A factor of safety method for quantitative estimates of grid-spacing and time-step uncertainties for solution verification is developed. It removes the two deficiencies of the grid convergence index and correction factor methods, namely, unreasonably small uncertainty when the estimated order of accuracy using the Richardson extrapolation method is greater than the theoretical order of accuracy and lack of statistical evidence that the interval of uncertainty at the 95% confidence level bounds the comparison error. Different error estimates are evaluated using the effectivity index. The uncertainty estimate builds on the correction factor method, but with significant improvements. The ratio of the estimated order of accuracy and theoretical order of accuracy P instead of the correction factor is used as the distance metric to the asymptotic range. The best error estimate is used to construct the uncertainty estimate. The assumption that the factor of safety is symmetric with respect to the asymptotic range was removed through the use of three instead of two factor of safety coefficients. The factor of safety method is validated using statistical analysis of 25 samples with different sizes based on 17 studies covering fluids, thermal, and structure disciplines. Only the factor of safety method, compared with the grid convergence index and correction factor methods, provides a reliability larger than 95% and a lower confidence limit greater than or equal to 1.2 at the 95% confidence level for the true mean of the parent population of the actual factor of safety. This conclusion is true for different studies, variables, ranges of P values, and single P values where multiple actual factors of safety are available. The number of samples is large and the range of P values is wide such that the factor of safety method is also valid for other applications including results not in the asymptotic range, which is typical in industrial and fluid engineering applications. An example for ship hydrodynamics is provided.

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Reduction-sensitive polymeric nanocarrier with near-infrared fluorescence probe has been prepared. Disulfide-cross-linked polypeptide nanogel with near-infrared fluorescence property (NIRF nanogel) was first synthesized, then the anticancer drug doxorubicin was encapsulated into polypeptide core of the NIRF nanogel to prepare a drug carrier with near-infrared fluorescence (NIRF prodrug). In vitro drug release study of the NIRF prodrug revealed an accelerated release behavior in the presence of 10 mM glutathione (GSH). Cellular uptake studies of both the NIRF nanogel and NIRF prodrug showed that they could enter cell via endocytosis. With the aid of NIRF labeling, direct imaging of the drug release from NIRF nanogel was accomplished, and drug molecules released subsequently migrated into nucleus while the NIRF nanogel still remained in cytoplasm. In vivo distribution of the NIRF nanogel and NIRF prodrug on tumor-bearing nude mice shows that both of them accumulated at tumor place at 24 h after tail veil injection via enhanced permeability and retention (EPR) effect. The NIRF prodrug prepared here has the potential application for the theranosis of cancer.

A novel disulfide core cross-linked PEGylated polypeptide nanogel has been synthesized by a one-step ring opening copolymerization of γ-benzyl L-glutamate N-carboxyanhydride and L-cystine N-carboxyanhydride using an amino group-terminated poly(ethylene glycol) methyl ether as initiator. Characterization of products confirms the formation of a core cross-linked PEGylated nanogel with disulfide linkages with a size of about 250 nm, and these studies also confirm that this nanogel can easily be broken by glutathione. Cell viability experiments show the good biocompatibility of the as-prepared polymer. Studies relating to loading and controlled release of indomethacin under reduction-sensitive conditions reveal that the nanogel is a good candidate for drug delivery systems.