The mechanical waves conceptual survey: An analysis of university students' performance, and recommendations for instruction

Indexación: Web of Science; Scopus.The Mechanical Waves Conceptual Survey (MWCS), presented in 2009, is the most important test to date that has been designed to evaluate university students' understanding of four main topics: propagation, superposition, reflection, and standing waves. In a literature review, we detected a significant need for a study that uses this test as an assessment tool and presents a complete analysis of students' difficulties on the test. This article addresses this need. We administered the MWCS at a private university in Mexico to 541 students. In this article, we present a complete description of these students' performance on the test, a description of their main difficulties, an elaboration of these main difficulties in terms of students' inappropriate conceptions, and recommendations for instruction based on the results obtained by the test. Our analyses may be used by instructors and researchers who intend to use the MWCS or create new instructional material.http://www.iserjournals.com/journals/eurasia/articles/10.12973/eurasia.2017.00651

Test of Understanding Graphs in Calculus: Test of Students’ Interpretation of Calculus Graphs

Indexación: Scopus.Studies show that students, within the context of mathematics and science, have difficulties understanding the concepts of the derivative as the slope and the concept of the antiderivative as the area under the curve. In this article, we present the Test of Understanding Graphs in Calculus (TUG-C), an assessment tool that will help to evaluate students' understanding of these two concepts by a graphical representation. Data from 144 students of introductory courses of physics and mathematics at a university was collected and analyzed. To evaluate the reliability and discriminatory power of this test, we used statistical techniques for individual items and the test as a whole, and proved that the test's results are satisfactory within the standard requirements. We present the design process in this paper and the test in the appendix. We discuss the findings of our research, students' understanding of the relations between these two concepts, using this new multiple-choice test. Finally, we outline specific recommendations. The analysis and recommendations can be used by mathematics or science education researchers, and by teachers that teach these concepts. © Authors.http://www.ejmste.com/Test-of-Understanding-Graphs-in-Calculus-Test-of-Students-Interpretation-of-Calculus,78085,0,2.htm

Deciphering the properties of the central engine in GRB collapsars

The central engine in long gamma-ray bursts (GRBs) is thought to be a compact object produced by the core collapse of massive stars, but its exact nature (black hole or millisecond magnetar) is still debatable. Although the central engine of GRB collapsars is hidden to direct observation, its properties may be imprinted on the accompanying electromagnetic signals. We aim to decipher the generic properties of central engines that are consistent with prompt observations of long GRBs detected by the Burst Alert Telescope (BAT) on board the Neil Gehrels Swift Observatory. Adopting a generic model for the central engine, in which the engine power and activity time-scale are independent of each other, we perform Monte Carlo simulations of long GRBs produced by jets that successfully breakout from the star. Our simulations consider the dependence of the jet breakout time-scale on the engine luminosity and the effects of the detector’s flux threshold. The two-dimensional (2D) distribution of simulated detectable bursts in the gamma-ray luminosity versus gamma-ray duration plane is consistent with the observed one for a range of parameter values describing the central engine. The intrinsic 2D distribution of simulated collapsar GRBs peaks at lower gamma-ray luminosities and longer durations than the observed one, a prediction that can be tested in the future with more sensitive detectors. Black hole accretors, whose power and activity time are set by the large-scale magnetic flux through the progenitor star and stellar structure, respectively, are compatible with the properties of the central engine inferred by our model

Inverse Compton cooling in Klein-Nishina regime and GRB prompt spectrum

Synchrotron radiation mechanism, when electrons are accelerated in a relativistic shock, is known to have serious problems to explain the observed gamma-ray spectrum below the peak for most Gamma-Ray Bursts (GRBs); the synchrotron spectrum below the peak is much softer than observed spectra. Recently, the possibility that electrons responsible for the radiation cool via Inverse Compton, but in the Klein-Nishina regime, has been proposed as a solution to this problem. We provide an analytical study of this effect and show that it leads to a hardening of the low energy spectrum but not by enough to make it consistent with the observed spectra for most GRBs (this is assuming that electrons are injected continuously over a time scale comparable to the dynamical time scale, as is expected for internal shocks of GRBs). In particular, we find that it is not possible to obtain a spectrum with \alpha>-0.1 (f_{\nu} \propto \nu^{\alpha}) whereas the typical observed value is \alpha\sim0. Moreover, extreme values for a number of parameters are required in order that \alpha\sim-0.1: the energy fraction in magnetic field needs to be less than about 10^{-4}, the thermal Lorentz factor of electrons should be larger than 10^6, and the radius where gamma-rays are produced should be not too far away from the deceleration radius. These difficulties suggest that the synchrotron radiation mechanism in internal shocks does not provide a self-consistent solution when \alpha>-0.2.Comment: 10 pages (single column), 2 figures, MNRAS in pres

Scattered Emission from A Relativistic Outflow and Its Application to Gamma-Ray Bursts

We investigate a scenario of photons scattering by electrons within a relativistic outflow. The outflow is composed of discrete shells with different speeds. One shell emits radiation for a short duration. Some of this radiation is scattered by the shell(s) behind. We calculate in a simple two-shell model the observed scattered flux density as a function of the observed primary flux density, the normalized arrival time delay between the two emission components, the Lorentz factor ratio of the two shells and the scattering shell's optical depth. Thomson scattering in a cold shell and inverse Compton scattering in a hot shell are both considered. The results of our calculations are applied to the Gamma-Ray Bursts and the afterglows. We find that the scattered flux from a cold slower shell is small and likely to be detected only for those bursts with very weak afterglows. A hot scattering shell could give rise to a scattered emission as bright as the X-ray shallow decay component detected in many bursts, on a condition that the isotropically equivalent total energy carried by the hot electrons is large, $\sim 10^{52-56}$ erg. The scattered emission from a faster shell could appear as a late short $\gamma$-ray/MeV flash or become part of the prompt emission depending on the delay of the ejection of the shell.Comment: 13 pages, 3 figures, MNRAS in press; a short intuitive estimation is added before detailed calculations; references update