Continuous contact force models for impact analysis in multibody systems

One method for predicting the impact response of a multibody system is based on the assumption that the impacting bodies undergo local deformations and the contact forces are continuous. In a continuous analysis, the integration of the system equations of motion is carried out during the period of contact; therefore, a model for evaluating the contact forces is required. In this paper, two such contact force models are presented, both Hertzian in nature and based upon the direct-central impact of two solid particles.At low impact velocities, the energy dissipation during impact can be represented by material damping. A model is constructed based on the general trend of the Hertz contact law in conjuction with a hysteresis damping function. The unknown parameters are determined in terms of a given coefficient of restitution and the impact velocity. When local plasticity effects are the dominant factor accounting for the dissipation of energy at high impact velocities, a Hertzian contact force model with permanent indentation is constructed. Utilizing energy and momentum considerations, the unknown parameters in the model are again evaluated. The two particle models are generalized to an impact analysis between two bodies of a multibody system.     

Determination of cerium(III) ions in soil and sediment samples by Ce(III) PVC-based membrane electrode based on 2,5-dioxo-4-imidazolidinyl

2,5-Dioxo-4-imidazolidinyl was used as an excellent sensing material in the preparation of a PVC membrane for a Ce(III)-selective sensor. The electrode shows a good selectivity for the Ce(III) ion with respect to most common cations including alkali, alkaline earth, transition, and heavy metal ions. The developed sensor exhibits a wide linear response with a slope of 19.6?±?0.3 mV per decade over the concentration range of 1.0?×?10^?6 to 1.0?×?10^?1 M, while the illustrated detection limit is 5.7?×?10^?7 M of Ce(III) ions. Moreover, it is concluded that the sensor response is pH-independent in the range of 3.1–9.8. The applications of the recommended electrode include the determination of concentration of Ce(III) ions in soil and sediment samples, validation with CRM's, and the Ce(III) ion potentiometric titration with EDTA as an indicator electrode.     

Rapid and sensitive determination of biphenyl and biphenyl oxide in water samples using dispersive liquid–liquid microextraction followed by gas chromatography

A rapid and sensitive method has been developed for the determination of biphenyl and biphenyl oxide in water samples using dispersive liquid–liquid microextraction followed by gas chromatography. This method involves the use of an appropriate mixture of extraction solvent (8.0?µL tetrachloroethylene) and disperser solvent (1.0?mL acetonitrile) for the formation of cloudy solution in 5.0?mL aqueous sample containing biphenyl and biphenyl oxide. After extraction, phase separation was performed by centrifugation and biphenyl and biphenyl oxide in sedimented phase (5.0?±?0.3?µL) were determined by gas chromatography-flame ionisation (GC-FID) system. Type of extraction and disperser solvents and their volumes, salt effect on the extraction recovery of biphenyl and biphenyl oxide from aqueous solution have been investigated. Under the optimum conditions and without salt addition, the enrichment factors for biphenyl and biphenyl oxide were 819 and 785, while the extraction recovery were 81.9% and 78.5%, respectively. The linear range was (0.125–100?µg L^?1) and limit of detection was (0.015?µg?L^?1) for both analytes. The relative standard deviation (RSD, n?=?4) for 5.0?µg?L^?1 of analytes were 8.4% and 6.7% for biphenyl and biphenyl oxide, respectively. The relative recoveries of biphenyl and biphenyl oxide from sea, river water and refined water (Paksan company) samples at spiking level of 5.0?µg?L^?1 were between 85.0% and 100 %.     

A selective modified nanoporous silica as sorbent for separation and preconcentration of dysprosium in water samples prior to ICP-OES determination

In this research a new physically functionalized nanoporous silica (SBA-15) using N′-[(2-hydroxy phenyl) methylene] benzohydrazide (BBH) was utilized as a selective sorbent for the separation, preconcentration and determination of dysprosium (Dy) in natural water by inductively coupled plasma optical emission spectrometry (ICP-OES). The selectivity of BBH to Dy (III) ion was previously tested by conductometric and spectroscopic methods. Conditions for effective adsorption of Dy were optimized with respect to experimental parameters in batch process. The extraction recovery was 96.5, analytical curve was linear in the range 0.2–1000?µgL^?1, and the detection limit was 0.05?ng?mL^?1. The relative standard deviation (RSD) under optimal conditions was 3.2% (n?=?10). The sorbent exhibited high adsorption capacity and fast rate of equilibrium for sorption of Dy ions. The method was applied for recovery and determination of dysprosium in different environmental water samples.     

Accurate fourteenth-order methods for solving nonlinear equations

We establish new iterative methods of local order fourteen to approximate the simple roots of nonlinear equations. The considered three-step eighth-order construction can be viewed as a variant of Newton’s method in which the concept of Hermite interpolation is used at the third step to reduce the number of evaluations. This scheme includes three evaluations of the function and one evaluation of the first derivative per iteration, hence its efficiency index is 1.6817. Next, the obtained approximation for the derivative of the Newton’s iteration quotient is again taken into consideration to furnish novel fourteenth-order techniques consuming four function and one first derivative evaluations per iteration. In providing such new fourteenth-order methods, we also take a special heed to the computational burden. The contributed four-step methods have 1.6952 as their efficiency index. Finally, various numerical examples are given to illustrate the accuracy of the developed techniques.     

An efficient glucose-based ligand for Heck and Suzuki coupling reactions in aqueous media

The glucose-based ligand, N-salicylidene-d-glucosamine (Sal-d-glsmN), was readily obtained by reaction of salicylaldehyde (Hsal) with the d-glucosamine hydrochloride. Ligand Sal-d-glsmN was found to be an efficient ligand in the palladium-catalyzed Suzuki and Heck C–C coupling reactions in aqueous medium under aerobic condition. It was found that the use of Sal-d-glsmN/Pd(OAc)₂ system as a catalyst, aryl halides undergo Suzuki and Heck cross-couplings, respectively, with arylboronic acids and olefins to give the desired products in moderate to excellent yields.