Analytical method for designing dispersion-managed fiber systems

This paper was published in Optics Letters and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/abstract.cfm?URI=ol-26-20-1544. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.Peer reviewedPublisher PD

Analytical maximum-likelihood method to detect patterns in real networks

In order to detect patterns in real networks, randomized graph ensembles that preserve only part of the topology of an observed network are systematically used as fundamental null models. However, their generation is still problematic. The existing approaches are either computationally demanding and beyond analytic control, or analytically accessible but highly approximate. Here we propose a solution to this long-standing problem by introducing an exact and fast method that allows to obtain expectation values and standard deviations of any topological property analytically, for any binary, weighted, directed or undirected network. Remarkably, the time required to obtain the expectation value of any property is as short as that required to compute the same property on the single original network. Our method reveals that the null behavior of various correlation properties is different from what previously believed, and highly sensitive to the particular network considered. Moreover, our approach shows that important structural properties (such as the modularity used in community detection problems) are currently based on incorrect expressions, and provides the exact quantities that should replace them.Comment: 26 pages, 10 figure

Using the stress function in the flow of generalized Newtonian fluids through pipes and slits

We use a generic and general numerical method to obtain solutions for the flow of generalized Newtonian fluids through circular pipes and plane slits. The method, which is simple and robust can produce highly accurate solutions which virtually match any analytical solutions. The method is based on employing the stress, as a function of the pipe radius or slit thickness dimension, combined with the rate of strain function as represented by the fluid rheological constitutive relation that correlates the rate of strain to stress. Nine types of generalized Newtonian fluids are tested in this investigation and the solutions obtained from the generic method are compared to the analytical solutions which are obtained from the Weissenberg-Rabinowitsch-Mooney-Schofield method. Very good agreement was obtained in all the investigated cases. All the required quantities of the flow which include local viscosity, rate of strain, flow velocity profile and volumetric flow rate, as well as shear stress, can be obtained from the generic method. This is an advantage as compared to some traditional methods which only produce some of these quantities. The method is also superior to the numerical meshing techniques which may be used for resolving the flow in these systems. The method is particularly useful when analytical solutions are not available or when the available analytical solutions do not yield all the flow parameters.Comment: 15 pages, 2 figures, 2 tables. arXiv admin note: text overlap with arXiv:1503.0126

On-line monitoring of the transesterification reaction between triglycerides and ethanol using near infrared spectroscopy combined with gas chromatography

Many analytical procedures have been developed to determine the composition of reaction mixtures during transesterification of vegetable oils with alcohols. However, despite their accuracy, these methods are time consuming and cannot be easily used for on-line monitoring. In this work, a fast analytical method was developed to on-line monitor the transesterification reaction of high oleic sunflower oil with ethanol using Near InfraRed spectroscopy and a multivariate approach. The reactions were monitored through sequential scans of the reaction medium with a probe in a one-liter batch reactor without collecting and preparing samples. To calibrate the NIR analytical method, gas chromatography-flame ionization detection was used as a reference method. The method was validated by studying the kinetics of the EtONa-catalyzed transesterification reaction. Activation energy (51.0 kJ/mol) was also determined by considering a pseudo second order kinetics model

An analytical method for designing low noise helicopter transmissions

The development and experimental validation of a method for analytically modeling the noise mechanism in the helicopter geared power transmission systems is described. This method can be used within the design process to predict interior noise levels and to investigate the noise reducing potential of alternative transmission design details. Examples are discussed