Modified Householder iterative method free from second derivatives for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method free from second derivatives for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We prove that the new iterative method is of fourth-order. Several examples are given to illustrate the efficiency of this new method and its comparison with other iterative methods. This method can be considered as a significant improvement of the Newton method and its variant forms.     

Closed solution to electromagnetic scattering of a plane wave by an eccentric cylinder coated with metamaterials

Closed series solution of electromagnetic scattering by an eccentric coated cylinder is achieved in matrix form. Diffracted field patterns are examined for an incident plane transverse magnetic (TM) wave. The solution is found by the classical separation of variables technique and the translational addition theorems. Wave transformation and orthogonality of the complex exponentials are employed to produce an infinite series. Numerical results are then shown by shortening the infinite series to a limited number of terms. Solutions are discussed for a dielectric or a metamaterial coating.     

Large signal performance of micromachined silicon inductive microphones

A mathematical model for the open-circuit output voltage of a micromachined silicon inductive microphone is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the amplitudes of the output components resulting from a multisinusoidal input acoustic pressure. The special case of an equal-amplitude two-tone acoustic pressure input is considered in detail. The results show that, the microphone generates both even and odd-order harmonic and intermodulation products.     

Empirical model for the current-voltage characteristic of resonant-tunneling devices

An empirical model is presented for the current-voltage characteristics of resonanttunneling (RT) devices. By using this model an analytical study of millimeter-band electronic circuits employing RT devices can be performed.     

Reaction kinetics and pathway of hydrothermal decomposition of aspartic acid

The kinetics and pathway of hydrothermal decomposition of aspartic acid were studied using a continuous‐flow tubular reactor. The reaction was carried out in the temperature range of 200–260°C and at a pressure of 20 MPa. Deamination was the primary reaction, indicated by the presence of significant amount of ammonia, fumaric acid, or maleic acid in the products. Other reaction products were pyruvic acid, malic acid, and traces of succinic and lactic acid. Traces of alanine were also detected, showing the possibility of decomposing high‐molecular weight amino acids to obtain simple amino acids such as glycine or alanine. Results on the effect of reaction parameters demonstrated that decomposition of aspartic acid is highly temperature dependent under hydrothermal conditions. For a slight temperature difference of 60°C (from 200 to 260°C), the first‐order reaction rate constants of 0.003 significantly increased to 0.231 s^?1. The activation energy was 144 kJ/mol, as calculated by the Arrhenius equation. No significant effect was exhibited by other reaction parameters such as pH and pressure. The results are useful in controlling the hydrolysis of proteinaceous materials toward high yield of aspartic acid under hydrothermal conditions. © 2007 Wiley Periodicals, Inc. 39: 175–180, 2007     

Exact solutions of solid-liquid phase-change heat transfer when subjected to convective boundary conditions

A closed-form expression is presented to find the location of solid-liquid interface motion in convection-dominated solidification and melting problems. In this regard, the solutions are expressed in terms of the generalized representations of error functions,E (u, v) andF (u, v), which are useful to heat-conduction problems with convective-type boundary conditions. It is demonstrated that for constant surface temperature, the interface solution reduces to the classical Neumann solution.     

Measurement and prediction of solubilities and diffusion coefficients of carbon dioxide in starch–water mixtures at elevated pressures

The solubility and diffusion coefficient of carbon dioxide in intermediate‐moisture starch–water mixtures were determined both experimentally and theoretically at elevated pressures up to 16 MPa at 50 °C. A high‐pressure decay sorption system was assembled to measure the equilibrium CO₂ mass uptake by the starch–water system. The experimentally measured solubilities accounted for the estimated swollen volume by Sanchez–Lacombe equation of state (S‐L EOS) were found to increase almost linearly with pressure, yielding 4.0 g CO₂/g starch–water system at 16 MPa. Moreover, CO₂ solubilities above 5 MPa displayed a solubility increase, which was not contributed by the water fraction in the starch–water mixture. The solubilities, however, showed no dependence on the degree of gelatinization (DG) of starch. The diffusion coefficient of CO₂ was found to increase with concentration of dissolved CO₂, which is pressure‐dependent, and decrease with increasing DG in the range of 50–100%. A free‐volume‐based diffusion model proposed by Areerat was employed to predict the CO₂ diffusivity in terms of pressure, temperature, and the concentration of dissolved CO₂. S‐L EOS was once more used to determine the specific free volume of the mixture system. The predicted diffusion coefficients showed to correlate well with the measured values for all starch–water mixtures. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 607–621, 2006     

Harmonic and intermodulation generation in quantum-well diodes

A Fourier-series model describing the current-voltage characteristic of a quantum-well diode (QWD) is presented. Using this model, closed-form expressions are obtained for the harmonic and intermodulation performance of a QWD excited by a multisinusoidal voltage superimposed on a dc voltage.     

Organic–inorganic nanocomposites prepared from fluoro-aramid and silica

Fluoro-aramid-based sol/gel-derived nanocomposites were synthesized by condensing a mixture of 4,4′-(hexafluoro-isopropylidene)dianiline and 1,3-phenylenediamine with terephthaloylchloride (TPC) in dimethylacetamide. TPC was added in slight excess to produce amide chains with carbonyl chloride end groups and then replaced with alkoxy groups using aminophenyltrimethoxysilane to develop bonding with the silica network. Mechanical, dynamic mechanical thermal, water absorption and morphological measurements were carried out on the thin hybrid films. Increase in the tensile strength and modulus was observed as compared to pristine polyamide. The thermal decomposition temperature was found in the range of 400–500 °C. The water absorption was found to be reduced with higher silica content. The glass transition temperature and the storage moduli increased with increasing silica concentration. The maximum increase in the T _g value (345 °C) was observed with 20 wt% silica. Scanning electron microscopy revealed the uniform distribution of silica in the matrix with an average particle size ranging from 8 to 50 nm.     

Studies with dithizone: Part XXI. The Relationship between pH12 and Molar Solubility

The effect of changes of ionic strength on the partition of an analytically important weak acid between a variety of aqueous and immiscible organic phases has been studied with respect to new measurements on dithizone (3-mercapto-1,5-diphenylformazan) and di(p-tolyl)thiocarbazone. A linear relationship has been deduced between the pH at which 50% extraction takes place and S_r,o (the solubility of the reactant in the organic phase), and confirmed by measurements of pH_{$\text{1}\text{2}$}, and S_r,o for a large number of organic solvents. The solubilities of the reagents in water, S_r, are also reported. The form of the relationship between pH and log D, and between pH_{$\text{1}\text{2}$} and log S_r,o is the same whether a solution of dithizone consists of a single species or a mixture of thiol and thione forms in tautomeric equilibrium.