Euler's theorem under the microscope

In this article Geoff Tennant summarises the first half of Imre Lakatos's seminal 1976 book, "Proofs and refutations: the logic of mathematical discovery". Implications are drawn for the classroom treatment of proof.

Water vapour continuum absorption in near-infrared windows derived from laboratory measurements

In most near-infrared atmospheric windows, absorption of solar radiation is dominated by the water vapor self-continuum and yet there is a paucity of measurements in these windows. We report new laboratory measurements of the self-continuum absorption at temperatures between 293 and 472 K and pressures from 0.015 to 5 atm in four near-infrared windows between 1 and 4 m (10000-2500 cm-1); the measurements are made over a wider range of wavenumber, temperatures and pressures than any previous measurements. They show that the self-continuum in these windows is typically one order of magnitude stronger than given in representations of the continuum widely used in climate and weather prediction models. These results are also not consistent with current theories attributing the self continuum within windows to the far-wings of strong spectral lines in the nearby water vapor absorption bands; we suggest that they are more consistent with water dimers being the major contributor to the continuum. The calculated global-average clear-sky atmospheric absorption of solar radiation is increased by 0.75 W/m2 (which is about 1% of the total clear-sky absorption) by using these new measurements as compared to calculations with the MT_CKD-2.5 self-continuum model.

Rhodium cationic complexes using dithioethers as chiral ligands. Application in styrene hydroformylation

Addition of the dithioethers (−)-DIOSR2 (R=Me, iPr) (2,3-O-isopropylidene-1,4-dimethyl (and diisopropyl) thioether-L-threitol) to a dichloromethane solution of [Rh(COD)2]ClO4 (COD=1,5-cyclooctadiene) yielded the mononuclear complexes [Rh(COD)(DIOSR2)]ClO4. X-ray diffraction methods showed that the [Rh(COD)(DIOSiPr2)]ClO4 complex had an square-planar coordination geometry at the rhodium atom with the iPr groups in anti position. Cyclooctadiene complexes react with carbon monoxide to form dinuclear tetracarbonylated complexes [(CO)2Rh(μ-DIOSR2)2(CO)2](ClO4)2. [Rh(COD)(DIOSR2)]ClO4 are active catalyst precursors in styrene hydroformylation at 30 atm and 65°C which give conversions of up to 99% with a regioselectivity in 2-phenylpropanal as high as 74%. In all cases enantioselectivities are low.

Mononuclear Pt(II) and Pd(II) 1,4-dithiolato complexes. Crystal structures of [Pt((−) DIOS) (PPh3)2] and [Pd(S(CH2) 4S)(Ph2P(CH2) 3PPh2)]. Application in styrene hydroformylation

Addition of 1,4-dithiols to dichloromethane solutions of [PtCl2(P-P)] (P-P = (PPh3)2, Ph2P(CH2)3PPh2, Phd2P(CH2)4PPh2; 1,4-dithiols = HS(CH2)4SH, (−)DIOSH2 (2,3-O-isopropylidene-1,4-dithiol-l-threitol), BINASH2 (1,1′-dinaphthalene-2,2′-dithiol)) in the presence of NEt3 yielded the mononuclear complexes [Pt(1,4-dithiolato)(P-P)]. Related palladium(II) complexes [Pd(dithiolato)(P-P)] (P-P=Ph2P(CH2)3PPh2, Ph2P(CH2)4PPh2; dithiolato = −S(CH2)4S−, (−)-DIOS) were prepared by the same method. The structure of [Pt((−)DIOS)(PPh3)2] and [Pd(S(CH2)4S)(Ph2P(CH2)3PPh2)] complexes was determined by X-ray diffraction methods. Pt—dithiolato—SnC12 systems are active in the hydroformylation of styrene. At 100 atm and 125°C [Pt(dithiolate)(P-P)]/SnCl2 (Pt:Sn = 20) systems provided aldehyde conversion up to 80%.

Transition of pupils from Key Stage 2 to 3 deemed gifted and talented in mathematics: an initial study

In this article Geoff Tennant and Dave Harries report on the early stages of a research project looking to examine the transition from Key Stage (KS) 2 to 3 of children deemed Gifted and Talented (G&T) in mathematics. An examination of relevant literature points towards variation in definition of key terms and underlying rationale for activities. Preliminary fieldwork points towards a lack of meaningful communication between schools, with primary school teachers in particular left to themselves to decide how to work with children deemed G&T. Some pointers for action are given, along with ideas for future research and a request for colleagues interested in working with us to get in touch.

SIMULATIONS OF WINDS OF WEAK-LINED T TAURI STARS. II. THE EFFECTS OF A TILTED MAGNETOSPHERE AND PLANETARY INTERACTIONS

Based on our previous work, we investigate here the effects on the wind and magnetospheric structures of weak-lined T Tauri stars due to a misalignment between the axis of rotation of the star and its magnetic dipole moment vector. In such a configuration, the system loses the axisymmetry presented in the aligned case, requiring a fully three-dimensional (3D) approach. We perform 3D numerical magnetohydrodynamic simulations of stellar winds and study the effects caused by different model parameters, namely the misalignment angle theta(t), the stellar period of rotation, the plasma-beta, and the heating index.. Our simulations take into account the interplay between the wind and the stellar magnetic field during the time evolution. The system reaches a periodic behavior with the same rotational period of the star. We show that the magnetic field lines present an oscillatory pattern. Furthermore, we obtain that by increasing theta(t), the wind velocity increases, especially in the case of strong magnetic field and relatively rapid stellar rotation. Our 3D, time-dependent wind models allow us to study the interaction of a magnetized wind with a magnetized extrasolar planet. Such interaction gives rise to reconnection, generating electrons that propagate along the planet`s magnetic field lines and produce electron cyclotron radiation at radio wavelengths. The power released in the interaction depends on the planet`s magnetic field intensity, its orbital radius, and on the stellar wind local characteristics. We find that a close-in Jupiter-like planet orbiting at 0.05 AU presents a radio power that is similar to 5 orders of magnitude larger than the one observed in Jupiter, which suggests that the stellar wind from a young star has the potential to generate strong planetary radio emission that could be detected in the near future with LOFAR. This radio power varies according to the phase of rotation of the star. For three selected simulations, we find a variation of the radio power of a factor 1.3-3.7, depending on theta(t). Moreover, we extend the investigation done in Vidotto et al. and analyze whether winds from misaligned stellar magnetospheres could cause a significant effect on planetary migration. Compared to the aligned case, we show that the timescale tau(w) for an appreciable radial motion of the planet is shorter for larger misalignment angles. While for the aligned case tau(w) similar or equal to 100 Myr, for a stellar magnetosphere tilted by theta(t) = 30 degrees, tau(w) ranges from similar to 40 to 70 Myr for a planet located at a radius of 0.05 AU. Further reduction on tau(w) might occur for even larger misalignment angles and/or different wind parameters.

SIMULATIONS OF WINDS OF WEAK-LINED T TAURI STARS: THE MAGNETIC FIELD GEOMETRY AND THE INFLUENCE OF THE WIND ON GIANT PLANET MIGRATION

By means of numerical simulations, we investigate magnetized stellar winds of pre-main-sequence stars. In particular, we analyze under which circumstances these stars will present elongated magnetic features (e.g., helmet streamers, slingshot prominences, etc). We focus on weak-lined T Tauri stars, as the presence of the tenuous accretion disk is not expected to have strong influence on the structure of the stellar wind. We show that the plasma-beta parameter (the ratio of thermal to magnetic energy densities) is a decisive factor in defining the magnetic configuration of the stellar wind. Using initial parameters within the observed range for these stars, we show that the coronal magnetic field configuration can vary between a dipole-like configuration and a configuration with strong collimated polar lines and closed streamers at the equator (multicomponent configuration for the magnetic field). We show that elongated magnetic features will only be present if the plasma-beta parameter at the coronal base is beta(0) << 1. Using our self-consistent three-dimensional magnetohydrodynamics model, we estimate for these stellar winds the timescale of planet migration due to drag forces exerted by the stellar wind on a hot-Jupiter. In contrast to the findings of Lovelace et al., who estimated such timescales using the Weber and Davis model, our model suggests that the stellar wind of these multicomponent coronae are not expected to have significant influence on hot-Jupiters migration. Further simulations are necessary to investigate this result under more intense surface magnetic field strengths (similar to 2-3 kG) and higher coronal base densities, as well as in a tilted stellar magnetosphere.

THREE-DIMENSIONAL NUMERICAL SIMULATIONS OF MAGNETIZED WINDS OF SOLAR-LIKE STARS

By means of self-consistent three-dimensional magnetohydrodynamics (MHD) numerical simulations, we analyze magnetized solar-like stellar winds and their dependence on the plasma-beta parameter (the ratio between thermal and magnetic energy densities). This is the first study to perform such analysis solving the fully ideal three-dimensional MHD equations. We adopt in our simulations a heating parameter described by gamma, which is responsible for the thermal acceleration of the wind. We analyze winds with polar magnetic field intensities ranging from 1 to 20 G. We show that the wind structure presents characteristics that are similar to the solar coronal wind. The steady-state magnetic field topology for all cases is similar, presenting a configuration of helmet streamer-type, with zones of closed field lines and open field lines coexisting. Higher magnetic field intensities lead to faster and hotter winds. For the maximum magnetic intensity simulated of 20 G and solar coronal base density, the wind velocity reaches values of similar to 1000 km s(-1) at r similar to 20r(0) and a maximum temperature of similar to 6 x 10(6) K at r similar to 6r(0). The increase of the field intensity generates a larger ""dead zone"" in the wind, i.e., the closed loops that inhibit matter to escape from latitudes lower than similar to 45 degrees extend farther away from the star. The Lorentz force leads naturally to a latitude-dependent wind. We show that by increasing the density and maintaining B(0) = 20 G the system recover back to slower and cooler winds. For a fixed gamma, we show that the key parameter in determining the wind velocity profile is the beta-parameter at the coronal base. Therefore, there is a group of magnetized flows that would present the same terminal velocity despite its thermal and magnetic energy densities, as long as the plasma-beta parameter is the same. This degeneracy, however, can be removed if we compare other physical parameters of the wind, such as the mass-loss rate. We analyze the influence of gamma in our results and we show that it is also important in determining the wind structure.

Template-based quadrilateral meshing

Generating quadrilateral meshes is a highly non-trivial task, as design decisions are frequently driven by specific application demands. Automatic techniques can optimize objective quality metrics, such as mesh regularity, orthogonality, alignment and adaptivity; however, they cannot make subjective design decisions. There are a few quad meshing approaches that offer some mechanisms to include the user in the mesh generation process; however, these techniques either require a large amount of user interaction or do not provide necessary or easy to use inputs. Here, we propose a template-based approach for generating quad-only meshes from triangle surfaces. Our approach offers a flexible mechanism to allow external input, through the definition of alignment features that are respected during the mesh generation process. While allowing user inputs to support subjective design decisions, our approach also takes into account objective quality metrics to produce semi-regular, quad-only meshes that align well to desired surface features. Published by Elsevier Ltd.

PedVis: A Structured, Space-Efficient Technique for Pedigree Visualization

Public genealogical databases are becoming increasingly populated with historical data and records of the current population`s ancestors. As this increasing amount of available information is used to link individuals to their ancestors, the resulting trees become deeper and more dense, which justifies the need for using organized, space-efficient layouts to display the data. Existing layouts are often only able to show a small subset of the data at a time. As a result, it is easy to become lost when navigating through the data or to lose sight of the overall tree structure. On the contrary, leaving space for unknown ancestors allows one to better understand the tree`s structure, but leaving this space becomes expensive and allows fewer generations to be displayed at a time. In this work, we propose that the H-tree based layout be used in genealogical software to display ancestral trees. We will show that this layout presents an increase in the number of displayable generations, provides a nicely arranged, symmetrical, intuitive and organized fractal structure, increases the user`s ability to understand and navigate through the data, and accounts for the visualization requirements necessary for displaying such trees. Finally, user-study results indicate potential for user acceptance of the new layout.