@article{gardner_liu_1999, title={Monte Carlo simulation of neutron porosity oil well logging tools: Combining the geometry-independent fine-mesh importance map and one-dimensional diffusion model approaches}, volume={133}, ISSN={["0029-5639"]}, DOI={10.13182/NSE99-A2074}, abstractNote={The generation of first estimate geometry-independent fine-mesh three-dimensional importance maps with simple one-dimensional diffusion models is demonstrated for the Monte Carlo simulation of the neutron porosity oil well logging tool response benchmark problem. By combining the approach of using simple one-dimensional steady-state diffusion models for calculating neutron adjoint flux with the geometry-independent fine-mesh-based Monte Carlo importance approach previously developed, an automated and efficient variance reduction method is obtained for this specific problem. A surprising result is that the converged figures of merit after iteration are consistently larger when the initial importance map is based on the one-dimensional diffusion model rather than that obtained from an analog Monte Carlo simulation.}, number={1}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Gardner, RP and Liu, LY}, year={1999}, month={Sep}, pages={80–91} }
 @article{liu_gardner_1997, title={A geometry-independent fine-mesh-based Monte Carlo importance generator}, volume={125}, ISSN={["1943-748X"]}, DOI={10.13182/NSE97-A24265}, abstractNote={A new importance map approach for Monte Carlo simulation that can be used in an adaptive fashion has been identified and developed. It is based on using a mesh-based system of weight windows that are independent of any physical geometric cells. It consists of an importance map generator and a splitting and Russian roulette algorithm for a mesh-based weight windows game that is used in an iterative fashion to obtain increasingly efficient results. The general purpose Monte Carlo code MCNP is modified to incorporate this new mesh-based importance map generator and matching weight window technique for variance reduction. Two nuclear well logging problems- one for neutrons and the other for gamma rays- are used to test the new importance map generator. Results show that the new generator is able to produce four to six times larger figures of merit than MCNP's physical geometry cell-based importance map generator. More importantly, the superior user friendliness of this new mesh-based generator makes variance reduction easy to accomplish.}, number={2}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Liu, LY and Gardner, RP}, year={1997}, month={Feb}, pages={188–195} }
 @article{gardner_liu_1997, title={On extending the accurate and useful counting rate range of GM counter detector systems}, volume={48}, ISSN={["0969-8043"]}, DOI={10.1016/S0969-8043(97)00161-9}, abstractNote={A study is described to extend the accurate and useful counting rate range of the GM (Geiger-Muller) counter detector system. The idealized simple one-parameter paralyzable and non-paralyzable models were first investigated with the decaying source method and were found to be inadequate for all the systems tested. The use of a slightly more complex two-parameter model was investigated next and, in spite of initial positive indications, the resulting model yielded inaccuracies larger than ± 10% for over one-third of the counting rate range. However, use of the decaying source method to provide a wide range of accurate useful counting rates was found to be reproducible to within ± 1%. Previous formulas for variance found in the literature were studied by Monte Carlo simulation and were found to be valid when the respective appropriate assumptions of the idealized models were applicable. Actual experimental variances were found to be fairly well predicted by a modified Kosten (1943) model that has a variable dead time. This model has the advantage that it always gives conservative estimates. At present the counting rate range of GM counter detector systems can be extended to the ± 1% accuracy level only at the cost of having to use the decaying source method, which involves the use of a pure short-lived radioisotope such as 56Mn. Use at this accuracy level without having to use the decaying source method must await further modeling or other experimental developments.}, number={10-12}, journal={APPLIED RADIATION AND ISOTOPES}, author={Gardner, RP and Liu, LY}, year={1997}, pages={1605–1615} }
 @article{gardner_sood_wang_liu_guo_gehrke_1997, title={Single peak versus library least-squares analysis methods for the PGNAA analysis of vitrified waste}, volume={48}, ISSN={["0969-8043"]}, DOI={10.1016/S0969-8043(97)00127-9}, abstractNote={A feasibility study (Gardner et al., 1995) for the neutron capture prompt gamma-ray analysis (PGNAA) of simulated vitrified nuclear waste containing SiO2/Al2O3 and SiO2/Fe2O3 mixtures has been carried out. Analyses for elements Al, Si, and Fe were made by both the single peak area and the library least-squares methods using measured and simulated data. It is shown that the library least-squares method is about 2.5 times better than the single peak analysis method.}, number={10-12}, journal={APPLIED RADIATION AND ISOTOPES}, author={Gardner, RP and Sood, A and Wang, YY and Liu, L and Guo, P and Gehrke, RJ}, year={1997}, pages={1331–1335} }