approximately 5 inverse femtobarns. Two complementary search strategies are employed. The first probes models with a specific dilepton production mechanism that leads to a characteristic kinematic edge in the dilepton mass distribution. The second strategy probes models of dilepton production with heavy, colored objects that decay to final states including invisible particles, leading to very large hadronic activity and missing transverse energy. No evidence for an event yield in excess of the standard model expectations is found. Upper limits on the BSM contributions to the signal regions are deduced from the results, which are used to exclude a region of the parameter space of the constrained minimal supersymmetric extension of the standard model. Additional information related to detector efficiencies and response is provided to allow testing specific models of BSM physics not considered in this paper.Comment: Replaced with published version. Added journal reference and DO