If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation.

The method of upper and lower solutions guarantees the interval of existence of nonlinear differential equations with initial conditions. To compute the solution on this interval, we need coupled lower and upper solutions on the interval of existence. We provide both theoretical as well as numerical methods to compute coupled lower and upper solutions by using a superlinear convergence method. Further, we develop monotone sequences which converge uniformly and monotonically, and with superlinear convergence, to the unique solution of the nonlinear problem on this interval. We accelerate the superlinear convergence by means of the Gauss-Seidel method. Numerical examples are developed for the logistic equation. Our method is applicable to more general nonlinear differential equations, including Riccati type differential equations.

Positron Annihilation Lifetime Spectroscopy (PALS) is used to study the nanoporosity and fractional free volume in Ultra High Molecular Weight Polyethylene (UHMWPE) and composites with the addition of Martian Regolith (UHMWPE-MR) as-made and irradiated with56Fe heavy ions at an energy of 600 MeV/u to three different doses (10, 32, 64 Gy). The positron lifetime spectra were obtained using22Na positron source and the spectra were analyzed to two lifetime components using POSFIT program. First short lifetime component around 0.28 ns is related to positron annihilation in material including vacancy defects and the second long lived component around 1.7 ns is due to Positronium formation in free volume pores. UHMWPE-MR composites were shown to be less porous with much lower nanopores concentration compared to the UHMWPE polymer. The average size of the nanopores is around 0.5 nm (obtained from a simple model). Larger variations in positron lifetime parameters are observed with increasing irradiation dose for UHMWPE polymer compared to UHMWPE+MR composites. The 3-point bend test results also showed larger variations with increasing irradiation dose for the UHMWPE polymer. The variations in PALS parameters may indicate an increasing competition between two processes at higher irradiation doses: 1) vacancy defects aggregation and 2) escape of vacancy defects as the local temperature increases at higher doses resulting in increased vacancy defects mobility. Present results clearly indicate a qualitative inverse relationship between nanoscale porosity measured by positron life time and mechanical properties of UHMWPE and its composite with MR.