The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena

Two mixed boundary value problems associated with two-dimensional Laplace equation, arising in the study of scattering of surface waves in deep water (or interface waves in two superposed fluids) in the linearised set up, by discontinuities in the surface (or interface) boundary conditions, are handled for solution by the aid of the Weiner-Hopf technique applied to a slightly more general differential equation to be solved under general boundary conditions and passing on to the limit in a manner so as to finally give rise to the solutions of the original problems. The first problem involves one discontinuity while the second problem involves two discontinuities. The reflection coefficient is obtained in closed form for the first problem and approximately for the second. The behaviour of the reflection coefficient for both the problems involving deep water against the incident wave number is depicted in a number of figures. It is observed that while the reflection coefficient for the first problem steadily increases with the wave number, that for the second problem exhibits oscillatory behaviour and vanishes at some discrete values of the wave number. Thus, there exist incident wave numbers for which total transmission takes place for the second problem. (C) 1999 Elsevier Science B.V. All rights reserved.

Vesicle formation from dimeric ion-paired amphiphiles. Control over vesicular thermotropic and ion-transport properties as a function of intra-amphiphilic headgroup separation

A novel series of vesicle-forming ion-paired amphiphiles, bis(hexadecyldimethylammonium)alkane dipalmitate (1a-1h), containing four chains were synthesized with two isolated headgroups. In each of these amphiphiles, the two headgroup charges are separated by a flexible polymethylene spacer chain -[(CH2)(m)]- of varying lengths (m) such that the length and the conformation of the spacer chain determine the intra-"monomer" headgroup separation. Transmission electron microscopy indicated that each of these forms bilayer membranes upon dispersion in aqueous media. The vesicular properties of these aggregates have been examined by differential scanning calorimetry and temperature-dependent fluorescence anisotropy measurements. Interestingly, their T-m values decreased with the increase in the m value. Thus while the apparent T-m of the lipid with m = 2 (1a) is 74.1 degrees C, the corresponding value observed for the lipid with m = 12 (1h) is 38.9 degrees C. The fluorescence anisotropy values (r) for 1b-1g were quite high (r similar to 0.3) compared to that of 1h (r similar to 0.23) at 20-30 degrees C in their gel states. On the other hand, the r value for vesicular 1b beyond melting was higher (0.1) compared to any of those for 1c-1h (similar to 0.04-0.06). X-ray diffraction of the cast films was performed to understand the nature and the thickness of these membrane organizations. The membrane widths ranged from 30 to 51 A as the m values varied. The entrapment of a small water-soluble solute, riboflavin, by the individual vesicular aggregates, and their sustenance: under an imposed transmembrane pH gradient have also been examined. These results show that all lipid vesicles entrap riboflavin and that generally the resistance to OH- permeation decreases with the increase in m value. Finally,all the above observations were comparatively analyzed, and on the basis of the calculated structures of these lipids, it was possible to conclude that membrane propel-ties can be modulated by spacer chain length variation of the ion-paired amphiphiles.

A study on determining the theoretical dispersion curve for Rayleigh wave propagation

A method has been presented to establish the theoretical dispersion curve for performing the inverse analysis for the Rayleigh wave propagation. The proposed formulation is similar to the one available in literature, and is based on the finite difference formulation of the governing partial differential equations of motion. The method is framed in such a way that it ultimately leads to an Eigen value problem for which the solution can be obtained quite easily with respect to unknown frequency. The maximum absolute value of the vertical displacement at the ground surface is formed as the basis for deciding the governing mode of propagation. With the proposed technique, the numerical solutions were generated for a variety of problems, comprising of a number of different layers, associated with both ground and pavements. The results are found to be generally satisfactory. (C) 2011 Elsevier Ltd. All rights reserved.

Enhanced lithium-ion transport in PEG-based composite polymer electrolyte with Mn0.03Zn0.97Al2O4 nanoparticles

The ion conduction and thermal properties of composite solid polymer electrolyte (SPE) comprising Poly(ethylene) Glycol (PEG, mol wt. 2000), lithium perchlorate (LiClO4) and insulating Mn0.03Zn0.97Al2O4 nanoparticle fillers were studied by complex impedance analysis and DSC techniques. The average size of the nanoparticles was determined by powder X-ray diffraction (XRD) using Scherrer's equation and was found to be similar to 8 nm. The same was also determined by TEM imaging and found to be similar to 12 nm. The glass transition temperature T, as measured by differential scanning calorimeter (DSC), showed a minimum at 5 mol% of narroparticles. Fractional crystallinity was determined using DSC. NMR was used to deter-mine crystallinity of a pure PEG sample, which was then used as the standard. Fractional crystallinity X. was the lowest for 5 mol% and beyond. The ionic conductivity of the composite polymer electrolyte containing 5 mol% Mn0.03Zn0.97Al2O4 nanoparticles was found to be 1.82 x 10(-5) S/cm, while for the pristine one, it was 7.27 x 10(-7) S/cm at room temperature. As a function of nanoparticle content, conductivity was observed to go through two maxima, one at around 5 mol% and another shallower one at around 12 mol%. The temperature dependence of conductivity could be divided into two regions, one consistent with Arrhenius behaviour and the other with VTF. We conclude that the enhancement of ionic conductivity on the addition of Mn0.03Zn0.97Al2O4 nanoparticles is a result of reduction in both the T, and the crystallinity. (C) 2002 Elsevier Science B.V. All rights reserved.

Study of translational and rotational mobility and orientational preference of ethane in one-dimensional channels

Structural and dynamical properties of ethane in one-dimensional channels of AlPO4-5 and carbon nanotube have been investigated at dilute concentration with the help of molecular dynamics simulation. Density distributions and orientational structure of ethane have been analyzed. Repulsive interactions seem to play an important role when ethane is located in the narrow part of the AlPO4-5 channel. In AlPO4-5, parallel orientation is predominant over perpendicular orientation except when ethane is located in the broader part of the channel. Unlike in the case of single-file diffusion, our results in carbon nanotube show that at dilute concentrations the mean squared displacement, mu(2)(t) approximate to t(alpha), alpha = 1.8. The autocorrelation function for the z-component of angular velocity of ethane in space-fixed frame of reference shows a pronounced negative correlation. This is attributed to the restriction in the movement of ethane along the x- and y- directions. It is seen that the ratio of reorientational correlation times does not follow the Debye model for confined ethane but it is closer to the predictions of the Debye model for bulk ethane.

Synthesis and characterization of mono- and bis-D-pi-A cryptand derivatives for second-order nonlinear optics and its modulation with different metal ion inputs

Two new classes of mono- and bis-D-pi-A cryptand derivatives with a flexible and a rigid cryptand core have been synthesized. The linear and nonlinear optical properties of these molecules are probed. The three dimensional cavity of the cryptand moiety has been utilized to modulate the SHG intensity to different extents in solution with metal ion inputs such as Ni-II,Cu-II,Zn-II, and Cd-II. We also report that decomplexation events can be used to reversibly modulate their NLO responses.

Electrochemical Properties of Li3N Dissolved in Molten LiCl at 900 K

Thermodynamic properties of Li3N dissolved in the molten LiCl salt at 900 K were explored using electrochemical methods. It was difficult to determine precisely the decomposition voltage of Li3N dissolved in the molten salt by cyclic voltammetry. The oxidation wave of N3– ion could not be located with high accuracy. However, the lithium activity of the Pb-Li alloy in equilibrium with the molten salt containing dissolved Li3N under nitrogen atmosphere could be measured electrochemically with high accuracy using the Li/Li + reference electrode. Under the conditions used in this study, the potential of the Li-Pb electrode is equal to the decomposition voltage of Li3N. The activity of Li3N in molten LiCl was determined for anionic fractions of N3– ranging from xN3– = 10–4 to 0.028. The nitride ion concentration in the salt was determined by chemical titration. The activity coefficient of the Li3N at high dilution was found to be very low, around 10–4. The activity coefficient increases sharply with composition and has a value of 0.25 at xN3– = 0.028. ©2001 The Electrochemical Society. All rights reserved.

Formation of amorphous xenon nanoclusters and microstructure evolution in pulsed laser deposited Ti(62.5)Si(37.5) thin films during Xe ion irradiation

As deposited amorphous and crystallized thin films of Ti 37.5% Si alloy deposited by pulsed laser ablation technique were irradiated with 100 keV Xe(+) ion beam to an ion fluence of about 10(16) ions-cm(-2). Transmission electron microscopy revealed that the implanted Xe formed amorphous nanosized clusters in both cases. The Xe ion-irradiation favors nucleation of a fcc-Ti(Si) phase in amorphous films. However, in crystalline films, irradiation leads to dissolution of the Ti(5)Si(3) intermetallic phase. In both cases, Xe irradiation leads to the evolution of similar microstructures. Our results point to the pivotal role of nucleation in the evolution of the microstructure under the condition of ion implantation.

A study of shock wave interaction with a rotating cylinder

Shock wave reflection over a rotating circular cylinder is numerically and experimentally investigated. It is shown that the transition from the regular reflection to the Mach reflection is promoted on the cylinder surface which rotates in the same direction of the incident shock motion, whereas it is retarded on the surface that rotates to the reverse direction. Numerical calculations solving the Navier-Stokes equations using extremely fine grids also reveal that the reflected shock transition from RRdouble right arrowMR is either advanced or retarded depending on whether or not the surface motion favors the incident shock wave. The interpretation of viscous effects on the reflected shock transition is given by the dimensional analysis and from the viewpoint of signal propagation.

Characterization of vesicles from ion-paired gemini surfactants by small angle neutron scattering

Detailed small angle neutron scattering ( SANS) studies were carried out with the aqueous vesicular (unilamellar) suspension of dimeric ion-paired lipids (2a-2c) for spacer lengths corresponding to n-values of 2, 6 and 10 and monomeric ion-paired lipid (3) below and above the phase transition temperature of each amphiphile. The vesicular structure strongly depends on the spacer chain length. The mean vesicle size is smallest for the lipid with a short spacer, n = 3 and it increases with the increase in the spacer chain length. The bilayer thickness also decreases with the increase in the spacer chain length. The size polydispersity increases with the increase in the spacer chain length (n-value).

High-pressure studies on lithium fast-ion conductors

The variation of resistivity of the lithium fast-ion conductor Li3+y Ge1−yO4 (y = 0.25, 0.6, 0.72) has been studied with hydrostatic pressure up to 70 kbar and compared with that of Li16−2x Znx (GeO4)4(x = 1, 2). Both types showed pronounced resistivity maxima between 20–30 kbar and marked decrease thereafter. Measurements as a function of temperature between 120–300 K permitted the determination of activation energies and prefactors that also showed corresponding maxima. The activation volumes (ΔV) of the first type of compound varied between 4.34 to −4.90 cm3/mol at 300 K and decreased monotonically with increasing temperature. For the second type ΔV was much smaller, varied with pressure between 0.58 and −0.24 cm3/mol, and went through a maximum with increasing temperature. High-pressure studies were also conducted on aged samples, and the results are discussed in conjunction with results of impedance measurements and nuclear magnetic resonance (NMR) studies. The principal effect of pressure appears to be variations of the sum of interatomic potentials and hence barrier height, which also causes significant changes in entropy.

Properties of Al2O3 films prepared by argon ion assisted deposition

Aluminum oxide films have been prepared by ion assisted deposition using argon ions with energy in the range 300 to 1000 eV and current density in the range 50 to 220 μA/cm2. The influence of ion energy and current density on the optical and structural properties has been investigated. The refractive index, packing density, and extinction coefficient are found to be very sensitive to the ion beam parameters and substrate temperatures. The as-deposited films were found to be amorphous and could be transformed into crystalline phase on annealing. However, the crystalline phases were different in films prepared at ambient and elevated substrate temperatures.

Stresses in Ion Assisted Deposited Oxide Thih Films

Thin films of Ceria, Titania and Ziroonia have been prepared using Ion Assisted Deposition(IAD). The energy of ions was varied between 0 and 1 keV and current densities up to 220 μA/cm were used. It was found that the stress behaviour is dependent on ion species, i.e. Argon or Oxygen, ion energy and current density and substrate temperature apart from the material. While oeria files showed tensile stresses under the influence of argon ion bombardment at ambient temperature, they showed a sharp transition from tensile to compressive stress with increase in substrate temperature. When bombarded with oxygen ions they showed a transition from tensile to compressive stress with increase in energy. The titania films deposited with oxygen ions, on the other hand showed purely tensile stresses. Zirconia films deposited with oxygen ions, however, showed a transition from tensile to compressive stress.

Formation of amorphous xenon nanoclusters and microstructure evolution in pulsed laser deposited Ti62.5Si37.5 thin films during Xe ion irradiation

As deposited amorphous and crystallized thin films of Ti 37.5% Si alloy deposited by pulsed laser ablation technique were irradiated with 100 keV Xe+ ion beam to an ion fluence of about 1016 ions-cm−2. Transmission electron microscopy revealed that the implanted Xe formed amorphous nanosized clusters in both cases. The Xe ion-irradiation favors nucleation of a fcc-Ti(Si) phase in amorphous films. However, in crystalline films, irradiation leads to dissolution of the Ti5Si3 intermetallic phase. In both cases, Xe irradiation leads to the evolution of similar microstructures. Our results point to the pivotal role of nucleation in the evolution of the microstructure under the condition of ion implantation.