Cantor and band spectra for periodic quantum graphs with magnetic fields

We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant (Lyapunov function) of a suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet eigenvalues the spectrum is a Cantor set for an irrational flux, and is absolutely continuous and has a band structure for a rational flux. The Dirichlet eigenvalues can be isolated or embedded, subject to the choice of parameters. Conditions for both possibilities are given. We show that generically there are infinitely many gaps in the spectrum, and the Bethe-Sommerfeld conjecture fails in this case.Comment: Misprints correcte

Thin accretion disc with a corona in a central magnetic field

We study the steady-state structure of an accretion disc with a corona surrounding a central, rotating, magnetized star. We assume that the magneto-rotational instability is the dominant mechanism of angular momentum transport inside the disc and is responsible for producing magnetic tubes above the disc. In our model, a fraction of the dissipated energy inside the disc is transported to the corona via these magnetic tubes. This energy exchange from the disc to the corona which depends on the disc physical properties is modified because of the magnetic interaction between the stellar magnetic field and the accretion disc. According to our fully analytical solutions for such a system, the existence of a corona not only increases the surface density but reduces the temperature of the accretion disc. Also, the presence of a corona enhances the ratio of gas pressure to the total pressure. Our solutions show that when the strength of the magnetic field of the central neutron star is large or the star is rotating fast enough, profiles of the physical variables of the disc significantly modify due to the existence of a corona.Comment: Accepted for publication in Astrophysics & Space Scienc

SPIDER: Probing the Early Universe with a Suborbital Polarimeter

We evaluate the ability of SPIDER, a balloon-borne polarimeter, to detect a divergence-free polarization pattern ("B-modes") in the Cosmic Microwave Background (CMB). In the inflationary scenario, the amplitude of this signal is proportional to that of the primordial scalar perturbations through the tensor-to-scalar ratio r. We show that the expected level of systematic error in the SPIDER instrument is significantly below the amplitude of an interesting cosmological signal with r=0.03. We present a scanning strategy that enables us to minimize uncertainty in the reconstruction of the Stokes parameters used to characterize the CMB, while accessing a relatively wide range of angular scales. Evaluating the amplitude of the polarized Galactic emission in the SPIDER field, we conclude that the polarized emission from interstellar dust is as bright or brighter than the cosmological signal at all SPIDER frequencies (90 GHz, 150 GHz, and 280 GHz), a situation similar to that found in the "Southern Hole." We show that two ~20-day flights of the SPIDER instrument can constrain the amplitude of the B-mode signal to r<0.03 (99% CL) even when foreground contamination is taken into account. In the absence of foregrounds, the same limit can be reached after one 20-day flight.Comment: 29 pages, 8 figures, 4 tables; v2: matches published version, flight schedule updated, two typos fixed in Table 2, references and minor clarifications added, results unchange

Designing a database for performance assessment: Lessons learned from WIPP

The Waste Isolation Pilot Plant (WIPP) Compliance Certification Application (CCA) Performance Assessment (PA) used a relational database that was originally designed only to supply the input parameters required for implementation of the PA codes. Reviewers used the database as a point of entry to audit quality assurance measures for control, traceability, and retrievability of input information used for analysis, and output/work products. During these audits it became apparent that modifications to the architecture and scope of the database would benefit the EPA regulator and other stakeholders when reviewing the recertification application. This paper contains a discussion of the WPP PA CCA database and lessons learned for designing a database

Soft sensors with white- and black-box approaches for a wastewater treatment process

The increasing degradation of water resources makes it necessary to monitor and control process variables that may disturb the environment, but which may be very difficult to measure directly, either because there are no physical sensors available, or because these are too expensive. In this work, two soft sensors are proposed for monitoring concentrations of nitrate (NO) and ammonium (NH) ions, and of carbonaceous matter (CM) during nitrification of wastewater. One of them is based on reintegration of a process model to estimate NO and NH and on a feedforward neural network to estimate CM. The other estimator is based on Stacked Neural Networks (SNN), an approach that provides the predictor with robustness. After simulation, both soft sensors were implemented in an experimental unit using FIX MMI (Intellution, Inc) automation software as an interface between the process and MATLAB 5.1 (The Mathworks Inc.) software