Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

Low-frequency degenerate surface modes of an electron-hole plasma

The computations of Flahive and Quinn1 of the dispersion curves of low frequency degenerate surface (DS) modes propagating along the magnetic field in an electron-hole plasma are extended to higher values of the wavenumber. We find that beyond a certain value of the wavenumber the DS mode re-enters the allowed region of surface wave propagation and tends to an asymptotic frequency ωR (<ωLH). These low frequency resonances of an electron-hole plasma are discussed with reference to the experimental observations.

Magnetoplasmon-type surface polaritons at the interface between two semiconductors

Magnetoplasmon-type surface polaritons are studied at the interfaces of sandwich structures in the configuration with a magnetic field oriented parallel to the interface but perpendicular to the direction of wave propagation. It is shown that the propagation window for the surface polaritons is shifted to higher frequencies in the presence of the magnetic field directed positively. On reversal of the magnetic field an additional low frequency propagation band appears. Irrespective of the direction and strength of the magnetic field there exists a certain frequency range in which interface polaritons cannot propagate. For sandwich structures for which the dielectric constant and the plasma frequency of one medium are simultaneously greater or less than those of the second medium gaps and multiple branches can appear in the propagation window either for n > 0 or n <; 0 waves. A graphical method for the estimation of critical ranges of B0 and dielectric constant ratios for different sandwich structures, within which gaps and multiple branches appear, is given

A conditional random field-based downscaling method for assessment of climate change impact on multisite daily precipitation in the Mahanadi basin

Downscaling to station-scale hydrologic variables from large-scale atmospheric variables simulated by general circulation models (GCMs) is usually necessary to assess the hydrologic impact of climate change. This work presents CRF-downscaling, a new probabilistic downscaling method that represents the daily precipitation sequence as a conditional random field (CRF). The conditional distribution of the precipitation sequence at a site, given the daily atmospheric (large-scale) variable sequence, is modeled as a linear chain CRF. CRFs do not make assumptions on independence of observations, which gives them flexibility in using high-dimensional feature vectors. Maximum likelihood parameter estimation for the model is performed using limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization. Maximum a posteriori estimation is used to determine the most likely precipitation sequence for a given set of atmospheric input variables using the Viterbi algorithm. Direct classification of dry/wet days as well as precipitation amount is achieved within a single modeling framework. The model is used to project the future cumulative distribution function of precipitation. Uncertainty in precipitation prediction is addressed through a modified Viterbi algorithm that predicts the n most likely sequences. The model is applied for downscaling monsoon (June-September) daily precipitation at eight sites in the Mahanadi basin in Orissa, India, using the MIROC3.2 medium-resolution GCM. The predicted distributions at all sites show an increase in the number of wet days, and also an increase in wet day precipitation amounts. A comparison of current and future predicted probability density functions for daily precipitation shows a change in shape of the density function with decreasing probability of lower precipitation and increasing probability of higher precipitation.

Probing the mechanism of benzaldehyde reduction to chiral hydrobenzoin on the CNT surface under near-UV light irradiation

Metal-free CNTs exhibit high activity (conversion rate 99.6%, 6 h) towards the synthesis of chiral hydrobenzoin from benzaldehyde under near-UV light irradiation (320–400 nm). The CNT structure before and after the reaction, the interaction between the molecule and the CNT surface, the intermediate products, the substitution effect and the influence of light on the reaction were examined using various techniques. A photo-excited conduction electron transfer (PECET) mechanism for the photocatalytic reduction using CNTs has been proposed. This finding provides a green photocatalytic route for the production of hydrobenzoin and highlights a potential photocatalytic application of CNTs.

Response of a turbulent boundary layer to a step change in surface heat flux

Measurements of both the velocity and the temperature field have been made in the thermal layer that grows inside a turbulent boundary layer which is subjected to a small step change in surface heat flux. Upstream of the step, the wall heat flux is zero and the velocity boundary layer is nearly self-preserving. The thermal-layer measurements are discussed in the context of a self-preserving analysis for the temperature disturbance which grows underneath a thick external turbulent boundary layer. A logarithmic mean temperature profile is established downstream of the step but the budget for the mean-square temperature fluctuations shows that, in the inner region of the thermal layer, the production and dissipation of temperature fluctuations are not quite equal at the furthest downstream measurement station. The measurements for both the mean and the fluctuating temperature field indicate that the relaxation distance for the thermal layer is quite large, of the order of 1000θ0, where θ0 is the momentum thickness of the boundary layer at the step. Statistics of the thermal-layer interface and conditionally sampled measurements with respect to this interface are presented. Measurements of the temperature intermittency factor indicate that the interface is normally distributed with respect to its mean position. Near the step, the passive heat contaminant acts as an effective marker of the organized turbulence structure that has been observed in the wall region of a boundary layer. Accordingly, conditional averages of Reynolds stresses and heat fluxes measured in the heated part of the flow are considerably larger than the conventional averages when the temperature intermittency factor is small.

Effects of environment on surface-wave characteristics of a dielectric-coated conductor .4.

The problem of excitation of 11zultilayercd-graded-dielectric-coatedc onductor by a magnetic ring source is fornzulated in the ,form of a contour integrul which is rolved by using the method of steepest descent. Numerical evaluation of launching efiiency shows that high value of about 90 percent can be attained by choosing proper dimensions of the launcher with respect to the dimension of the surface wave line.

Interaction of surfactants with DNA. Role of hydrophobicity and surface charge on intercalation and DNA melting

A probe, 9-(anthrylmethyl)trimethylammonium chloride, 1, was prepared. 1 binds to calf-thymus DNA or Escherichia coli genomic DNA with high affinity, as evidenced from the absorption titration. Strong hypochromism, spectral broadening and red-shifts in the absorption spectra were observed. Half-reciprocal plot constructed from this experiment gave binding constant of 5±0.5×104 M−1 in base molarity. We employed this anthryl probe-DNA complex for studying the effects of addition of various surfactant to DNA. Surfactants of different charge types and chain lengths were used in this study and the effects of surfactant addition to such probe-DNA complex were compared with that of small organic cations or salts. Addition of either salts or cationic surfactants led to structural changes in DNA and under these conditions, the probe from the DNA-bound complex appeared to get released. However, the cationic surfactants could induce such release of the probe from the probe-DNA complex at a much lower concentration than that of the small organic cations or salts. In contrast the anionic surfactants failed to promote any destabilization of such probe-DNA complexes. The effects of additives on the probe-DNA complexes were also examined by using a different technique (fluorescence spectroscopy) using a different probe ethidium bromide. The association complexes formed between the cationic surfactants and the plasmid DNA pTZ19R, were further examined under agarose gel electrophoresis and could not be visualized by ethidium bromide staining presumably due to cationic surfactant-induced condensation of DNA. Most of the DNA from such association complexes can be recovered by extraction of surfactants with phenol-chloroform. Inclusion of surfactants and other additives into the DNA generally enhanced the DNA melting temperatures by a few °C and at high [surfactant], the corresponding melting profiles got broadened.

On the relationship of thermodynamic parameters with the buried surface area in protein-ligand complex formation

Prediction of thermodynamic parameters of protein-protein and antigen-antibody complex formation from high resolution structural parameters has recently received much attention, since an understanding of the contributions of different fundamental processes like hydrophobic interactions, hydrogen bonding, salt bridge formation, solvent reorganization etc. to the overall thermodynamic parameters and their relations with the structural parameters would lead to rational drug design. Using the results of the dissolution of hydrocarbons and other model compounds the changes in heat capacity (DeltaCp), enthalpy (DeltaH) and entropy (DeltaS) have been empirically correlated with the polar and apolar surface areas buried during the process of protein folding/unfolding and protein-ligand complex formation. In this regard, the polar and apolar surfaces removed from the solvent in a protein-ligand complex have been calculated from the experimentally observed values of changes in heat capacity (DeltaCp) and enthalpy (DeltaH) for protein-ligand complexes for which accurate thermodynamic and high resolution structural data are available, and the results have been compared with the x-ray crystallographic observations. Analyses of the available results show poor correlation between the thermodynamic and structural parameters. Probable reasons for this discrepancy are mostly related with the reorganization of water accompanying the reaction which is indeed proven by the analyses of the energetics of the binding of the wheat germ agglutinin to oligosaccharides.

Underwater Sustainability of the ``Cassie'' State of Wetting

A rough hydrophobic surface when immersed in water can result in a ``Cassie'' state of wetting in which the water is in contact with both the solid surface and the entrapped air. The sustainability of the entrapped air on such surfaces is important for underwater applications such as reduction of flow resistance in microchannels and drag reduction of submerged bodies such as hydrofoils. We utilize an optical technique based oil total internal reflection of light at the water-air interface to quantify the spatial distribution of trapped air oil such a surface and its variation with immersion time. With this technique, we evaluate the sustainability of the Cassie state on hydrophobic surfaces with four different kinds of textures. The textures studied are regular arrays of pillars, ridges, and holes that were created in silicon by a wet etching technique, and also a texture of random craters that was obtained through electrodischarge machining of aluminum. These surfaces were rendered hydrophobic with a self-assembled layer Of fluorooctyl trichlorosilane. Depending on the texture, the size and shape of the trapped air pockets were found to vary. However, irrespective of the texture, both the size and the number of air pockets were found to decrease with time gradually and eventually disappear, suggesting that the sustainability of the ``Cassie'' state is finite for all the microstructures Studied. This is possibly due to diffusion of air from the trapped air pockets into the water. The time scale for disappearance of air pockets was found to depend on the kind of microstructure and the hydrostatic pressure at the water-air interface. For the surface with a regular array of pillars, the air pockets were found to be in the form of a thin layer perched on top of the pillars with a large lateral extent compared to the spacing between pillars. For other surfaces studied, the air pockets are smaller and are of the same order as the characteristic length scale of the texture. Measurements for the surface with holes indicate that the time for air-pocket disappearance reduces as the hydrostatic pressure is increased.

Influence of Hydrophilic Surface Specificity on the Structural Properties of Confined Water

The influence of chemical specificity of hydrophilic surfaces on the structure of confined water in the subnanometer regime is investigated using grand canonical Monte Carlo Simulations. The structural variations for water confined between hydroxylated silica surfaces are contrasted with water confined between mica surfaces. Although both surfaces are hydrophilic, our Study shows that hydration of potassium ions on the mica surface has a strong influence on the water Structure and solvation force response of confined water. In contrast to the disrupted hydrogen bond network observed for water confined between Mica Surfaces, water between silica surfaces retains its hydrogen bond network displaying bulklike structural features down to surface separations as small as 0.45 nm. Hydrogen bonding of all invariant contact water layer with the surface silanol groups aids in maintaining a constant number of hydrogen bonds per water molecule for the silica surfaces. As a consequence water depletion and rearrangement upon decreasing confinement is a strong function of the hydrophilic surface specificity, particularly at smaller separations. An oscillatory solvation force response is only observed for water confined between Silica surfaces, and bulklike features are observed for both Surfaces above a surface separation of about 1.2 nm. We evaluate and contrast the water density, dipole moment distributions, pi pair correlation functions, and solvation forces as a function of the surface separation.

On Multi-Dimensional Packets of Surface Waves

By using the method of operators of multiple scales, two coupled nonlinear equations are derived, which govern the slow amplitude modulation of surface gravity waves in two space dimensions. The equations of Davey and Stewartson, which also govern the two-dimensional modulation of the amplitude of gravity waves, are derived as a special case of our equations. For a fully dispersed wave, symmetric about a point which moves with the group velocity, the coupled equations reduce to a nonlinear Schrödinger equation with extra terms representing the effect of the curvature of the wavefront.