Beyond velocity and acceleration: Jerk, snap and higher derivatives

© 2016 IOP Publishing Ltd. The higher derivatives of motion are rarely discussed in the teaching of classical mechanics of rigid bodies; nevertheless, we experience the effect not only of acceleration, but also of jerk and snap. In this paper we will discuss the third and higher order derivatives of displacement with respect to time, using the trampolines and theme park roller coasters to illustrate this concept. We will also discuss the effects on the human body of different types of acceleration, jerk, snap and higher derivatives, and how they can be used in physics education to further enhance the learning and thus the understanding of classical mechanics concepts

Solar wind and seasonal influence on ionospheric currents from Swarm and CHAMP measurements

We present a new climatological model of the ionospheric current system, determined from magnetic measurements taken by the Challenging Minisatellite Payload (CHAMP) and Swarm satellites. The model describes the horizontal currents in the ionosphere, below the satellites, and the field-aligned (Birkeland) currents that connect the ionosphere with the magnetosphere. The model provides ionospheric current values at any location as continuous functions of solar wind speed, interplanetary magnetic field, dipole tilt angle, and the F10.7 index of solar flux. Geometric distortions due to variations in the Earth’s main magnetic field are taken into account, thus allowing for precise comparisons between the two hemispheres. The model is the first of its kind to describe the full 3-D electric currents and not only the field-aligned or the equivalent horizontal current. We use this capability to demonstrate a key difference between seasons: During winter, the total horizontal current is almost entirely confined to the auroral oval, for all interplanetary magnetic field orientations, where it connects upward and downward Birkeland currents. During more sunlit conditions, the horizontal current extends beyond the auroral oval and is a sum of currents connecting Birkeland currents and currents that circulate in the ionosphere. The westward electrojet is the only large-scale current structure that is persistent across seasons. Comparison with average convection maps suggests that it is comprised largely of Hall currents, which connect to Birkeland currents in the winter but not in summer.publishedVersio

How the IMF By\mathit{B}_{y} Induces a Local By\mathit{B}_{y} Component During Northward IMF Bz\mathit{B}_{z} and Characteristic Timescales

We use the Lyon-Fedder-Mobarry global magnetohydrodynamics model to study the effects of the interplanetary magnetic field (IMF) $\mathit{B}_{y}$ component on the coupling between the solar wind and magnetosphere-ionosphere system when IMF $\mathit{B}_{z}$ $>$0. We describe the evolution of how a magnetospheric $\mathit{B}_{y}$ component is induced on closed field lines during these conditions. Starting from dayside lobe reconnection, the magnetic tension on newly reconnected field lines redistribute the open flux asymmetrically between the two hemispheres. This results in asymmetric magnetic energy density in the lobes. Shear flows are induced to restore equilibrium, and these flows are what effectively induces a local $\mathit{B}_{y}$ component. We show the radial dependence of the induced $\mathit{B}_{y}$ and compare the results to the induced $\mathit{B}_{y}$ during southward IMF conditions. We also show the response and reconfiguration time of the inner magnetosphere to IMF $\mathit{B}_{y}$ reversals during northward IMF $\mathit{B}_{z}$. A superposed epoch analysis of magnetic field measurements from seven Geostationary Operational Environmental Satellite spacecraft at different local times both for negative-to-positive and positive-to-negative IMF $\mathit{B}_{y}$ reversals is presented. We find that the induced $\mathit{B}_{y}$ responds within 16 min of the arrival of IMF $\mathit{B}_{y}$ at the bow shock, and it completely reconfigures within 47 min

Dynamic effects of restoring footpoint symmetry on closed magnetic field lines

Here we present an event where simultaneous global imaging of the aurora from both hemispheres reveals a large longitudinal shift of the nightside aurora of about 3 h, being the largest relative shift reported on from conjugate auroral imaging. This is interpreted as evidence of closed field lines having very asymmetric footpoints associated with the persistent positive y component of the interplanetary magnetic field before and during the event. At the same time, the Super Dual Auroral Radar Network observes the ionospheric nightside convection throat region in both hemispheres. The radar data indicate faster convection toward the dayside in the dusk cell in the Southern Hemisphere compared to its conjugate region. We interpret this as a signature of a process acting to restore symmetry of the displaced closed magnetic field lines resulting in flux tubes moving faster along the banana cell than the conjugate orange cell. The event is analyzed with emphasis on Birkeland currents (BC) associated with this restoring process, as recently described by Tenfjord et al. (2015). Using data from the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) during the same conditions as the presented event, the large-scale BC pattern associated with the event is presented. It shows the expected influence of the process of restoring symmetry on BCs. We therefore suggest that these observations should be recognized as being a result of the dynamic effects of restoring footpoint symmetry on closed field lines in the nightside

Results from the intercalibration of optical low light calibration sources 2011

Following the 38th Annual European Meeting on Atmospheric Studies by Optical Methods in Siuntio in Finland, an intercalibration workshop for optical low light calibration sources was held in Sodankylä, Finland. The main purpose of this workshop was to provide a comparable scale for absolute measurements of aurora and airglow. All sources brought to the intercalibration workshop were compared to the Fritz Peak reference source using the Lindau Calibration Photometer built by Wilhelm Barke and Hans Lauche in 1984. The results were compared to several earlier intercalibration workshops. It was found that most sources were fairly stable over time, with errors in the range of 5–25%. To further validate the results, two sources were also intercalibrated at UNIS, Longyearbyen, Svalbard. Preliminary analysis indicates agreement with the intercalibration in Sodankylä within about 15–25%

The Wind Energy Potential of Iceland

AbstractDownscaling simulations performed with the Weather Research and Forecasting (WRF) model were used to determine the large-scale wind energy potential of Iceland. Local wind speed distributions are represented by Weibull statistics. The shape parameter across Iceland varies between 1.2 and 3.6, with the lowest values indicative of near-exponential distributions at sheltered locations, and the highest values indicative of normal distributions at exposed locations in winter. Compared with summer, average power density in winter is increased throughout Iceland by a factor of 2.0–5.5. In any season, there are also considerable spatial differences in average wind power density. Relative to the average value within 10 km of the coast, power density across Iceland varies between 50 and 250%, excluding glaciers, or between 300 and 1500 W m−2 at 50 m above ground level in winter. At intermediate elevations of 500–1000 m above mean sea level, power density is independent of the distance to the coast. In addition to seasonal and spatial variability, differences in average wind speed and power density also exist for different wind directions. Along the coast in winter, power density of onshore winds is higher by 100–700 W m−2 than that of offshore winds. Based on these results, 14 test sites were selected for more detailed analyses using the Wind Atlas Analysis and Application Program (WAsP)