Solitons and other nonlinear waves of the Boussinesq equation

This paper studies the dynamics of shallow water waves that are governed by the Boussinesq equations. A few perturbation terms are taken into account. The ansatz method is used to carry out the perturbed Boussinesq equation. Later on, the mapping method is used to extract a few more analytical solutions. Additionally, the Weierstrass elliptic function method is also used to obtain solitary waves and singular soliton solutions. Finally, the Lie symmetry approach is used to extract a few more additional solutions.     

The Active Phase of Nickel/Ordered Ce(2) Zr(2) O(x) Catalysts with a Discontinuity (x=7-8) in Methane Steam Reforming

Breaking news: A unique discontinuous property and an active phase of Ni/ordered Ce(2) Zr(2) O(x) (x=7-8) solid-solution catalysts were observed during methane steam reforming. The catalytic performance of Ni/Ce(2) Zr(2) O(x) strongly depended on the phase and oxygen content of the Ce(2) Zr(2) O(x) support.     

7-Deazapurine and 8-aza-7-deazapurine nucleoside and oligonucleotide pyrene "click" conjugates: synthesis, nucleobase controlled fluorescence quenching, and duplex stability

7-Deazapurine and 8-aza-7-deazapurine nucleosides related to dA and dG bearing 7-octadiynyl or 7-tripropargylamine side chains as well as corresponding oligonucleotides were synthesized. "Click" conjugation with 1-azidomethyl pyrene (10) resulted in fluorescent derivatives. Octadiynyl conjugates show only monomer fluorescence, while the proximal alignment of pyrene residues in the tripropargylamine derivatives causes excimer emission. 8-Aza-7-deazapurine pyrene "click" conjugates exhibit fluorescence emission much higher than that of 7-deazapurine derivatives. They are quenched by intramolecular charge transfer between the nucleobase and the dye. Oligonucleotide single strands decorated with two "double clicked" pyrenes show weak or no excimer fluorescence. However, when duplexes carry proximal pyrenes in complementary strands, strong excimer fluorescence is observed. A single replacement of a canonical nucleoside by a pyrene conjugate stabilizes the duplex substantially, most likely by stacking interactions: 6-12 °C for duplexes with a modified "adenine" base and 2-6 °C for a modified "guanine" base. The favorable photophysical properties of 8-aza-7-deazapurine pyrene conjugates improve the utility of pyrene fluorescence reporters in oligonucleotide sensing as these nucleoside conjugates are not affected by nucleobase induced quenching.     

Novel synthesis of 1,2,4‐triazolophanes and 1,3,4‐oxadiazolophanes: A dieckmann condensation approach

The Dieckmann condensation has been used for the first time for the syntheses of novel 1,2,4‐triazolophanes and 1,3,4‐oxadiazolophanes. The bis‐1,3,4‐oxadiazol‐2‐thiols 1a and 1b were reacted with ethyl bromoacetate to give the diesters 2a and 2b . Diesters 2a and 2b were treated under dry conditions with sodium methoxide in methanol to afford desired symmetrical 1,3,4‐oxadiazolophanes 3a and 3b . Similarly, diesters of macrocycle precursors containing 1,2,4‐triazole moiety, that is, 6a , 6b , 10 , 13a , 13b , and 13c were synthesized from 5a , 5b , 9 , 12a , 12b , and 12c , respectively. Dieckmann condensation of these diesters afforded symmetrical ketones 7a , 7b , 11 , 14a , 14b , and 14c . Extrusion of CO₂ was observed after in situ hydrolysis of the conventional Dieckmann product during neutralization by dilute mineral acids to afford highly symmetrical ketone in good yields. Further, the ketones 14a , 14b , and 14c were converted into their respective thiones by the reaction with Lawesson's reagent. All the products were synthesized with good yields, and structures were confirmed by various spectroscopic tools and elemental analyses. J. Heterocyclic Chem.,, (2012).     

The t-analog of the level one string function for twisted affine Kac–Moody algebras

We study Lusztig?s t-analog of weight multiplicities, or affine Kostka–Foulkes polynomials, associated to level one representations of twisted affine Kac–Moody algebras. We obtain an explicit closed form expression for the unique t-string function, using constant term identities of Macdonald and Cherednik. This extends previous work on t-string functions for the untwisted simply-laced affine Kac–Moody algebras.     

Analytical rheology of blends of linear and star polymers using a Bayesian formulation

A Bayesian data analysis technique is presented as a general tool for inverting linear viscoelastic models of branched polymers. The proposed method takes rheological data of an unknown polymer sample as input and provides a distribution of compositions and structures consistent with the rheology, as its output. It does so by converting the inverse problem of analytical rheology into a sampling problem, using the idea of Bayesian inference. A Markov chain Monte Carlo method with delayed rejection is proposed to sample the resulting posterior distribution. As an example, the method is applied to pure linear and star polymers and linear–linear, star–star, and star–linear blends. It is able to (a) discriminate between pure and blend systems, (b) accurately predict the composition of the mixtures, in the absence of degenerate solutions, and (c) describe multiple solutions, when more than one possible combination of constituents is consistent with the rheology.     

Interfacially active particles in droplet/matrix blends of model immiscible homopolymers: Particles can increase or decrease drop size

Particles have been shown to adsorb at the interface between immiscible homopolymer melts and to affect the morphology of blends of those homopolymers. We examined the effect of such interfacially active particles on the morphology of droplet/matrix blends of model immiscible homopolymers. Experiments were conducted on blends of polydimethylsiloxane and 1,4-polyisoprene blended in either a 20:80 or 80:20 weight ratio. The effects of three different particle types, fluoropolymer particles, iron particles, and iron oxyhydroxide particles, all at a loading of 0.5 vol.%, were examined by rheology and by direct flow visualization. Particles were found to significantly affect the strain recovery behavior of polymer blends, increasing or decreasing the ultimate recovery, slowing down or accelerating the recovery kinetics, and changing the dependence of these parameters on the applied stress prior to cessation of shear. These rheological observations were found to correlate reasonably well with particle-induced changes in drop size. The particles can both increase as well as decrease the drop size, depending on the particle type, as well as on which phase is continuous. The cases in which particles cause a decrease in drop size are analogous to the particle stabilization of “Pickering emulsions” well-known from the literature on oil/water systems. We hypothesize that cases in which particles increase drop size are analogous to the “bridging–dewetting” mechanism known in the aqueous foam literature.     

Non-linear dynamic intertwining of rods with self-contact

Twisted marine cables on the sea floor can form highly contorted three-dimensional loops that resemble tangles. Such tangles or ‘hockles’ are topologically equivalent to the plectomenes that form in supercoiled DNA molecules. The dynamic evolution of these intertwined loops is studied herein using a computational rod model that explicitly accounts for dynamic self-contact. Numerical solutions are presented for an illustrative example of a long rod subjected to increasing twist at one end. The solutions reveal the dynamic evolution of the rod from an initially straight state, through a buckled state in the approximate form of a helix, through the dynamic collapse of this helix into a near-planar loop with one site of self-contact, and the subsequent intertwining of this loop with multiple sites of self-contact. This evolution is controlled by the dynamic conversion of torsional strain energy to bending strain energy or, alternatively, by the dynamic conversion of twist (Tw) to writhe (Wr).     

Molecular dynamics simulations of ion-irradiation induced deflection of 2D graphene films

Ion-irradiation induced surface stress generation and the resulting deflection of 2D cantilever graphene films is studied using molecular dynamics (MD) simulations. The simulation results show that the free-end deflection is strongly dependent on the kinetic energy of the incident ions. At low incident energies (?10 eV), the graphene film bends towards the irradiated side (upward deflection in our simulations); a transition from bending towards the irradiated side (upward deflection) to bending away from the irradiated side (downward deflection) occurs when the incident energy is ～10 eV; the downward deflection peaks at ～50 eV. Further increases of the incident energy cause the magnitude of downward deflection to decrease. The evolution of free-end deflection with respect to the number of incidences is also dependent on the incident energy. The dependence of the deflection behavior of the graphene films on the incident energy revealed by our atomistic simulations suggests the generation of intrinsic stress of different levels in the growing films. Such behavior may be attributed to competing mechanisms of production and annihilation of interstitial- and vacancy-like defects in the growing film. Understanding the dependence of thin film deflection on the incident energy provides guidelines for controlling thin film shapes at the nanometer scale using ion-beam machining.