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.

On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions

Closed-form analytical expressions are derived for the reflection and transmission coefficients for the problem of scattering of surface water waves by a sharp discontinuity in the surface-boundary-conditions, for the case of deep water. The method involves the use of the Havelock-type expansion of the velocity potential along with an analysis to solve a Carleman-type singular integral equation over a semi-infinite range. This method of solution is an alternative to the Wiener-Hopf technique used previously.

Solution of a class of surface water wave scattering problems involving non-reflecting vertical barriers

A large class of scattering problems of surface water waves by vertical barriers lead to mixed boundary value problems for Laplace equation. Specific attentions are paid, in the present article, to highlight an analytical method to handle this class of problems of surface water wave scattering, when the barriers in question are non-reflecting in nature. A new set of boundary conditions is proposed for such non-reflecting barriers and tile resulting boundary value problems are handled in the linearized theory of water waves. Three basic poblems of scattering by vertical barriers are solved. The present new theory of non-reflecting vertical barriers predict new transmission coefficients and tile solutions of tile mathematical problems turn out to be extremely simple and straight forward as compared to the solution for other types of barriers handled previously.

Interconnected, ultrafine osmium nanoclusters: preparation and surface enhanced Raman scattering activity

Interconnected Os nanochains consisting of ultrafine particles prepared using a simple procedure yield a coupled surface plasmon peak in the visible region and can be used as substrates for surface enhanced Raman scattering of various analytes.

Spontaneous assembly of iridium nanochain-like structures: surface enhanced Raman scattering activity using visible light

A facile, environmentally friendly approach to synthesize branched Ir nanochain-like structures under mild conditions, using polyfunctional capping molecules in an aqueous medium is reported; the nanostructures exhibit a surface plasmon resonance peak (SPR) in the visible region and serve as an active substrate for surface enhanced Raman scattering studies.

Dispersion of polymer grafted nanoparticles in polymer nanocomposite films: Insights from surface x-ray scattering and microscopy

Dispersion of nanoparticles in polymer nanocomposite films determines the application potential of these systems as novel materials with unique physical properties. Grafting polymers to, mostly inorganic, nanoparticles has been suggested as an effective strategy to enhance dispersion and hence the efficacy of materials. In this review, we discuss the various parameters which control dispersion of polymer grafted nanoparticles in polymer nanocomposite films. We discuss how surface x-ray scattering and microscopy can provide complementary and unique information in thin polymer nanocomposite films to unravel the subtle interplay of entropic and surface interactions, mediated by confinement, that leads to enhanced dispersion of the nanoparticles in these films. (C) 2014 AIP Publishing LLC.

Surface Enhanced Raman Scattering on Anodized Alumina Templates for Bio-sensing Applications

SERS substrate was fabricated by depositing silver on anodized aluminum oxide (AAO) template. The thickness of the AA0 template was 200 nm with 40 nm circular pore and 15 nm spacing. SERS effect was observed on these metal coated structures due to electric field enhancement around the edge of the pores. Para-Nitrophenol (pnp) solution of 10(-6) M concentration was detected which refers to an enhancement factor of 10(4).

Surface-waves, stability, and scattering for a lined duct with flow

We consider a straight cylindrical duct with a steady subsonic axial flow and a reacting boundary (e.g. an acoustic lining). The wave modes are separated into ordinary acoustic duct modes, and surface modes confined to a small neighbourhood of the boundary. Many researchers have used a mass-spring-damper boundary model, for which one surface mode has previously been identified as a convective instability; however, we show the stability analysis used in such cases to be questionable. We investigate instead the stability of the surface modes using the Briggs-Bers criterion for a Flügge thin-shell boundary model. For modest frequencies and wavenumbers the thin-shell has an impedance which is effectively that of a mass-spring-damper, although for the large wavenumbers needed for the stability analysis the thin-shell and mass-spring-damper impedances diverge, owing to the thin shell's bending stiffness. The thin shell model may therefore be viewed as a regularization of the mass-spring-damper model which accounts for nonlocally-reacting effects. We find all modes to be stable for realistic thin-shell parameters, while absolute instabilities are demonstrated for extremely thin boundary thicknesses. The limit of vanishing bending stiffness is found to be a singular limit, yielding absolute instabilities of arbitrarily large temporal growth rate. We propose that the problems with previous stability analyses are due to the neglect of something akin to bending stiffness in the boundary model. Our conclusion is that the surface mode previously identified as a convective instability may well be stable in reality. Finally, inspired by Rienstra's recent analysis, we investigate the scattering of an acoustic mode as it encounters a sudden change from a hard-wall to a thin-shell boundary, using a Wiener-Hopf technique. The thin-shell is considered to be clamped to the hard-wall. The acoustic mode is found to scatter into transmitted and reflected acoustic modes, and surface modes strongly linked to the solid waves in the boundary, although no longitudinal or transverse waves within the boundary are excited. Examples are provided that demonstrate total transmission, total reflection, and a combination of the two. This thin-shell scattering problem is preferable to the mass-spring-damper scattering problem presented by Rienstra, since the thin-shell problem is fully determined and does not need to appeal to a Kutta-like condition or the inclusion of an instability in order to avoid a surface-streamline cusp at the boundary change.

Probing single-molecule by surface-enhanced resonance Raman scattering with linearly and circularly polarized laser

Rhodamine 6G (R6G) was incubated in silver sols with different low concentrations and its surface-enhanced resonance Raman scattering (SERRS) spectra, excited by linearly and circularly polarized light, respectively, were studied. At the single-molecule level the SERRS spectra were recorded in 10(-13) M dye colloidal solution. Spectral inhomogeneous behaviors from single-molecule were observed such as spectral polarization, spectral diffusion and intensity fluctuations of vibrational lines. Difference between SERRS spectra of R6G excited by linearly and circularly polarized light and the effect of the polarizing angle of Raman signal relative to the slit of spectrograph on the Raman spectral polarization were analyzed and measured experimentally. Circularly polarized laser and the correction of the polarizing angle of Raman signal are necessary to avoid fake results in the measuring of Raman spectral of single-molecule, which was not noticed in initial papers. (c) 2005 Elsevier B.V. All rights reserved.

Surface-enhanced Raman scattering substrate fabricated by femtosecond laser direct writing

We report the fabrication of a novel surface-enhanced Raman scattering (SERS) substrate with a controllable enhancement factor (EF) using femtosecond laser direct writing on Ag+-doped phosphate glass followed by chemical plating at similar to 40 degrees C. Silver seeds were first photoreduced using a femtosecond laser in a laser-irradiated area and then transformed into silver nanoparticles of suitable size for SERS application in the subsequent chemical plating. Rhodamine 6G was used as a probing molecule to investigate the enhancement effect of a Raman signal on the substrate. Nearly homogenous enhancement of the Raman signal over the Substrate was achieved, and the EF of the substrate was controlled to some extent by adjusting fabrication parameters. Moreover, the ability of forming a SERS platform in an embedded microfluidic chamber would be of great use for establishing a compact lab-on-a-chip device based on Raman analysis.

Single-molecule detection in a liquid by surface-enhanced resonance Raman scattering

Surface-enhanced resonance Raman scattering (SERRS) of Rhodamine 6G (R6G) adsorbed on colloidal silver clusters in a liquid has been studied. The first observation of single molecule resonance Raman scattering in a liquid in a probed volume of 10 pL was achieved. Anisotropy of SERRS spectra of single R6G molecule and huge SERRS spectra were observed and compared with that of single molecule fixed in the dried films of sols, which revealed the intricate complex interaction between R6G molecules and the environment in a liquid.

Surface-enhanced resonance Raman scattering spectroscopy of single R6G molecules

Surface-enhanced resonance Raman scattering (SERRS) of Rhodamine 6G (R6G) adsorbed on colloidal silver clusters has been studied. Based on the great enhancement of the Raman signal and the quench of the fluorescence, the SERRS spectra of R6G were recorded for the samples of dye colloidal solution with different concentrations. Spectral inhomogeneity behaviours from single molecules in the dried sample films were observed with complementary evidences, such as spectral polarization, spectral diffusion, intensity fluctuation of vibrational lines and even "breathing" of the molecules. Sequential spectra observed from a liquid sample with an average of 0.3 dye molecules in the probed volume exhibited the expected Poisson distribution for actually measuring 0, 1 or 2 molecules. Difference between the SERRS spectra of R6G excited by linearly and circularly polarized light were experimentally measured.

Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface

By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions. (c) 2006 Optical Society of America.