Use of Abel integral equations in water wave scattering by two surface-piercing barriers

In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.

Simplified theory of carrier back-scattering in semiconducting carbon nanotubes: A Kane's model approach

We present a simplified yet analytical formulation of the carrier backscattering coefficient for zig-zag semiconducting single walled carbon nanotubes under diffusive regime. The electron-phonon scattering rate for longitudinal acoustic, optical, and zone-boundary phonon emissions for both inter- and intrasubband transition rates have been derived using Kane's nonparabolic energy subband model.The expressions for the mean free path and diffusive resistance have been formulated incorporating the aforementioned phonon scattering. Appropriate overlap function in Fermi's golden rule has been incorporated for a more general approach. The effect of energy subbands on low and high bias zones for the onset of longitudinal acoustic, optical, and zone-boundary phonon emissions and absorption have been analytically addressed. 90% transmission of the carriers from the source to the drain at 400 K for a 5 mu m long nanotube at 105 V m(-1) has been exhibited. The analytical results are in good agreement with the available experimental data. (c) 2010 American Institute of Physics.

Convergence correction in colloid scattering

The error introduced in depolarisation measurements due to the convergence of the incident beam has been investigated theoretically as well as experimentally for the case of colloid scattering, where the particles are not small compared to the wavelength of light. Assuming the scattering particles to be anisotropic rods, it is shown that, when the incident unpolarised light is condensed by means of a lens with a circular aperture, the observed depolarisation ratio ϱ u is given by ϱ u = ϱ u0 + 5/3 θ2 where ϱ u0 is the true depolarisation for incident parallel light, and θ the semi-angle of convergence. Appropriate formulae are derived when the incident beam is polarised vertically and horizontally. Experiments performed on six typical colloids support the theoretical conclusions. Other immediate consequences of the theory are also discussed.

Phonon-mediated two-magnon light scattering from ferromagnetic insulators

An indirect mechanism of light scattering from spin-waves in ferromagnetic insulators via two-magnon one-phonon process is proposed. Following linear response theory, an expression has been derived for the differential scattering cross-section in the mean-field-approximation.

Vertical profile of aerosol single scattering albedo over west coast of India during W_ICARB

Altitude profile of aerosol Single Scattering Albedo (SSA), derived from simultaneous in-situ airborne measurements of the coefficients of aerosol absorption and scattering off the west coast of India over the Arabian Sea (AS), during January 2009 is presented. While both the absorption and scattering coefficients decreased with altitude, their vertical structure differed significantly. Consequently, the derived SSA, with a surface value of 0.94, decreased with altitude, illustrating increasing relative dominance of aerosol absorption at higher altitudes. Altitude profile of SSA, when examined in conjunction with that of hemispheric backscatter fraction, revealed that the continental influence on the aerosol properties was higher at higher altitude, rather than the effect of marine environment. During an east-west transect across the peninsular India at an altitude of similar to 2500 m (free troposphere), it was found that the aerosol scattering coefficients remained nearly the same over both east and west coasts. (C) 2010 Elsevier Ltd. All rights reserved.

Assessment of ultrasound modulation of near infrared light on the quantification of scattering coefficient

Purpose: To assess the effect of ultrasound modulation of near infrared (NIR) light on the quantification of scattering coefficient in tissue-mimicking biological phantoms.Methods: A unique method to estimate the phase of the modulated NIR light making use of only time averaged intensity measurements using a charge coupled device camera is used in this investigation. These experimental measurements from tissue-mimicking biological phantoms are used to estimate the differential pathlength, in turn leading to estimation of optical scattering coefficient. A Monte-Carlo model base numerical estimation of phase in lieu of ultrasound modulation is performed to verify the experimental results. Results: The results indicate that the ultrasound modulation of NIR light enhances the effective scattering coefficient. The observed effective scattering coefficient enhancement in tissue-mimicking viscoelastic phantoms increases with increasing ultrasound drive voltage. The same trend is noticed as the ultrasound modulation frequency approaches the natural vibration frequency of the phantom material. The contrast enhancement is less for the stiffer (larger storage modulus) tissue, mimicking tumor necrotic core, compared to the normal tissue. Conclusions: The ultrasound modulation of the insonified region leads to an increase in the effective number of scattering events experienced by NIR light, increasing the measured phase, causing the enhancement in the effective scattering coefficient. The ultrasound modulation of NIR light could provide better estimation of scattering coefficient. The observed local enhancement of the effective scattering coefficient, in the ultrasound focal region, is validated using both experimental measurements and Monte-Carlo simulations. (C) 2010 American Association of Physicists in Medicine. [DOI: 10.1118/1.3456441]

Magnetic excitations in charge-ordered Nd0.5Ca0.5MnO3: A Brillouin scattering study

Brillouin scattering studies on single crystals of a charge-ordered manganite, Nd0.5Ca0.5MnO3, have been carried out for the first time. The spectra show two modes at similar to 27 GHz (B-mode) and 60 GHz (S-mode). The B-mode frequency and intensity from 300 K to 27 K, covering both the charge ordering transition at 250 K and the antiferromagnetic transition, at 170 K, exactly follow the same temperature dependence as the d.c. magnetic susceptibility. The B-mode is associated With bulk magnetic excitations and the S-mode with surface magnetic excitations of the manganite with ferromagnetic correlations. The study is strongly indicative of the presence of ferromagnetic inhomogeneities in the charge-ordered as well as antiferromagnetic phases.

Electromagnetic wave propagation at the interface between two polar semiconductors

The interface between two polar semiconductors can support three types of phonon-plasmon-polariton modes propagating in three well-defined frequency windows ??1?[min(?1,?3),?R1], ??2?[max(?2,?4),?R2], and ??3?[min(?2,?4),?R3]. The limiting frequencies ?1,2,3,4 are defined by ?1(?)=0, ?2(?)=0, and ?R1,2,3 by ?1(?)+?2(?)=0, where ?i(?) are dielectric functions of the two media with i=1,2. The dispersion, decay distances, and polarization of the three modes are discussed. The variation of the limiting frequencies with the interface plasma parameter ???p22/?p12 reveals an interesting feature in the dispersion characteristics of these modes. For the interfaces for which the bulk coupled phonon-plasmon frequencies of medium 1 are greater than the LO frequency or are less than the TO frequency of medium 2, there exist two values of ?=?1 and ?2(

Experimental studies and phase field modeling of microstructure evolution during solidification with electromagnetic stirring

Thixocasting requires manufacturing of billets with non-dendritic microstructure. Aluminum alloy A356 billets were produced by rheocasting in a mould placed inside a linear electromagnetic stirrer. Subsequent heat treatment was used to produce a transition from rosette to globular microstructure. The current and the duration of stirring were explored as control parameters. Simultaneous induction heating of the billet during stirring was quantified using experimentally determined thermal profiles. The effect of processing parameters on the dendrite fragmentation was discussed. Corresponding computational modeling of the process was performed using phase-field modeling of alloy solidification in order to gain insight into the process of morphological changes of a solid during this process. A non-isothermal alloy solidification model was used for simulations. The morphological evolution under such imposed thermal cycles was simulated and compared with experimentally determined one. Suitable scaling using the thermosolutal diffusion distances was used to overcome computational difficulties in quantitative comparison at system scale. The results were interpreted in the light of existing theories of microstructure refinement and globularisation.

Propagation Of Vlf Electromagnetic-Waves In An Idealized Earth-Crust Wave-Guide With Overburden

Theoretical study of propagation characteristics of VLF electromagnetic waves through an idealised parallel-plane earth-crust waveguide with overburden, experimental verification of some of these characteristics with the aid of a model tank and use of range equation reveal the superiority of radio communication between land and a deeply submerged terminal inside a ocean via the earth-crust over direct link communication through the ocean.

Absorption of Electromagnetic Waves in Astrophysical Plasmas

We study parametric Decay Instabilities (PDI) using the kinetic description, in the homogeneous and unmagnetic plasmas. These instabilities cause anomalous absorption of the incident electromagnetic (e.m) radiations. The maximum plasma temperatures reached are functionas of luminocity of the non-thermal radio radiation and the plasma parameters.

Theory of the effects of destruction of localization by inelastic scattering in the resistivity of pure thin potassium wires

Measurements of the electrical resistivity of thin potassium wires at temperatures near 1 K have revealed a minimum in the resistivity as a function of temperature. By proposing that the electrons in these wires have undergone localization, albeit with large localization length, and that inelastic-scattering events destroy the coherence of that state, we can explain both the magnitude and shape of the temperature-dependent resistivity data. Localization of electrons in these wires is to be expected because, due to the high purity of the potassium, the elastic mean free path is comparable to the diameters of the thinnest samples, making the Thouless length lT (or inelastic diffusion length) much larger than the diameter, so that the wire is effectively one dimensional. The inelastic events effectively break the wire into a series of localized segments, whose resistances can be added to obtain the total resistance of the wire. The ensemble-averaged resistance for all possible segmented wires, weighted with a Poisson distribution of inelastic-scattering lengths along the wire, yields a length dependence for the resistance that is proportional to [L3/lin(T)], provided that lin(T)?L, where L is the sample length and lin(T) is some effective temperature-dependent one-dimensional inelastic-scattering length. A more sophisticated approach using a Poisson distribution in inelastic-scattering times, which takes into account the diffusive motion of the electrons along the wire through the Thouless length, yields a length- and temperature-dependent resistivity proportional to (L/lT)4 under appropriate conditions. Inelastic-scattering lifetimes are inferred from the temperature-dependent bulk resistivities (i.e., those of thicker, effectively three-dimensional samples), assuming that a minimum amount of energy must be exchanged for a collision to be effective in destroying the phase coherence of the localized state. If the dominant inelastic mechanism is electron-electron scattering, then our result, given the appropriate choice of the channel number parameter, is consistent with the data. If electron-phason scattering were of comparable importance, then our results would remain consistent. However, the inelastic-scattering lifetime inferred from bulk resistivity data is too short. This is because the electron-phason mechanism dominates in the inelastic-scattering rate, although the two mechanisms may be of comparable importance for the bulk resistivity. Possible reasons why the electron-phason mechanism might be less effective in thin wires than in bulk are discussed.