Recent Developments

Context. Tracing nuclear inflows and outflows in active galactic nuclei (AGNs), determining the mass of gas involved in them, and their impact on the host galaxy and nuclear black hole requires 3D imaging studies of both the ionized and molecular gas. Aims. We map the distribution and kinematics of molecular and ionized gas in a sample of active galaxies to quantify the nuclear inflows and outflows. Here, we analyze the nuclear kinematics of NGC 1566 via ALMA observations of the CO J:2-1 emission at 24 pc spatial and ∼2.6 km s−1 spectral resolution, and Gemini-GMOS/IFU observations of ionized gas emission lines and stellar absorption lines at similar spatial resolution, and 123 km s−1 of intrinsic spectral resolution. Methods. The morphology and kinematics of stellar, molecular (CO), and ionized ([N II]) emission lines are compared to the expectations from rotation, outflows, and streaming inflows. Results. While both ionized and molecular gas show rotation signatures, there are significant non-circular motions in the innermost 200 pc and along spiral arms in the central kpc (CO). The nucleus shows a double-peaked CO profile (full width at zero intensity of 200 km s−1), and prominent (∼80 km s−1) blue- and redshifted lobes are found along the minor axis in the inner arcseconds. Perturbations by the large-scale bar can qualitatively explain all features in the observed velocity field. We thus favor the presence of a molecular outflow in the disk with true velocities of ∼180 km s−1 in the nucleus and decelerating to 0 by ∼72 pc. The implied molecular outflow rate is 5.6 M⊙ yr−1, with this gas accumulating in the nuclear 2″ arms. The ionized gas kinematics support an interpretation of a similar but more spherical outflow in the inner 100 pc, with no signs of deceleration. There is some evidence of streaming inflows of ∼50 km s−1 along specific spiral arms, and the estimated molecular mass inflow rate, ∼0.1 M⊙ yr−1, is significantly higher than the SMBH accretion rate (ṁ = 4.8 × 10−5 M⊙ yr−1)

Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schroedinger Hamiltonians

Some exactly solvable potentials in the position dependent mass background are generated whose bound states are given in terms of Laguerre- or Jacobi-type $X_1$ exceptional orthogonal polynomials. These potentials are shown to be shape invariant and isospectral to the potentials whose bound state solutions involve classical Laguerre or Jacobi polynomials.Comment: To appear in Physics Letters

Subresultants in multiple roots: an extremal case

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\alpha)^m and (x-\beta)^n with respect to the set of Bernstein polynomials \{(x-\alpha)^j(x-\beta)^{d-j}, \, 0\le j\le d\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.Comment: 18 pages, uses elsart. Revised version accepted for publication at Linear Algebra and its Application

Fostering student engagement through a real-world, collaborative project across disciplines and institutions

Ample research has identified several features of a learning experience likely to enhance student learning, including collaboration, open-ended exploration, and problem-based learning in real-life scenarios. Missing is a model of how instructors might combine these elements into a single project that works flexibly across disciplines and institutions. This article fills this gap by offering such a model and reporting on its effectiveness in fostering student engagement. It describes a project that instructors at four colleges and universities in Flint, Michigan (USA) piloted during the height of the Flint water crisis. The project asked students to apply class content to the real-world problem unfolding around them, and offered students an opportunity to collaborate with peers. We collected qualitative and quantitative data on students’ reactions to the project, and found that the project succeeded in engaging students. We offer recommendations for how instructors can create similar projects in their own classrooms

A study of the bound states for square potential wells with position-dependent mass

A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the variation of the energy of the bound states are calculated as a function of the well-width and mass.Comment: To appear in Phys. Lett. A (Present e-mail of A.G: [email protected]

Group 2A: Speed gun

This document describes the research, design, and testing of the speed gun designed by Group 2A for the School of ECEN 4024 Capstone Design class of spring 2017. The project was assigned at the beginning of the semester to be turned in after demonstrating its functionality at the end of the semester. The purpose of this project was to demonstrate the skills obtained through the School of Electrical and Computer Engineering curriculum in one project covering many areas of electrical and computer engineering. The specifications are set by the group, and the end design must match these specifications. In this report, the responsibility breakdown, budget and schedule, background information and research, methodology, detailed design, and end results are all described.The group was allotted $250 by the School of Electrical and Computer Engineering department to design and build a functional project. Group 2A broke apart the workload based on skills and comfortability working with certain areas of the overall system. These sections included RF circuitry for Roy, electronics circuitry for Tyler, software development for Matheus, and packaging design for Andrew. Each member performed their share of the work as well as contributed to the other sections as needed. After researching the respective sections, the group came together to design an overall system to perform at the specified goals. After many challenges, hard work, and collaboration, the group was able to complete the project ahead of schedule and reach some of the stretch goals for the project including a PCB design, BLE implementation, and multimode operation. The device met the specifications, successfully measuring the speed of a baseball. In normal operation, the speed gun does not exceed a total current draw of 120mA, consuming 600mW. The group stayed well under budget coming in at a grand total of$162.64

An outflow in the Seyfert ESO 362-G18 revealed by Gemini-GMOS/IFU Observations

We present two-dimensional stellar and gaseous kinematics of the inner 0.7 $\times$ 1.2 kpc$^{2}$ of the Seyfert galaxy ESO 362-G18, derived from optical spectra obtained with the GMOS/IFU on the Gemini South telescope at a spatial resolution of $\approx$170 pc and spectral resolution of 36 km s$^{-1}$. ESO 362-G18 is a strongly perturbed galaxy of morphological type Sa or S0/a, with a minor merger approaching along the NE direction. Previous studies have shown that the [OIII] emission shows a fan-shaped extension of $\approx$ 10\arcsec\ to the SE. We detect the [OIII] doublet, [NII] and H${\alpha}$ emission lines throughout our field of view. The stellar kinematics is dominated by circular motions in the galaxy plane, with a kinematic position angle of $\approx$137$^{\circ}$. The gas kinematics is also dominated by rotation, with kinematic position angles ranging from 122$^{\circ}$ to 139$^{\circ}$. A double-Gaussian fit to the [OIII]$\lambda$5007 and H${\alpha}$ lines, which have the highest signal to noise ratios of the emission lines, reveal two kinematic components: (1) a component at lower radial velocities which we interpret as gas rotating in the galactic disk; and (2) a component with line of sight velocities 100-250 km s$^{-1}$ higher than the systemic velocity, interpreted as originating in the outflowing gas within the AGN ionization cone. We estimate a mass outflow rate of 7.4 $\times$ 10$^{-2}$ M$_{\odot}$ yr$^{-1}$ in the SE ionization cone (this rate doubles if we assume a biconical configuration), and a mass accretion rate on the supermassive black hole (SMBH) of 2.2 $\times$ 10$^{-2}$ M$_{\odot}$ yr$^{-1}$. The total ionized gas mass within $\sim$84 pc of the nucleus is 3.3 $\times$ 10$^{5}$ M$_{\odot}$; infall velocities of $\sim$34 km s$^{-1}$ in this gas would be required to feed both the outflow and SMBH accretion.Comment: 18 pages, 14 figure

Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential

The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.Comment: 10 page

Irregular Input Data in Convergence Acceleration and Summation Processes: General Considerations and Some Special Gaussian Hypergeometric Series as Model Problems

Sequence transformations accomplish an acceleration of convergence or a summation in the case of divergence by detecting and utilizing regularities of the elements of the sequence to be transformed. For sufficiently large indices, certain asymptotic regularities normally do exist, but the leading elements of a sequence may behave quite irregularly. The Gaussian hypergeometric series 2F1 (a, b; c; z) is well suited to illuminate problems of that kind. Sequence transformations perform quite well for most parameters and arguments. If, however, the third parameter $c$ of a nonterminating hypergeometric series 2F1 is a negative real number, the terms initially grow in magnitude like the terms of a mildly divergent series. The use of the leading terms of such a series as input data leads to unreliable and even completely nonsensical results. In contrast, sequence transformations produce good results if the leading irregular terms are excluded from the transformation process. Similar problems occur also in perturbation expansions. For example, summation results for the infinite coupling limit k_3 of the sextic anharmonic oscillator can be improved considerably by excluding the leading terms from the transformation process. Finally, numerous new recurrence formulas for the 2F1 (a, b; c; z) are derived.Comment: 25 pages, 7 tables, REVTe