Rotordynamic analysis of a bearing tester

The properties of the solutions of a system of four coupled nonlinear differential equations that model the behavior of the rotating shaft of a bearing tester are studied. In particular, it is shown how the bounds for the rotations of these equations can be obtained from bounds for the solutions of the linearized equations. By studying the behavior of the Fourier transforms of the solution, the approach to the stability boundary can also be predicted. These conclusions are verified by means of numerical solutions of the equations, and of power spectrum density (PSD) plots

The Jeffcott equations in nonlinear rotordynamics

The Jeffcott equations are a system of coupled differential equations representing the behavior of a rotating shaft. This is a simple model which allows investigation of the basic dynamic behavior of rotating machinery. Nolinearities can be introduced by taking into consideration deadband, side force, and rubbing, among others. The properties of the solutions of the Jeffcott equations with deadband are studied. In particular, it is shown how bounds for the solution of these equations can be obtained from bounds for the solutions of the linearized equations. By studying the behavior of the Fourier transforms of the solutions, we are also able to predict the onset of destructive vibrations. These conclusions are verified by means of numerical solutions of the equations, and of power spectrum density (PSD) plots. This study offers insight into a possible detection method to determine pump stability margins during flight and hot fire tests, and was motivated by the need to explain a phenomenon observed in the development phase of the cryogenic pumps of the Space Shuttle, during hot fire ground testing; namely, the appearance of vibrations at frequencies that could not be accounted for by means of linear models

A method for the early detection of instabilities in rotordynamics

For a simple Jeffcott model with deadband, a method is developed to determine stability margins by an analysis of the Discrete Fourier transform of the system response. The viability of this method is demonstrated by means of numerical simulations. The circular behavior of the system response on the stability boundary is also explained

Bases of translates and multiresolution analyses

AbstractUsing the theory of basis generators we study various properties of multivariate Riesz and orthonormal sequences of translates, with emphasis on those associated with multiresolution analyses and their connection with wavelets. In particular, we show that every multiresolution analysis of multiplicity n generated by a dilation matrix preserving the lattice Zd has an orthonormal wavelet system associated with it, and give a closed form representation in Fourier space for such wavelet systems. We illustrate these results by applying them to the case of univariate wavelets associated with multiresolution analyses with binary dilations

Some smooth compactly supported tight framelets associated to the quincunx matrix

We construct several families of tight wavelet frames in L2(R2)L2(R2) associated to the quincunx matrix. A couple of those families has five generators. Moreover, we construct a family of tight wavelet frames with three generators. Finally, we show families with only two generators. The generators have compact support, any given degree of regularity, and any fixed number of vanishing moments. Our construction is made in Fourier space and involves some refinable functions, the Oblique Extension Principle and a slight generalization of a theorem of Lai and Stöckler. In addition, we will use well known results on construction of tight wavelet frames with two generators on RR with the dyadic dilation. The refinable functions we use are constructed from the Daubechies low pass filters and are compactly supported. The main difference between these families is that while the refinable functions associated to the five generators have many symmetries, the refinable functions used in the construction of the others families are merely even.The first author was partially supported by MEC/MICINN grant #MTM2011-27998 (Spain)

A family of nonseparable scaling functions and compactly supported tight framelets

Given integers b and d, with d>1 and |b|>1, we construct even nonseparable compactly supported refinable functions with dilation factor bb that generate multiresolution analyses on L2(Rd). These refinable functions are nonseparable, in the sense that they cannot be expressed as the product of two functions defined on lower dimensions. We use these scaling functions and a slight generalization of a theorem of Lai and Stöckler to construct smooth compactly supported tight framelets. Both the refinable functions and the framelets they generate can be made as smooth as desired. Estimates for the supports of these refinable functions and framelets, are given.The first author was partially supported by Spanish Science Ministry grant JC2010-0012

Some Smooth Compactly Supported Tight Wavelet Frames with Vanishing Moments

Let A∈Rd×d, d≥1 be a dilation matrix with integer entries and |detA|=2. We construct several families of compactly supported Parseval framelets associated to A having any desired number of vanishing moments. The first family has a single generator and its construction is based on refinable functions associated to Daubechies low pass filters and a theorem of Bownik. For the construction of the second family we adapt methods employed by Chui and He and Petukhov for dyadic dilations to any dilation matrix A. The third family of Parseval framelets has the additional property that we can find members of that family having any desired degree of regularity. The number of generators is 2d+d and its construction involves some compactly supported refinable functions, the Oblique Extension Principle and a slight generalization of a theorem of Lai and Stöckler. For the particular case d=2 and based on the previous construction, we present two families of compactly supported Parseval framelets with any desired number of vanishing moments and degree of regularity. None of these framelet families have been obtained by means of tensor products of lower-dimensional functions. One of the families has only two generators, whereas the other family has only three generators. Some of the generators associated with these constructions are even and therefore symmetric. All have even absolute values.The first author was partially supported by MEC/MICINN Grant #MTM2011-27998 (Spain)

Epidemiological risk factors for clinical malaria infection in the highlands of Western Kenya.

BackgroundUnderstanding the complex heterogeneity of risk factors that can contribute to an increased risk of malaria at the individual and household level will enable more effective use of control measures. The objective of this study was to understand individual and household factors that influence clinical malaria infection among individuals in the highlands of Western Kenya.MethodsThis was a matched case-control study undertaken in the Western Kenya highlands. Clinical malaria cases were recruited from health facilities and matched to asymptomatic individuals from the community who served as controls. Each participant was screened for malaria using microscopy. Follow-up surveys were conducted with individual households to collect socio-economic data. The houses were also checked using pyrethrum spray catches to collect mosquitoes.ResultsA total of 302 malaria cases were matched to 604 controls during the surveillance period. Mosquito densities were similar in the houses of both groups. A greater percentage of people in the control group (64.6%) used insecticide-treated bed nets (ITNs) compared to the families of malaria cases (48.3%). Use of ITNs was associated with lower level of clinical malaria episodes (odds ratio 0.51; 95% CI 0.39-0.68; P < 0.0001). Low income was the most important factor associated with higher malaria infections (adj. OR 4.70). Use of malaria prophylaxis was the most important factor associated with less malaria infections (adj OR 0.36). Mother's (not fathers) employment status (adj OR 0.48) and education level (adj OR 0.54) was important malaria risk factor. Houses with open eaves was an important malaria risk factor (adj OR 1.72).ConclusionThe identification of risk factors for clinical malaria infection provides information on the local malaria epidemiology and has the potential to lead to a more effective and targeted use of malaria control measures. These risk factors could be used to assess why some individuals acquire clinical malaria whilst others do not and to inform how intervention could be scaled at the local level

An Environmental Genocide: Counting the Human and Environmental Cost of Oil in Bayelsa, Nigeria

NoBayelsa, in the Niger Delta, in Southern Nigeria, is in the grip of a human and environmental catastrophe of unimaginable proportions. At one time, the area was home to one of the largest mangrove forests on the planet; an area of unrivalled ecological value. Today, it is one of the most polluted places on Earth. Oil extraction and its impact is the overwhelmingly evident cause of this disaster

A cohort study of Plasmodium falciparum infection dynamics in Western Kenya Highlands

Abstract Background The Kenyan highlands were malaria-free before the 1910s, but a series of malaria epidemics have occurred in the highlands of western Kenya since the 1980s. Longitudinal studies of the genetic structure, complexity, infection dynamics, and duration of naturally acquired Plasmodium falciparum infections are needed to facilitate a comprehensive understanding of malaria epidemiology in the complex Kenyan highland eco-epidemiological systems where malaria recently expanded, as well as the evaluation of control measures. Methods We followed a cohort of 246 children residing in 3 villages at altitudes 1430 - 1580 m in western Kenya. Monthly parasitological surveys were undertaken for one year, yielding 866 P. falciparum isolates that were analyzed using 10 microsatellite markers. Results Infection complexity and genetic diversity were high (HE = 0.787-0.816), with ≥83% of infections harboring more than one parasite clone. Diversity remained high even during the low malaria transmission season. There was no significant difference between levels of genetic diversity and population structure between high and low transmission seasons. Infection turn-over rate was high, with the average infection duration of single parasite genotypes being 1.11 months, and the longest genotype persistence was 3 months. Conclusions These data demonstrate that despite the relatively recent spread of malaria to the highlands, parasite populations seem to have stabilized with no evidence of bottlenecks between seasons, while the ability of residents to clear or control infections indicates presence of effective anti-plasmodial immune mechanisms