A New Approach to the Problem of Scattering of Water Waves by Vertical Barriers

Using a modified Green's function technique the two well-known basic problems of scattering of surface water waves by vertical barriers are reduced to the problem of solving a pair of uncoupled integral equations involving the “jump” and “sum” of the limiting values of the velocity potential on the two sides of the barriers in each case. These integral equations are then solved, in closed form, by the aid of an integral transform technique involving a general trigonometric kernel as applicable to the problems associated with a radiation condition.

Influence of Raman scattering on the cross phase modulation in optical fibers

The effect of Raman scattering on co-propagation of two short optical pulses is considered. The intra pulse Raman scattering causes the self-frequency shift of each pulse. The effect of the inter pulse Raman scattering is to enhance the frequency shift while the stimulated Raman scattering (SRS) term suppresses (enhances) the frequency shift if the center frequency difference between the optical pulses falls to the right (left) of the Raman gain peak. An expression for the frequency shift as a function of the propagation distance is obtained.

Numerical Electromagnetic Analysis of Current and Voltage Distribution along Down Conductors and Towers Hit by Direct Lightning

In order to answer the practically important question of whether the down conductors of lightning protection systems to tall towers and buildings can be electrically isolated from the structure itself, this work is conducted. As a first step in this regard, it is presumed that the down conductor placed on metallic tower will be a pessimistic representation of the actual problem. This opinion was based on the fact that the proximity of heavy metallic structure will have a large damping effect. The post-stroke current distributions along the down conductors and towers, which can be quite different from that in the lightning channel, govern the post-stroke near field and the resulting gradient in the soil. Also, for a reliable estimation of the actual stroke current from the measured down conductor currents, it is essential to know the current distribution characteristics along the down conductors. In view of these, the present work attempts to deduce the post-stroke current and voltage distribution along typical down conductors and towers. A solution of the governing field equations on an electromagnetic model of the system is sought for the investigation. Simulation results providing the spatio-temporal distribution of the post-stroke current and voltage has provided very interesting results. It is concluded that it is almost impossible to achieve electrical isolation between the structure and the down conductor. Furthermore, there will be significant induction into the steel matrix of the supporting structure.

The Determination of the Surface Tensions of Liquid-Iron, Nickel and Iron-Nickel Alloys using the electromagnetic Oscillating Droplet Technique

An oscillating droplet method combined with electromagnetic levitation has been applied to determine the surface tensions of liquid pure iron, nickel and iron-nickel alloys as a function of the temperature. The natural frequency of the oscillating droplet is evaluated using a Fourier analyser. The theoretical background of this method and the experimental set-up were described, and the influence of magnetic field strength was also discussed. The experimental results were compared with those of other investigators and interpreted using theoretical models (Butler's equation, subregular and perfect solution model for the surface phase).

The Determination of the Surface Tensions of Nickel Sulfur Alloys using the Electromagnetic Oscillating Droplet Technique

An oscillating droplet method combined with electromagnetic levitation technique has been applied to determine the surface tensions of liquid nickel sulphur alloys as a function of the temperature and composition. The natural frequency of the oscillating droplet is evaluated using a Fourier analyser, and the influence of magnetic field strength on the surface tension was considered. Furthermore, the applicability of Butler's equation and subregular solution model for the surface was shown to predict the surface tension of the systems containing the surface active elements.

Geometry and quadratic nonlinearity of charge transfer complexes in solution using depolarized hyper-Rayleigh scattering

We report large quadratic nonlinearity in a series of 1:1 molecular complexes between methyl substituted benzene donors and quinone acceptors in solution. The first hyperpolarizability, beta(HRS), which is very small for the individual components, becomes large by intermolecular charge transfer (CT) interaction between the donor and the acceptor in the complex. In addition, we have investigated the geometry of these CT complexes in solution using polarization resolved hyper-Rayleigh scattering (HRS). Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D = I-2 omega,I-X,I-X/I-2 omega,I-Z,I-X and D' = I-2 omega,I-X,I-C/I-2 omega,I-Z,I-C in the laboratory fixed XYZ frame by detecting the second harmonic scattered light in a polarization resolved fashion. The experimentally obtained first hyperpolarizability, beta(HRS), and the value of macroscopic depolarization ratios, D and D', are then matched with the theoretically deduced values from single and double configuration interaction calculations performed using the Zerner's intermediate neglect of differential overlap self-consistent reaction field technique. In solution, since several geometries are possible, we have carried out calculations by rotating the acceptor moiety around three different axes keeping the donor molecule fixed at an optimized geometry. These rotations give us the theoretical beta(HRS), D and D' values as a function of the geometry of the complex. The calculated beta(HRS), D, and D' values that closely match with the experimental values, give the dominant equilibrium geometry in solution. All the CT complexes between methyl benzenes and chloranil or 1,2-dichloro-4,5-dicyano-p-benzoquinone investigated here are found to have a slipped parallel stacking of the donors and the acceptors. Furthermore, the geometries are staggered and in some pairs, a twist angle as high as 30 degrees is observed. Thus, we have demonstrated in this paper that the polarization resolved HRS technique along with theoretical calculations can unravel the geometry of CT complexes in solution. (C) 2011 American Institute of Physics. doi:10.1063/1.3514922]

Higher twist and higher order contributions to the pion electromagnetic form factor

The O(m(pi)4/(m(u) + (d))2Q2) and O(alpha(S)2) corrections to the leading term of the perturbative QCD calculation of the pion electromagnetic form factor are examined numerically. Both sets of terms provide significant corrections for values of Q2 between 1 and 15 GeV2/c2.

The structure of amorphous platinum disulfide as studied by anomalous x-ray-scattering

Anomalous X-ray scattering (AXS) has been applied to study the structure of amorphous platinum disulfide, Pt1-xS2, prepared by the precipitation process. The local atomic arrangement in amorphous Pt1-xS2 was determined by the least-squares variational method so as to reproduce the experimental differential interference function at the Pt L(III) absorption edge by the AXS method as well as the ordinary interference function by MoK alpha. The structural unit in amorphous Pt1-xS2 is found to be a PtS6 octahedron, similar to that in crystalline PtS2. These octahedra share both their corners and edges, while only edge-sharing linkages occur in crystalline PtS2.

Anomalous X-ray scattering study of local structures in the superionic conducting class (CuI)(0.3)(Cu2O)(0.35)(MoO3)(0.35)

The anomalous X-ray scattering (AXS) method using Cu and Mo K absorption edges has been employed for obtaining the local structural information of superionic conducting glass having the composition (CuI)(0.3)(Cu2O)(0.35)(MoO3)(0.35). The possible atomic arrangements in near-neighbor region of this glass were estimated by coupling the results with the least-squares analysis so as to reproduce two differential intensity profiles for Cu and Mo as well as the ordinary scattering profile. The coordination number of oxygen around Mo is found to be 6.1 at the distance of 0.187 nm. This implies that the MoO6 octahedral unit is a more probable structural entity in the glass rather than MoO4 tetrahedra which has been proposed based on infrared spectroscopy. The pre-peak shoulder observed at about 10 nm(-1) may be attributed to density fluctuation originating from the MoO6 octahedral units connected with the corner sharing linkage, in which the correlation length is about 0.8 nm. The value of the coordination number of I- around Cu+ is estimated as 4.3 at 0.261 nm, suggesting an arrangement similar to that in molten CuI.

Magnetic Raman scattering from 1D antiferromagnets

We study Raman scattering from 1D antiferromagnets within the Fleury-Loudon scheme by applying a finite temperature Lanczos method to a 1D spin-half Heisenberg model with nearest-neighbor (J(1)) and second-neighbor (J(2)) interactions. The low-temperature spectra are analyzed in terms of the known elementary excitations of the system for J(2) = 0 and J(2) = 1/2. We find that the low-T Raman spectra are very broad for \J(2)/J(1)\ less than or equal to 0.3. This broad peak gradually diminishes and shifts with temperature, so that at T > J(1) the spectra are narrower and peaked at low frequencies. The experimental spectra for CuGeO3 are discussed in light of our calculations.

Role of spacer chain length in dimeric micellar organization. Small angle neutron scattering and fluorescence studies

Micelles of different dimeric amphiphiles Br-, n-C(16)H(33)NMe(2)(+) -(CH)(m)-N(+)Me(2)-n-C16H33, Br- (where m = 3, 4, 5, 6, 8, 10, and 12) adapt different morphologies and internal packing arrangements in aqueous media depending on their spacer chain length (m). Detailed measurements of small angle neutron scattering (SANS) cross sections from different bis-cationic, dimeric surfactant micelles in aqueous media (D2O) are reported. The data have been analyzed using the Hayter and Penfold model for macro ion solution to compute the interparticle structure factor S(Q) taking into account the screened Coulomb interactions between the dimeric micelles. The SANS analysis clearly indicated that the extent of aggregate growth and the variations of shapes of the dimeric micelles depend primarily on the spacer chain length. With spacer chain length, m less than or equal to 4, the propensity of micellar growth was particularly pronounced. The effects of the variation of the concentration of dimeric surfactants with m = 5 and 10 on the SANS spectra and the effects of the temperature variation for the micellar system with m = 10 were also examined. The critical micelle concentrations (cmc) and their microenvironmental feature, namely, the microviscosities that the dimeric micellar aggregates offer to a solubilized, extrinsic fluorescence probe, 1,6-diphenyl-1,3,5-hexatriene, were also determined. The changes of cmcs and microviscosities as a function of spacer chain length have been explained in terms of conformational variations and progressive looping of the spacer in micellar core upon increasing m values.

Airborne measurements of aerosol scattering properties above the MABL over Bay of Bengal during W_ICARB - characteristics and spatial gradients

Realizing the importance of aerosol characterization and addressing its spatio-temporal heterogeneities over Bay of Bengal (BoB), campaign mode observations of aerosol parameters were carried out using simultaneous cruise, aircraft and land-based measurements during the Winter Integrated Campaign for Aerosols gases and Radiation Budget (W_ICARB). Under this, airborne measurements of total and hemispheric backscatter coefficients were made over several regions of coastal India and eastern BoB using a three wavelength integrating nephelometer. The measurements include high resolution multi-level (ML) sorties for altitude profiles and bi-level (BL) sorties for spatial gradients within and above the Marine Atmospheric Boundary Layer (MABL) over BoB. The vertical profiles of the scattering coefficients are investigated in light of the information on the vertical structure of the atmospheric stability, which was derived from the collocated GPS (Global Positioning System) aided radiosonde ascents. In general, the altitude profiles revealed that the scattering coefficient remained steady in the convectively well-mixed regions and dropped off above the MABL. This decrease was quite rapid off the Indian mainland, while it was more gradual in the eastern BoB. Investigation on horizontal gradients revealed that the scattering coefficients over northern BoB are 3 to 4 times higher compared to that of central BoB within and above the MABL. A north-south gradient in scattering coefficients is observed over Port Blair in the eastern BoB, with values decreasing from south to north, which is attributed to the similar gradient in the surface wind speed, which can be replicated in the sea salt abundance. The gradients are parameterized using best-fit analytical functions.

Small-angle neutron scattering studies of different mixed micelles composed of dimeric and monomeric cationic surfactants

Measurements of small-angle neutron scattering (SANS) cross sections from different mixed micelles composed of CTAB and Br-, n-C16H33N+Me2-(CH2)(m)N+Me2-n-C16H33, Br- (16-m-16, 2Br(-), where m = 3, 5, and 10), in aqueous media (D2O) are reported. The data have been analyzed using the Hayter and Penfold model for macroion solution to compute the interparticle structure factor S(Q) taking into account the screened Coulomb interactions between the micelles. The aggregate composition matches with that predicted from an ideal mixing model. The SANS analysis further indicates that the extent of aggregate growth and the Variations of shapes of the mixed micelles could be modulated by the amount of dimeric surfactant present in these mixtures. With the spacer chain length m less than or equal to 4 in the dimeric surfactant, the propensity of micellar growth is particularly pronounced. The effect of the variation of the temperature for the mixed micellar system (23.1 mol % of 16-3-16, 2Br(-)) was also examined. The systemic microviscosities that the mixed micellar aggregates offer to a solubilized, extrinsic fluorescence probe, 1,6-diphenyl-1,3,5-hexatriene, were determined. The variation of the microviscosities of the mixed micelles as a function of percentages of the dimeric surfactants could be explained in terms of conformational variations and progressive looping of the spacer chain of dimeric surfactants in mixed micellar aggregates with increasing m values.

Local environmental structures of Mo in the superionic conducting glass (AgI)(0.6)(Ag2MoO4)(0.4) by anomalous X-ray scattering

The anomalous X-ray scattering (AXS) method using Mo K absorption edges has been employed for obtaining the local structural information of superionic conducting glass having the composition (AgI)(0.6)(Ag2MoO4)(0.4). The possible atomic arrangements in the near-neighbor region of this glass were estimated by coupling the results with the least-squares variational analysis so as to reproduce the differential intensity profile for Mo as well as the ordinary scattering profile. The coordination number of oxygen around Mo is found to be about 4 at the distance of 0.180 mn. This implies that the most probable structural entity in the glass is the MoO4 tetrahedral unit which has been proposed based on infrared spectroscopy. The value of the coordination number of I- around Ag+ is estimated as 4.4 at 0.287 nm, suggesting an arrangement similar to that of crystalline or molten AgI.

Micellar structures of dimeric surfactants with phosphate head groups and wettable spacers: A small-angle neutron scattering study

Dimeric or gemini surfactants consist of two hydrophobic chains and two hydrophilic head groups covalently connected by a hydrophobic or hydrophilic spacer. This paper reports the small-angle neutron scattering (SANS) measurements from aqueous micellar solutions of two different recently developed types of dimeric surfactants: (i) bis-anionic C16H33PO4--(CH2)(m)-PO4-C16H33,2Na(+) dimeric surfactants composed of phosphate head groups and a hydrophobic polymethylene spacer, referred to as 16-m-16,2Na(+), for spacer lengths m = 2, 4, 6, and 10, (ii) bis-cationic C16H33N+(CH3)(2)-CH2-(CH2-O-CH2)(p)-CH2-N+ (CH3)(2)C16H33,2Br(-) dimeric surfactants composed of dimethylammonium head groups and a wettable polyethylene oxide spacer, referred to as 16-CH2-p-CH2-16,2Br(-), for spacer lengths p = 1 - 3. The micellar structures of these surfactants are compared with the earlier studied bis-cationic C16H33N+ (CH3)(2)-(CH2)(m)-N+ (CH3)(2)C16H33,2Br(-) dimeric surfactants composed of dimethylammonium head groups and a hydrophobic polymethylene spacer, referred to as 16-m-16,2Br(-). It is found that 16-m-16,2Na(+), similar to 16-m-16,2Br(-), form various micellar structures depending on the spacer length. Micelles an disklike for rn = 2, rodlike for m = 4, and prolate ellipsoidal fur m = 6 and 10. The micelles of 16-CH2-p-CH2-16,2Br(-) are prolate ellipsoidal for all the values of p = 1 - 3. It is also found that micelles of 16-m-16,2Na(+) and 16-CH2-p-CH2-16,2Br(-) are large in comparison to those of 16-in-16,2Br(-) for similar spacer lengths. This is connected with the fact that both in 16-m-16,2Na(+) and 16-CH2-p-CH2-16,2Br(-), the head group or the spacer is more hydrated as compared to that in the 16-m-16,2Br(-). An increase in the hydration of the spacer or the head group increases the screening of the Coulomb repulsion between the charged head groups. This effect has been found to be more pronounced in the dimeric surfactants having wettable spacers. [S1063-651X(99)00303-7].