Solution of a System of Generalized Abel Integral Equations Using Fractional Calculus

A method is presented for obtaining useful closed form solution of a system of generalized Abel integral equations by using the ideas of fractional integral operators and their applications. This system appears in solving certain mixed boundary value problems arising in the classical theory of elasticity.

Hydrogel-polymer electrolytes for electrochemical capacitors: an overview

Electrochemical capacitors are electrochemical devices with fast and highly reversible charge-storage and discharge capabilities. The devices are attractive for energy storage particularly in applications involving high-power requirements. Electrochemical capacitors employ two electrodes and an aqueous or a non-aqueous electrolyte, either in liquid or solid form; the latter provides the advantages of compactness, reliability, freedom from leakage of any liquid component and a large operating potential-window. One of the classes of solid electrolytes used in capacitors is polymer-based and they generally consist of dry solid-polymer electrolytes or gel-polymer electrolyte or composite-polymer electrolytes. Dry solid-polymer electrolytes suffer from poor ionic-conductivity values, between 10(-8) and 10(-7) S cm(-1) under ambient conditions, but are safer than gel-polymer electrolytes that exhibit high conductivity of ca. 10(-3) S cm(-1) under ambient conditions. The aforesaid polymer-based electrolytes have the advantages of a wide potential window of ca. 4 V and hence can provide high energy-density. Gel-polymer electrolytes are generally prepared using organic solvents that are environmentally malignant. Hence, replacement of organic solvents with water in gel-polymer electrolytes is desirable which also minimizes the device cost substantially. The water containing gel-polymer electrolytes, called hydrogel-polymer electrolytes, are, however, limited by a low operating potential-window of only about 1.23 V. This article reviews salient features of electrochemical capacitors employing hydrogel-polymer electrolytes.

Effect of Dietary Unsaturated Oils on the Biosynthesis of Cholesterol, and on Biliary and Fecal Excretion of Cholesterol and Bile Acids in Rats1

The aim of the present work was to investigate whether the hypocholesterolemic effect of polyunsaturated oils is due to inhibition of cholesterol synthesis or increased excretion of cholesterol and bile acids through the bile and feces of animals. Separate groups of rats were fed diets containing 10% safflower oil, coconut oil or hydrogenated vegetable oils for 30 days, after which the hepatic cholesterol and bile acid synthesis and their excretion through the bile and feces were studied. As compared to the rats in the other two groups, those given the diet containing 10% safflower oil showed markedly increased rates of bile flow and excreted through their bile and feces markedly higher amounts of cholesterol and bile acids. At the same time incorporation of [1-14C] acetate and [2-14C] mevalonate into the liver cholesterol and conversion of [4-14C] cholesterol into 14C-bile acids were also higher in the same rats. In the light of these observations it has been discussed that in the animals given polyunsaturated oils, biliary and fecal loss of cholesterol and bile acids far outweighs the activation of cholesterol synthesis and thereby effectively lowers the serum cholesterol levels.

Thermodynamics of cobalt-manganese alloys using fluoride and oxide electrolytes

Abstract is not available.

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

Fractional power dependence of rate on activation energy for reactions with very low internal barriers

The dynamics of reactions with low internal barriers are studied both analytically and numerically for two different models. Exact expressions for the average rate,kI, are obtained by solving the associated first passage time problems. Both the average rate constant, kI, and the numerically calculated long-time rate constant, kL, show a fractional power law dependence on the barrier height for very low barriers. The crossover of the reaction dynamics from low to high barrier is investigated.

Characterization of a toxin from Parthenium hysterophorus and its mode of excretion in animals

Fractionation of methanolic extracts of air dried aerial parts ofParthenium resulted in the isolation of a toxic constituent which was identified as parthenin, the major sesquiterpene lactone from the weed. The LD50 (minimal lethal dose required to cause 50% mortality) for parthenin in rats was 42 mg/kg body weight. When [3H]-parthenin was given orally or by intravenous administration, radioactivity appeared in the milk of lactating laboratory and dairy animals. Tissue distribution of radioactivity revealed that maximum label was detectable in kidneys.

Mordenite-incorporated PVA-PSSA membranes as electrolytes for DMFCs

Composite membranes with mordenite (MOR) incorporated in poly vinyl alcohol (PVA)–polystyrene sulfonic acid (PSSA) blend tailored with varying degree of sulfonation are reported. Such a membrane comprises a dispersed phase of mordenite and a continuous phase of the polymer that help tuning the flow of methanol and water across it. The membranes on prolonged testing in a direct methanol fuel cell (DMFC) exhibit mitigated methanol cross-over from anode to the cathode. The membranes have been tested for their sorption behaviour, ion-exchange capacity, electrochemical selectivity and mechanical strength as also characterized by Fourier transform infrared spectroscopy and thermogravimetric analysis. Water release kinetics has been measured by magnetic resonance imaging (NMR imaging) and is found to be in agreement with the sorption data. Similarly, methanol release kinetics studied by volume-localized NMR spectroscopy (point resolved spectroscopy, PRESS) clearly demonstrates that the dispersion of mordenite in PVA–PSSA retards the methanol release kinetics considerably. A peak power-density of 74 mW/cm2 is achieved for the DMFC using a PVA–PSSA membrane electrolyte with 50% degree of sulfonation and 10 wt.% dispersed mordenite phase. A methanol cross-over current as low as 7.5 mA/cm2 with 2 M methanol feed at the DMFC anode is observed while using the optimized composite membrane as electrolyte in the DMFC, which is about 60% and 46% lower than Nafion-117 and PVA–PSSA membranes, respectively, when tested under identical conditions.

Physicochemical, Electrochemical, and Spectroscopic Characterization of Zinc-Based Room-Temperature Molten Electrolytes and Their Application in Rechargeable Batteries

Room-temperature zinc ion-conducting molten electrolytes based on acetamide, urea, and zinc perchlorate or zinc triflate have been prepared and characterized by various physicochemical, spectroscopic, and electrochemical techniques. The ternary molten electrolytes are easy to prepare and can be handled under ambient conditions. They show excellent stability, high ionic conductivity, relatively low viscosity, and other favorable physicochemical and electrochemical properties that make them good electrolytes for rechargeable zinc batteries. Specific conductivities of 3.4 and 0.5 mS cm(-1) at 25 degrees C are obtained for zinc-perchlorate-and zinc-triflate-containing melts, respectively. Vibrational spectroscopic data reveal that the free ion concentration is high in the optimized composition. Rechargeable Zn batteries have been assembled using the molten electrolytes, with gamma-MnO2 as the positive electrode and Zn as the negative electrode. They show excellent electrochemical characteristics with high discharge capacities. This study opens up the possibility of using acetamide-based molten electrolytes as alternate electrolytes in rechargeable zinc batteries. (C) 2009 The Electrochemical Society.

Magnesium ion conducting, room temperature molten electrolytes

Room temperature, magnesium ion conducting binary molten electrolyte consisting of acetamide and magnesium perchlorate has been prepared and characterized. The molten liquid is very stable and shows high ionic conductivity, of the order of several mS cm(-1) at 25 degrees C with other favourable physicochemical properties. Vibrational spectroscopic studies reveal that the free ion concentration is higher than that of ion pairs and aggregates in the melt. The electrochemical reversibility of magnesium deposition and dissolution is demonstrated using voltammetry and impedance studies. Preliminary studies on rechargeable batteries assembled using gamma-MnO2 and Mg metal as the electrodes together with the molten electrolyte show high discharge capacity.

Soft matter lithium salt electrolytes: ion conduction and application to rechargeable batteries

Soft matter provides diverse opportunities for the development of electrolytes for all solid state lithium batteries. Here we review soft matter solid electrolytes for lithium batteriesthat are primarily obtained starting from liquid electrolytic systems. This concept of solid electrolyte synthesis from liquid is significantly different from prevalent approaches. The novelty of our approach is discussed in the light of various fundamental issues and in relation to its application to rechargeable lithium batteries.

Spin-Probe ESR Studies on Nanocomposite Polymer Electrolytes

The possibility of using spin-probe electron spin resonance (ESR) as a tool to study glass transition temperature, T g, of polymer electrolytes is explored in 4 hydroxy 2,2,6,6 tetramethylpiperidine N oxyl (TEMPOL) doped composite polymer electrolyte (PEG)46LiClO4 dispersed with nanoparticles of hydrotalcite. The T g is estimated from the measured values of T 50G, the temperature at which the extrema separation 2A zz of the broad powder spectrum decreases to 50 G. In another method, the correlation time τc for the spin probe dynamics was determined by computer simulation of the ESR spectra and T g has been identified as the temperature at which τc begins to show temperature dependence. While both methods give values of T g close to those obtained from differential scanning calorimetry, it is concluded that more work is required to establish spin-probe ESR as a reliable technique for the determination of T g.

Beyond fractional derivatives: local approximation of other convolution integrals

Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

Oxide Particle Surface Chemistry and Ion Transport in "Soggy Sand" Electrolytes

The crucial role of oxide surface chemical composition on ion transport in "soggy sand" electrolytes is discussed in a systematic manner. A prototype soggy sand electrolytic system comprising aerosil silica functionalized with various hydrophilic and hydrophobic moieties dispersed in lithium perchlorate-ethylene glycol solution was used for the study. Detailed rheology studies show that the attractive particle network in the case of the composite with unmodified aerosil silica (with surface silanol groups) is most favorable for percolation in ionic conductivity, as well as rendering the composite with beneficial elastic mechanical properties: Though weaker in strength compared to the composite with unmodified aerosil particles, attractive particle networks are also observed in composites of aerosil particles with surfaces partially substituted with hydrophobic groups. The percolation in ionic conductivity is, however, dependent on the size of the hydrophobic moiety. No spanning attractive particle network was formed for aerosil particles with surfaces modified with stronger hydrophilic groups (than silanol), and as a result, no percolation in ionic conductivity was observed. The composite with hydrophilic particles was a sol, contrary to gels obtained in the case of unmodified aerosil, and partially substituted with hydrophobic groups.