Laminar compressible flow in a tube

A two-dimensional solution for the velocity and pressure distributions in steady, laminar, isothermal flow of an ideal gas in a long tube is obtained as a double perturbation expension in β, the radius to length ratio, and ε, the relative pressure drop. It is found that simple approximations estimate the exact flow rate-pressure drop relationship accurately.     

Intramolecular Heck reactions of aryl chlorides with alkynes

We have developed a reaction that affords the selective preparation of hexahydro-2H-pyrido[2,1-a]isoquinoline dienes, allenes, or alkenes via an intramolecular Heck cyclization of an aryl chloride with an alkyne. Tricyclic isoquinoline core structures of this nature are difficult to access by alternative methods. The unsaturated product formed can be partially controlled by choice of ligand and reaction solvent.     

Pronounced negative thermal expansion from a simple structure: cubic ScF(3)

Scandium trifluoride maintains a cubic ReO(3) type structure down to at least 10 K, although the pressure at which its cubic to rhombohedral phase transition occurs drops from >0.5 GPa at ～300 K to 0.1-0.2 GPa at 50 K. At low temperatures it shows strong negative thermal expansion (NTE) (60-110 K, α(l) ≈ -14 ppm K(-1)). On heating, its coefficient of thermal expansion (CTE) smoothly increases, leading to a room temperature CTE that is similar to that of ZrW(2)O(8) and positive thermal expansion above ～1100 K. While the cubic ReO(3) structure type is often used as a simple illustration of how negative thermal expansion can arise from the thermally induced rocking of rigid structural units, ScF(3) is the first material with this structure to provide a clear experimental illustration of this mechanism for NTE.     

Low frequency deep ocean ambient noise trend in the Northeast Pacific Ocean

Concern about effects of anthropogenic noise on marine life has stimulated new studies to establish present-day ocean noise levels and compare them to noise levels from previous times. This paper reports on the trend in low-frequency (10-400 Hz) ambient noise levels and presents measurements made using a calibrated multi-element volume array at deep ocean sites in the Northeast Pacific from 1978 to 1986. The experiments provided spectral noise levels as well as horizontal and vertical noise directionality. The data presented here provide evidence that the trend derived from 1960s data extended to around 1980, but has since continued at a lower rate.     

Autoresonant excitation of antiproton plasmas

We demonstrate controllable excitation of the center-of-mass longitudinal motion of a thermal antiproton plasma using a swept-frequency autoresonant drive. When the plasma is cold, dense, and highly collective in nature, we observe that the entire system behaves as a single-particle nonlinear oscillator, as predicted by a recent theory. In contrast, only a fraction of the antiprotons in a warm plasma can be similarly excited. Antihydrogen was produced and trapped by using this technique to drive antiprotons into a positron plasma, thereby initiating atomic recombination.     

Anisotropic ion heating and tail generation during tearing mode magnetic reconnection in a high-temperature plasma

Complementary measurements of ion energy distributions in a magnetically confined high-temperature plasma show that magnetic reconnection results in both anisotropic ion heating and the generation of suprathermal ions. The anisotropy, observed in the C(+6) impurity ions, is such that the temperature perpendicular to the magnetic field is larger than the temperature parallel to the magnetic field. The suprathermal tail appears in the majority ion distribution and is well described by a power law to energies 10 times the thermal energy. These observations may offer insight into the energization process.     

Bifurcation to 3D helical magnetic equilibrium in an axisymmetric toroidal device

We report the first direct measurement of the internal magnetic field structure associated with a 3D helical equilibrium generated spontaneously in the core of an axisymmetric toroidal plasma containment device. Magnetohydrodynamic equilibrium bifurcation occurs in a reversed-field pinch when the innermost resonant magnetic perturbation grows to a large amplitude, reaching up to 8% of the mean field strength. Magnetic topology evolution is determined by measuring the Faraday effect, revealing that, as the perturbation grows, toroidal symmetry is broken and a helical equilibrium is established.     

Elementary school teachers’ growth in inquiry-based teaching of mathematics

This article reports on a self-directed, school-based, practice-based professional development (PD) experience aimed at helping elementary school teachers to develop knowledge and expertise in inquiry-based teaching of mathematics. It discusses the characteristics of the self-directed orientation of this PD that supported the teachers’ learning, the nature of the inquiry-based knowledge they constructed, and the impact on their teaching. It highlights the centrality of agency, practical knowledge, and situated learning in this PD approach. The findings suggest that this approach can help mathematics teachers who want to be the architect of their own learning to transform their classrooms in meaningful and desirable ways.     

A high-field solid-state 35/37Cl NMR and quantum chemical investigation of the chlorine quadrupolar and chemical shift tensors in amino acid hydrochlorides

A series of six L-amino acid hydrochloride salts has been studied by 35/37Cl solid-state NMR spectroscopy (at 11.75 and 21.1 T) and complementary quantum chemical calculations. Analyses of NMR spectra acquired under static and magic-angle-spinning conditions for the six hydrochloride salts, those of aspartic acid, alanine, cysteine, histidine, methionine and threonine, allowed the extraction of information regarding the chlorine electric field gradient (EFG) and chemical shift tensors, including their relative orientation. Both tensors are found to be highly dependent on the local environment, with chlorine-35 quadrupolar coupling constants (CQ) ranging from -7.1 to 4.41 MHz and chemical shift tensor spans ranging from 60 to 100 ppm; the value of CQ for aspartic acid hydrochloride is the largest in magnitude observed to date for an organic hydrochloride salt. Quantum chemical calculations performed on cluster models of the chloride ion environment demonstrated agreement between experiment and theory, reproducing CQ to within 18%. In addition, the accuracy of the calculated values of the NMR parameters as a function of the quality of the input structure was explored. Selected X-ray structures were determined (L-Asp HCl; L-Thr HCl) or re-determined (L-Cys HCl.H2O) to demonstrate the benefits of having accurate crystal structures for calculations. The self-consistent charge field perturbation model was also employed and was found to improve the accuracy of calculated quadrupolar coupling constants, demonstrating the impact of the neighbouring ions on the EFG tensor of the central chloride ion. Taken together, the present work contributes to an improved understanding of the factors influencing 35/37Cl NMR interaction tensors in organic hydrochlorides.     

Recursions associated to trapezoid,symmetric and rotation symmetric functions over Galois fields

Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential sums of rotation symmetric Boolean functions satisfy homogeneous linear recurrences with integer coefficients. In this work, a generalization of this result is proved over any Galois field. That is, exponential sums over Galois fields of some rotation symmetric polynomials satisfy linear recurrences with integer coefficients. In the particular case of ${\mathbb{F}}_2$, an elementary method is used to obtain explicit recurrences for exponential sums of some of these functions. The concept of trapezoid Boolean function is also introduced and it is showed that the linear recurrences that exponential sums of trapezoid Boolean functions satisfy are the same as the ones satisfied by exponential sums of the corresponding rotations symmetric Boolean functions. Finally, it is proved that exponential sums of trapezoid and symmetric polynomials also satisfy linear recurrences with integer coefficients over any Galois field ${\mathbb{F}}_q$. Moreover, the Discrete Fourier Transform matrix and some Complex Hadamard matrices appear as examples in some of our explicit formulas of these recurrences.