Incorporating engineering design challenges into STEM courses

Successful strategies for incorporating engineering design challenges into science, technology, engineering, and mathematics (STEM) courses in American high schools are presented in this paper. The developers have taken the position that engineering design experiences should be an important component of the high school education of all American youth. In most instances, these experiences in engineering design are infused into instruction programs in standards-based courses in science, technology, or mathematics. Sometimes the courses are designated as engineering courses and the engineering design component is emphasized. A growing number of researchers seek to understand whether the development of engineering habits of thought and action in high school STEM courses leads to improvements in problem solving abilities, systems thinking, integration of STEM content, increased interest in engineering, and feelings of self- efficacy about pursuing additional engineering activities. We have attempted to integrate these findings, to draw inferences that reflect the current body of knowledge, and to call attention to promising contemporary practices. This paper is intended to provide guidelines for the development of authentic engineering design challenges, to describe instructional strategies for introducing engineering design experiences to high school students, and to offer suggestions for the assessment of the outcomes of engineering design activities. The information is intended to be useful in planning, organizing, and implementing the infusion of engineering design challenges in high school STEM courses. The paper is not intended as a detailed guide for curriculum development, comprehensive instructional design, or the assessment of achievement across the range of high school STEM courses

Chaotic root-finding for a small class of polynomials

In this paper we present a new closed-form solution to a chaotic difference equation, $y_{n+1} = a_2 y_{n}^2 + a_1 y_{n} + a_0$ with coefficient $a_0 = (a_1 - 4)(a_1 + 2) / (4 a_2)$, and using this solution, show how corresponding exact roots to a special set of related polynomials of order $2^p, p \in \mathbb{N}$ with two independent parameters can be generated, for any $p$

The potential natural vegetation of large river floodplains - from dynamic to static equilibrium

Article in PressThe potential natural vegetation (PNV) is a useful benchmark for the restoration of large river floodplains because very few natural reference reaches exist. Expert-based approaches and different types of ecological models (static and dynamic) are commonly used for its estimation despite the conceptual differences they imply. For natural floodplains a static concept of PNV is not reasonable, as natural disturbances cause a constant resetting of succession. However, various forms of river regulation have disrupted the natural dynamics of most large European rivers for centuries. Therefore, we asked whether the consideration of succession dynamics and time dependent habitat turnover are still relevant factors for the reconstruction of the PNV. To answer this we compared the results of a simulation of the vegetation succession (1872–2016) of a segment of the upper Rhine river after regulation (damming, straightening and bank protection) to different statistic and expert-based modelling approaches for PNV reconstruction. The validation of the different PNV estimation methods against a set of independent reference plots and the direct comparison of their results revealed very similar performances. We therefore conclude that due to a lack of large disturbances, the vegetation of regulated large rivers has reached a near-equilibrium state with the altered hydrologic regime and that a static perception of its PNV may be justified. Consequently, statistical models seem to be the best option for its reconstruction since they need relatively few resources (data, time, expert knowledge) and are reproducibleinfo:eu-repo/semantics/acceptedVersio

Dynamics of finite Fermi-Hubbard and Bose-Hubbard systems

This paper analyzes dynamical properties of small Fermi-Hubbard and Bose-Hubbard systems, focusing on the structure of the underlying Hilbert space. We evaluate time-dependent quantities such as the return probability to the initial state and the spin imbalance of spin-1/2 fermions. The results are compared with recent experimental observations in ultracold gases. For the symmetric two-site Fermi-Hubbard model we find that the spin imbalance and the return probability are controlled by two and three frequencies, respectively. The spin imbalance and the return probability are identical for the asymmetric Falicov-Kimball limit and controlled by only one frequency. In general, the transition probabilities between the initial state and energy eigenstates depend strongly on the particle-particle interaction. This is discussed for "self trapping" of spinless bosons in a double-well potential. We observe that the available Hilbert space is reduced significantly by strong interaction.Comment: 12 pages, 5 figure

Maximum Likelihood, Minimum Effort

We provide an efficient method for computing the maximum likelihood mixed quantum state (with density matrix rho) given a set of measurement outcome in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix mu which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst O(d^4) for the basis change plus O(d^3) for finding rho where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only O(d^3) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one.Comment: 4 pages, 5 pdf figures. Replaced with corrections and expanded figure

Investigating the Atmospheric Mass Loss of the Kepler-105 Planets Straddling the Radius Gap

An intriguing pattern among exoplanets is the lack of detected planets between approximately $1.5$ R$_\oplus$ and $2.0$ R$_\oplus$. One proposed explanation for this "radius gap" is the photoevaporation of planetary atmospheres, a theory that can be tested by studying individual planetary systems. Kepler-105 is an ideal system for such testing due to the ordering and sizes of its planets. Kepler-105 is a sun-like star that hosts two planets straddling the radius gap in a rare architecture with the larger planet closer to the host star ($R_b = 2.53\pm0.07$ R$_\oplus$, $P_b = 5.41$ days, $R_c = 1.44\pm0.04$ R$_\oplus$, $P_c = 7.13$ days). If photoevaporation sculpted the atmospheres of these planets, then Kepler-105b would need to be much more massive than Kepler-105c to retain its atmosphere, given its closer proximity to the host star. To test this hypothesis, we simultaneously analyzed radial velocities (RVs) and transit timing variations (TTVs) of the Kepler-105 system, measuring disparate masses of $M_b = 10.8\pm2.3$ M$_\oplus$ ($\rho_b = 0.97\pm0.22$ g cm$^{-3}$) and $M_c = 5.6\pm1.2$ M$_\oplus$ ($\rho_c = 2.64\pm0.61$ g cm$^{-3}$). Based on these masses, the difference in gas envelope content of the Kepler-105 planets could be entirely due to photoevaporation (in 76\% of scenarios), although other mechanisms like core-powered mass loss could have played a role for some planet albedos.Comment: 14 pages, 3 figures, 2 table

A mathematical framework for contact detection between quadric and superquadric surfaces

The calculation of the minimum distance between surfaces plays an important role in computational mechanics, namely, in the study of constrained multibody systems where contact forces take part. In this paper, a general rigid contact detection methodology for non-conformal bodies, described by ellipsoidal and superellipsoidal surfaces, is presented. The mathematical framework relies on simple algebraic and differential geometry, vector calculus, and on the C2 continuous implicit representations of the surfaces. The proposed methodology establishes a set of collinear and orthogonal constraints between vectors defining the contacting surfaces that, allied with loci constraints, which are specific to the type of surface being used, formulate the contact problem. This set of non-linear equations is solved numerically with the Newton-Raphson method with Jacobian matrices calculated analytically. The method outputs the coordinates of the pair of points with common normal vector directions and, consequently, the minimum distance between both surfaces. Contrary to other contact detection methodologies, the proposed mathematical framework does not rely on polygonal-based geometries neither on complex non-linear optimization formulations. Furthermore, the methodology is extendable to other surfaces that are (strictly) convex, interact in a non-conformal fashion, present an implicit representation, and that are at least C2 continuous. Two distinct methods for calculating the tangent and binormal vectors to the implicit surfaces are introduced: (i) a method based on the Householder reflection matrix; and (ii) a method based on a square plate rotation mechanism. The first provides a base of three orthogonal vectors, in which one of them is collinear to the surface normal. For the latter, it is shown that, by means of an analogy to the referred mechanism, at least two non-collinear vectors to the normal vector can be determined. Complementarily, several mathematical and computational aspects, regarding the rigid contact detection methodology, are described. The proposed methodology is applied to several case tests involving the contact between different (super)ellipsoidal contact pairs. Numerical results show that the implemented methodology is highly efficient and accurate for ellipsoids and superellipsoids.Fundação para a Ciência e a Tecnologia (FCT

Risks to carbon storage from land-use change revealed by peat thickness maps of Peru

This work was funded by NERC (grant ref. NE/R000751/1) to I.T.L., A.H., K.H.R., E.T.A.M., C.M.A., T.R.B., G.D. and E.C.D.G.; Leverhulme Trust (grant ref. RPG-2018-306) to K.H.R., L.E.S.C. and C.E.W.; Gordon and Betty Moore Foundation (grant no. 5439, MonANPeru network) to T.R.B., E.N.H.C. and G.F.; Wildlife Conservation Society to E.N.H.C.; Concytec/British Council/Embajada Británica Lima/Newton Fund (grant ref. 220–2018) to E.N.H.C. and J.D.; Concytec/NERC/Embajada Británica Lima/Newton Fund (grant ref. 001–2019) to E.N.H.C. and N.D.; the governments of the United States (grant no. MTO-069018) and Norway (grant agreement no. QZA-12/0882) to K.H.; and NERC Knowledge Exchange Fellowship (grant ref no. NE/V018760/1) to E.N.H.C.Tropical peatlands are among the most carbon-dense ecosystems but land-use change has led to the loss of large peatland areas, associated with substantial greenhouse gas emissions. To design effective conservation and restoration policies, maps of the location and carbon storage of tropical peatlands are vital. This is especially so in countries such as Peru where the distribution of its large, hydrologically intact peatlands is poorly known. Here field and remote sensing data support the model development of peatland extent and thickness for lowland Peruvian Amazonia. We estimate a peatland area of 62,714 km2 (5th and 95th confidence interval percentiles of 58,325 and 67,102 km2, respectively) and carbon stock of 5.4 (2.6–10.6) PgC, a value approaching the entire above-ground carbon stock of Peru but contained within just 5% of its land area. Combining the map of peatland extent with national land-cover data we reveal small but growing areas of deforestation and associated CO2 emissions from peat decomposition due to conversion to mining, urban areas and agriculture. The emissions from peatland areas classified as forest in 2000 represent 1–4% of Peruvian CO2 forest emissions between 2000 and 2016. We suggest that bespoke monitoring, protection and sustainable management of tropical peatlands are required to avoid further degradation and CO2 emissions.PostprintPeer reviewe