Optimum take-off angle in the long jump

In this study, we found that the optimum take-off angle for a long jumper may be predicted by combining the equation for the range of a projectile in free flight with the measured relations between take-off speed, take-off height and take-off angle for the athlete. The prediction method was evaluated using video measurements of three experienced male long jumpers who performed maximum-effort jumps over a wide range of take-off angles. To produce low take-off angles the athletes used a long and fast run-up, whereas higher take-off angles were produced using a progressively shorter and slower run-up. For all three athletes, the take-off speed decreased and the take-off height increased as the athlete jumped with a higher take-off angle. The calculated optimum take-off angles were in good agreement with the athletes' competition take-off angles

Gauge dependence and self-force from Galilean to Einsteinian free fall, compact stars falling into black holes, Hawking radiation and the Pisa tower at the general relativity centennial

(Short abstract). In Galilean physics, the universality of free fall implies an inertial frame, which in turns implies that the mass m of the falling body is omitted. Otherwise, an additional acceleration proportional to m/M would rise either for an observer at the centre of mass of the system, or for an observer at a fixed distance from the centre of mass of M. These elementary, but overlooked, considerations fully respect the equivalence principle and the identity of an inertial or a gravitational pull for an observer in the Einstein cabin. They value as fore-runners of the self-force and gauge dependency in general relativity. The approximate nature of Galilei's law of free fall is explored herein. When stepping into general relativity, we report how the geodesic free fall into a black hole was the subject of an intense debate again centred on coordinate choice. Later, we describe how the infalling mass and the emitted gravitational radiation affect the free fall motion of a body. The general relativistic self-force might be dealt with to perfectly fit into a geodesic conception of motion. Then, embracing quantum mechanics, real black holes are not classical static objects any longer. Free fall has to handle the Hawking radiation, and leads us to new perspectives on the varying mass of the evaporating black hole and on the varying energy of the falling mass. Along the paper, we also estimate our findings for ordinary masses being dropped from a Galilean or Einsteinian Pisa-like tower with respect to the current state of the art drawn from precise measurements in ground and space laboratories, and to the constraints posed by quantum measurements. The appendix describes how education physics and high impact factor journals discuss the free fall. Finally, case studies conducted on undergraduate students and teachers are reviewed

Constraints on porosity and mass loss in O-star winds from modeling of X-ray emission line profile shapes

We fit X-ray emission line profiles in high resolution XMM-Newton and Chandra grating spectra of the early O supergiant Zeta Pup with models that include the effects of porosity in the stellar wind. We explore the effects of porosity due to both spherical and flattened clumps. We find that porosity models with flattened clumps oriented parallel to the photosphere provide poor fits to observed line shapes. However, porosity models with isotropic clumps can provide acceptable fits to observed line shapes, but only if the porosity effect is moderate. We quantify the degeneracy between porosity effects from isotropic clumps and the mass-loss rate inferred from the X-ray line shapes, and we show that only modest increases in the mass-loss rate (<~ 40%) are allowed if moderate porosity effects (h_infinity <~ R_*) are assumed to be important. Large porosity lengths, and thus strong porosity effects, are ruled out regardless of assumptions about clump shape. Thus, X-ray mass-loss rate estimates are relatively insensitive to both optically thin and optically thick clumping. This supports the use of X-ray spectroscopy as a mass-loss rate calibration for bright, nearby O stars.Comment: 20 pages, 20 figures. Accepted by Ap

On the origin of exponential growth in induced earthquakes in Groningen

The Groningen gas field shows exponential growth in earthquakes event counts around a magnitude M1 with a doubling time of 6-9 years since 2001. This behavior is identified with dimensionless curvature in land subsidence, which has been evolving at a constant rate over the last few decades {essentially uncorrelated to gas production.} We demonstrate our mechanism by a tabletop crack formation experiment. The observed skewed distribution of event magnitudes is matched by that of maxima of event clusters with a normal distribution. It predicts about one event $<$\,M5 per day in 2025, pointing to increasing stress to human living conditions.Comment: 12 pages, 7 figures, to appear in Earthquakes and Structure

Evidence for the importance of resonance scattering in X-ray emission line profiles of the O star ζ\zeta Puppis

We fit the Doppler profiles of the He-like triplet complexes of \ion{O}{7} and \ion{N}{6} in the X-ray spectrum of the O star $\zeta$ Puppis, using XMM-Newton RGS data collected over $\sim 400$ ks of exposure. We find that they cannot be well fit if the resonance and intercombination lines are constrained to have the same profile shape. However, a significantly better fit is achieved with a model incorporating the effects of resonance scattering, which causes the resonance line to become more symmetric than the intercombination line for a given characteristic continuum optical depth $\tau_*$. We discuss the plausibility of this hypothesis, as well as its significance for our understanding of Doppler profiles of X-ray emission lines in O stars.Comment: 29 pages, 8 figures, revised version accepted by Ap

On the three-dimensional temporal spectrum of stretched vortices

The three-dimensional stability problem of a stretched stationary vortex is addressed in this letter. More specifically, we prove that the discrete part of the temporal spectrum is only associated with two-dimensional perturbations.Comment: 4 pages, RevTeX, submitted to PR

Nonlinear model of short-scale electrodynamics in the auroral ionosphere

International audienceThe optical detection of auroral subarcs a few tens of m wide as well as the direct observation of shears several m/s per m over km to sub km scales by rocket instrumentation both indicate that violent and highly localized electrodynamics can occur at times in the auroral ionosphere over scales 100 m or less in width. These observations as well as the detection of unstable ion-acoustic waves observed by incoherent radars along the geomagnetic field lines has motivated us to develop a detailed time-dependent two-dimensional model of short-scale auroral electrodynamics that uses current continuity, Ohm's law, and 8-moment transport equations for the ions and electrons in the presence of large ambient electric fields to describe wide auroral arcs with sharp edges in response to sharp cut-offs in precipitation (even though it may be possible to describe thin arcs and ultra-thin arcs with our model, we have left such a study for future work). We present the essential elements of this new model and illustrate the model's usefulness with a sample run for which the ambient electric field is 100 mV/m away from the arc and for which electron precipitation cuts off over a region 100 m wide. The sample run demonstrates that parallel current densities of the order of several hundred µA m-2 can be triggered in these circumstances, together with shears several m/s per m in magnitude and parallel electric fields of the order of 0.1 mV/m around 130 km altitude. It also illustrates that the local ionospheric properties like densities, temperature and composition can strongly be affected by the violent localized electrodynamics and vice-versa.Key words: Ionosphere (auroral ionosphere, electric fields and currents, ionosphere-magnetosphere interactions)</p

Velocity shear and current driven instability in a collisional F-region

We have studied how the presence of collisions affects the behavior of instabilities triggered by a combination of shears and parallel currents in the ionosphere under a variety of ion to electron temperature ratios. To this goal we have numerically solved a kinetic dispersion relation, using a relaxation model to describe the effects of ion and electron collisions. We have compared our solutions to expressions derived in a fluid limit which applied only to large electron to ion temperature ratios. We have limited our study to threshold conditions for the current density and the shears. We have studied how the threshold varies as a function of the wave-vector angle direction and as a function of frequency. As expected, we have found that for low frequencies and/or elevated ion to electron temperature ratios, the kinetic dispersion relation has to be used to evaluate the threshold conditions. We have also found that ion velocity shears can significantly lower the field-aligned threshold current needed to trigger the instability, especially for wave-vectors close to the perpendicular to the magnetic field. However the current density and shear requirements remain significantly higher than if collisions are neglected. Therefore, for ionospheric F-region applications, the effect of collisions should be included in the calculation of instabilities associated with horizontal shears in the vertical flow. Furthermore, in many situations of interest the kinetic solutions should be used instead of the fluid limit, in spite of the fact that the latter can be shown to produce qualitatively valid solutions