A comparison of best fit lines for data with outliers

Three techniques for determining a straight line fit to data are compared. The methods are applied to a range of datasets containing one or more outliers, and to a specific example from the field of chemistry. For the method which is the most resistant to the presence of outliers, a Microsoft Excel spreadsheet, as well as two Matlab routines, are included which can be used to determine the slope and intercept estimates.     

Hierarchical fractal‐structured allophanate‐derived network formation in bulk polyurethane synthesis

Polyurethanes are among the most applied and researched polymers worldwide. Nevertheless, polyurethane synthesis is accompanied by a side‐reaction occurring between isocyanate groups and the secondary nitrogen of already formed urethane groups, leading to the formation of crosslinking allophanates. This inevitably requires the development of highly diagnostic direct analytical methods that can be performed in the solid state of the polymer. The present research focused on the direct investigation and diagnostic determination of the chemical structure formation in bulk polyurethane synthesis, using a combination of Fourier transform infrared and solid‐state ¹³C nuclear magnetic resonance analysis. Polyurethane syntheses were performed in bulk and designed as to obtain significantly strong diagnostic analytical measurements signals for the accurate identification of each of the investigated chemical structures. The present research results led to the conclusive analytical identification of allophanate formation during polyurethane synthesis. In addition, the occurrence of a new reaction mechanism was discovered in the present research. It was demonstrated in the present research that this newly described reaction occurs via the further reaction of the allophanate secondary nitrogen with an isocyanate group, the reaction creating a tertiary nitrogen and an additional reactive secondary nitrogen, and so on, in a consecutive step progression, leading to the formation of a 3‐dimensional hierarchical fractal‐like crosslinked polymeric structure. Solid‐state ¹³C nuclear magnetic resonance analysis results were highly consistent with the Fourier transform infrared results. The discovery of this newly described reaction can facilitate the optimization of industrial processes and potentially opens a new door to the development of a vast variety of biomedical and nanotechnology applications.     

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-II hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size, we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively, and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.     

Autonomously Propelled Motors for Value‐Added Product Synthesis and Purification

A proof‐of‐concept design for autonomous, self‐propelling motors towards value‐added product synthesis and separation is presented. The hybrid motor design consists of two distinct functional blocks. The first, a sodium borohydride (NaBH₄) granule, serves both as a reaction prerequisite for the reduction of vanillin and also as a localized solid‐state fuel in the reaction mixture. The second capping functional block consisting of a graphene–polymer composite serves as a hydrophobic matrix to attract the reaction product vanillyl alcohol (VA), resulting in facile separation of this edible value‐added product. These autonomously propelled motors were fabricated at a length scale down to 400 μm, and once introduced in the reaction environment showed rapid bubble‐propulsion followed by high‐purity separation of the reaction product (VA) by the virtue of the graphene–polymer cap acting as a mesoporous sponge. The concept has excellent potential towards the synthesis/isolation of industrially important compounds, affinity‐based product separation, pollutant remediation (such as heavy metal chelation/adsorption), as well as localized fuel‐gradients as an alternative to external fuel dependency.     

Dynamic modeling of the morphology of latex particles with in situ formation of graft copolymer

Modification of the polymer–polymer interfacial tension is a way to tailor‐make particle morphology of waterborne polymer–polymer hybrids. This allows achieving a broader spectrum of application properties and maximizing the synergy of the positive properties of both polymers, avoiding their drawbacks. In situ formation of graft copolymer during polymerization is an efficient way to modify the polymer–polymer interfacial tension. Currently, no dynamic model is available for polymer–polymer hybrids in which a graft copolymer is generated during polymerization. In this article, a novel model based on stochastic dynamics is developed for predicting the dynamics of the development of particle morphology for composite waterborne systems in which a graft copolymer is produced in situ during the process. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Validation of a novel very large eddy simulation method for simulation of turbulent separated flow

The paper describes the validation of a newly developed very LES (VLES) method for the simulation of turbulent separated flow. The new VLES method is a unified simulation approach that can change seamlessly from Reynolds‐averaged Navier–Stokes to DNS depending on the numerical resolution. Four complex test cases are selected to validate the performance of the new method, that is, the flow past a square cylinder at Re = 3000 confined in a channel (with a blockage ratio of 20%), the turbulent flow over a circular cylinder at Re = 3900 as well as Re = 140,000, and a turbulent backward‐facing step flow with a thick incoming boundary layer at Re = 40,000. The simulation results are compared with available experimental, LES, and detached eddy simulation‐type results. The new VLES model performs well overall, and the predictions are satisfactory compared with previous experimental and numerical results. It is observed that the new VLES method is quite efficient for the turbulent flow simulations; that is, good predictions can be obtained using a quite coarse mesh compared with the previous LES method. Discussions of the implementation of the present VLES modeling are also conducted on the basis of the simulations of turbulent channel flow up to high Reynolds number of Re_τ = 4000. The efficiency of the present VLES modeling is also observed in the channel flow simulation. From a practical point of view, this new method has considerable potential for more complex turbulent flow simulations at relative high Reynolds numbers. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical simulation and convergence analysis for a system of nonlinear singularly perturbed differential equations arising in population dynamics

In this article, we consider a system of nonlinear singularly perturbed differential equations with two different parameters. To solve this system, we develop a weighted monotone hybrid scheme on a nonuniform mesh. The proposed scheme is a combination of the midpoint scheme and the upwind scheme involving the weight parameters. The weight parameters enable the method to switch automatically from the midpoint scheme to the upwind scheme as the nodal points start moving from the inner region to the outer region. The nonuniform mesh in particular the adaptive grid is constructed using the idea of equidistributing a positive monitor function involving the solution gradient. The method is shown to be second order convergent with respect to the small parameters. Numerical experiments are presented to show the robustness of the proposed scheme and indicate that the estimate is optimal.     

Study of flame-retardant finishing of cellulose fibres: Organic–inorganic hybrid versus conventional organophosphonate

The aim of this study was to introduce a non-formaldehyde inorganic–organic hybrid sol–gel flame-retardant precursor (SiOP) containing phosphorous, nitrogen, and silicon and to compare its functional properties with those of the conventional formaldehyde-containing organic flame-retardant agent, organophosphonate (OP). SiOP was used at concentrations of 2%, 4%, and 8%, and OP was used at a concentration of 200 g/dm³. Both agents were applied to 100% cotton (CO) woven fabric by the pad-dry-cure method under the appropriate conditions. The presence of the SiOP and OP coatings on the CO fabric was confirmed by scanning electron microscopy, energy dispersive X-ray spectroscopy and Fourier-transform infrared spectroscopy. The results of the vertical tests of flammability and the thermogravimetric analyses showed that the presence of the SiOP coating changed the thermal degradation pathway of the CO fabric and resulted in an increase in the thermo-oxidative stability of the cellulose fibres. The thermo-oxidative stability was enhanced by the addition of higher amount of dry solids. At comparable dry solids contents, OP preserved significantly greater flame retardancy and thermo-oxidative stability than did SiOP. These results indicated that the SiOP precursor could not act as an effective alternative to the OP agent in the flame-retardant protection of CO fabric.