Solitons and conservation laws of Klein–Gordon equation with power law and log law nonlinearities

This paper obtains the conservation laws of the Klein–Gordon equation with power law and log law nonlinearities. The multiplier approach with Lie symmetry analysis is employed to obtain the conserved densities. The 1-soliton solutions are subsequently used to compute the conserved quantities from the conserved densities. Later the perturbation terms are added and the conservation laws of the perturbed Klein–Gordon equation are studied.     

Binuclear meta‐xylyl‐linked Ag(I)‐N‐heterocyclic carbene complexes of N‐alkyl/aryl‐alkyl‐substituted bis‐benzimidazolium salts: synthesis,crystal structures and in vitro anticancer studies

Salts of meta‐xylyl‐linked N‐ethyl/n‐butyl/benzyl‐substituted bis‐benzimidazolium having hexafluorophosphate counterions have been synthesized. The corresponding binuclear Ag(I)‐N‐heterocyclic carbene complexes were prepared by the reaction of Ag₂O. The N‐heterocyclic carbene (NHC) ligand precursor 7 and Ag(I)–NHC complexes 10 and 11 have been structurally characterized by single‐crystal X‐ray diffraction technique. All of the reported compounds have been tested for their anticancer activity using human colorectal (HCT 116) cancer cell lines. Sterically varied benzimidazolium salts displayed significant activity against HCT 116 cell line, yielding IC₅₀ values in the range 0.1–19.4 µ m , while Ag(I)–carbene complexes showed exceptionally good activity (0.2–1.3 µ m ) against tested cancer cell lines. Copyright © 2013 John Wiley & Sons, Ltd.     

Control of iron nanoparticle size by manipulating PEG–ethanol colloidal solutions and spin-coating parameters for the growth of single-walled carbon nanotubes

Iron catalyst nanoparticles were prepared on silicon wafers by spin-coating colloidal solutions containing iron nitrate, polyethylene glycol (PEG) and absolute ethanol. The effects of various spin-coating conditions were investigated. The findings showed that the size of the iron particles was governed by the composition of the colloidal solution used and that a high angular speed was responsible for the formation of a thin colloidal film. The effect of angular acceleration on the size and distribution of the iron particles were found to be insignificant. It was observed that a longer spin-coating duration provoked the agglomeration of iron particles, leading to the formation of large particles. We also showed that single-walled carbon nanotubes could be grown from the smallest iron catalyst nanoparticles after the chemical vapor deposition of methane.     

Constant heat flux solution for mixed convection boundary layer viscoelastic fluid

The mixed convection boundary layer of a viscoelastic fluid past a circular cylinder with constant heat flux is discussed. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. The governing non-similar partial differential equations are transformed into dimensionless forms and then solved numerically using the Keller-box method by augmenting an extra boundary condition at infinity. Numerical results obtained in the form of velocity distributions and temperature profiles are presented for a range of values of the dimensionless viscoelastic fluid parameter. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the momentum boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point.