3-Dimensional hopf bifurcation via averaging theory

We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br - b, r - 1), in the Lorenz case, and at s± = (c+√c2-4ab/2, -c+√c2-4ab/2a, c±√c2-4ab/2a) in the Rössler case. As usual this Hopf bifurcation is in the sense that an one-parameter family in ε of limit cycles bifurcates from the singular point when ε = 0. Moreover, we can determine the kind of stability of these limit cycles. In fact, for both systems we can prove that all the bifurcated limit cycles in a neighborhood of the singular point are either a local attractor, or a local repeller, or they have two invariant manifolds, one stable and the other unstable, which locally are formed by two 2-dimensional cylinders. These results are proved using averaging theory. The method of studying the Hopf bifurcation using the averaging theory is relatively general and can be applied to other 3- or n-dimensional differential systems.

A Method for Detecting Population Genetic Structure in Diverse, High Gene-Flow Species

Detecting small amounts of genetic subdivision across geographic space remains a persistent challenge. Often a failure to detect genetic structure is mistaken for evidence of panmixia, when more powerful statistical tests may uncover evidence for subtle geographic differentiation. Such slight subdivision can be demographically and evolutionarily important as well as being critical for management decisions. We introduce here a method, called spatial analysis of shared alleles (SAShA), that detects geographically restricted alleles by comparing the spatial arrangement of allelic co-occurrences with the expectation under panmixia. The approach is allele-based and spatially explicit, eliminating the loss of statistical power that can occur with user-defined populations and statistical averaging within populations. Using simulated data sets generated under a stepping-stone model of gene flow, we show that this method outperforms spatial autocorrelation (SA) and UST under common real-world conditions: at relatively high migration rates when diversity is moderate or high, especially when sampling is poor. We then use this method to show clear differences in the genetic patterns of 2 nearshore Pacific mollusks, Tegula funebralis (5 Chlorostoma funebralis) and Katharina tunicata, whose overall patterns of within-species differentiation are similar according to traditional population genetics analyses. SAShA meaningfully complements UST/FST, SA, and other existing geographic genetic analyses and is especially appropriate for evaluating species with high gene flow and subtle genetic differentiation.

Real-time analysis of δ13C- and δD-CH4 in ambient air with laser spectroscopy: method development and first intercomparison results

In situ and simultaneous measurement of the three most abundant isotopologues of methane using mid-infrared laser absorption spectroscopy is demonstrated. A field-deployable, autonomous platform is realized by coupling a compact quantum cascade laser absorption spectrometer (QCLAS) to a preconcentration unit, called trace gas extractor (TREX). This unit enhances CH4 mole fractions by a factor of up to 500 above ambient levels and quantitatively separates interfering trace gases such as N2O and CO2. The analytical precision of the QCLAS isotope measurement on the preconcentrated (750 ppm, parts-per-million, µmole mole−1) methane is 0.1 and 0.5 ‰ for δ13C- and δD-CH4 at 10 min averaging time. Based on repeated measurements of compressed air during a 2-week intercomparison campaign, the repeatability of the TREX–QCLAS was determined to be 0.19 and 1.9 ‰ for δ13C and δD-CH4, respectively. In this intercomparison campaign the new in situ technique is compared to isotope-ratio mass spectrometry (IRMS) based on glass flask and bag sampling and real time CH4 isotope analysis by two commercially available laser spectrometers. Both laser-based analyzers were limited to methane mole fraction and δ13C-CH4 analysis, and only one of them, a cavity ring down spectrometer, was capable to deliver meaningful data for the isotopic composition. After correcting for scale offsets, the average difference between TREX–QCLAS data and bag/flask sampling–IRMS values are within the extended WMO compatibility goals of 0.2 and 5 ‰ for δ13C- and δD-CH4, respectively. This also displays the potential to improve the interlaboratory compatibility based on the analysis of a reference air sample with accurately determined isotopic composition.

Parametric aggregation in ordered weighted averaging

Incorporating further information into the ordered weighted averaging (OWA) operator weights is investigated in this paper. We first prove that for a constant orness the minimax disparity model [13] has unique optimal solution while the modified minimax disparity model [16] has alternative optimal OWA weights. Multiple optimal solutions in modified minimax disparity model provide us opportunity to define a parametric aggregation OWA which gives flexibility to decision makers in the process of aggregation and selecting the best alternative. Finally, the usefulness of the proposed parametric aggregation method is illustrated with an application in metasearch engine. © 2011 Elsevier Inc. All rights reserved.

Indirect ties in knowledge networks:a social network analysis with ordered weighted averaging operators

This PhD thesis analyses networks of knowledge flows, focusing on the role of indirect ties in the knowledge transfer, knowledge accumulation and knowledge creation process. It extends and improves existing methods for mapping networks of knowledge flows in two different applications and contributes to two stream of research. To support the underlying idea of this thesis, which is finding an alternative method to rank indirect network ties to shed a new light on the dynamics of knowledge transfer, we apply Ordered Weighted Averaging (OWA) to two different network contexts. Knowledge flows in patent citation networks and a company supply chain network are analysed using Social Network Analysis (SNA) and the OWA operator. The OWA is used here for the first time (i) to rank indirect citations in patent networks, providing new insight into their role in transferring knowledge among network nodes; and to analyse a long chain of patent generations along 13 years; (ii) to rank indirect relations in a company supply chain network, to shed light on the role of indirectly connected individuals involved in the knowledge transfer and creation processes and to contribute to the literature on knowledge management in a supply chain. In doing so, indirect ties are measured and their role as means of knowledge transfer is shown. Thus, this thesis represents a first attempt to bridge the OWA and SNA fields and to show that the two methods can be used together to enrich the understanding of the role of indirectly connected nodes in a network. More specifically, the OWA scores enrich our understanding of knowledge evolution over time within complex networks. Future research can show the usefulness of OWA operator in different complex networks, such as the on-line social networks that consists of thousand of nodes.

Application of ensemble averaging to the analysis of electromyography recordings under whole body vibratory stimulation

The aim of this study is to evaluate the application of ensemble averaging to the analysis of electromyography recordings under whole body vibratory stimulation. Recordings from Rectus Femoris, collected during vibratory stimulation at different frequencies, are used. Each signal is subdivided in intervals, which time duration is related to the vibration frequency. Finally the average of the segmented intervals is performed. By using this method for the majority of the recordings the periodic components emerge. The autocorrelation of few seconds of signals confirms the presence of a pseudosinusoidal components strictly related to the soft tissues oscillations caused by the mechanical waves. © 2014 IEEE.

A laser induced breakdown spectroscopy quantitative analysis method based on the robust least squares support vector machine regression model

Data fluctuation in multiple measurements of Laser Induced Breakdown Spectroscopy (LIBS) greatly affects the accuracy of quantitative analysis. A new LIBS quantitative analysis method based on the Robust Least Squares Support Vector Machine (RLS-SVM) regression model is proposed. The usual way to enhance the analysis accuracy is to improve the quality and consistency of the emission signal, such as by averaging the spectral signals or spectrum standardization over a number of laser shots. The proposed method focuses more on how to enhance the robustness of the quantitative analysis regression model. The proposed RLS-SVM regression model originates from the Weighted Least Squares Support Vector Machine (WLS-SVM) but has an improved segmented weighting function and residual error calculation according to the statistical distribution of measured spectral data. Through the improved segmented weighting function, the information on the spectral data in the normal distribution will be retained in the regression model while the information on the outliers will be restrained or removed. Copper elemental concentration analysis experiments of 16 certified standard brass samples were carried out. The average value of relative standard deviation obtained from the RLS-SVM model was 3.06% and the root mean square error was 1.537%. The experimental results showed that the proposed method achieved better prediction accuracy and better modeling robustness compared with the quantitative analysis methods based on Partial Least Squares (PLS) regression, standard Support Vector Machine (SVM) and WLS-SVM. It was also demonstrated that the improved weighting function had better comprehensive performance in model robustness and convergence speed, compared with the four known weighting functions.

Volume averaging of multiphase flows with hydrate formation in subsea pipelines

In oil and gas pipeline operations, the gas, oil, and water phases simultaneously move through pipe systems. The mixture cools as it flows through subsea pipelines, and forms a hydrate formation region, where the hydrate crystals start to grow and may eventually block the pipeline. The potential of pipe blockage due to hydrate formation is one of the most significant flow-assurance problems in deep-water subsea operations. Due to the catastrophic safety and economic implications of hydrate blockage, it is important to accurately predict the simultaneous flow of gas, water, and hydrate particles in flowlines. Currently, there are few or no studies that account for the simultaneous effects of hydrate growth and heat transfer on flow characteristics within pipelines. This thesis presents new and more accurate predictive models of multiphase flows in undersea pipelines to describe the simultaneous flow of gas, water, and hydrate particles through a pipeline. A growth rate model for the hydrate phase is presented and then used in the development of a new three-phase model. The conservation equations of mass, momentum, and energy are formulated to describe the physical phenomena of momentum and heat transfer between the fluid and the wall. The governing equations are solved based on an analytical-numerical approach using a Newton-Raphson method for the nonlinear equations. An algorithm was developed in Matlab software to solve the equations from the inlet to the outlet of the pipeline. The developed models are validated against a single-phase model with mixture properties, and the results of comparative studies show close agreement. The new model predicts the volume fraction and velocity of each phase, as well as the mixture pressure and temperature profiles along the length of the pipeline. The results from the hydrate growth model reveal the growth rate and location where the initial hydrates start to form. Finally, to assess the impact of certain parameters on the flow characteristics, parametric studies have been conducted. The results show the effect of a variation in the pipe diameter, mass flow rate, inlet pressure, and inlet temperature on the flow characteristics and hydrate growth rates.

Characterization of Chimney Flue Gas Flows : Flow Rate Measurements with Averaging Pitot Probes

Performance testing methods of boilers in transient operating conditions (start, stop and combustion power modulation sequences) need the combustion rate quantified to allow for the emissions to be quantified. One way of quantifying the combustion rate of a boiler during transient operating conditions is by measuring the flue gas flow rate. The flow conditions in chimneys of single family house boilers pose a challenge however, mainly because of the low flow velocity. The main objectives of the work were to characterize the flow conditions in residential chimneys, to evaluate the use of the Pitot-static method and the averaging Pitot method, and to develop and test a calibration method for averaging Pitot probes for low

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.