Many problems in science and engineering require the solution of a long sequence of slowly changing linear systems. We propose and analyze two methods that significantly reduce the total number of matrix-vector products required to solve all systems. We consider the general case where both the matrix and right-hand side change, and we make no assumptions regarding the change in the right-hand sides. Furthermore, we consider general nonsingular matrices, and we do not assume that all matrices are pairwise close or that the sequence of matrices converges to a particular matrix. Our methods work well under these general assumptions, and hence form a significant advancement with respect to related work in this area. We can reduce the cost of solving subsequent systems in the sequence by recycling selected subspaces generated for previous systems. We consider two approaches that allow for the continuous improvement of the recycled subspace at low cost. We consider both Hermitian and non-Hermitian problems, and we analyze our algorithms both theoretically and numerically to illustrate the effects of subspace recycling. We also demonstrate the effectiveness of our algorithms for a range of applications from computational mechanics, materials science, and computational physics.

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Single‐walled carbon nanotube (SWNT)/poly(methyl methacrylate) (PMMA) composites were prepared using coagulation method. The electrical conductivity and the electromagnetic interference (EMI) shielding of SWNT/PMMA composites over the X‐band (8–12 GHz) and the microwave (200–2000 MHz) frequency range have been investigated. The electrical conductivity of composites increases with SWNT loading by 13 orders of magnitude, from 10−15 to 10−2 Ω−1 cm−1 with a percolation threshold of about 3 wt% SWNTs. The effect of the sample thickness on the shielding effectiveness has been studied, and correlated to the electrical conductivity of composites. The data suggest that SWNT/PMMA composites containing higher SWNT loading (above 10 wt%) be useful for EMI shielding and those with lower SWNT loading be useful for electrostatic charge dissipation. The dominant shielding mechanism of SWNT/PMMA composites was also discussed. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

Recently, magnesium (Mg) alloys have received significant attention as a potential biomaterial for degradable implants, and this study was directed at evaluating the suitability of Mg for craniofacial bone screws. The objective was to implant screws fabricated from commercially available Mg-alloys (pure Mg and AZ31) in-vivo in a rabbit mandible. First, Mg-alloy screws were compared to stainless steel screws in an in-vitro pull-out test and determined to have a similar holding strength (~40N). A finite element model of the screw was created using the pull-out test data, and the model can be used for future Mg-alloy screw design. Then, Mg-alloy screws were implanted for 4, 8, and 12 weeks, with two controls of an osteotomy site (hole) with no implant and a stainless steel screw implanted for 12 weeks. MicroCT (computed tomography) was used to assess bone remodeling and Mg-alloy degradation, both visually and qualitatively through volume fraction measurements for all time points. Histologic analysis was also completed for the Mg-alloys at 12 weeks. The results showed that craniofacial bone remodeling occurred around both Mg-alloy screw types. Pure Mg had a different degradation profile than AZ31, however bone growth occurred around both screw types. The degradation rate of both Mg-alloy screw types in the bone marrow space and the muscle were faster than in the cortical bone space at 12 weeks. Furthermore, it was shown that by alloying Mg, the degradation profile could be changed. These results indicate the promise of using Mg-alloys for craniofacial applications.

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