Anomalies and entanglement renormalization

We study 't Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general topological restrictions on conformal data are derived. An ansatz class allowing for optimization of MERA with an anomalous symmetry is introduced. We utilize this class to numerically study a family of Hamiltonians with a symmetric critical line. Conformal data is obtained for all irreducible projective representations of each anomalous symmetry twist, corresponding to definite topological sectors. It is numerically demonstrated that this line is a protected gapless phase. Finally, we implement a duality transformation between a pair of critical lines using our subclass of MERA.Comment: 12+18 pages, 6+5 figures, 0+2 tables, v2 published versio

Status and prospects of computational fluid dynamics for unsteady transonic viscous flows

Applications of computational aerodynamics to aeronautical research, design, and analysis have increased rapidly over the past decade, and these applications offer significant benefits to aeroelasticians. The past developments are traced by means of a number of specific examples, and the trends are projected over the next several years. The crucial factors that limit the present capabilities for unsteady analyses are identified; they include computer speed and memory, algorithm and solution methods, grid generation, turbulence modeling, vortex modeling, data processing, and coupling of the aerodynamic and structural dynamic analyses. The prospects for overcoming these limitations are presented, and many improvements appear to be readily attainable. If so, a complete and reliable numerical simulation of the unsteady, transonic viscous flow around a realistic fighter aircraft configuration could become possible within the next decade. The possibilities of using artificial intelligence concepts to hasten the achievement of this goal are also discussed

NASA/GE Energy Efficient Engine low pressure turbine scaled test vehicle performance report

The low pressure turbine for the NASA/General Electric Energy Efficient Engine is a highly loaded five-stage design featuring high outer wall slope, controlled vortex aerodynamics, low stage flow coefficient, and reduced clearances. An assessment of the performance of the LPT has been made based on a series of scaled air-turbine tests divided into two phases: Block 1 and Block 2. The transition duct and the first two stages of the turbine were evaluated during the Block 1 phase from March through August 1979. The full five-stage scale model, representing the final integrated core/low spool (ICLS) design and incorporating redesigns of stages 1 and 2 based on Block 1 data analysis, was tested as Block 2 in June through September 1981. Results from the scaled air-turbine tests, reviewed herein, indicate that the five-stage turbine designed for the ICLS application will attain an efficiency level of 91.5 percent at the Mach 0.8/10.67-km (35,000-ft), max-climb design point. This is relative to program goals of 91.1 percent for the ICLS and 91.7 percent for the flight propulsion system (FPS)

Absent posterior interventricular artery

During the dissection of the thorax of a 79-year-old Caucasian male cadaver, the posterior interventricular coronary artery was found to be completely absent. Congenital heart abnormalities are frequent but absent arteries are uncommon and when occurring are often associated with replacement vessels from the existing circulation, making complete absence rare. This condition may well have been asymptomatic in life, but such variations could have serious implications in patients with underlying heart pathology

Iterative, Small-Signal L2 Stability Analysis of Nonlinear Constrained Systems

This paper provides a method to analyze the small-signal L2 gain of control-affine nonlinear systems on compact sets via iterative semi-definite programs (SDPs). First, a continuous piecewise affine (CPA) storage function and the corresponding upper bound on the L2 gain are found on a bounded, compact set's triangulation. Then, to ensure that the state does not escape this set, a (CPA) barrier function is found that is robust to small-signal inputs. Small-signal L2 stability then holds inside each sublevel set of the barrier function inside the set where the storage function was found. The bound on the inputs is also found while searching for a barrier function. The method's effectiveness is shown in a numerical example

Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Sets

Imitation learning enables the synthesis of controllers for complex objectives and highly uncertain plant models. However, methods to provide stability guarantees to imitation learned controllers often rely on large amounts of data and/or known plant models. In this paper, we explore an input-output (IO) stability approach to dissipative imitation learning, which achieves stability with sparse data sets and with little known about the plant model. A closed-loop stable dynamic output feedback controller is learned using expert data, a coarse IO plant model, and a new constraint to enforce dissipativity on the learned controller. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to successfully learn the controller. This new imitation learning method is applied to two unknown plants and compared to traditionally learned dynamic output feedback controller and neural network controller. With little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance

A matrix isolation and computational study of molecular palladium fluorides : does PdF₆ exist?

Palladium atoms generated by thermal evaporation and laser ablation were reacted with and trapped in F₂ /Ar, F₂ /Ne, and neat F₂ matrices. The products were characterized by electronic absorption and infrared spectroscopy, together with relativistic density functional theory calculations as well as coupled cluster calculations. Vibrational modes at 540 and 617 cm⁻¹ in argon matrices were assigned to molecular PdF and PdF₂ , and a band at 692 cm⁻¹ was assigned to molecular PdF₄ . A band at 624 cm⁻¹ can be assigned to either PdF₃ or PdF₆, with the former preferred from experimental considerations. Although calculations might support the latter assignment, our conclusion is that in these detailed experiments there is no convincing evidence for PdF₆

Portable LED fluorescence instrumentation for the rapid assessment of potable water quality

Characterising the organic and microbial matrix of water are key issues in ensuring a safe potable water supply. Current techniques only confirm water quality retrospectively via laboratory analysis of discrete samples. Whilst such analysis is required for regulatory purposes, it would be highly beneficial to monitor water quality in-situ in real time, enabling rapid water quality assessment and facilitating proactive management of water supply systems. A novel LED-based instrument, detecting fluorescence peaks C and T (surrogates for organic and microbial matter, respectively), was constructed and performance assessed. Results from over 200 samples taken from source waters through to customer tap from three UK water companies are presented. Excellent correlation was observed between the new device and a research grade spectrophotometer (r 2 = 0.98 and 0.77 for peak C and peak T respectively), demonstrating the potential of providing a low cost, portable alternative fluorimeter. The peak C/TOC correlation was very good (r 2 = 0.75) at low TOC levels found in drinking water. However, correlations between peak T and regulatory measures of microbial matter (2 day/3 day heterotrophic plate counts (HPC), E. coli, and total coliforms) were poor, due to the specific nature of these regulatory measures and the general measure of peak T. A more promising correlation was obtained between peak T and total bacteria using flow cytometry. Assessment of the fluorescence of four individual bacteria isolated from drinking water was also considered and excellent correlations found with peak T (Sphingobium sp. (r 2 = 0.83); Methylobacterium sp. (r 2 = 1.0); Rhodococcus sp. (r 2 = 0.86); Xenophilus sp. (r 2 = 0.96)). It is notable that each of the bacteria studied exhibited different levels of fluorescence as a function of their number. The scope for LED based instrumentation for insitu, real time assessment of the organic and microbial matrix of potable water is clearly demonstrated

Collaborative and Active eLearning: Contributing, Ranking and Tagging Web Resources in First Year Chemistry

To enhance peer-to-peer and student-to-educator collaboration and to promote active eLearning, students and educators are invited to contribute, tag and vote on web-based resources via an application hosted on the eLearning site. These resources are organised according to the topics in the syllabus and hence are available in a succinct, week-by-week format as well as by common tags and by contributor. The resources are also feed to social networking sites to act as external resource libraries and to promote a sense of community and shared learning amongst the large and diverse groups taking our first year chemistry units. By encouraging our learners to contribute in this way and by utilising the large numbers of student in a positive way, the project also seeks to provide a manageable and reliable way of sourcing checking and ranking the vast amount of existing and ever-growing resources on the web

Lattice-Boltzmann coupled models for advection–diffusion flow on a wide range of Péclet numbers

Traditional Lattice-Boltzmann modelling of advection–diffusion flow is affected by numerical instability if the advective term becomes dominant over the diffusive (i.e., high-Péclet flow). To overcome the problem, two 3D one-way coupled models are proposed. In a traditional model, a Lattice-Boltzmann Navier–Stokes solver is coupled to a Lattice-Boltzmann advection–diffusion model. In a novel model, the Lattice-Boltzmann Navier–Stokes solver is coupled to an explicit finite-difference algorithm for advection–diffusion. The finite-difference algorithm also includes a novel approach to mitigate the numerical diffusivity connected with the upwind differentiation scheme. The models are validated using two non-trivial benchmarks, which includes discontinuous initial conditions and the case Pe$_{g}$->$\infty$ for the first time, where Pe$_{g}$ is the grid Péclet number. The evaluation of Pe$_{g}$ alongside Pe is discussed. Accuracy, stability and the order of convergence are assessed for a wide range of Péclet numbers. Recommendations are then given as to which model to select depending on the value Pe$_{g}$ - in particular, it is shown that the coupled finite-difference/Lattice-Boltzmann provide stable solutions in the case Pe->$\infty$, Pe$_{g}$->$\infty