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.

Effect of viscosity on internal waves from a source in a wall

The solution for a line source of oscillatory strength kept at the origin in a wall bounding a semi-infinite viscous imcompressible stratified fluid is presented in an integral form. The behaviour of the flow at far field and near field is studied by an asymptotic expansion procedure. The streamlines for different parameters are drawn and discussed. The real characteristic straight lines present in the inviscid problem are modified by the viscosity and the solutions obtained are valid even at the resonance frequency.

Quasi-simple wave solutions for acoustic gravity waves

The special class of quasi-simple wave solutions is studied for the system of partial differential equations governing inviscid acoustic gravity waves. It is shown that these traveling wave solutions do not admit shocks. Periodic solutions are found to exist when there is no propagation in the vertical direction. The solutions for some particular cases are depicted graphically. Physics of Fluids is copyrighted by The American Institute of Physics.

A One-Step Method for the Growth of Ga2O3-Nanorod-Based White-Light-Emitting Phosphors

A one-step synthesis of Ga2O3 nanorods by heating molten gallium in ambient air at high temperatures is presented. The high-temperature synthesis creates oxygen vacancies and incorporates nitrogen from the environment. The oxygen vacancy in Ga2O3 is responsible for the emission in the blue-green region, while nitrogen in Ga2O3 is responsible for red emission.

Light- and cytokinin-induced changes in the levels of leucine and tyrosine isoaccepting tRNA species and modified nucleotide contents of total tRNA in cucumber seedlings

We have determined relative levels of chloroplast leucine and tyrosine isoaccepting tRNAs and modified nucleotide contents from total tRNAs isolated from dark-grown, light-grown, N6-isopentenyladenine (i6A)-treated dark-grown and i6A-treated light-grown cucumber seedlings. Significant increases in the relative amounts of tRNA(Leu)2 and tRNA(Leu)3 were observed in the i6A-treated dark-grown seedlings compared to dark-grown, light-grown and i6A-treated light-grown seedlings. On the other hand, i6A-treated light-grown seedlings tRNA(Tyr)1 increased to 85% of total tRNAs(Tyr) from about 9% in light-grown seedlings and tRNA(Tyr)2 decreased to 15% compared with 91% in light-grown seedlings. Analysis of modified nucleotide of total tRNAs indicated that pT, pI, pm1A, pm5C, pGm, pm1G, pm2G and pm7G contents were significantly higher in the total tRNA of i6A-treated dark-grown seedlings than those from untreated dark-grown seedlings. Illumination of 8-day-old dark-grown seedlings for 12 h increased the contents of pT, pI, pGm and pm1G when compared to 8-day-old dark-grown seedlings with extended growth for 12 h in dark. On the contrary, i6A had no stimulatory effect in the contents of modified nucleotide in the light-grown seedlings.

Light and heat induced interdiffusion in Sb/As2S3 nano-multilayered film

The light and heat induced changes in the optical band gap of Sb/As2S3 nanomultilayered chalcogenide film has been studied. Even though the changes in optical bandgap are attributed to the light and heat induced interdiffusion, the diffusional intermixing between the layers is rather different with light and heat. The observed difference in the light and heat induced interdiffusion is due to unequal diffusion coefficients of light and heat predicted by thermal spike model.

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.

Time reversal technique for health monitoring of metallic structure using Lamb waves

Time reversal active sensing using Lamb waves is investigated for health monitoring of a metallic structure. Experiments were conducted on an aluminum plate to study the time reversal behavior of A(0) and S-0 Lamb wave modes under narrow band and broad band pulse excitation. Damage in the form of a notch was introduced in the plate to study the changes in the characteristics of the time reversed Lamb wave modes experimentally. Time-frequency analysis of the time reversed signal was carried out to extract the damage information. A measure of damage based on wavelet transform was derived to quantify the hidden damage information in the time reversed signal. It has been shown that time reversal can be used to achieve temporal recompression of Lamb waves under broadband signal excitation. Further, the broad band excitation can also improve the resolution of the technique in detecting closely located defects. This is demonstrated by picking up the reflection of waves from the edge of the plate, from a defect close to the edge of the plate and from defects located near to each other. This study shows the effectiveness of Lamb wave time reversal for temporal recompression of dispersive Lamb waves for damage detection in health monitoring applications. (C) 2009 Elsevier B.V. All rights reserved.

Photocytotoxic Oxovanadium(IV) Complexes Showing Light-Induced DNA and Protein Cleavage Activity

Oxovanadium(IV) complexes [VO(L)(B)]Cl-2 (1-3), where L is bis(2-benzimidazolylmethyl)amine and B is 1,10-phenanthroline(phen),dipyrido[3,2-d:2',3'-f]quinoxaline(dpq) or dipyrido[3,2-a:2',3'-c]phenazine (dppz), have been prepared, characterized, and their photo-induced DNA and protein cleavage activity studied. The photocytotoxicity of complex 3 has been studied using adenocarcinoma A549 cells, The phen complex 1, structurally characterized by single-crystal X-ray crystallography, shows the presence of a vanadyl group in six-coordinate VON5 coordination geometry. The ligands L and phen display tridentate and bidentate N-donor chelating binding modes, respectively. The complexes exhibit a d-d band near 740 nm in 15% DMF-Tris-HCl buffer (pH 7.2). The phen and dpq complexes display an irreversible cathodic cyclic voltammetric response near -0.8 V in 20% DMF-Tris-HCl buffer having 0.1 M KCl as supporting electrolyte. The dppz complex 3 exhibits a quasi-reversible voltammogram near -0.6 V (vs SCE) that is assignable to the V(IV)-V(III)couple. The complexes bind to calf thymus DNA giving binding constant values in the range of 6.6 x 10(4)-2.9 x 10(5) M-1. The binding site size, thermal melting and viscosity binding data suggest DNA surface and/or groove binding nature of the complexes. The complexes show poor ``chemical nuclease'' activity in dark in the presence of 3-mercaptopropionic acid or hydrogen peroxide. The dpq and dppz complexes are efficient photocleavers of plasmid DNA in UV-A light of 365 nm via a mechanistic pathway that involves formation of both singlet oxygen and hydroxyl radicals. The complexes show significant photocleavage of DNA in near-IR light (>750 nm) via hydroxyl radical pathway. Among the three complexes, the dppz complex 3 shows significant BSA and lysozyme protein cleavage activity in UV-A light of 365 nm via hydroxyl radical pathway. The dppz complex 3 also exhibits photocytotoxicity in non-small cell lung carcinoma/human lung adenocarcinoma A549 cells giving IC50 value of 17 mu M in visible light(IC50 = 175 mu M in dark).

Cucumber chloroplast trnL(CAA) gene: nucleotide sequence and in vivo expression analysis in etiolated cucumber seedlings treated with benzyladenine and light.

The nucleotide sequence of a 714 bp BamHI-EcoRI fragment of cucumber chloroplast DNA was determined. The fragment contained a gene for tRNA(Leu) together with its flanking regions. The trnL(CAA) gene sequence is about 99% in similarity to broad bean, cauliflower, maize, spinach and tobacco corresponding genes. The relative expression level of the gene was determined by Northern (tRNA) gel blot and Northern (total cellular RNA) slot-blot analyses using the trnL gene probe in 6-day old etiolated cucumber seedlings and the seedlings that had been kept in the dark (dark-grown), treated with benzyladenine (BA) and kept in the dark (BA-treated dark-grown), illuminated (light-grown), and treated with BA and illuminated (BA-treated light-grown), for additional 4, 8 or 12 hr. The trnL transcripts and tRNA(Leu) levels in BA-treated dark-grown seedlings were 5 and 3 times higher, respectively after 4 hr BA treatment, while in the BA treated light-grown seedlings the level of trnL transcripts was only 3 times higher and had no detectable effect on mature tRNA(Leu) when compared to the time-4 hr dark-grown seedlings. However, the level of mature tRNA(Leu) did not show marked changes in the light-grown seedlings, whereas the level of trnL transcripts increases 3 times after 8 hr illumination of dark-grown seedlings. These data indicate that both light and cytokinin can signal changes in plastid tRNA gene expression. The possible regulatory mechanisms for such changes are discussed.

Enhanced catharanthine and vindoline production in suspension cultures of Catharanthus roseus by ultraviolet-B light

Suspension cultures of Catharanthus roseus were used to evaluate ultraviolet-B (UV-B) treatment as an abiotic elicitor of secondary metabolites. A dispersed cell suspension culture from C. roseus leaves in late exponential phase and stationary phase were irradiated with UV-B for 5 min. The stationary phase cultures were more responsive to UV-B irradiation than late exponential phase cultures. Catharanthine and vindoline increased 3-fold and 12-fold, respectively, on treatment with a 5-min UV-B irradiation.

Cucumber chloroplast trnL(CAA) gene: nucleotide sequence and in vivo expression analysis in etiolated cucumber seedlings treated with benzyladenine and light

The nucleotide sequence of a 714 bp BamHI-EcoRI fragment of cucumber chloroplast DNA was determined. The fragment contained a gene for tRNA(Leu) together with its flanking regions. The trnL(CAA) gene sequence is about 99% in similarity to broad bean, cauliflower, maize, spinach and tobacco corresponding genes. The relative expression level of the gene was determined by Northern (tRNA) gel blot and Northern (total cellular RNA) slot-blot analyses using the trnL gene probe in 6-day old etiolated cucumber seedlings and the seedlings that had been kept in the dark (dark-grown), treated with benzyladenine (BA) and kept in the dark (BA-treated dark-grown), illuminated (light-grown), and treated with BA and illuminated (BA- treated light-grown), for additional 4, 8 or 12 hr. The trnL transcripts and tRNA(Leu) levels in BA-treated dark-grown seedlings were 5 and 3 times higher, respectively after 4 hr BA treatment, while in the BA treated light-grown seedlings the level of trnL transcripts was only 3 times higher and had not detectable effect on mature tRNA(Leu) when compared to the time-4 hr dark-grown seedlings. However, the level of mature tRNA(Leu) did not show marked changes in the light-grown seedlings, whereas the level of trnL transcripts increases 3 times after 8 hr illumination of dark-grown seedlings. These date indicate that both light and cytokinin can signal changes in plastid tRNA gene expression. The possible regulatory mechanisms for such changes are discussed.

A complete characterization of pre-Mueller and Mueller matrices in polarization optics

The Mueller-Stokes formalism that governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could require of a 4 x 4 real matrix M in order that it qualify to be the Mueller matrix of some physical system would be that M map Omega((pol)), the positive solid light cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is a need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability brings in additional constraints that a pre-Mueller matrix M mapping Omega((pol)) into itself needs to meet in order to be an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized. (C) 2010 Optical Society of America

Anaerobic DNA cleavage activity in red light and photocytotoxicity of (pyridine-2-thiol)cobalt(III) complexes of phenanthroline bases

Cobalt(III) complexes [Co(pnt)(B)(2)](NO3)(2) (1-3) of pyridine-2-thiol (pnt) and phenanthroline bases (B), viz. 1,10-phenanthroline (phen in 1), dipyrido[3,2-d: 2',3'-f]quinoxaline (dpq in 2) and dipyrido[3,2-a:2',3'-c] phenazine (dppz in 3), have been prepared, characterized and their photo-induced anaerobic DNA cleavage activity studied. The crystal structure of 1a as mixed ClO4- and PF6- salt of 1 shows a (CoN5S)-N-III coordination geometry in which the pnt and phen showed N,S- and N,N-donor binding modes, respectively. The complexes exhibit Co(III)/Co(II) redox couple near -0.3 V (vs. SCE) in 20% DMF-Tris-HCl buffer having 0.1 M TBAP. The complexes show binding propensity to calf thymus DNA giving K-b values within 2.2 x 10(4)-7.3 x 10(5) M-1. Thermal melting and viscosity data suggest DNA surface and/or groove binding of the complexes. The complexes show significant anaerobic DNA cleavage activity in red light under argon atmosphere possibly involving sulfide anion radical or thiyl radical species. The DNA cleavage reaction under aerobic medium in red light is found to involve both singlet oxygen and hydroxyl radical pathways. The dppz complex 3 shows non-specific BSA and lysozyme protein cleavage activity in UV-A light of 365 nm via both hydroxyl and singlet oxygen pathways. The dppz complex 3 exhibits photocytotoxicity in HeLa cervical cancer cells giving IC50 values of 767 nM and 19.38 mu M in UV-A light of 365 nm and in the dark, respectively. A significant reduction of the dark toxicity of the dppz base (IC50 = 8.34 mu M in dark) is observed on binding to the cobalt(III) center.