The method of Glowinski and Pironneaufor the unsteady stokes problem

AbstractThe unsteady Stokes problem, i.e., the Stokes problem with a constant multiple of the velocity included in the velocity-pressure equation, is often central to methods used to solve the nonstationary Navier-Stokes equations and the equations governing viscoelastic flows. The Glowinski-Pironneau finite-element method for the Stokes problem decomposes the problem into a series of Poisson's equations, providing a potentially efficient approach for large problems in two or three dimensions. The goal of this paper is to present a complete development and analysis of the Glowinski-Pironneau method for the unsteady Stokes problem, along with numerical results which confirm the analytical estimates

On the Notion of Conceptual Learning in Undergraduate Physics

Methods for improving the quality of student learning continues to be central to research and practice in teaching and learning in tertiary education. Extensive studies have shown that student learning approaches influence their learning conception and outcomes. In particular, it has been shown that learning as simple reproduction of knowledge leads to surface learning approaches, while learning as transformation of knowledge leads to deep learning approaches [1,2]. An important factor in the way students learn appears to be the way knowledge is structured when presented. In this paper we illustrate how concept maps of the hierarchical organisation of cognitive structure may benefit the preparation, presentation and assessment of course material. The results of a comparison between the concepts presented with those actually assessed in a one semester first year university, introductory physics course show a large imbalance. Concept maps may be effectively used to improve the planning and structure of all components of course presentation in order to more realistically match assessment tasks. Concept maps also help develop relationships and perspectives related to the physics ideas by the students. We illustrate how the maps were used to organize the discussed concepts, and how the new concepts could be incorporated into the map so that the new knowledge becomes an integral part of the existing structure

Field-Aligned and Ionospheric Currents by AMPERE and SuperMAG During HSS/SIR-Driven Storms

This study considers 28 geomagnetic storms with Dst $\leq-50$ nT driven by high-speed streams (HSSs) and associated stream interaction regions (SIRs) during 2010-2017. Their impact on ionospheric horizontal and field-aligned currents (FACs) have been investigated using superposed epoch analysis of SuperMAG and AMPERE data, respectively. The zero epoch ($t_0$) was set to the onset of the storm main phase. Storms begin in the SIR with enhanced solar wind density and compressed southward oriented magnetic field. The integrated FAC and equivalent currents maximise 40 and 58 min after $t_0$, respectively, followed by a small peak in the middle of the main phase ($t_0$+4h), and a slightly larger peak just before the Dst minimum ($t_0$+5.3h). The currents are strongly driven by the solar wind, and the correlation between the Akasofu $\varepsilon$ and integrated FAC is $0.90$. The number of substorm onsets maximises near $t_0$. The storms were also separated into two groups based on the solar wind dynamic pressure p_dyn in the vicinity of the SIR. High p_dyn storms reach solar wind velocity maxima earlier and have shorter lead times from the HSS arrival to storm onset compared with low p_dyn events. The high p_dyn events also have sudden storm commencements, stronger solar wind driving and ionospheric response at $t_0$, and are primarily responsible for the first peak in the currents after $t_0$. After $t_0+2$ days, the currents and number of substorm onsets become higher for low compared with high p_dyn events, which may be related to higher solar wind speed.publishedVersio

Effect of ICME-Driven Storms on Field-Aligned and Ionospheric Currents From AMPERE and SuperMAG

Funding Information: This work was supported by the Academy of Finland project 314664 and 314670. We thank the AMPERE team and the AMPERE Science Center for providing the Iridium derived data products ( https://ampere.jhuapl.edu/ ). For the ground magnetometer data and substorm onset list, we gratefully thank the SuperMAG collaboration and all organizations involved ( https://supermag.jhuapl.edu/info/ ). For the geomagnetic indices, solar wind and interplanetary magnetic field data, we gratefully thank NASA/GSFC's Space Physics Data Facility's OMNIWeb ( https://omniweb.gsfc.nasa.gov/ ). Funding Information: This work was supported by the Academy of Finland project 314664 and 314670. We thank the AMPERE team and the AMPERE Science Center for providing the Iridium derived data products (https://ampere.jhuapl.edu/). For the ground magnetometer data and substorm onset list, we gratefully thank the SuperMAG collaboration and all organizations involved (https://supermag.jhuapl.edu/info/). For the geomagnetic indices, solar wind and interplanetary magnetic field data, we gratefully thank NASA/GSFC's Space Physics Data Facility's OMNIWeb (https://omniweb.gsfc.nasa.gov/). Publisher Copyright: © 2022. The Authors.Peer reviewe

Natural and sail-displaced doubly-symmetric Lagrange point orbits for polar coverage

This paper proposes the use of doubly-symmetric, eight-shaped orbits in the circular restricted three-body problem for continuous coverage of the high-latitude regions of the Earth. These orbits, for a range of amplitudes, spend a large fraction of their period above either pole of the Earth. It is shown that they complement Sun-synchronous polar and highly eccentric Molniya orbits, and present a possible alternative to low thrust pole-sitter orbits. Both natural and solar-sail displaced orbits are considered. Continuation methods are described and used to generate families of these orbits. Starting from ballistic orbits, other families are created either by increasing the sail lightness number, varying the period or changing the sail attitude. Some representative orbits are then chosen to demonstrate the visibility of high-latitude regions throughout the year. A stability analysis is also performed, revealing that the orbits are unstable: it is found that for particular orbits, a solar sail can reduce their instability. A preliminary design of a linear quadratic regulator is presented as a solution to stabilize the system by using the solar sail only. Finally, invariant manifolds are exploited to identify orbits that present the opportunity of a ballistic transfer directly from low Earth orbit

Results of the BiPo-1 prototype for radiopurity measurements for the SuperNEMO double beta decay source foils

The development of BiPo detectors is dedicated to the measurement of extremely high radiopurity in $^{208}$Tl and $^{214}$Bi for the SuperNEMO double beta decay source foils. A modular prototype, called BiPo-1, with 0.8 $m^2$ of sensitive surface area, has been running in the Modane Underground Laboratory since February, 2008. The goal of BiPo-1 is to measure the different components of the background and in particular the surface radiopurity of the plastic scintillators that make up the detector. The first phase of data collection has been dedicated to the measurement of the radiopurity in $^{208}$Tl. After more than one year of background measurement, a surface activity of the scintillators of $\mathcal{A}$($^{208}$Tl) $=$ 1.5 $\mu$Bq/m$^2$ is reported here. Given this level of background, a larger BiPo detector having 12 m$^2$ of active surface area, is able to qualify the radiopurity of the SuperNEMO selenium double beta decay foils with the required sensitivity of $\mathcal{A}$($^{208}$Tl) $<$ 2 $\mu$Bq/kg (90% C.L.) with a six month measurement.Comment: 24 pages, submitted to N.I.M.

Spectral modeling of scintillator for the NEMO-3 and SuperNEMO detectors

We have constructed a GEANT4-based detailed software model of photon transport in plastic scintillator blocks and have used it to study the NEMO-3 and SuperNEMO calorimeters employed in experiments designed to search for neutrinoless double beta decay. We compare our simulations to measurements using conversion electrons from a calibration source of $\rm ^{207}Bi$ and show that the agreement is improved if wavelength-dependent properties of the calorimeter are taken into account. In this article, we briefly describe our modeling approach and results of our studies.Comment: 16 pages, 10 figure

D* Production in Deep Inelastic Scattering at HERA

This paper presents measurements of D^{*\pm} production in deep inelastic scattering from collisions between 27.5 GeV positrons and 820 GeV protons. The data have been taken with the ZEUS detector at HERA. The decay channel $D^{*+}\to (D^0 \to K^- \pi^+) \pi^+$ (+ c.c.) has been used in the study. The $e^+p$ cross section for inclusive D^{*\pm} production with $5<Q^2<100 GeV^2$ and $y<0.7$ is 5.3 \pms 1.0 \pms 0.8 nb in the kinematic region {$1.3<p_T(D^{*\pm})<9.0$ GeV and $| \eta(D^{*\pm}) |<1.5$}. Differential cross sections as functions of p_T(D^{*\pm}), $\eta(D^{*\pm}), W$ and $Q^2$ are compared with next-to-leading order QCD calculations based on the photon-gluon fusion production mechanism. After an extrapolation of the cross section to the full kinematic region in p_T(D^{*\pm}) and $\eta$(D^{*\pm}), the charm contribution $F_2^{c\bar{c}}(x,Q^2)$ to the proton structure function is determined for Bjorken $x$ between 2 $\cdot$ 10$^{-4}$ and 5 $\cdot$ 10$^{-3}$.Comment: 17 pages including 4 figure