What the Integral Does: Physics Students\u27 Efforts at Making Sense of Integration

Students use a variety of resources to make sense of integration, and interpreting the definite integral as a sum of infinitesimal products (rooted in the concept of a Riemann sum) is particularly useful in many physical contexts. This study of beginning and upper-level undergraduate physics students examines some obstacles students encounter when trying to make sense of integration, as well as some discomforts and skepticism some students maintain even after constructing useful conceptions of the integral. In particular, many students attempt to explain what integration does by trying to interpret the algebraic manipulations and computations involved in finding antiderivatives. This tendency, perhaps arising from their past experience of making sense of algebraic expressions and equations, suggests a reluctance to use their understanding of what a Riemann sum does to interpret what an integral does.

Measurement of event-shape observables in Z→ℓ+ℓ− events in pp collisions at √ s=7 TeV with the ATLAS detector at the LHC

Event-shape observables measured using charged particles in inclusive $Z$-boson events are presented, using the electron and muon decay modes of the $Z$ bosons. The measurements are based on an integrated luminosity of $1.1 {\rm fb}^{-1}$ of proton--proton collisions recorded by the ATLAS detector at the LHC at a centre-of-mass energy $\sqrt{s}=7$ TeV. Charged-particle distributions, excluding the lepton--antilepton pair from the $Z$-boson decay, are measured in different ranges of transverse momentum of the $Z$ boson. Distributions include multiplicity, scalar sum of transverse momenta, beam thrust, transverse thrust, spherocity, and $\mathcal{F}$-parameter, which are in particular sensitive to properties of the underlying event at small values of the $Z$-boson transverse momentum. The Sherpa event generator shows larger deviations from the measured observables than Pythia8 and Herwig7. Typically, all three Monte Carlo generators provide predictions that are in better agreement with the data at high $Z$-boson transverse momenta than at low $Z$-boson transverse momenta and for the observables that are less sensitive to the number of charged particles in the event.Comment: 36 pages plus author list + cover page (54 pages total), 14 figures, 4 tables, submitted to EPJC, All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2014-0

The development of a scale of the Guttman Type for the assessment of mobility disability in multiple sclerosis

Objective: The aim of the study was to develop a valid and reliable unidimensional scale of the Guttman type for the assessment of mobility disability in multiple sclerosis (MS). Subjects: Sixty-eight subjects with a definite diagnosis of MS participated.They were attending as outpatients at a MS unit at a District General Hospital. Thirty had the primary progressive pattern of disease, and 38 had the relapsing-remitting pattern. Methods: Formal assessments used for neurological disability were inspected, and 14 test items of gross motor function were extracted and ordered according to two criteria. These were that actions progressed from lying, to sitting, to standing and walking tasks, and that they progressed from broader to narrower bases of support. All subjects carried out all test items which were scored as ‘pass’ or ‘fail’. Analysis: Data were tested for internal consistency, reliability, inter item correlation, reproducibility and scalability. On the basis of the results, the items were re-ordered in rank, and reduced to eleven tests. The eleven item scale was re-analysed. Results: Results showed that the scale had an internal consistency of 0.88 (alpha coefficient) and a coefficient of reproducibility (CR) of 0.95 and above for both MS subject groups. The coefficient of scalability (CS) for items was 0.78 for primary progressive subjects and 0.74 for the relapsing-remitting group. Reliability ranged from good (kappa = 0.49) for one item, to perfect for six items. Conclusion: The scale was demonstrated to be a hierarchical scale of the Guttman type exhibiting homogeneous unidimensionality and good reliability. The high CR indicated that scores may be summed, and the very acceptable levels of CS indicated that the cumulative scores are meaningful within the defined concept of hierarchy used in this study

Search for Diphoton Events with Large Missing Transverse Energy in 7 TeV Proton-Proton Collisions with the ATLAS Detector

A search for diphoton events with large missing transverse energy is presented. The data were collected with the ATLAS detector in proton-proton collisions at √s=7  [square root of s=7] TeV at the CERN Large Hadron Collider and correspond to an integrated luminosity of 3.1  pb-1 [pb superscript -1]. No excess of such events is observed above the standard model background prediction. In the context of a specific model with one universal extra dimension with compactification radius R and gravity-induced decays, values of 1/R<729  GeV are excluded at 95% C. L., providing the most sensitive limit on this model to date.United States. Dept. of EnergyNational Science Foundation (U.S.

Measurement of the isolated diphoton cross-section in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The ATLAS experiment has measured the production cross-section of events with two isolated photons in the final state, in proton-proton collisions at sqrt(s) = 7 TeV. The full data set acquired in 2010 is used, corresponding to an integrated luminosity of 37 pb^-1. The background, consisting of hadronic jets and isolated electrons, is estimated with fully data-driven techniques and subtracted. The differential cross-sections, as functions of the di-photon mass, total transverse momentum and azimuthal separation, are presented and compared to the predictions of next-to-leading-order QCD.Comment: 15 pages plus author list (27 pages total), 9 figures, 2 tables, final version to appear in Physical Review

Search for a heavy Standard Model Higgs boson in the channel H→ZZ→l+l−qqˉH\rightarrow ZZ\rightarrow l^{+}l^{-} q\bar{q} using the ATLAS detector

A search for a heavy Standard Model Higgs boson decaying via H->ZZ->llqq, where l=e,mu, is presented. The search is performed using a data set of pp collisions at sqrt(s)=7 TeV, corresponding to an integrated luminosity of 1.04 fb^-1 collected in 2011 by the ATLAS detector at the CERN LHC collider. No significant excess of events above the estimated background is found. Upper limits at 95% confidence level on the production cross section (relative to that expected from the Standard Model) of a Higgs boson with a mass in the range between 200 and 600 GeV are derived. Within this mass range, there is at present insufficient sensitivity to exclude a Standard Model Higgs boson. For a Higgs boson with a mass of 360 GeV, where the sensitivity is maximal, the observed and expected cross section upper limits are factors of 1.7 and 2.7, respectively, larger than the Standard Model prediction.Comment: 11 pages plus author list (26 pages total), 4 figures, 1 table, final version to appear in Physics Letters

Charged-particle multiplicities in <i>pp</i> interactions at &#8730;s = 900 GeV measured with the ATLAS detector at the LHC

The first measurements from proton–proton collisions recorded with the ATLAS detector at the LHC are presented. Data were collected in December 2009 using a minimum-bias trigger during collisions at a centre-of-mass energy of 900 GeV. The charged-particle multiplicity, its dependence on transverse momentum and pseudorapidity, and the relationship between mean transverse momentum and charged-particle multiplicity are measured for events with at least one charged particle in the kinematic range |η|&#60;2.5 and pT&#62;500 MeV. The measurements are compared to Monte Carlo models of proton–proton collisions and to results from other experiments at the same centre-of-mass energy. The charged-particle multiplicity per event and unit of pseudorapidity at η=0 is measured to be1.333&#177;0.003(stat.)&#177;0.040(syst.), which is 5–15% higher than the Monte Carlo models predict

The ATLAS experiment at the CERN Large Hadron Collider

The ATLAS detector as installed in its experimental cavern at point 1 at CERN is described in this paper. A brief overview of the expected performance of the detector when the Large Hadron Collider begins operation is also presented

Measurement of the isolated diphoton cross section in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

15 pages plus author list (27 pages total), 9 figures, 2 tables, submitted to Phys. Rev. DThe ATLAS experiment has measured the production cross-section of events with two isolated photons in the final state, in proton-proton collisions at sqrt(s) = 7 TeV. The full data set acquired in 2010 is used, corresponding to an integrated luminosity of 37 pb-1. The background, consisting of hadronic jets and isolated electrons, is estimated with fully data-driven techniques and subtracted. The differential cross-sections, as functions of the di-photon mass, total transverse momentum and azimuthal separation, are presented and compared to the predictions of next-to-leading-order QCD