On Ward Identities in Lifshitz-like Field Theories

In this work, we develop a normal product algorithm suitable to the study of anisotropic field theories in flat space, apply it to construct the symmetries generators and describe how their possible anomalies may be found. In particular, we discuss the dilatation anomaly in a scalar model with critical exponent z=2 in six spatial dimensions.Comment: Clarifications adde

Radiative Corrections to the Aharonov-Bohm Scattering

We consider the scattering of relativistic electrons from a thin magnetic flux tube and perturbatively calculate the order $\alpha$, radiative correction, to the first order Born approximation. We show also that the second order Born amplitude vanishes, and obtain a finite inclusive cross section for the one-body scattering which incorporates soft photon bremsstrahlung effects. Moreover, we determine the radiatively corrected Aharonov-Bohm potential and, in particular, verify that an induced magnetic field is generated outside of the flux tube.Comment: 14 pages, revtex, 3 figure

Four Fermion Field Theories and the Chern-Simons Field: A Renormalization Group Study

In (2+1) dimensions, we consider the model of a $N$ flavor, two-component fermionic field interacting through a Chern-Simons field besides a four fermion self-interaction which consists of a linear combination of the Gross-Neveu and Thirring like terms. The four fermion interaction is not perturbatively renormalizable and the model is taken as an effective field theory in the region of low momenta. Using Zimmerman procedure for reducing coupling constants, it is verified that, for small values of the Chern-Simons parameter, the origin is an infrared stable fixed point but changes to ultraviolet stable as $\alpha$ becomes bigger than a critical $\alpha_c$. Composite operators are also analyzed and it is shown that a specific four fermion interaction has an improved ultraviolet behavior as $N$ increases.Comment: 9 pages, revte

Runtime Distributions and Criteria for Restarts

Randomized algorithms sometimes employ a restart strategy. After a certain number of steps, the current computation is aborted and restarted with a new, independent random seed. In some cases, this results in an improved overall expected runtime. This work introduces properties of the underlying runtime distribution which determine whether restarts are advantageous. The most commonly used probability distributions admit the use of a scale and a location parameter. Location parameters shift the density function to the right, while scale parameters affect the spread of the distribution. It is shown that for all distributions scale parameters do not influence the usefulness of restarts and that location parameters only have a limited influence. This result simplifies the analysis of the usefulness of restarts. The most important runtime probability distributions are the log-normal, the Weibull, and the Pareto distribution. In this work, these distributions are analyzed for the usefulness of restarts. Secondly, a condition for the optimal restart time (if it exists) is provided. The log-normal, the Weibull, and the generalized Pareto distribution are analyzed in this respect. Moreover, it is shown that the optimal restart time is also not influenced by scale parameters and that the influence of location parameters is only linear

Optimal control strategies for tuberculosis treatment: a case study in Angola

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions. Numerical simulations are given using data from Angola.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 15-March-201

Topological Superconductor from the Quantum Hall Phase: Effective Field Theory Description

We derive low-energy effective field theories for the quantum anomalous Hall and topological superconducting phases. The quantum Hall phase is realized in terms of free fermions with nonrelativistic dispersion relation, possessing a global $U(1)$ symmetry. We couple this symmetry with a background gauge field and compute the effective action by integrating out the gapped fermions. In spite of the fact that the corresponding Dirac operator governing the dynamics of the original fermions is nonrelativistic, the leading contribution in the effective action is a usual Abelian $U(1)$ Chern-Simons term. The proximity to a conventional superconductor induces a pairing potential in the quantum Hall state, favoring the formation of Cooper pairs. When the pairing is strong enough, it drives the system to a topological superconducting phase, hosting Majorana fermions. Even though the continuum $U(1)$ symmetry is broken down to a $\mathbb{Z}_2$ one, we can forge fictitious $U(1)$ symmetries that enable us to derive the effective action for the topological superconducting phase, also given by a Chern-Simons theory. To eliminate spurious states coming from the artificial symmetry enlargement, we demand that the fields in the effective action are $O(2)$ instead of $U(1)$ gauge fields. In the $O(2)$ case we have to sum over the $\mathbb{Z}_2$ bundles in the partition function, which projects out the states that are not $\mathbb{Z}_2$ invariants. The corresponding edge theory is the $U(1)/\mathbb{Z}_2$ orbifold, which contains Majorana fermions in its operator content.Comment: 40 pages, 5 figures, journal versio

Quantum Rod Emission Coupled to Plasmonic Lattice Resonances: A Collective Directional Source of Polarized Light

We demonstrate that an array of optical antennas may render a thin layer of randomly oriented semiconductor nanocrystals into an enhanced and highly directional source of polarized light. The array sustains collective plasmonic lattice resonances which are in spectral overlap with the emission of the nanocrystals over narrow angular regions. Consequently, different photon energies of visible light are enhanced and beamed into definite directions.Comment: 4 pages, 3 figure

Influence of operating parameters on the biodegradation of steroid estrogens and nonylphenolic compounds during biological wastewater treatment processes

This document is the unedited author's version of a Submitted Work that was subsequently accepted for publication in Environmental Science & Technology, copyright © American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/es901612v.This study investigated operational factors influencing the removal of steroid estrogens and nonylphenolic compounds in two sewage treatment works, one a nitrifying/denitrifying activated sludge plant and the other a nitrifying/denitrifying activated sludge plant with phosphorus removal. Removal efficiencies of >90% for steroid estrogens and for longer chain nonylphenol ethoxylates (NP4−12EO) were observed at both works, which had equal sludge ages of 13 days. However, the biological activity in terms of milligrams of estrogen removed per day per tonne of biomass was found to be 50−60% more efficient in the nitrifying/denitrifying activated sludge works compared to the works which additionally incorporated phosphorus removal. A temperature reduction of 6 °C had no impact on the removal of free estrogens, but removal of the conjugated estrone-3-sulfate was reduced by 20%. The apparent biomass sorption (LogKp) values were greater in the nitrifying/denitrifying works than those in the nitrifying/denitrifying works with phosphorus removal for both steroid estrogens and nonylphenolic compounds possibly indicating a different cell surface structure and therefore microbial population. The difference in biological activity (mg tonne−1 d−1) identified in this study, of up to seven times, suggests that there is the potential for enhancing the removal of estrogens and nonylphenols if more detailed knowledge of the factors responsible for these differences can be identified and maximized, thus potentially improving the quality of receiving waters.Public Utilities Board (Singapore), Anglian Water Ltd, Severn Trent Water Ltd, Thames Water Utilities Ltd, United Utilities 393 Plc and Yorkshire Water Services