Use of the reciprocity theorem for axially symmetric transient problems

Summary A fundamental solution, to be used in reciprocal theorem for the solutions of axially symmetric transient problem of elastodynamics, is presented. A cylindrical cavity problem has been solved to check the formulation. The strong singularity of the resulting integral equation for this problem has been reduced to the weak form. The new formulation provides the initial velocity on the surface for a transient loading. Some differences have been introduced for the use of generalized functions.     

Quantitative Determination of Underivatized α-Tocopherol in Cow Milk, Vitamin and Multivitamin Drugs by GC-FID

A simple and rapid method for direct determination of α-tocopherol (α-T, vitamin E) in pharmaceutical preparations (vitamin and multivitamin tablets) and cow milk obtained from different villages of Erzurum in Turkey was developed and validated by GC-FID. Separation of underivatized α-T in pure substance, milk samples, vitamin and multivitamin tablets was performed in about 8.4 min, using an HP-5 capillary column. The range of quantification for the GC-FID was 1–30 μg mL^?1. Within-day and between-day precision (RSD %) were less than 8.5%, and accuracy (relative error) was less than 11.0% (n = 6). LOQ and LOD values were found to be 0.35 and 0.30 μg mL^?1, respectively. The developed method was applied directly and easily to the analysis of α-T in vitamin and multivitamin preparations and cow milk. RSD values were found to be 6.59% (Grandpherol soft gelatine capsule: 200 I.U.), 0.59% (Megadyn film tablet: 10 mg) and 1.54% (Supradyn drage: 10 I.U.). The developed method was also applied to cow milk samples and mean values of α-T content was found 2.99 μg mL^?1 in cow milk samples. This developed and validated GC–FID method, in conjunction with other methods, could be successfully applied for routine laboratory because of its simplicity, rapidity, sensitivity, precision and accuracy.     

Reasons of different colors in the ignimbrite lithology: micro-XRF and confocal Raman spectrometry method

Medium to large volume ignimbrites usually show vertical changes in terms of color, mineral components, texture and geochemistry. Determination of vertical changes in single extensive ignimbrite flow unit is difficult and requires careful studies. Color changes in ignimbrite flow units are very important for earth scientists. This may cause to identify the same ignimbrite series with different definition. Incesu ignimbrite has a wide distribution in the Central Anatolian Volcanic Province (CAVP). It is classified into three levels as lower, middle and upper according to color and welding degree. There is a sharp contact between the lower and middle level. The lower level is dark brown to black in color and the middle level has pinkish red to red color. The present paper focuses on the investigation of color changes between the ignimbrite levels by using micro-XRF and confocal Raman spectrometry. Micro-XRF and Raman spectrometry studies were performed on the polished thin sections of the lower and middle levels with different compositions. These differences were because of the compositional changes of K and slightly Fe elements distribution within the matrix. The dark brown to black color of the lower level was related to the high concentration of the K and Fe relatively to the middle level. Confocal Raman spectrometry investigations exhibited the matrix of the lower level mainly composed of anorthoclase, supporting the results of the micro-XRF.     

Determination of mineral element concentrations in wheat,sunflower, chickpea and lentil cultivars in response to P fertilization by polarized energy dispersive X‐ray fluorescence

Concentrations of elements (P, K, S, Ca, Mg, Si, Cl, Fe, Zn, Cu, Mn, Mo, Na, Al, Ti, Ni, Ba, As, Br, Rb and Sr) of wheat, sunflower, chickpea and lentil cultivars grown in low and high phosphorus soil were investigated by polarized energy dispersive X‐ray fluorescence (PEDXRF). The phosphorus treatment x cultivars interaction was significant for the growth and element concentrations, and cultivars within plant species differed considerably with respect to element concentrations as the result of P fertilization. Shoot growth of the cultivars of each plant species was increased in response to phosphorus fertilization. Application of P increased the P concentrations of wheat, sunflower, chickpea and lentil cultivars. Under high P conditions, mean K concentrations of wheat and sunflower cultivars were decreased while the mean K concentrations of chickpea and lentil were increased. With the exception of sunflower cultivars, applied P significantly increased S concentration of the cultivars of wheat, chickpea and lentil. Calcium concentrations of wheat and sunflower cultivars were reduced by P fertilization and that of chickpea and lentil were increased. Applied P decreased mean Mg concentrations in sunflower, increased in chickpea and lentil cultivars and showed no effects on the wheat cultivars. Applied P significantly decreased mean Si concentrations of wheat and sunflower while mean Si concentrations of the chickpea and lentil cultivars were increased. Chloride concentrations of the wheat and sunflower cultivars were decreased and those of the chickpea and lentil cultivars were increased by applied P. In general, Fe concentrations of the wheat and chickpea cultivars were significantly increased by applied P. Zinc and Cu concentrations of all the cultivars of the four plant species were reduced by P, particularly Zn concentrations. However, applied P increased mean Mn concentrations of wheat and chickpea and decreased those of chickpea cultivars. Mean Mo concentrations of wheat and chickpea increased but decreased in sunflower and lentil cultivars. In general, applied P increased mean Na concentration of wheat and decreased that of chickpea and lentil. Aluminum concentrations of wheat and chickpea cultivars were decreased by applied P. Applied P decreased Ti concentrations of wheat and sunflower cultivars and increased Ti concentrations of chickpea and lentil. Nickel concentrations of wheat and chickpea were increased and those of sunflower and lentil were decreased by applied P. Applied P reduced the Ba and increased As and Rb concentrations of all the cultivars within the plant species. Bromine concentrations of wheat and lentil were decreased and those of sunflower and chickpea were increased by applied P. Finally, Sr concentrations in wheat and sunflower cultivars were reduced, and increased in chickpea cultivars with applied P. Copyright © 2009 John Wiley & Sons, Ltd.     

A second order self-consistent IMEX method for radiation hydrodynamics

We present a second order self-consistent implicit/explicit (methods that use the combination of implicit and explicit discretizations are often referred to as IMEX (implicit/explicit) methods ,  and ) time integration technique for solving radiation hydrodynamics problems. The operators of the radiation hydrodynamics are splitted as such that the hydrodynamics equations are solved explicitly making use of the capability of well-understood explicit schemes. On the other hand, the radiation diffusion part is solved implicitly. The idea of the self-consistent IMEX method is to hybridize the implicit and explicit time discretizations in a nonlinearly consistent way to achieve second order time convergent calculations. In our self-consistent IMEX method, we solve the hydrodynamics equations inside the implicit block as part of the nonlinear function evaluation making use of the Jacobian-free Newton Krylov (JFNK) method ,  and . This is done to avoid order reductions in time convergence due to the operator splitting. We present results from several test calculations in order to validate the numerical order of our scheme. For each test, we have established second order time convergence.     

GC Determination of Prilocaine HCl in Human Plasma: Analytical Application to Real Samples

A gas chromatographic (GC) method with a rapid and simple sample preparation was developed and validated for determination of prilocaine in human plasma. The validation parameters of linearity, precision, accuracy, recovery, specificity, limit of detection and limit of quantification were studied. The range of quantification for the GC method was 50–300 ng mL^?1 in plasma. Intra- and inter-day precision, expressed as the relative standard deviation (RSD) were less than 4.5%, and accuracy (relative error) was better than 8.0% (n = 6). The analytical recovery of prilocaine HCl from plasma has averaged 96.5% and the recovery of internal standard (lidocaine HCl) reached 96.8%. The limit of quantification (LOQ) and the limit of detection (LOD) of the method for plasma were 50 and 40 ng mL^?1, respectively. Also the developed and validated method was applied to three healthy volunteers to whom a local anaesthesia with citanest was administered.     

Determination of Carbamazepine in Pharmaceutical Dosage Form Using GC-FID

The present work describes the methodology and validation of gas chromatography with flame ionization detection (GC-FID) for the determination of carbamazepine with internal standard (diazepam) in pharmaceutical preparations. The method was linear from 2–30 μg mL⁻¹. The RSD values for precision was less than 9%, accuracy (relative error) was better than 11% (n = 6). The developed method was successfully applied for the assay of pharmaceutical dosage forms which do not require any preliminary separation or treatment of the samples. The RSD values for Tegretol^® tablets (200 mg) and Karberol^® tablets (200 mg) was found to be 4.03 and 3.25%, respectively. The results obtained from this method were compared with the reference method (LC) reported in literature and no significant difference was found statistically.

     

Adaptive solution techniques for simulating underwater explosions and implosions

Adaptive solution techniques are presented for simulating underwater explosions and implosions. The liquid is assumed to be an adiabatic fluid and the solution in the gas is assumed to be uniform in space. The solution in water is integrated in time using a semi-implicit time discretization of the adiabatic Euler equations. Results are presented either using a non-conservative semi-implicit algorithm or a conservative semi-implicit algorithm. A semi-implicit algorithm allows one to compute with relatively large time steps compared to an explicit method. The interface solver is based on the coupled level set and volume-of-fluid method (CLSVOF) [M. Sussman, A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles, J. Comput. Phys. 187 (2003) 110–136; M. Sussman, E.G. Puckett, A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows, J. Comput. Phys. 162 (2000) 301–337]. Several underwater explosion and implosion test cases are presented to show the performances of our proposed techniques.     

Effects of shear stresses and rotary inertia on the stability and vibration of sandwich cylindrical shells with FGM core surrounded by elastic medium

The vibration and stability of axially loaded sandwich cylindrical shells with the functionally graded (FG) core with and without shear stresses and rotary inertia resting Pasternak foundation are investigated. The dynamic stability is derived based on the first order shear deformation theory (FSDT) including shear stresses. The axial load and dimensionless fundamental frequency for FG sandwich shell with shear stresses and rotary inertia and resting on the Pasternak foundation. Finally, the influences of variations of FG core, elastic foundations, shear stresses and rotary inertia on the fundamental frequencies and critical axial loads are investigated.