Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Dilute solution properties of methyl methacrylate�acrylonitrile copolymer (MA1)

This paper deals with studies on the dilute solution properties of methyl methacrylate�acrylonitrile copolymer of 0.289 mole fraction (mf) of acrylonitrile composition. Mark�Houwink parameters for this copolymer have been evaluated in acetonitrile (MeCN), 2-butanone (MEK), dimethylformamide (DMF) and γ-butyrolactone (γ-BL). The solvent power is found to be in the order of MEK < MeCN < DMF < γ-BL at 30°C. Herein, probably for the first time, the steric factor for the copolymer is found to be lower than that for the parent homopolymers and the excess interaction parameter, �AB is found to be negative. This probably suggests that the units are compatible to each other.

Synthesis, structural and ferromagnetic properties of La1-xKxMnO3 (0.0 <= x <= 0.25) phases by solution combustion method

We describe the solution combustion synthesis and characterization of La1-xKxMnO3 (0.0 <= x <= 0.25) perovskite phases, which is a low temperature initiated, rapid route to prepare metal oxides. As-synthesized compounds are amorphous in nature; crystallinity was observed on heating at 800 degrees C for 5 min. Structural parameters were determined by the Rietveld refinement method using powder XRD data. Parent LaMnO3 compound crystallizes in the orthorhombic structure (space group Pbnm, No. 62). Potassium substituted compounds were crystallized with rhombohedral symmetry (space group R-3c, No. 167). The ratio of the Mn3+/Mn4+ was determined by the iodometric titration. The Fourier transform infrared spectrum (FTIR) shows two absorption bands for Mn-O stretching vibration (v, mode), Mn-O-Mn deformation vibration (v(b) mode) around 600 cm(-1) and 400 cm(-1) for the compositions, x = 0.0, 0.05 and 0-10. Four-probe electrical resistivity measurements reveal a composition controlled metal to insulator transition (TM-1), the maximum TM-1 was observed for the composition La0.85K0.15MnO3 at 287 K. Room temperature vibrating sample magnetometer data indicate that for the composition up to x = 0-10, the compounds are paramagnetic whereas composition with x = 0.15, 0.20 and 0.25 show magnetic moments of 27, 29 and 30 emu/g, respectively.

Solution NMR studies of acetohydroxy acid synthase I: Identification of the sites of inter-subunit interactions using multidimensional NMR methods

The novel multidomain organization in the multimeric Escherichia coli AHAS I (ilvBN) enzyme has been dissected to generate polypeptide fragments. These fragments when cloned, expressed and purified reassemble in the presence of cofactors to yield a catalytically competent enzyme. Structural characterization of AHAS has been impeded due to the fact that the holoenzyme is prone to dissociation leading to heterogeneity in samples. Our approach has enabled the structural characterization using high-resolution nuclear magnetic resonance methods. Near complete sequence specific NMR assignments for backbone H-N, N-15, C-13 alpha and C-13(beta) atoms of the FAD binding domain of ilvB have been obtained on samples isotopically enriched in H-2, C-13 and N-15. The secondary structure determined on the basis of observed C-13(alpha) secondary chemical shifts and sequential NOEs indicates that the secondary structure of the FAD binding domain of E. coli AHAS large Subunit (ilvB) is similar to the structure of this domain in the catalytic subunit of yeast AHAS. Protein-protein interactions involving the regulatory subunit (ilvN) and the domains of the catalytic subunit (ilvB) were studied using circular dichroic and isotope edited solution nuclear magnetic resonance spectroscopic methods. Observed changes in circular dichroic spectra indicate that the regulatory subunit (ilvN) interacts with ilvB alpha and ilvB beta domains of the catalytic subunit and not with the ilvB gamma domain. NMR chemical shift mapping methods show that ilvN binds close to the FAD binding site in ilvB beta and proximal to the intrasubunit ilvB alpha/ilvB beta domain interface. The implication of this interaction on the role of the regulatory subunit oil the activity of the holoenzyme is discussed. NMR studies of the regulatory domains show that these domains are structured in solution. Preliminary evidence for the interaction of ilvN with the metabolic end product of the pathway, viz., valine is also presented.

Coupled Solution for Forced Recharge in Confined Aquifers

Analytical solutions for forced well recharge currently in use were initially developed for pumping scenarios and applied for recharge cases assuming that radial flow in the recharge well replicates a mirror image of that in to a pumping well. Moreover these solutions were not extended to multiaquifer systems. Well bore numerical solutions were generally not considering the effect of well bore interaction, which has a significant effect in the case of a recharge well. In the present paper, improved analytical solutions are developed for a well fully penetrating either single or multiaquifers in respect.to of well storage, well loss, and interactions between the individual aquifers through well bore. The solution developed for constant and variable rates of injection and well loss is applied to the experimental data of the Hansol well injection project near the city of Ahmedabad in the Gujarat state in India. The paper also discusses the difference in well hydraulics of recharge and recovery wells.

Surfactant-Mediated Synthesis of Functional Metal Oxide Nanostructures Via Microwave Irradiation-Assisted Chemical Synthesis

In the present work we report a rapid microwave irradiation-assisted chemical synthesis technique for the growth of nanoparticles, nanorods, and nanotubes of a variety of metal oxides in the presence of an appropriate surfactant (cationic, anionic, non ionic and polymeric), without the use of any templates. The method is simple, inexpensive, and helps one to prepare nanostructures in quick time, measured in seconds and minutes. This method has been applied successfully to synthesize nanostructures of a variety of binary and ternary metal oxides such as ZnO, CdO, Fe2O3, CuO, Ga2O3, Gd2O3, ZnFe2O4, etc. There is an observed variation in the morphology of the nanostructures with changes in different process parameters, such as microwave power, irradiation time, identity of solvent, type of surfactant, and its concentration.

X-Pro peptides: Synthesis and solution conformation of benzyloxycarbonyl-(Aib-Pro)4methyl ester. Evidence for a novel helical structure

The synthesis of the octapeptide, benzyloxycarbonyl-(-aminoisobutyryl-L-prolyl)4-methyl ester [Z-(Aib-Pro)4-OMe] and an analysis of its solution conformation is reported. The octapeptide is shown to possess three strong intramolecular hydrogen bonds on the basis of studies of the solvent and temperature dependence of NH chemical shifts and rates of hydrogen-deuterium exchange. 13C studies are consistent with a structure involving only trans Aib-Pro bonds, while ir experiments support a hydrogen-bonded conformation. The Aib 3, 5, and 7 NH groups are shown to participate in hydrogen bonding. A 310 helical conformation compatible with the spectroscopic data is suggested. The proposed conformation consists of three type III -turns with Aib and Pro at the corners and stabilized by 4 1 intramolecular hydrogen bonds.

A new framework for solution of multidimensional population balance equations

A new framework is proposed in this work to solve multidimensional population balance equations (PBEs) using the method of discretization. A continuous PBE is considered as a statement of evolution of one evolving property of particles and conservation of their n internal attributes. Discretization must therefore preserve n + I properties of particles. Continuously distributed population is represented on discrete fixed pivots as in the fixed pivot technique of Kumar and Ramkrishna [1996a. On the solution of population balance equation by discretization-I A fixed pivot technique. Chemical Engineering Science 51(8), 1311-1332] for 1-d PBEs, but instead of the earlier extensions of this technique proposed in the literature which preserve 2(n) properties of non-pivot particles, the new framework requires n + I properties to be preserved. This opens up the use of triangular and tetrahedral elements to solve 2-d and 3-d PBEs, instead of the rectangles and cuboids that are suggested in the literature. Capabilities of computational fluid dynamics and other packages available for generating complex meshes can also be harnessed. The numerical results obtained indeed show the effectiveness of the new framework. It also brings out the hitherto unknown role of directionality of the grid in controlling the accuracy of the numerical solution of multidimensional PBEs. The numerical results obtained show that the quality of the numerical solution can be improved significantly just by altering the directionality of the grid, which does not require any increase in the number of points, or any refinement of the grid, or even redistribution of pivots in space. Directionality of a grid can be altered simply by regrouping of pivots.

A solution framework for scheduling a BPM with non-identical job dimensions

A Batch Processing Machine (BPM) is one which processes a number of jobs simultaneously as a batch with common beginning and ending times. Also, a BPM, once started cannot be interrupted in between (Pre-emption not allowed). This research is motivated by a BPM in steel casting industry. There are three main stages in any steel casting industry viz., pre-casting stage, casting stage and post-casting stage. A quick overview of the entire process, is shown in Figure 1. There are two BPMs : (1) Melting furnace in the pre-casting stage and (2) Heat Treatment Furnace (HTF) in the post casting stage of steel casting manufacturing process. This study focuses on scheduling the latter, namely HTF. Heat-treatment operation is one of the most important stages of steel casting industries. It determines the final properties that enable components to perform under demanding service conditions such as large mechanical load, high temperature and anti-corrosive processing. In general, different types of castings have to undergo more than one type of heat-treatment operations, where the total heat-treatment processing times change. To have a better control, castings are primarily classified into a number of job-families based on the alloy type such as low-alloy castings and high alloy castings. For technical reasons such as type of alloy, temperature level and the expected combination of heat-treatment operations, the castings from different families can not be processed together in the same batch.

Diffusion of flexible, charged, nanoscopic molecules in solution: Size and pH dependence for PAMAM dendrimer

In order to understand self-diffusion (D) of a charged, flexible, and porous nanoscopic molecule in water, we carry out very long, fully atomistic molecular dynamics simulation of PAMAM dendrimer up to eight generations in explicit salt water under varying pH. We find that while the radius of gyration (R-g) varies as N-1/3, the self-diffusion constant (D) scales, surprisingly, as N-alpha, with alpha=0.39 at high pH and 0.5 at neutral pH, indicating a dramatic breakdown of Stokes-Einstein relation for diffusion of charged nanoscopic molecules. The variation in D as a function of radius of gyration demonstrates the importance of treating water and ions explicitly in the diffusion process of a flexible nanoscopic molecule. In agreement with recent experiments, the self-diffusion constant increases with pH, revealing the importance of dielectric friction in the diffusion process. The shape of a dendrimer is found to fluctuate on a nanosecond time scale. We argue that this flexibility (and also the porosity) of the dendrimer may play an important role in determining the mean square displacement of the dendrimer and the breakdown of the Stokes-Einstein relation between diffusion constant and the radius.

Delamination of Surfactant-Intercalated Brucite-Like Hydroxy Salts of Cobalt and Copper and Solvothermal Decomposition of the Resultant Colloidal Dispersions

Surfactant anion intercalated hydroxy salts of copper and cobalt of the formula M(OH)(2-x)(surf)(x)center dot mH(2)O [M = Cu, Co; surf = dodecyl sulfate. dodecyl benzene sulfonate. and x = 0.5 for Cu and 0.67 for Co] delaminate readily in 1-butanol to give translucent colloidal dispersions that are stable for months. The extent of delamination and the colloidal dispersion observed in these solids is higher than what had been observed for layered double hydroxides. The dispersions yield the corresponding nanoparticulate oxides on solvothermal decomposition. While the copper hydroxy salt forms similar to 300 nm dendrimer-like CuO nanostructures comprising nanorods of similar to 10 nm diameter, the cobalt analogue forms similar to 20 nm superparamagnetic particles of Co3O4.

Induced swelling of kaolinitic soil in alkali solution

Unexpected swelling induced in foundation soils can cause distress to structures founded on them. In this paper, the swelling of kaolinitic soils due to interaction with alkali solution has been reported. The induced swelling is attributed to the formation of new minerals, which has been confirmed by X-ray diffraction patters and SEM studies. To understand the effect of alkali concentration and duration of interaction, two series of consolidation experiments have been carried out. In series 1, the specimen were remoulded with water and inundated with alkali solutions and in series 2, the specimen were remoulded and inundated with same alkali solutions. A steep compression during loading cycle and no abnormal swelling during unloading cycle has been noticed for the specimen remoulded with water and inundated with 1 N NaOH solutions. The steep compression is due to the segregation or break down of clay minerals due to alkali interactions. In case of specimen inundated with 4 N NaOH solutions, abnormal swelling has been observed during unloading cycle of the consolidation test. New minerals are formed on interaction of soil with 4 N solution as confirmed by X-ray diffraction patterns. These minerals are known to have very fine pores and possess high water holding capacity. The differences in the amount of swelling of samples remoulded with water and remoulded with alkali solution are due to variations in the concentration of alkali and duration of interaction.

Influence of surfactant and annealing temperature on optical properties of sol-gel derived nano-crystalline TiO2 thin films

Titanium dioxide thin films have been synthesized by sol-gel spin coating technique on glass and silicon substrates with and without surfactant polyethylene glycol (PEG). XRD and SEM results confirm the presence of nano-crystalline (anatase) phase at an annealing temperature of 300 degrees C. The influence of surfactant and annealing temperature on optical properties of TiO2 thin films has been studied. Optical constants and film thickness were estimated by Swanepoel's (envelope) method and by ellipsometric measurements in the visible spectral range. The optical transmittance and reflectance were found to decrease with an increase in PEG percentage. Refractive index of the films decreased and film thickness increased with the increase in percentage of surfactant. The refractive index of the un-doped TiO2 films was estimated at different annealing temperatures and it has increased with the increasing annealing temperature. The optical band gap of pure TiO2 films was estimated by Tauc's method at different annealing temperature. (C) 2010 Elsevier B.V. All rights reserved.

Quadratic Nonlinearity of One- and Two-Electron Oxidized Metalloporphyrins and Their Switching in Solution

We report the quadratic nonlinearity of one- and two-electron oxidation products of the first series of transition metal complexes of meso-tetraphenylporphyrin (TPP). Among many MTPP complexes, only CuTPP and ZnTPP show reversible oxidation/reduction cycles as seen from cyclic voltammetry experiments. While centrosymmetric neutral metalloporphyrins have zero first hyperpolarizability, β, as expected, the cation radicals and dications of CuTPP and ZnTPP have very high β values. The one- and two-electron oxidation of the MTPPs leads to symmetry-breaking of the metal−porphyrin core, resulting in a large β value that is perhaps aided in part by contributions from the two-photon resonance enhancement. The calculated static first hyperpolarizabilities, β0, which are evaluated in the framework of density functional theory by a coupled perturbed Hartree−Fock method, support the experimental trend. The switching of optical nonlinearity has been achieved between the neutral and the one-electron oxidation products but not between the one- and the two-electron oxidation products since dications that are electrochemically reversible are unstable due to the formation of stable isoporphyrins in the presence of nucleophiles such as halides.