The Star-Forming Torus and Stellar Dynamical Black Hole Mass in the Seyfert 1 Nucleus of NGC3227

We report R~4300 VLT SINFONI adaptive optics integral field K-band spectroscopy of the nucleus of the Seyfert 1 galaxy NGC3227 at a spatial resolution of 0.085" (7pc). We present the morphologies and kinematics of emission lines and absorption features, and give the first derivation of a black hole mass in a Seyfert 1 nucleus from spatially resolved stellar dynamics. We show that the gas in the nucleus has a mean column density of order 10^{24}-10^{25}cm^{-2} and that it is geometrically thick, in agreement with the standard `molecular torus' scenario. We discuss which heating processes may be responsible for maintaining the vertical height of the torus. We have also resolved the nuclear stellar distribution, and find that within a few parsecs of the AGN there has been an intense starburst, the most recent episode of which began ~40Myr ago but has now ceased. The current luminosity of stars within 30pc of the AGN, ~3x10^9L_sun, is comparable to that of the AGN. Based on a comparison of the respective size scales, we argue that the star formation has been occuring in the obscuring torus. Finally, we present the first derivation of a black hole mass in a Seyfert 1 nucleus from stellar dynamics which marginally spatially resolve the black hole's sphere of influence. We apply Schwarzschild orbit superposition models to our full 2-dimensional data and derive the mass of the black hole, paying careful attention to the input parameters which are often uncertain: the contribution of the large scale bulge and its mass-to-light ratio; the recent star formation in the nucleus and its mass-to-light ratio; the contribution of the gas mass to the potential; and the inclination. Our models yield a 1sigma range for the black hole mass of M_{BH} = 7x10^6-2x10^7M_sun.Comment: Accepted by ApJ, 42 pages with 20 figure

Quantum Computation with Topological Codes: from qubit to topological fault-tolerance

This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer formalism, and measurement-based quantum computation, are also provided in a pedagogical way. Topological quantum computation by brading the defects on the surface code is explained in both circuit-based and measurement-based models in such a way that their relation is clear. The interdisciplinary connections between quantum error correction codes and subjects in other fields such as topological order in condensed matter physics and spin glass models in statistical physics are also discussed. This manuscript will be appeared in SpringerBriefs.Comment: 155 pages, 133 figures, this manuscript will be appeared in SpringerBriefs, comments are welcom

Isogeometric Analysis for High Order Geometric Partial Differential Equations with Applications

In this thesis, we consider the numerical approximation of high order geometric Partial Differential Equations (PDEs). We first consider high order PDEs defined on surfaces in the 3D space that are represented by single-patch tensor product NURBS. Then, we spatially discretize the PDEs by means of NURBS-based Isogeometric Analysis (IGA) in the framework of the Galerkin method. With this aim, we consider the construction of periodic NURBS function spaces with high degree of global continuity, even on closed surfaces. As benchmark problems for the proposed discretization, we propose Laplace-Beltrami problems of the fourth and sixth orders, as well as the corresponding eigenvalue problems, and we analyze the impact of the continuity of the basis functions on the accuracy as well as on computational costs. The numerical solution of two high order phase field problems on both open and closed surfaces is also considered: the fourth order Cahn-Hilliard equation and the sixth order crystal equation, both discretized in time with the generalized-alpha method. We then consider the numerical approximation of geometric PDEs, derived, in particular, from the minimization of shape energy functionals by L^2-gradient flows. We analyze the mean curvature and the Willmore gradient flows, leading to second and fourth order PDEs, respectively. These nonlinear geometric PDEs are discretized in time with Backward Differentiation Formulas (BDF), with a semi-implicit formulation based on an extrapolation of the geometry, leading to a linear problem to be solved at each time step. Results about the numerical approximation of the two geometric flows on several geometries are analyzed. Then, we study how the proposed mathematical framework can be employed to numerically approximate the equilibrium shapes of lipid bilayer biomembranes, or vesicles, governed by the Canham-Helfrich curvature model. We propose two numerical schemes for enforcing the conservation of the area and volume of the vesicles, and report results on benchmark problems. Then, the approximation of the equilibrium shapes of biomembranes with different values of reduced volume is presented. Finally, we consider the dynamics of a vesicle, e.g. a red blood cell, immersed in a fluid, e.g. the plasma. In particular, we couple the curvature-driven model for the lipid membrane with the incompressible Navier-Stokes equations governing the fluid. We consider a segregated approach, with a formulation based on the Resistive Immersed Surface method applied to NURBS geometries. After analyzing benchmark fluid simulations with immersed NURBS objects, we report numerical results for the investigation of the dynamics of a vesicle under different flow conditions

Geometry and tool motion planning for curvature adapted CNC machining

CNC machining is the leading subtractive manufacturing technology. Although it is in use since decades, it is far from fully solved and still a rich source for challenging problems in geometric computing. We demonstrate this at hand of 5-axis machining of freeform surfaces, where the degrees of freedom in selecting and moving the cutting tool allow one to adapt the tool motion optimally to the surface to be produced. We aim at a high-quality surface finish, thereby reducing the need for hard-to-control post-machining processes such as grinding and polishing. Our work is based on a careful geometric analysis of curvature-adapted machining via so-called second order line contact between tool and target surface. On the geometric side, this leads to a new continuous transition between “dual” classical results in surface theory concerning osculating circles of surface curves and oscu- lating cones of tangentially circumscribed developable surfaces. Practically, it serves as an effective basis for tool motion planning. Unlike previous approaches to curvature-adapted machining, we solve locally optimal tool positioning and motion planning within a single optimization framework and achieve curvature adaptation even for convex surfaces. This is possible with a toroidal cutter that contains a negatively curved cutting area. The effectiveness of our approach is verified at hand of digital models, simulations and machined parts, including a comparison to results generated with commercial software

Shock-excited molecular hydrogen in the outflows of post-asymptotic giant branch stars

Since the identi cation of proto-planetary nebulae (PPNe) as transition objects between the asymptotic giant branch stars and planetary nebulae more than two decades ago, astronomers have attempted to characterise these exciting objects. Today many questions still elude a conclusive answer, partly due to the sheer diversity observed within this small subset of stellar objects, and partly due to the low numbers detected. Fortunately, many of these objects display a rich spectrum of emission/absorption lines that can be used as diagnostics for these nebulae. This dissertation presents a study of six PPNe using the relatively new (at NIR wavelengths) integral eld spectroscopy technique. This method has allowed the investigation of distinct regions of these nebulae, and in certain cases the application of magneto-hydrodynamic shock models to the data. The goal of this research has been to investigate the evolution of PPNe by detailed examination of a small sample of objects consisting of a full range of evolutionary types. Near-IR ro-vibrational lines were employed as the primary tool to tackle this problem. In all six sources the 1!0S(1) line is used to map the spatial extent of the H2. In three of these objects the maps represent the rst images of their H2 emission nebulae. In the case of the earliest-type object (IRAS 14331-6435) in this sample, the line map gives the rst image of its nebula at any wavelength. In the only M-type object (OH 231.8+4.2) in the sample, high-velocity H2 is detected in discrete clumps along the edges of the bipolar out ow, while a possible ring of slower moving H2 is found around the equatorial region. This is the rst detection of H2 in such a late-type object but due its peculiarities, it is possibly not representative of what is expected of M-type objects. In IRAS 19500-1709, an intermediate-type object, the line map shows the H2 emission to originate in clumpy structures along the edges of a bipolar shell/out ow. The remaining three objects have all been the subject of previous studies but in each case new H2 lines are detected in this work along with other emission lines (Mg ii, Na i & CO). In the case of IRAS 16594-4656, MHD shock models have been used to determine the gas density and shock velocity. Two new python modules/classes have been written. The rst one to deal with the data cubes, extract ux measurements, rebin regions of interest, and produce line maps. The second class allows the easy calculation of many important parameters, for example, excitation temperatures, column density ratio values, extinction estimates from several line-pairs, column density values, and total mass of the H2. The class also allows the production of input les for the shock tting procedure, and simulated shocks for testing this tting process. A new framework to t NIR shock models to data has been developed, employing Monte Carlo techniques and the extensive computing cluster at the University of Hertfordshire (UH). This method builds on the approach used by many other authors, with the added advantages that this framework provides a method of correctly sampling the shock model parameter space, and providing error estimates on the model t. Using this approach, data from IRAS 16594-4656 have been successfully modelled using the shock models. A full description of this class of stellar objects from such a small sample is not possible due to their diverse nature. Although H2 was detected across the full spectral vi range of post-AGB objects, the phase at which H2 emission begins is still not clear. The only M-type object in this work is a peculiar object and may not be representative of a typical post-AGB star. The H2 PPNe appear to be located at lower Galactic latitudes (b 20 ) than the total PPNe population, possibly pointing to an above average mass and hence younger age of these objects

Applications of Locality and Asymmetry to Quantum Fault-Tolerance

Quantum computing sounds like something out of a science-fiction novel. If we can exert control over unimaginably small systems, then we can harness their quantum mechanical behavior as a computational resource. This resource allows for astounding computational feats, and a new perspective on information-theory as a whole. But there's a caveat. The events we have to control are so fast and so small that they can hardly be said to have occurred at all. For a long time after Feynman's proposal and even still, there are some who believe that the barriers to controlling such events are fundamental. While we have yet to find anything insurmountable, the road is so pockmarked with challenges both experimental and theoretical that it is often difficult to see the road at all. Only a marriage of both engineering and theory in concert can hope to find the way forward. Quantum error-correction, and more broadly quantum fault-tolerance, is an unfinished answer to this question. It concerns the scaling of these microscopic systems into macroscopic regimes which we can fully control, straddling practical and theoretical considerations in its design. We will explore and prove several results on the theory of quantum fault-tolerance, but which are guided by the ultimate goal of realizing a physical quantum computer. In this thesis, we demonstrate applications of locality and asymmetry to quantum fault-tolerance. We introduce novel code families which we use to probe the behavior of thresholds in quantum subsystem codes. We also demonstrate codes in this family that are well-suited to efficiently correct asymmetric noise models, and determine their parameters. Next we show that quantum error-correcting encodings are incommensurate with transversal implementations of universal classical-reversible computation. Along the way, we resolve an open question concerning almost information-theoretically secure quantum fully homomorphic encryption, showing that it is impossible. Finally, we augment a framework for transversally mapping between stabilizer subspace codes, and discuss prospects for fault-tolerance.PHDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145948/1/mgnewman_1.pd