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.

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.

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.

Detection of a periodic structure embedded in surface roughness, for various correlation functions

This paper deals with surface profilometry, where we try to detect a periodic structure, hidden in randomness using the matched filter method of analysing the intensity of light, scattered from the surface. From the direct problem of light scattering from a composite rough surface of the above type, we find that the detectability of the periodic structure can be hindered by the randomness, being dependent on the correlation function of the random part. In our earlier works, we had concentrated mainly on the Cauchy-type correlation function for the rough part. In the present work, we show that this technique can determine the periodic structure of different kinds of correlation functions of the roughness, including Cauchy, Gaussian etc. We study the detection by the matched filter method as the nature of the correlation function is varied.

RCS ENHANCEMENT DUE TO BRAGG SCATTERING

With the advances of techniques for RCS reduction, it has become practical to develop aircraft which are invisible to modern day radars. In order to detect such low visible targets it is necessary to explore other phenomenon that contributes to the scattering of incident electromagnetic wave. It is well known from the developments from the clear air scattering using RASS induced acoustic wave could be used to create dielectric constant fluctuation. The scattering from these fluctuations rather than from the aircraft have been observed to enhance the RCS of clear air, under the condition when the incident EM wave is half of the acoustic wave, the condition of Bragg scattering would be met and RCS would be enhanced. For detecting low visibility targets which are at significant distance away from the main radar, inducement of EM fluctuation from acoustic source collocated with the acoustic source is infeasible. However the flow past aircraft produces acoustic disturbances around the aircraft can be exploited to detect low visibility targets. In this paper numerical simulation for RCS enhancement due to acoustic disturbances is presented. In effect, this requires the solution of scattering from 3D inhomogeneous complex shaped bodies. In this volume surface integral equation (VSIE) is used to compute the RCS from fluctuation introduced through the acoustic disturbances. Though the technique developed can be used to study the scattering from radars of any shape and acoustic disturbances of any shape. For illustrative condition, enhancement due to the Bragg scattering are shown to improve the RCS by nearly 30dB, for air synthetic sinusoidal acoustic variation profile for a spherical scattering volume

Intensity profile of light scattered from a rough surface

We present in this paper, approximate analytical expressions for the intensity of light scattered by a rough surface, whose elevation. xi(x,y) in the z-direction is a zero mean stationary Gaussian random variable. With (x,y) and (x',y') being two points on the surface, we have h. = 0 with a correlation, = sigma(2)g(r), where r = (x - x')(2) + ( y - y')(2)](1/2) is the distance between these two points. We consider g(r) = exp-r/l)(beta)] with 1 <= beta <= 2, showing that g(0) = 1 and g(r) -> 0 for r >> l. The intensity expression is sought to be expressed as f(v(xy)) = {1 + (c/2y)v(x)(2) + v(y)(2)]}(-y), where v(x) and v(y) are the wave vectors of scattering, as defined by the Beckmann notation. In the paper, we present expressions for c and y, in terms of sigma, l, and beta. The closed form expressions are verified to be true, for the cases beta = 1 and beta = 2, for which exact expressions are known. For other cases, i.e., beta not equal 1, 2 we present approximate expressions for the scattered intensity, in the range, v(xy) = (v(x)(2) + v(y)(2))(1/2) <= 6.0 and show that the relation for f(v(xy)), given above, expresses the scattered intensity quite accurately, thus providing a simple computational methods in situations of practical importance.

Small-Angle Neutron Scattering Studies of Hemoglobin Confined Inside Silica Tubes of Varying Sizes

In addition to the chemical nature of the surface, the dimensions of the confining host exert a significant influence on confined protein structures; this results in immense biological implications, especially those concerning the enzymatic activities of the protein. This study probes the structure of hemoglobin (Hb), a model protein, confined inside silica tubes with pore diameters that vary by one order of magnitude (approximate to 20-200 nm). The effect of confinement on the protein structure is probed by comparison with the structure of the protein in solution. Small-angle neutron scattering (SANS), which provides information on protein tertiary and quaternary structures, is employed to study the influence of the tube pore diameter on the structure and configuration of the confined protein in detail. Confinement significantly influences the structural stability of Hb and the structure depends on the Si-tube pore diameter. The high radius of gyration (R-g) and polydispersity of Hb in the 20 nm diameter Si-tube indicates that Hb undergoes a significant amount of aggregation. However, for Si-tube diameters greater or equal to 100 nm, the R-g of Hb is found to be in very close proximity to that obtained from the protein data bank (PDB) reported structure (R-g of native Hb=23.8 angstrom). This strongly indicates that the protein has a preference for the more native-like non-aggregated state if confined inside tubes of diameter greater or equal to 100 nm. Further insight into the Hb structure is obtained from the distance distribution function, p(r), and ab initio models calculated from the SANS patterns. These also suggest that the Si-tube size is a key parameter for protein stability and structure.

Flame surface statistics of constant-pressure turbulent expanding premixed flames

In this paper we investigate the local flame surface statistics of constant-pressure turbulent expanding flames. First the statistics of local length ratio is experimentally determined from high-speed planar Mie scattering images of spherically expanding flames, with the length ratio on the measurement plane, at predefined equiangular sectors, defined as the ratio of the actual flame length to the length of a circular-arc of radius equal to the average radius of the flame. Assuming isotropic distribution of such flame segments we then convolute suitable forms of the length-ratio probability distribution functions (pdfs) to arrive at the corresponding area-ratio pdfs. It is found that both the length ratio and area ratio pdfs are near log-normally distributed and shows self-similar behavior with increasing radius. Near log-normality and rather intermittent behavior of the flame-length ratio suggests similarity with dissipation rate quantities which stimulates multifractal analysis. (C) 2014 AIP Publishing LLC.

Implications of multiple scattering on the assessment of black carbon aerosol radiative forcing

The effects of radiative coupling between scattering and absorbing aerosols, in an external mixture, on the aerosol radiative forcing (ARF) due to black carbon (BC), its sensitivity to the composite aerosol loading and composition, and surface reflectance are investigated using radiative transfer model simulations. The ARF due to BC is found to depend significantly on the optical properties of the `neighboring' (non-BC) aerosol species. The scattering due to these species significantly increases the top of the atmospheric warming due to black carbon aerosols, and significant changes in the radiative forcing efficiency of BC. This is especially significant over dark surfaces (such as oceans), despite the ARF due to BC being higher over snow and land-surfaces. The spatial heterogeneity of this effect (coupling or multiple scattering by neighboring aerosol species) imposes large uncertainty in the estimation ARF due to BC aerosols, especially over the oceans. (C) 2014 Elsevier Ltd. All rights reserved.

Anomalous structural relaxations in PVDF rich blends with PMMA in the presence of surface functionalized CNTs

The structural relaxations in PVDF rich blends with PMMA can be quite interesting in understanding the origin of the different molecular relaxations associated with the crystalline and amorphous phases, crystal-amorphous interphase and the segmental motions. In light of our recent findings, we understood that the origin of these molecular relaxations were strongly contingent on the concentration of PMMA in the blend, crystalline morphology and the surface functional moieties on multiwall carbon nanotubes (CNTs). In addition, for the blends with concentration of PMMA >= 25 wt%, the structural relaxations often merge and are dielectrically indistinguishable. In this study, we attempted to determine the critical width in composition where the structural relaxations can be distinctly realized both in the control as well as blends with amine functionalized CNTs (NH2-CNTs). Intriguingly, we observed that in a narrow zone in composition (with PMMA concentration >= 10 wt% and <= 25 wt%), the molecular relaxations can be dielectrically distinguished and they often merge for all other compositions. Furthermore, we attempted to understand how this critical width in composition is related to the crystalline morphology using small angle X-ray scattering and polarizing optical microscopy and the crystal structure using FTIR and Raman spectroscopy. We now understand that although the formation of beta crystals in the blends has no direct correlation with the observed molecular relaxations, the amorphous miscibility and the interphase regions seem to be dictating the origin of different molecular relaxations in the blends. The latter was observed to be strongly contingent on the concentration of PMMA in the blends.

Exciton-phonon scattering and nonradiative relaxation of excited carriers in hydrothermally synthesized CdTe quantum dots

Naturally formed CdTe/CdS core/shell quantum dot (QD) structures in the presence of surface stabilizing agents have been synthesized by a hydrothermal method. Size and temperature dependent photoluminescence (PL) spectra have been investigated to understand the exciton-phonon interaction, and radiative and nonradiative relaxation of carriers in these QDs. The PL of these aqueous CdTe QDs (3.0-4.8 nm) has been studied in the temperature range 15-300 K. The strength of the exciton-LO-phonon coupling, as reflected in the Huang-Rhys parameter `S' is found to increase from 1.13 to 1.51 with the QD size varying from 4.8 to 3.0 nm. The PL linewidth (FWHM) increases with increase in temperature and is found to have a maximum in the case of QDs of 3.0 nm in size, where the exciton-acoustic phonon coupling coefficient is enhanced to 51 mu eV K-1, compared to the bulk value of 0.72 mu eV K-1. To understand the nonradiative processes, which affect the relaxation of carriers, the integrated PL intensity is observed as a function of temperature. The integrated PL intensity remains constant until 50 K for relatively large QDs (3.9-4.8 nm) beyond which a thermally activated process takes over. Below 150 K, a small activation energy, 45-19 meV, is found to be responsible for the quenching of the PL. Above 150 K, the thermal escape from the dot assisted by scattering with multiple longitudinal optical (LO) phonons is the main mechanism for the fast quenching of the PL. Besides this high temperature quenching, interestingly for relatively smaller size QDs (3.4-3.0 nm), the PL intensity enhances as the temperature increases up to 90-130 K, which is attributed to the emission of carriers from interface/trap states having an activation energy in the range of 6-13 meV.

Scattering of electromagnetic waves from chirally coated cylinders

The problem of electromagnetic scattering from an isotropic homogeneous chirally coated conducting cylinder is analysed. The cylinder is assumed to be illuminated by either a transverse magnetic or a transverse electric wave. Mie's analysis is used to evaluate the scattering characteristics. The computed results include the evaluation of the normalized scattering width and the absorption efficiency. The results show that there is a significant reduction in the normalized scattering width as compared to a RAM coated cylinder. This reduction has been attributed to increased absorption.

Small-angle neutron scattering study of micellar structures of dimeric surfactants

Dimeric or gemini surfactants consist of two hydrophobic chains and two hydrophilic head groups co; valently connected by a hydrocarbon spacer. Small-angle neutron scattering measurements from bis-cationic C16H33N+(CH3)(2)-(CH2)(m)-N+(CH3)(2)C(16)H(33)2Br(-) dimeric surfactants, referred to-as 16-m-16, for different length of hydrocarbon spacers m-3-6, 8, 10, and 12, are reported. The measurements have been carried out at various concentrations: C=2.5 and 10 mM for all m and C=30 and 50 mM for m greater than or equal to 5. It is found that micellar structure depends on the length of the spacer. Micelles are disks for m=3, cylindrical for m=4, and prolate ellipsoidals for other values of m. These structural results are in agreement with the theoretical predictions based on the packing parameter. It has also been observed that conformation of the spacer and the hydrophobic chains in the interior of the micelle change as the length of the spacer is increased. The concentration dependence for m greater than or equal to 5 shows that the effect of surfactant concentration on the size of the micelle is more pronounced for m=5 and 12 than for the intermediate spacers. The fractional charge on the micelle increases with the increase in spacer length and decreases when the concentration is increased.

Evidence of clustering in an aqueous electrolyte solution: a small-angle X-ray scattering study

The work reported hen was motivated by a desire to verify the existence of structure - specifically MP-rich clusters induced by sodium bromide (NaBr) in the ternary liquid mixture 3-methylpyridine (Mf) + water(W) + NaBr. We present small-angle X-ray scattering (SAXS) measurements in this mixture. These measurements were obtained at room temperature (similar to 298 K) in the one-phase region (below the relevant lower consolute points, T(L)s) at different values of X (i.e., X = 0.02 - 0.17), where X is the weight fraction of NaBr in the mixture. Cluster-size distribution, estimated on the assumption that the clusters are spherical, shows systematic behaviour in that the peak of the distribution shifts rewards larger values of cluster radius as X increases. The largest spatial extent of the clusters (similar to 4.5 nm) is seen at X = 0.17. Data analysis assuming arbitrary shapes and sizes of clusters gives a limiting value of cluster size (- 4.5 nm) that is not very sensitive to X. It is suggested that the cluster size determined may not be the same as the usual critical-point fluctuations far removed from the critical point (T-L). The influence of the additional length scale due to clustering is discussed from the standpoint of crossover from Ising to mean-field critical behaviour, when moving away from the T-L.

Surface chemical studies of Thiobacillus ferrooxidans with reference to copper tolerance

A strain of Thiobacillus ferrooxidans was adapted to grow at higher concentrations of copper by single step culturing in the presence of 20 g/L (0.314 mol/L) cupric ions added to 9K medium. Exposure to copper results in change in the surface chemistry of the microorganism. The isoelectric point of the adapted strain (pI=4.7) was observed to be at a higher pH than that of the wild unadapted strain(pI=2.0). Compared to the wild strain, the copper adapted strain was found to be more hydrophobic and showed enhanced attachment efficiency to the pyrite mineral. The copper adsorption ability of the adapted strain was also found to be higher than that of the wild strain. Fourier transform infrared spectroscopy of adapted cells suggested that a proteinaceous new cell surface component is synthesized by the adapted strain. Treatment of adapted cells with proteinase-K, resulted in complete loss of tolerance to copper, reduction in copper adsorption and hydrophobicity of the adapted cells. These observations strongly suggest a role played by cell surface modifications of Thiobacillus ferrooxidans in imparting the copper tolerance to the cells and bioleaching of sulphide minerals.