Analysis of Nonlinear Optical Properties of Photonic Crystal Beam-splitters

The paper analyses electromagnetic wave propagation through nonlinear photonic crystal beam-splitters. Different lattice configurations of Y-junction beam-splitters are simulated and propagation properties are investigated with introducing nonlinearity with varying the rod size in crystal lattice. It is seen that nonlinear photonic crystal shows a considerable band-gap even at low refractive contrast. The division of power in both arms of beam-splitters can be controlled by varying the nonlinearity.

Probing of unusual DNA structures in topologically constrained form V DNA: use of restriction enzymes as structural probe

The ability of DNA sequences to adopt unusual structures under the superhelical torsional stress has been studied. Sequences that are forced to adopt unusual conformation in topologically constrained pBR322 form V DNA (Lk=0) were mapped using restriction enzymes as probes. Restriction enzymes such as BamHI, Pstl, Aval and HindIII could not cleave their recognition sequences. The removal of topological constraint relieved this inhibition. The influence of neighbouring sequences on the ability of a given sequence to adopt unusual DNA structure, presumably left handed Z conformation, was studied through single hit analysis. Using multiple cut restriction enzymes such as Narl and Fspl, it could be shown that under identical topological strain, the extent of structural alteration is greatly influenced by the neighbouring sequences. In the light of the variety of sequences and locations that could be mapped to adopt non-6 conformation in pBR322 form V DNA, restriction enzymes appear as potential structural probes for natural DNA sequences.

Local variability and base sequence effects in DNA crystal structures.

The importance and usefulness of local doublet parameters in understanding sequence dependent effects has been described for A- and B-DNA oligonucleotide crystal structures. Each of the two sets of local parameters described by us in the NUPARM algorithm, namely the local doublet parameters, calculated with reference to the mean z-axis, and the local helical parameters, calculated with reference to the local helix axis, is sufficient to describe the oligonucleotide structures, with the local helical parameters giving a slightly magnified picture of the variations in the structures. The values of local doublet parameters calculated by NUPARM algorithm are similar to those calculated by NEWHELIX90 program, only if the oligonucleotide fragment is not too distorted. The mean values obtained using all the available data for B-DNA crystals are not significantly different from those obtained when a limited data set is used, consisting only of structures with a data resolution of better than 2.4 A and without any bound drug molecule. Thus the variation observed in the oligonucleotide crystals appears to be independent of the quality of their crystallinity. No strong correlation is seen between any pair of local doublet parameters but the local helical parameters are interrelated by geometric relationships. An interesting feature that emerges from this analysis is that the local rise along the z-axis is highly correlated with the difference in the buckle values of the two basepairs in the doublet, as suggested earlier for the dodecamer structures (Bansal and Bhattacharyya, in Structure & Methods: DNA & RNA, Vol. 3 (Eds., R.H. Sarma and M.H. Sarma), pp. 139-153 (1990)). In fact the local rise values become almost constant for both A- and B-forms, if a correction is applied for the buckling of the basepairs. In B-DNA the AA, AT, TA and GA basepair sequences generally have a smaller local rise (3.25 A) compared to the other sequences (3.4 A) and this seems to be an intrinsic feature of basepair stacking interaction and not related to any other local doublet parameter. The roll angles in B-DNA oligonucleotides have small values (less than +/- 8 degrees), while mean local twist varies from 24 degrees to 45 degrees. The CA/TG doublet sequences show two types of preferred geometries, one with positive roll, small positive slide and reduced twist and another with negative roll, large positive slide and increased twist.(ABSTRACT TRUNCATED AT 400 WORDS)

Exact nonlinear travelling hydromagnetic wave solutions

Exact travelling wave solutions for hydromagnetic waves in an exponentially stratified incompressible medium are obtained. With the help of two integrals it becomes possible to reduce the system of seven nonlinear PDE's to a second order nonlinear ODE which describes an one dimensional harmonic oscillator with a nonlinear friction term. This equation is studied in detail in the phase plane. The travelling waves are periodic only when they propagate either horizontally or vertically. The reduced second order nonlinear differential equation describing the travelling waves in inhomogeneous conducting media has rather ubiquitous nature in that it also appears in other geophysical systems such as internal waves, Rossby waves and topographic Rossby waves in the ocean.

Conformational Polymorphism in Telomeric Structures: Loop Orientation and Interloop Pairing in d(G4TnG4),

Sequence repeats constituting the telomeric regions of chromosomes are known to adopt a variety of unusual structures, consisting of a G tetraplex stem and short stretches of thymines or thymines and adenines forming loops over the stem. Detailed model building and molecular mechanics studies have been carried out for these telomeric sequences to elucidate different types of loop orientations and possible conformations of thymines in the loop. The model building studies indicate that a minimum of two thymines have to be interspersed between guanine stretches to form folded-back structures with loops across adjacent strands in a G tetraplex (both over the small as well as large groove), while the minimum number of thymines required to build a loop across the diagonal strands in a G tetraplex is three. For two repeat sequences, these hairpins, resulting from different types of folding, can dimerize in three distinct ways-i.e., with loops across adjacent strands and on same side, with loops across adjacent strands and on opposite sides, and with loops across diagonal strands and on opposite sides-to form hairpin dimer structures. Energy minimization studies indicate that all possible hairpin dimers have very similar total energy values, though different structures are stabilized by different types of interactions. When the two loops are on the same side, in the hairpin dimer structures of d(G(4)T(n)G(4)), the thymines form favorably stacked tetrads in the loop region and there is interloop hydrogen bonding involving two hydrogen bonds for each thymine-thymine pair. Our molecular mechanics calculations on various folded-back as well as parallel tetraplex structures of these telomeric sequences provide a theoretical rationale for the experimentally observed feature that the presence of intervening thymine stretches stabilizes folded-back structures, while isolated stretches of guanines adopt a parallel tetraplex structure

Conformational Polymorphism in G-tetraplex Structures: Strand Reversal by Base Flipover or Sugar Flipover

Guanine rich sequences adopt a variety of four stranded structures, which differ in strand orientation and conformation about the glycosidic bond even though they are all stabilised by Hoogsteen hydrogen bonded guanine tetrads. Detailed model building and molecular mechanics calculations have been carried out to investigate various possible conformations of guanines along a strand and different possible orientations of guanine strands in a G-tetraplex structure. It is found that for an oligo G stretch per se, a parallel four stranded structure with all guanines in anti conformation is favoured over other possible tetraplex structures. Hence an alternating syn-anti arrangement of guanines along a strand is likely to occur only in folded back tetraplex structures with antiparallel G strands. Our study provides a theoretical rationale for the observed alternation of glycosidic conformation and the inverted stacking arrangement arising from base flipover, in antiparallel G-tetraplex structures and also highlights the various structural features arising due to different types of strand orientations. The molecular mechanics calculations help in elucidating the various interactions which stabilize different G-tetraplex structures and indicate that screening of phosphate charge by counterions could have a dramatic effect on groove width in these four stranded structures.

1, 2-Bis (diphenylphosphino) etane bridged dinuclear copper (I) complexes: Investigations of solid state and solution structures by CP/MAS31P NMR spectroscopy, X-ray crystallography, IR spectroscopy and solution 31P NMR and 63Cu NMR spectroscopy

Three different complexes of copper (I) with bridging 1, 2-bis(diphenylphosphino)ethane (dppe), namely [Cu2 (mu-dppe) (CH3CN)6] (ClO4)2 (1), [Cu2 (mu-dppe)2 (CH3 CN)2] (ClO4)2 (2), and [Cu2 (mu-dppe) (dppe)2 (CH3CN)2] (ClO4)2 (3) have been prepared. The structure of [Cu2 (mu-dppe) (dPPe)2 (CH3CH)2] (ClO4)2 has been determined by X-ray crystallography. It crystallizes in the space group PT with a=12.984(6) angstrom, b=13.180(6) angstrom, c=14.001(3) angstrom, alpha=105.23(3), beta=105.60(2), gamma=112.53 (4), V=1944 (3) angstrom3, and Z=1. The structure was refined by least-squares method with R=0.0365; R(w)=0.0451 for 6321 reflections with F0 greater-than-or-equal-to 3 sigma (F0). The CP/MAS P-31 and IR spectra of the complexes have been analysed in the light of available crystallographic data. IR spectroscopy is particularly helpful in identifying the presence of chelating dppe. P-31 chemical shifts observed in solid state are very different from those observed in solution, and change significantly with slight changes in structure. In solution, complex 1 remains undissociated but complexes 2 and 3 undergo extensive dissociation. With a combination of room temperature H-1, Cu-63, and variable temperature P-31 NMR spectra, it is possible to understand the various processes occurring in solution.

Conformational polymorphism in G-tetraplex structures: strand reversal by base flipover or sugar flipover

Guanlne rich sequences adopt a variety of four stranded structures, which differ in strand orientation and conformation about the glycosldic bond even though they are all stabilised by Hoogsteen hydrogen bonded guanlne tetrads. Detailed model building and molecular mechanics calculations have been carried out to investigate various possible conformations of guanlnes along a strand and different possible orientations of guanlne strands In a G-tetraplex structure. It is found that for an ollgo G stretch per se, a parallel four stranded structure with all guanines In anti conformation is favoured over other possible tetraplex structures. Hence an alternating syn-anti arrangement of guanlnes along a strand is likely to occur only in folded back tetraplex structures with antiparallel G strands. Our study provides a theoretical rationale for the observed alternation of glycosldic conformation and the inverted stacking arrangement arising from base filpover, In antlparallel G-tetraplex structures and also highlights the various structural features arising due to different types of strand orientations. The molecular mechanics calculations help in elucidating the various interactions which stabilize different G-tetraplex structures and indicate that screening of phosphate charge by counterions could have a dramatic effect on groove width in these four stranded structures.

Coupled substitution of niobium and silicon in potassium titanyl phosphate and arsenate (KTiOPO4 and KTiOAsO4. Synthesis and nonlinear optical properties of KTi1-xNbxOX1-xSixO4 (X = P, As)

Coupled substitution of Nb(V) and Si(IV) for Ti(IV) and P(V)/As(V) in KTiOP04 (KTP) and KTiOAsO4 (KTA) giving new series of nonlinear optical materials, KTi1-xNbxOX1-xSixO4 (X=P,As), has been investigated. Substitution up to x = 0.40 readily occurs, the members retaining the orthorhombic (Pna2(1)) structure of KTP. The second harmonic generation (SHG) property of the parent KTP and KTA is not adversely affected by the coupled substitution. SHG intensity of the powder samples of the X = P series shows a slight increase with x up to x = 0.15; for 0.15 < x less-than-or-equal-to 0.40, there is a decrease in SHG intensity as compared to that for KTP. A similar trend in SHG intensity is seen for the arsenic analogs.

Crystal structures, spectral and magnetic properties of (µ-hydroxo)(µ-acetato)dicopper(II) complexes containing chelating amines

The reaction of [Cu2(O2CMe)4(H2O)2] with N, N, N′, N′-tetramethylethane- 1,2-diamine (tmen) in ethanol yielded the dicopper(II) complex [Cu2(OH)(O2CMe)(tmen)2][ClO4]21. A similar reaction with N, N- dimethylethane- 1,2-diamine (dmen) afforded a crystalline product 2 in which two dicopper(II) complexes, [Cu2(OH)(O2CMe)(dmen)2][ClO4]22a and [Cu2(OH)(O2CMe)(H2O)2(dmen)2][ClO4]22b, are cocrystallized in a 1 : 1 molar ratio along with 2NaClO4. The crystal structures of 1 and 2 have been determined. The complexes have an asymmetrically dibridged [Cu2(µ-OH)(µ-O2CMe)]2+ core. The co-ordination geometry of the metal is square planar (CuO2N2). The copper atoms in 2b have a square-pyramidal CuO3N2 co-ordination sphere. The Cu Cu distances and Cu–O–Cu angles in 1, 2a and 2b are 3.339(2), 3.368(3), 3.395(7)Å, 120.1(2), 116.4(1) and 123.6(2)°, respectively. Complex 1 exhibits an axial ESR spectrum in a methanol glass giving g∥= 2.26 (A∥= 164 × 10–4 cm–1) and g⊥= 2.04. The ESR spectra obtained from the bulk material of the dmen product are indicative of the presence of two dimers, viz. complex 2a(g∥= 2.25, A∥= 165 × 10–4 cm–1; g⊥= 2.03) and 2b(g∥= 2.19, A∥= 184 × 10–4 cm–1; g⊥= 2.0). Variable-temperature magnetic susceptibility measurements on these complexes show an intramolecular antiferromagnetic coupling in the dimeric core. The fitting parameters are J=–27.8 cm–1, g= 2.1 for complex 1 and J=–10.1 cm–1, g= 2.0 for 2. The magnetostructural properties of the complexes are discussed. There is a linear correlation of the –2J values with the Cu Cu distances among dibridged complexes having square-planar copper(II) centres.

Decentralized Parallel Operation of Inverters Sharing Unbalanced and Nonlinear Loads

In this paper, a wireless control strategy for parallel operation of three-phase four-wire inverters is proposed. A generalized situation is considered where the inverters are of unequal power ratings and the loads are nonlinear and unbalanced in nature. The proposed control algorithm exploits the potential of sinusoidal domain proportional+multiresonant controller ( in the inner voltage regulation loop) to make the system suitable for nonlinear and unbalanced loads with a simple and generalized structure of virtual output-impedance loop. The decentralized operation is achieved by using three-phase P/Q droop characteristics. The overall control algorithm helps to limit the harmonic contents and the degree of unbalance in the output-voltage waveform and to achieve excellent power-sharing accuracy in spite of mismatch in the inverter output impedances. Moreover, a synchronized turn on with consequent change over to the droop mode is applied for the new incoming unit in order to limit the circulating current completely. The simulation and experimental results from-1 kVA and -0.5 kVA paralleled units validate the effectiveness of the scheme.

Nonlinear hydrodynamics of a hard-sphere fluid near the glass transition

We conduct a numerical study of the dynamic behavior of a dense hard-sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free-energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through a stretched exponential decay and a two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wave-number dependence of the kinetics is extensively explored. The connection of our results with experiment, mode-coupling theory, and molecular-dynamics results is discussed.

Spectral approach for the soliton and periodic solutions of the nonlinear wave equation

A spectral method that obtains the soliton and periodic solutions to the nonlinear wave equation is presented. The results show that the nonlinear group velocity is a function of the frequency shift as well as of the soliton power. When the frequency shift is a function of time, a solution in terms of the Jacobian elliptic function is obtained. This solution is periodic in nature, and, to generate such an optical pulse train, one must simultaneously amplitude- and frequency-modulate the optical carrier. Finally, we extend the method to include the effect of self-steepening.