Integrability and singularity structure of coupled nonlinear Schrödinger equations

Multimode propagation of electromagnetic waves in optical fibre is often described by coupled nonlinear Schrödinger (NLS) equations. To understand the integrability properties of such coupled NLS systems, we extend the Painlevé singularity structure analysis of two coupled systems to three coupled systems and identify four integrable sets of parameters. We bilinearize these cases to obtain soliton solutions. The results are extended to N-coupled systems, completing the earlier analysis of Sahadevan, Tamizhmani and Lakshmanan.     

Synthesis of novel highly functionalized biologically active polycyclic caged amides

The synthesis of novel polycyclic amides has been achieved through the reaction of bishalomethyl pentacyclo[5.4.0.0^2,6.0^3,10.0^5,9]undecane diones with acyclic and cyclic secondary amines in the presence of an ionic liquid. Three of the compounds prepared have been found to possess antituberculosis activity.     

Ir6In32S21, a polar,metal-rich semiconducting subchalcogenide

Subchalcogenides are uncommon, and their chemical bonding results from an interplay between metal–metal and metal–chalcogenide interactions. Herein, we present Ir₆In₃₂S₂₁, a novel semiconducting subchalcogenide compound that crystallizes in a new structure type in the polar P31m space group, with unit cell parameters a = 13.9378(12) Å, c = 8.2316(8) Å, α = β = 90°, γ = 120°. The compound has a large band gap of 1.48(2) eV, and photoemission and Kelvin probe measurements corroborate this semiconducting behavior with a valence band maximum (VBM) of −4.95(5) eV, conduction band minimum of −3.47(5) eV, and a photoresponse shift of the Fermi level by ∼0.2 eV in the presence of white light. X-ray absorption spectroscopy shows absorption edges for In and Ir do not indicate clear oxidation states, suggesting that the numerous coordination environments of Ir₆In₃₂S₂₁ make such assignments ambiguous. Electronic structure calculations confirm the semiconducting character with a nearly direct band gap, and electron localization function (ELF) analysis suggests that the origin of the gap is the result of electron transfer from the In atoms to the S 3p and Ir 5d orbitals. DFT calculations indicate that the average hole effective masses near the VBM (1.19m_e) are substantially smaller than the average electron masses near the CBM (2.51m_e), an unusual feature for most semiconductors. The crystal and electronic structure of Ir₆In₃₂S₂₁, along with spectroscopic data, suggest that it is neither a true intermetallic nor a classical semiconductor, but somewhere in between those two extremes.

Subchalcogenides are uncommon, and their chemical bonding results from an interplay between metal–metal and metal–chalcogenide interactions.     

Phase behavior of concentrated aqueous solutions of cetyltrimethylammonium bromide (CTAB) and sodium hydroxy naphthoate (SHN)

We have characterized the phase behavior of mixtures of the cationic surfactant cetyltrimethylammonium bromide (CTAB) and the organic salt 3-sodium-2-hydroxy naphthoate (SHN) over a wide range of surfactant concentrations using polarizing optical microscopy and X-ray diffraction. A variety of liquid crystalline phases, such as hexagonal, lamellar with and without curvature defects, and nematic, are observed in these mixtures. At high temperatures the curvature defects in the lamellar phase are annealed gradually on decreasing the water content. However, at lower temperatures these two lamellar structures are separated by an intermediate phase, where the bilayer defects appear to order into a lattice. The ternary phase diagram shows a high degree of symmetry about the line corresponding to equimolar CTAB/SHN composition, as in the case of mixtures of cationic and anionic surfactants.     

Generating finite dimensional integrable nonlinear dynamical systems

In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties, including quantum aspects. Particularly we concentrate on Lienard type nonlinear oscillators and their generalizations and coupled versions. Specific systems include Mathews-Lakshmanan oscillators, modified Emden equations, isochronous oscillators and generalizations. Nonstandard Lagrangian and Hamiltonian formulations of some of these systems are also briefly touched upon. Nonlocal transformations and linearization aspects are also discussed.     

On symmetry preserving and symmetry broken bright,dark and antidark soliton solutions of nonlocal nonlinear Schrödinger equation

We construct symmetry preserving and symmetry broken N-bright, dark and antidark soliton solutions of a nonlocal nonlinear Schrödinger equation. To obtain these solutions, we use appropriate eigenfunctions in Darboux transformation (DT) method. We present explicit one and two bright soliton solutions and show that they exhibit stable structures only when we combine the field and parity transformed complex conjugate field. Further, we derive two dark/antidark soliton solution with the help of DT method. Unlike the bright soliton case, dark/antidark soliton solution exhibits stable structure for the field and the parity transformed conjugate field separately. In the dark/antidark soliton solution case we observe a contrasting behaviour between the envelope of the field and parity transformed complex conjugate envelope of the field. For a particular parametric choice, we get dark (antidark) soliton for the field while the parity transformed complex conjugate field exhibits antidark (dark) soliton. Due to this surprising result, both the field and PT transformed complex conjugate field exhibit sixteen different combinations of collision scenario. We classify the parametric regions of dark and antidark solitons in both the field and parity transformed complex conjugate field by carrying out relevant asymptotic analysis. Further we present 2N-dark/antidark soliton solution formula and demonstrate that this solution may have $2^{2N}\times 2^{2N}$ combinations of collisions.     

Radical-Pair Formation in Hydrocarbon (Aut)Oxidation

The reaction profiles for the uni- and bimolecular decomposition of benzyl hydroperoxide have been studied in the context of initiation reactions for the (aut)oxidation of hydrocarbons. The unimolecular dissociation of benzyl hydroperoxide was found to proceed through the formation of a hydrogen-bonded radical-pair minimum located +181 kJ mol⁻¹ above the hydroperoxide substrate and around 15 kJ mol⁻¹ below the separated radical products. The reaction of toluene with benzyl hydroperoxide proceeds such that O−O bond homolysis is coupled with a C−H bond abstraction event in a single kinetic step. The enthalpic barrier of this molecule-induced radical formation (MIRF) process is significantly lower than that of the unimolecular O−O bond cleavage. The same type of reaction is also possible in the self-reaction between two benzyl hydroperoxide molecules forming benzyloxyl and hydroxyl radical pairs along with benzaldehyde and water as co-products. In the product complexes formed in these MIRF reactions, both radicals connect to a centrally placed water molecule through hydrogen-bonding interactions.     

Stiffness based technique to probe cyclic damage accumulation in micro-structurally graded bond coats via micro-beam bending tests

This paper highlights a novel technique to delineate the fatigue response of different regions within thin microstructurally graded platinum nickel aluminide bond coats. Notched clamped beam structures fabricated from distinct microstructural zones of these coatings are subjected to programmed cyclic bending using the nano-indentation system. A methodical approach is established herein to quantify the cyclic damage preceding crack pop-in by using the cyclic stiffness of the beam as an indicator to mark failure. Preliminary results from these tests show that there is a characteristic change in the stiffness of the beam before a crack pop-in event occurs and different regions within the coating show different stiffening characteristics. Factors affecting the measured stiffness such as offsets in the loading position and blunting of the notch tip have been estimated using the finite element method. A graded flow stress model has been proposed and implemented in FEM to quantify the local flow stress changes accompanying the measured rise in stiffness. Electron transparent foils lifted off from the notched region of the beam post-testing suggests that the cyclic stiffening of the beams occurs due to dislocation hardening in the plastically deformed region close to the notch tip. Toughening mechanisms active in the crack wake have thus been investigated and correlated to the measured cyclic stiffness.     

New Synthesis of Analogues of the Antihypertensive Active Pharmaceutical Ingredient Irbesartan

A simple and new synthetic approach to various analogues of Irbesartan is described.