Approximate solutions of Fredholm integral equations of the second kind

This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail. (c) 2009 Elsevier Inc. All rights reserved.

Simplified Mathematical Model for Effects of Freezing on the Low-Temperature Performance of the Lead-Acid Battery

Discharge periods of lead-acid batteries are significantly reduced at subzero centigrade temperatures. The reduction is more than what can he expected due to decreased rates of various processes caused by a lowering of temperature and occurs despite the fact that active materials are available for discharge. It is proposed that the major cause for this is the freezing of the electrolyte. The concentration of acid decreases during battery discharge with a consequent increase in the freezing temperature. A battery freezes when the discharge temperature falls below the freezing temperature. A mathematical model is developed for conditions where charge-transfer reaction is the rate-limiting step. and Tafel kinetics are applicable. It is argued that freezing begins from the midplanes of electrodes and proceeds toward the reservoir in-between. Ionic conduction stops when one of the electrodes freezes fully and the time taken to reach that point, namely the discharge period, is calculated. The predictions of the model compare well to observations made at low current density (C/5) and at -20 and -40 degrees C. At higher current densities, however, diffusional resistances become important and a more complicated moving boundary problem needs to be solved to predict the discharge periods. (C) 2009 The Electrochemical Society.

Growth and physical properties of a new chiral open-framework crystal for NLO applications: Cesium hydrogen l-malate monohydrate

Cesium hydrogen l-malate monohydrate, CsH(C4H4O5)·H2O, is a new chiral open-framework semi-organic crystalline material with a second-harmonic generation efficiency one order of magnitude greater than KDP. Single crystals of this new material have been grown by the conventional slow cooling technique from aqueous solution. Grown crystals display both platy and prismatic morphologies depending on the imposed supersaturation. Hardness values measured using Vickers hardness indenter show considerable anisotropy. The resistivity behavior at room temperature and above, places the crystal between an ionic conductor and a dielectric. The single-crystal SHG efficiency estimated through Maker fringes experiment gives deff which is 4.24 times that of KDP. Single and multiple shot experiments performed on the grown crystals for the fundamental and second harmonic of pulsed Nd:YAG laser (1064 and 532 nm) show that it exhibits a high laser damage threshold which is a favorable property for nonlinear optical applications.

Comparative study of lead-acid batteries for photovoltaic stand-alone lighting systems

The lead-acid battery is often the weakest link in photovoltaic (PV) installations. Accordingly, various versions of lead-acid batteries, namely flooded, gelled, absorbent glass-mat and hybrid, have been assembled and performance tested for a PV stand-alone lighting system. The study suggests the hybrid VRLA batteries, which exhibit both the high power density of absorbent glass-mat design and the improved thermal properties of the gel design, to be appropriate for such an application. Among the VRLA-type batteries studied here water loss for the hybrid VRLA batteries is minimal and charge-acceptance during the service at high temperatures is better in relation to their AGM counterparts.

A low-cost lead-acid battery with high specific-energy

Lightweight grids for lead-acid battery grids have been prepared from acrylonitrile. butadiene styrene (ABS) copolymer followed by coating with lead. Subsequently, the grids have been electrochemically coated with a conductive and corrosion-resistant layer of polyaniline. These grids are about 75% lighter than those employed in conventional lead-acid batteries. Commercial-grade 6V/3.5 Ah (C-20-rate) lead-acid batteries have been assembled and characterized employing positive and negative plates constituting these grids. The specific energy of such a lead-acid battery is about 50 Wh/kg. The batteries can withstand fast charge-discharge duty cycles.

Laser damage threshold studies on urea L-malic acid: A nonlinear optical crystal

A detailed study of surface laser damage performed on a nonlinear optical crystal, urea L-malic acid, using 7 ns laser pulses at 10 Hz repetition rate from a Q-switched Nd:YAG laser at wavelengths of 532 and 1064 nm is reported. The single shot and multiple shot surface laser damage threshold values are determined to be 26.64±0.19 and 20.60±0.36 GW cm−2 at 1064 nm and 18.44±0.31 and 7.52±0.22 GW cm−2 at 532 nm laser radiation, respectively. The laser damage anisotropy is consistent with the Vickers mechanical hardness measurement performed along three crystallographic directions. The Knoop polar plot also reflects the damage morphology. Our investigation reveals a direct correlation between the laser damage profile and hardness anisotropy. Thermal breakdown of the crystal is identified as the possible mechanism of laser induced surface damage.

THREE-LAYER FLUID FLOW OVER A SMALL OBSTRUCTION ON THE BOTTOM OF A CHANNEL

Many boundary value problems occur in a natural way while studying fluid flow problems in a channel. The solutions of two such boundary value problems are obtained and analysed in the context of flow problems involving three layers of fluids of different constant densities in a channel, associated with an impermeable bottom that has a small undulation. The top surface of the channel is either bounded by a rigid lid or free to the atmosphere. The fluid in each layer is assumed to be inviscid and incompressible, and the flow is irrotational and two-dimensional. Only waves that are stationary with respect to the bottom profile are considered in this paper. The effect of surface tension is neglected. In the process of obtaining solutions for both the problems, regular perturbation analysis along with a Fourier transform technique is employed to derive the first-order corrections of some important physical quantities. Two types of bottom topography, such as concave and convex, are considered to derive the profiles of the interfaces. We observe that the profiles are oscillatory in nature, representing waves of variable amplitude with distinct wave numbers propagating downstream and with no wave upstream. The observations are presented in tabular and graphical forms.

A modified approach to numerical solution of Fredholm integral equations of the second kind

A modified approach to obtain approximate numerical solutions of Fredholin integral equations of the second kind is presented. The error bound is explained by the aid of several illustrative examples. In each example, the approximate solution is compared with the exact solution, wherever possible, and an excellent agreement is observed. In addition, the error bound in each example is compared with the one obtained by the Nystrom method. It is found that the error bound of the present method is smaller than the ones obtained by the Nystrom method. Further, the present method is successfully applied to derive the solution of an integral equation arising in a special Dirichlet problem. (C) 2015 Elsevier Inc. All rights reserved.

An alternative approach to study nonlinear inviscid flow over arbitrary bottom topography

This paper deals with a new approach to study the nonlinear inviscid flow over arbitrary bottom topography. The problem is formulated as a nonlinear boundary value problem which is reduced to a Dirichlet problem using certain transformations. The Dirichlet problem is solved by applying Plemelj-Sokhotski formulae and it is noticed that the solution of the Dirichlet problem depends on the solution of a coupled Fredholm integral equation of the second kind. These integral equations are solved numerically by using a modified method. The free-surface profile which is unknown at the outset is determined. Different kinds of bottom topographies are considered here to study the influence of bottom topography on the free-surface profile. The effects of the Froude number and the arbitrary bottom topography on the free-surface profile are demonstrated in graphical forms for the subcritical flow. Further, the nonlinear results are validated with the results available in the literature and compared with the results obtained by using linear theory. (C) 2015 Elsevier Inc. All rights reserved.