On the fractal characteristics of a stabilised Newton method

In this report, we present a complete theory for the fractal that is obtained when applying Newton's Method to find the roots of a complex cubic. We show that a modified Newton's Method improves convergence and does not yield a fractal, but basins of attraction with smooth borders. Extensions to higher-order polynomials and the numerical relevance of this fractal analysis are discussed

Fractal Characteristics of Newton's Method on Polynomials

In this report, we present a simple geometric generation principle for the fractal that is obtained when applying Newton's method to find the roots of a general complex polynomial with real coefficients. For the case of symmetric polynomials $z^{\nu}-1$ , the generation mechanism is derived from first principles. We discuss the case of a general cubic and are able to give a description of the arising fractal structure depending on the coefficients of the cubic. Special cases are analysed and their characteristics, including scale factors and an approximate fractal dimension, are derived. The theoretical results are confirmed via computational experiments. An application of the theory in turbulence modelling is presented

A Successful Cool Storage Rate

Houston Lighting & Power (HL&P) initiated design and development of its commercial cool storage program as part of an integrated resource planning process with a targeted 225 MW of demand reduction through DSM. Houston's extensive commercial air conditioning load, which is highly coincident with HL&P's system peak, provided a large market for cool storage technologies. Initial market research made it very clear that a special cool storage rate was required to successfully market the technology. Development of the rate required an integrated, multidepartment effort and extensive use of DSManager, an integrated resource planning model. An experimental version of the rate was initially implemented as part of the initial phase of the cool storage program. A permanent rate, incorporating lessons learned from the experimental rate, was then developed for the long term implementation of the program. The permanent rate went through a lengthy regulatory approval process which included intervention by a local natural gas distribution company. The end result is a very successful cool storage program with 52 projects and 31 megawatts of demand reduction in the first three and one-half years of program implementation

The response of Oregon shelf waters to wind fluctuations : differences and the transition between winter and summer

The physical characteristics of continental shelf waters off Oregon during late winter and spring of 1975 are described and compared with observations taken previously during summer. The currents in winter are barotropic in the monthly means while in summer the currents are baroclinic. Alongshore current fluctuations on the time scale of a few days are depth dependent in winter but become depth independent in summer. The current shear changes sign on the several day time scale in winter while in summer the deeper currents are always northward with respect to the near surface currents. Alongshore coherences of sea level and currents indicate that winter fluctuations generally propagate southward rather than northward as previously observed in summer. These winter fluctuations in alongshore currents also have onshore/offshore phase speeds that are comparable in magnitude to their alongshore phase speeds. There is no evidence for free continental shelf wave activity in winter although forced waves (travelling predominately southward, as do the meteorological disturbances) may exist. The Gill and Schumann (1974) model, which predicts sea level from a knowledge of the alongshore components of winds along the coastline, is tested for winter and summer in 1975 and found to have some predictive ability for fluctuations on the time scale of several days. The transition from winter to summer is initiated in a dramatic barotropic event and continues as a longer period baroclinic adjustment. The former is marked by a sudden reversal of currents and a lowering of sea level while the latter is marked by a slow rising of the pycnocline and with it the layer of maximum vertical shear. Both the barotropic changes at the transition event and the adjustment of the density field, which occurs after the transition event, are directly forced by the local wind

Nox1 oxidase suppresses influenza a virus-induced lung inflammation and oxidative stress

Influenza A virus infection is an ongoing clinical problem and thus, there is an urgent need to understand the mechanisms that regulate the lung inflammation in order to unravel novel generic pharmacological strategies. Evidence indicates that the Nox2-containing NADPH oxidase enzyme promotes influenza A virus-induced lung oxidative stress, inflammation and dysfunction via ROS generation. In addition, lung epithelial and endothelial cells express the Nox1 isoform of NADPH oxidase, placing this enzyme at key sites to regulate influenza A virus-induced lung inflammation. The aim of this study was to investigate whether Nox1 oxidase regulates the inflammatory response and the oxidative stress to influenza infection in vivo in mice. Male WT and Nox1-deficient (Nox1−/y) mice were infected with the moderately pathogenic HkX-31 (H3N2, 1×104 PFU) influenza A virus for analysis of bodyweight, airways inflammation, oxidative stress, viral titre, lung histopathology, and cytokine/chemokine expression at 3 and 7 days post infection. HkX-31 virus infection of Nox1−/y mice resulted in significantly greater: loss of bodyweight (Day 3); BALF neutrophilia, peri-bronchial, peri-vascular and alveolar inflammation; Nox2-dependent inflammatory cell ROS production and peri-bronchial, epithelial and endothelial oxidative stress. The expression of pro-inflammatory cytokines including CCL2, CCL3, CXCL2, IL-1β, IL-6, GM-CSF and TNF-α was higher in Nox1−/y lungs compared to WT mice at Day 3, however, the expression of CCL2, CCL3, CXCL2, IFN-γ and the anti-inflammatory cytokine IL-10 were lower in lungs of Nox1−/y mice vs. WT mice at Day 7. Lung viral titre, and airways infiltration of active CD8+ and CD4+ T lymphocytes, and of Tregs were similar between WT and Nox1−/y mice. In conclusion, Nox1 oxidase suppresses influenza A virus induced lung inflammation and oxidative stress in mice particularly at the early phases of the infection. Nox1 and Nox2 oxidases appear to have opposing roles in the regulation of inflammation caused by influenza A viruses

Nitrite is produced by elicited but not by circulating neutrophils

The generation of nitrite (NO2-) was used as an index of the production of nitric oxide by human and rat polymorphonuclear leukocytes (PMN) and rat peritoneal macrophages. Human peripheral blood PMN did not produce significant levels of NO2-. Attempts to induce NO2- generation in human PMN by incubation with GM–CSF (1 nM), TNFα (0.3 nM), endotoxin (1 μg/ml) or formyl-Met-Leu-Phe (100 nM) for up to 16 h were not successful. Addition of human PMN primed by GM–CSF (1 nM) to rabbit aortic ring preparations precontracted with phenylephrine had no effect on tone. In contrast to these observations, PMN, isolated from the peritoneum of oyster glycogen treated rats, generated NO2- via a pathway sensitive to inhibition by the nitric oxide synthase inhibitor, NG-monomethyl L-arginine. However, peripheral blood rat PMN obtained from the same animals did not produce NO2-, even during prolonged incubation for periods of up to 16 h. It is suggested that detectable NO production by PMN requires NO synthase activity to be induced either by the process of PMN migration or by exposure to certain cytokines produced locally at the site of inflammation