Dissipative Waves in a Relaxing Gas Exhibiting Mixed Nonlinearity

We consider a weakly dissipative quasilinear system of PDEs, governingthe unsteady one-dimensional motion of a relaxing gas, and investigatethe effects ofhigher order terms and the source term, present in the differentialsystem, on the wave motion associated with it. The undisturbed stateof the medium, which is assumed to be uniform and at restadmits mixed nonlinearity, i.e., the quadratic nonlinearity parameter inherent in the system changes sign depending on the basestate. The method of multiple scales is employed to determine theevolution equation governing small perturbations to the state where is of O(), and the effects of nonlinearity arenoticeable over times of order O(^–2).     

On Doi–Naganuma and Shimura liftings

The Ramanujan Journal - In this paper, we extend the Doi–Naganuma lifting to higher levels by following the methods of Zagier and Kohnen. We prove that there is a Hecke-equivariant linear map...     

Solvent‐free and nonisocyanate melt transurethane reaction for aliphatic polyurethanes and mechanistic aspects

A novel melt transurethane polycondensation route for polyurethanes under solvent‐free and nonisocyanate condition was developed for soluble and thermally stable aliphatic or aromatic polyurethanes. The new transurethane process was investigated for A + B, A‐A + B, and A‐A + B‐B (A‐urethane and B‐hydroxyl) ‐type condensation reactions, and also monomers bearing primary and secondary urethane or hydroxyl functionalities. The transurethane process was confirmed by ¹H and ¹³C NMR, and molecular weight of the polymers were obtained as M_n = 10–15 × 10³ and M_w = 15–45 × 10³ g/mol. The mechanistic aspects of the melt transurethane process and role of the catalyst were investigated using model reactions, ¹H NMR, and MALDI‐TOF‐MS. The model reactions indicated the occurrence of 97% reaction in the presence of catalyst, whereas its absence gave only less than 2% of the product. The polymer samples were subjected for end‐group analysis using MALDI‐TOF‐MS, which confirms the Ti‐catalyst mediated nonisocyanate pathway in the melt transurethane process. Almost all the polyurethanes were stable up to 280 °C, and the T_g of the polyurethanes can be easily fine‐tuned from ?30 to 120 °C by using appropriate diols in the melt transurethane process. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2445–2458, 2008     

2-(Trimethylsilyl)ethanesulfonyl amide as a new ammonia equivalent for palladium-catalyzed amination of aryl halides

2-(Trimethylsilyl)ethanesulfonyl amide (SES-NH₂) is an ammonia equivalent for the palladium-catalyzed amination of aryl bromides and aryl chlorides. Using these amine derivatives, it has been observed that anilines and anilines with sensitive functional groups can be readily prepared.     

Probing the pi-stacking induced molecular aggregation in pi-conjugated polymers, oligomers, and their blends of p-phenylenevinylenes

The role of pi-stack induced molecular aggregation on solution and solid-state luminescent properties was investigated for the tricyclodecane substituted bulky (p-phenylenevinylene)s (BTCD-60, with 60% bulky group), oligophenylenevinylenes (MEH-OPV and BTCD-OPV)s, and their polymer-oligomer binary blends. The natures of the solvent, concentration, solvent combinations (good or bad), and temperature were employed as stimuli to probe the origin of the molecular aggregates in bulky conducting polymers. Absorption, photoluminescence (PL), and time-resolved fluorescence spectroscopic techniques were employed as tools to trace aggregation in solvents such as toluene, tetrahydrofuran (THF), THF and methanol, or THF and water as well as in the solid state. The absorbance spectra of poly(2-methoxy-5-(2-ethylhexyloxy))-1,4-phenylenevinylene (MEH-PPV) and BTCD-60 indicated that the films obtained from polymers that were dissolved in aromatic solvents such as toluene were found to possess more pi-stacking as compared to that of films obtained from a good solvent such as THF. The solid-state emission spectrum of BTCD-60 was found to show almost a 5-6 times enhancement in PL intensity as compared to that of MEH-PPV. Concentration dependent excitation spectra of the polymers confirmed the presence of aggregated polymer chains in MEH-PPV, which is the main reason for the quenching of luminescence intensity in the polymer. Solvent induced aggregation studies of polymers in THF and methanol mixture further supports the existence of strong aggregation in MEH-PPV as compared to that of bulky BTCD-60. Variable temperature absorption studies confirmed the reversibility of molecular aggregation on heating/cooling cycles, and the extent of aggregation was found more in MEH-PPV chains as compared to that of BTCD-60. MEH-PPV/OPV binary blends were prepared in the entire composition range from 0 to 100% via solution blending techniques. Through selective PL excitation techniques, the effect of oligomer-to-polymer energy transfer and also luminescent enhancement in MEH-PPV via interchain separation were investigated. Both the energy transfer and the interchain separation were found to be more effective on the enhancement of luminescence properties in the BTCD blends as compared to that of MEH blends. Time-resolved fluorescence studies confirmed the existence of two types of species corresponding to the free and aggregated chains in the polymer matrix with lifetimes in the range of 0.5-2.0 ns. In the present investigation, we have successfully shown that the molecular aggregation of the pi-conjugated polymers, oligomers, and their binary blends can be controlled via suitable bulky substitution to tune their emission properties in solution as well as in the solid state.     

Computational insights into octyl-D-xyloside isomers towards understanding the liquid crystalline structure: physico-chemical features

We applied density functional theory to study octyl-D-xyloside isomers in order to explain the features responsible for the liquid crystal mesophases. Compared to a glucoside, the xylose headgroup has a proton instead of the hydroxymethyl group on C5. Thus, a xyloside has a reduced headgroup volume that renders it less hydrophilic. Our results have shown that the xylose headgroup may adopt stable pyranose and furanose conformations, which may lead to different effective headgroup hydrophilicities. These features are probably responsible for forming two non-equivalent inverse micelles, which are self-assembled into a cubic discontinuous phase with a space group of Fd3m commonly found for xylosides. While different factors are responsible for controlling the relative stability of each isomer, the role of intramolecular hydrogen bonding was highlighted for the investigated single molecule. The polarisable continuum model was used to take into account the solvent effect in order to understand the molecular behaviour in very polar systems. Results from calculations carried out in gas phase were used for comparative purposes. The molecular electrostatic potential calculations for these xylolipids demonstrate sugar amphoterism, which is implicated in the heterogeneity nature of lipid self-assembly.     

A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation

A second-order splitting method is applied to a KdV-like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L² and L^∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin–Bona–Mahony) and BBMB (Benjamin–Bona–Mahony–Burgers) equations and the well-known decay estimates are demonstrated for the computed solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 695–716, 1998