Generalized negative flows in hierarchies of integrable evolution equations

A one-parameter generalization of the hierarchy of negative flows is introduced for integrable hierarchies of evolution equations, which yields a wider (new) class of non-evolutionary integrable nonlinear wave equations. As main results, several integrability properties of these generalized negative flow equation are established, including their symmetry structure, conservation laws, and bi-Hamiltonian formulation. (The results also apply to the hierarchy of ordinary negative flows). The first generalized negative flow equation is worked out explicitly for each of the following integrable equations: Burgers, Korteweg-de Vries, modified Korteweg-de Vries, Sawada-Kotera, Kaup-Kupershmidt, Kupershmidt.     

The effect of anodising time on the electrochemical behaviour of the Ti/TiO<Subscript>2</Subscript> NTs/IrO<Subscript>2</Subscript>-RuO<Subscript>2</Subscript>-Ta<Subscript>2</Subscript>O<Subscript>5</Subscript> anode

Nowadays, mixed metal oxide (MMO) anodes are a superior alternative to lead alloys in electrowinning processes. Passivation of titanium substrate is the most common mechanism of deactivation in these anodes. In this research, titanium oxide nanotubes have been utilised as an interlayer between the substrate and a mixed metal oxide coating in order to improve the anode electrochemical behaviour and life via retardation of titanium passivation. Anodising of the substrate was done in 0.5 wt% hydrofluoric acid for 30, 60 and 240 min. The samples were subsequently coated with a coating composed of IrO₂-RuO₂-Ta₂O₅. The microstructure of different samples was observed by scanning with an electron microscope, and the electrochemical behaviour of the samples was studied by accelerated life test, cyclic voltammetry and electrochemical impedance spectroscopy. The studies showed that formation of titanium oxide nanotubes with anodising times of 60 and 240 min increases the life of the anode through the provision of a compact coating. The life of the anode which was anodised for 240 min lasted about 20% longer than the sample which had a substrate without any anodised layer.     

Effect of frequency on sonochemical reactions. I: Oxidation of iodide

The effect of continuous sonication on the kinetics of iodine formation in aqueous iodide solutions was studied in the presence of air and argon at two frequencies, 20 and 900 kHz. Most workers in this area assume that frequency has a negligible effect on sonochemical reactions. The present results indicate, however, that there is a significant effect in the above solutions. The rate of sonochemical oxidation of iodide in aqueous solution is 3.1 times greater in presence of air than argon at 900 kHz, in contrast to the situation at 20 kHz, where the ratio is 0.9 A 900 kHz apparatus was specially designed to make it possible to measure the absolute acoustic power delivered into the solution. The rate of oxidation per unit power in this new 900 kHz apparatus can be more than 30 times greater than that at 20 kHz for the oxidation of iodide in the presence of air.     

Analysis of the AC electrical data in the Davidson-Cole dielectric representation

The representation of the AC electrical data in the complex plane reveal two major classifications of the relaxation processes known as ideal (Debye) and non-ideal (non-Debye) types. The non-Debye relaxation has been empirically observed via Cole-Cole (C-C), Davidson-Cole (D-C), and Havriliak-Negami (H-N) responses. Each of these non-Debye relaxations is visualized with an equivalent circuit similar to the ideal relaxation. Both ideal and C-C relaxations reveal semicircular behavior in the complex plane while D-C and H-N relaxations deviate from the usual semicircular loci known as skewed behavior. The extracted equivalent circuit elements are essentially non-Debye for both D-C and H-N relaxations possessing complexity in the relaxation time. The analytical method of extracting these elements in conjunction with the empirical parameters of the D-C relaxation is described using conventional (real) domain and complex domain. The curve fitting procedure provided extremely small error for the complex domain analysis. The behavior of the D-C relaxation function and the depression parameter β are also discussed using ωτ=1 and ωτ≠1 corresponding to the maximum of the imaginary part of the impedance (Z^*) or permittivity (ε^*).     

Z-scan measurement for the nonlinear absorption and the nonlinear refraction of poly1,4-diazophenylene-bridged-tris(8-hydroxy-quinoline) aluminum (PDPAlq3)

The nonlinear optical properties of the poly1,4-diazophenylene-bridged-tris(8-hydroxy-quinoline) aluminum (PDPAlq₃) solution were studied using single beam Z-scan technique with a continuous-wave Diode laser radiation at 657.2 nm with 10 Hz repetition rate. The results show that the solution of PDPAlq₃ exhibits large nonlinear refractive index (n₂ = −1.7642 × 10⁻¹² m²/W) and nonlinear absorption coefficient (β = 1.12 × 10⁻⁶ m/W). The negative sign of the nonlinear refractive index n₂ indicates that the material exhibits self-defocusing optical nonlinearity. The evaluation of the figure of merit (W = 1.8) shows that the solution of PDPAlq₃ is sufficient for application in all-optical switching technology. These results show that the solution of PDPAlq₃ have potential application in nonlinear optics.     

Acoustic radiation force of a Bessel beam on a porous sphere

The possibility of using acoustic Bessel beams to produce an axial pulling force on porous particles is examined in an exact manner. The mathematical model utilizes the appropriate partial-wave expansion method in spherical coordinates, while Biot's model is used to describe the wave motion within the poroelastic medium. Of particular interest here is to examine the feasibility of using Bessel beams for (a) acoustic manipulation of fine porous particles and (b) suppression of particle resonances. To verify the viability of the technique, the radiation force and scattering form-function are calculated for aluminum and silica foams at various porosities. Inspection of the results has shown that acoustic manipulation of low porosity (<0.3) spheres is similar to that of solid elastic spheres, but this behavior significantly changes at higher porosities. Results have also shown a strong correlation between the backscattered form-function and the regions of negative radiation force. It has also been observed that the high-order resonances of the particle can be effectively suppressed by choosing the beam conical angle such that the acoustic contribution from that particular mode vanishes. This investigation may be helpful in the development of acoustic tweezers for manipulation of micro-porous drug delivery carrier and contrast agents.     

Estimates of B-decays into K-resonances and dileptons

Short and long distance contributions to the exclusive B-decays into various K-resonances and dileptons, i.e. $B \to K^i \ell \bar \ell (\ell = e,\mu ,\nu )$ , are examined. The heavy quark effective theory has been used to calculate the hadronic matrix elements. Substantial branching fractions are obtained for the dileptonic B-decays into some higher excited states of K-mesons. The long distance (resonance) contributions to these exclusive rare B-decay modes dominate the short distance contributions mostly by two orders of magnitude. It is pointed out that, excluding the resonance contributions, the P-wave channels are dominant, accounting for about 50% of the inclusiveB??X _s ? ⁺ ? ^? branching fraction.     

Subwavelength-size solid immersion lens

We report on the fabrication and characterization of nanoscale solid immersion lenses (nano-SILs) with sizes down to a subwavelength range. Submicrometer-scale cylinders fabricated by electron-beam lithography are thermally reflowed to form a spherical shape. Subsequent soft lithography leads to nano-SILs on transparent substrates for optical characterization. The optical characterization is performed using a high-resolution interference microscope with illumination at 642 nm wavelength. The focal spots produced by the nano-SILs show both spot-size reduction and enhanced optical intensity, which are consistent with the immersion effect.     

Phase-field modeling of void evolution and swelling in materials under irradiation

Void swelling is an important phenomenon observed in both nuclear fuels and cladding materials in operating nuclear reactors. In this work we develop a phase-field model to simulate void evolution and void volume change in irradiated materials. Important material processes, including the generation of defects such as vacancies and self-interstitials, their diffusion and annihilation, and void nucleation and evolution, have been taken into account in this model. The thermodynamic and kinetic properties, such...