Monte Carlo Efficiency Research Articles

Development of concrete reference material for quality assurance/quality control of gamma radioactivity measurement for nuclear power plant decommissioning waste

The Korea Research Institute of Standards and Science has developed a new concrete reference material (RM) for measuring gamma-emitting radionuclides, such as 134Cs, 137Cs, 65Zn, 241Am, and 60Co, to improve and maintain the quality assurance and quality control of the radioactivity measurement in radioactive waste generated during the decommissioning of nuclear power plants. In this study, cement, SiO2, and bentonite, which are the main components of concrete, were mixed in an appropriate ratio with radionuclides. For certification and homogeneity assessment, 10 bottles were randomly selected, two sub-samples were collected from each bottle, and radionuclides were measured via HPGe gamma spectrometry. The results of the homogeneity tests using a one-way analysis of variance on 241Am, 134Cs, 137Cs, 65Zn, and 60Co in the concrete RM fulfilled the requirements of ISO Guide 35. Coincidence summing and self-absorption correction were performed on measurement results by introducing the Monte Carlo efficiency transfer code and Monte Carlo N-Particle transport code. The reference values for five radionuclides (60Co, 65Zn, 241Am, 134Cs, and 137Cs) in the RM were in the range of 15–40 Bq/kg, and the expanded uncertainty was within 10% (k = 2). To the best of our knowledge, this was the first study to develop concrete RM for measuring gamma-emitting radionuclides.

Effect of the geometrical parameters of an HPGe detector on efficiency calculations using Monte Carlo methods

This paper describes a procedure for constructing a Monte Carlo model of an HPGe detector used to measure activity. The purpose of this parametric study is to obtain a single model that effectively reproduces the detection efficiency for both small (< 1 cm) and large (> 40 cm) source–detector distances. We therefore investigated the effect of the HPGe detector’s geometrical parameters on the Monte Carlo efficiency calculations. The results highlight detector parameters with the greatest effect on the calculations within a wide range of gamma energy levels (60–1900 keV) and source–detector distances (1 to 50 cm): the air gap, the dead layers thicknesses and the crystal height (see Figure 1). Analysis of these results has made it possible to determine the key parameters, together with the optimal energy and distance ranges, significantly reducing the computational time required. A broad range of calibrated point-like radioactive sources were used to ensure a high level of experimental efficiency when constructing the detector model. A single Monte Carlo model for this detector was thus optimised by minimising the difference between the experimental efficiency and the calculations. The single HPGe model resulting from this optimisation process led to an average deviation between experimental and simulated efficiency of 3% for both small and large source–detector distances.

Optimization and validation of a LaBr3(Ce) detector model for use in Monte Carlo simulations

A reliable detector model is needed for Monte Carlo efficiency calibration. A LaBr3(Ce) detector model was optimized and verified using different radioactive sources (241Am,133Ba,137Cs,60Co and152Eu) and geometries (point, extended and surface). PENELOPE and MCNP were used for Monte Carlo simulations. A good agreement was observed between simulated and experimental full energy peak efficiencies (FEPE) as their mean relative difference was 2.84% ± 1.93% and 2.79% ± 1.99% for PENELOPE and MCNP simulation, respectively. The differences between simulated FEPEs of two Monte Carlo codes were negligible except for low energies (< 100 keV).

Efficiency calibration for HPGe detector by Monte Carlo efficiency transfer method

In this paper, the Monte Carlo efficiency transfer method was used to calibrate the full energy peak efficiency (FEPE) of a coaxial p-type HPGe detector. The gamma standard radioactive sources including 22Na, 54Mn, 57Co, 60Co, 65Zn, 109Cd,133Ba, 137Cs, 154Eu, 207Bi, 241Am were measured at different positions on-center of detector with the distance of 5, 10, 15, 20, 25 cm. Besides, a cylindrical sample containing standard mixed nuclides solution was also measured at surface of the detector. The experimental FEPE curves as function of gamma energy for these geometries were determined with the coincidence-summing corrections. A HPGe detector model based on the specifications of manufacturer was built to directly calculate the FEPE for the geometries by Monte Carlo simulations with MCNP6 code. However, these simulated FEPEs show a quite high discrepancy from experimental FEPEs. Then, the FEPEs were calculated by the efficiency transfer method with the efficiency curve for point source at distance of 25 cm as the reference data. A good agreement was obtained between the calculated results by the Monte Carlo efficiency transfer method and experimental results. The comparisons between experimental and calculated FEPE showed that the relative deviations were mostly within +/-4% in the energy range of 53-1770 keV.&#x0D;

Lattice Monte Carlo for quantum Hall states on a torus

Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum to lattice. We first apply this new technique to study the Berry phase of transporting composite fermions along different closed paths enclosing or not enclosing the Fermi surface center in the half filled Landau level problem. The Monte Carlo result agrees with the phase structure we found on small systems and confirms it on much larger sizes. Several other quantities including the Coulomb energy in different Landau levels, structure factor, particle-hole symmetry are computed and discussed for various model states. In the end, based on certain knowledge of structure factor, we introduce a algorithm by which the lattice Monte Carlo efficiency is further boosted by several orders.

Bayesian Inference for the One-Factor Copula Model

ABSTRACTWe develop efficient Bayesian inference for the one-factor copula model with two significant contributions over existing methodologies. First, our approach leads to straightforward inference on dependence parameters and the latent factor; only inference on the former is available under frequentist alternatives. Second, we develop a reversible jump Markov chain Monte Carlo algorithm that averages over models constructed from different bivariate copula building blocks. Our approach accommodates any combination of discrete and continuous margins. Through extensive simulations, we compare the computational and Monte Carlo efficiency of alternative proposed sampling schemes. The preferred algorithm provides reliable inference on parameters, the latent factor, and model space. The potential of the methodology is highlighted in an empirical study of 10 binary measures of socio-economic deprivation collected for 11,463 East Timorese households. The importance of conducting inference on the latent factor is motivated by constructing a poverty index using estimates of the factor. Compared to a linear Gaussian factor model, our model average improves out-of-sample fit. The relationships between the poverty index and observed variables uncovered by our approach are diverse and allow for a richer and more precise understanding of the dependence between overall deprivation and individual measures of well-being.

Monte Carlo efficiency improvement by multiple sampling of conditioned integration variables

We present a technique that permits to increase the efficiency of multidimensional Monte Carlo algorithms when the sampling of the first, unconditioned random variable consumes much more computational time than the sampling of the remaining, conditioned random variables while its variability contributes only little to the total variance. This is in particular relevant for transport problems in complex and randomly distributed geometries. The proposed technique is based on an new Monte Carlo estimator in which the conditioned random variables are sampled more often than the unconditioned one. A significant contribution of the present Short Note is an automatic procedure for calculating the optimal number of samples of the conditioned random variable per sample of the unconditioned one. The technique is illustrated by a current research example where it permits to increase the efficiency by a factor 100.

Applied tools for determining low-activity radionuclides in large environmental samples

Considerable amounts of biological material contaminated with artificial radionuclides were generated to obtain the efficiency curves for low-activity radionuclide analyses of large environmental samples. Likewise, improving detection geometry is also an important task, mainly for studies involving conservation units with a high level of biodiversity preservation. This study aimed to evaluate the Monte Carlo efficiency curves without generating contaminated material with artificial radionuclides for water and vegetation measurements. An in-house adapted Marinelli geometry was applied to reduce the sampled amount of biological material in the ecosystem, which was combined with the Monte Carlo assisted efficiency curve for a more sustainable radiometric analysis.

Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms

To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano’s theorem. Additionally, Lewis’ approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano’s and Lewis’ approaches are stated in this new equation. Fano’s theorem is found not to apply in the presence of electromagnetic fields. Lewis’ theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms.

SU‐E‐T‐666: Radionuclides and Activity of the Patient Apertures Used in a Proton Beam of Wobbling System

Purpose:To identify the radionuclides and quantify the activity of the patient apertures used in a 190‐MeV proton beam of wobbling system.Methods:A proton beam of wobbling system in the first proton center in Taiwan, Chang Gung Memorial Hospital at Linkou, was used to bombard the patient apertures. The patient aperture was composed of 60.5 % copper, 39.4 % Zinc, 0.05 % iron, 0.05 % lead. A protable high‐purity germanium (HPGe) coaxial detector was used to measure the spectra of the induced nuclides of patient apertures. The analysis of the spectra and the identification of the radionuclides were preliminarily operated by the Nuclide Navigator III Master Library. On the basis of the results by Nuclide Navigator III Master Library, we manually selected the reliable nuclides by the gamma‐ray energies, branching ratio, and half life. In the spectra, we can quantify the activity of radionuclides by the Monte Carlo efficiency transfer method.Results:In this study, the radioisotopes activated in patient apertures by the 190‐MeV proton beam were divided into two categories. The first category is long half‐life radionuclides, such as Co‐56 (half life, 77.3 days). Other radionuclides of Cu‐60, Cu‐61, Cu‐62, Cu‐66, and Zn‐62 have shorter half life. The radionuclide of Cu‐60 had the highest activity. From calculation with the efficiency transfer method, the deviations between the computed results and the measured efficiencies were mostly within 10%.Conclusion:To identify the radionuclides and quantify the activity helps us to estimate proper time intervals for cooling the patient apertures.This study was supported by the grants from the Chang Gung Memorial Hospital (CMRPD1C0682).

Application of the Monte Carlo efficiency transfer method to an HPGe detector with the purpose of environmental samples measurement

Monte Carlo efficiency transfer method was used to determine the full energy peak efficiency of a coaxial n-type HPGe detector. The efficiencies calibration curves for three Certificate Reference Materials were determined by efficiency transfer using a 152Eu reference source. The efficiency values obtained after efficiency transfer were used to calculate the activity concentration of the radionuclides detected in the three materials, which were measured in a low-background gamma spectrometry system. Reported and calculated activity concentration show a good agreement with mean deviations of 5%, which is satisfactory for environmental samples measurement.

Using standard calibrated geometries to characterize a coaxial high purity germanium gamma detector for Monte Carlo simulations.

A detector model optimization procedure based on matching Monte Carlo simulations with measurements for two experimentally calibrated sample geometries which are frequently used in radioactivity measurement laboratories results in relative agreement within 5% between simulated and measured efficiencies for a high purity germanium detector. The optimization procedure indicated that the increase in dead layer thickness is largely responsible for a detector efficiency decrease in time. The optimized detector model allows Monte Carlo efficiency calibration for all other samples of which the geometry and bulk composition is known. The presented method is a competitive and economic alternative to more elaborate detector scanning methods and results in a comparable accuracy.

EXPERIMENTAL LIMITS ON PRIMORDIAL BLACK HOLE DARK MATTER FROM THE FIRST 2 YR OFKEPLERDATA

We present the analysis on our new limits of the dark matter (DM) halo consisting of primordial black holes (PBHs) or massive compact halo objects (MACHOs). We present a search of the first two years of publicly available Kepler mission data for potential signatures of gravitational microlensing caused by these objects, as well as an extensive analysis of the astrophysical sources of background error. These include variable stars, flare events, and comets or asteroids which are moving through the Kepler field. We discuss the potential of detecting comets using the Kepler lightcurves, presenting measurements of two known comets and one unidentified object, most likely an asteroid or comet. After removing the background events with statistical cuts, we find no microlensing candidates. We therefore present our Monte Carlo efficiency calculation in order to constrain the PBH DM with masses in the range of 2 x 10^-9 solar masses to 10^-7 solar masses. We find that PBHs in this mass range cannot make up the entirety of the DM, thus closing a full order of magnitude in the allowed mass range for PBH DM.

Statistical Run-Time Verification of Analog Circuits in Presence of Noise and Process Variation

Noise and process variation present a practical limit on the performance of analog circuits. This paper proposes a methodology for modeling and verification of analog designs in the presence of shot noise, thermal noise, and process variations. The idea is to use stochastic differential equations to model noise in additive and multiplicative form and then combine process variation due to 0.18 μm technology in a statistical run-time verification environment. The efficiency of Monte-Carlo and Bootstrap statistical techniques are compared for a Colpitts oscillator and a phase locked loop-based frequency synthesizer circuit.

Monte Carlo and experimental efficiency calibration of gamma-spectrometers for non-destructive analysis of large volume samples of irregular shapes

A comparison of efficiency calibration of a HPGe gamma-ray spectrometer applied for non-destructive analysis of gamma-ray emitters in large volume samples of irregular shape is presented. The detector efficiency calibration was carried out during the analysis of cosmogenic radionuclides (60Co, 54Mn, 22Na and 26Al) in fragments of the Kosice meteorite. Fourteen meteorite fragments were available for the analysis with masses from 27 to 2,163 g. A reasonable agreement in the estimation of the HPGe detector efficiency was obtained using the Monte Carlo simulation GEANT 3 code, and the experimental calibration using radioactive standards mixed with iron–silica–copper powder housed in mock-ups of similar shapes as the original samples. The differences in the efficiency estimation obtained by both methods were within 10 %. It is recommended that the Monte Carlo simulation of the detector efficiency can be applied in routine analysis of gamma-ray emitters in large volume samples of regular or irregular shapes.

Estimating statistical uncertainty of Monte Carlo efficiency-gain in the context of a correlated sampling Monte Carlo code for brachytherapy treatment planning with non-normal dose distribution

Correlated sampling Monte Carlo methods can shorten computing times in brachytherapy treatment planning. Monte Carlo efficiency is typically estimated via efficiency gain, defined as the reduction in computing time by correlated sampling relative to conventional Monte Carlo methods when equal statistical uncertainties have been achieved. The determination of the efficiency gain uncertainty arising from random effects, however, is not a straightforward task specially when the error distribution is non-normal. The purpose of this study is to evaluate the applicability of the F distribution and standardized uncertainty propagation methods (widely used in metrology to estimate uncertainty of physical measurements) for predicting confidence intervals about efficiency gain estimates derived from single Monte Carlo runs using fixed-collision correlated sampling in a simplified brachytherapy geometry. A bootstrap based algorithm was used to simulate the probability distribution of the efficiency gain estimates and the shortest 95% confidence interval was estimated from this distribution. It was found that the corresponding relative uncertainty was as large as 37% for this particular problem. The uncertainty propagation framework predicted confidence intervals reasonably well; however its main disadvantage was that uncertainties of input quantities had to be calculated in a separate run via a Monte Carlo method. The F distribution noticeably underestimated the confidence interval. These discrepancies were influenced by several photons with large statistical weights which made extremely large contributions to the scored absorbed dose difference. The mechanism of acquiring high statistical weights in the fixed-collision correlated sampling method was explained and a mitigation strategy was proposed.

Comparative Monte Carlo efficiency by Monte Carlo analysis

We propose a modified power method for computing the subdominant eigenvalue λ{2} of a matrix or continuous operator. While useful both deterministically and stochastically, we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfunction. Accordingly, the methods must cancel these signs properly in order to sample this eigenfunction faithfully. We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing λ{2} of various Markov chain transition matrices. As |λ{2}| of this matrix controls the rate at which Monte Carlo sampling relaxes to a stationary condition, its computation also enabled us to compare efficiencies of several Monte Carlo algorithms as applied to two quite different types of problems. We first computed λ{2} for several one- and two-dimensional Ising models, which have a discrete phase space, and compared the relative efficiencies of the Metropolis and heat-bath algorithms as functions of temperature and applied magnetic field. Next, we computed λ{2} for a model of an interacting gas trapped by a harmonic potential, which has a mutidimensional continuous phase space, and studied the efficiency of the Metropolis algorithm as a function of temperature and the maximum allowable step size Δ. Based on the λ{2} criterion, we found for the Ising models that small lattices appear to give an adequate picture of comparative efficiency and that the heat-bath algorithm is more efficient than the Metropolis algorithm only at low temperatures where both algorithms are inefficient. For the harmonic trap problem, we found that the traditional rule of thumb of adjusting Δ so that the Metropolis acceptance rate is around 50% is often suboptimal. In general, as a function of temperature or Δ , λ{2} for this model displayed trends defining optimal efficiency that the acceptance ratio does not. The cases studied also suggested that Monte Carlo simulations for a continuum model are likely more efficient than those for a discretized version of the model.

Parameterization based on randomized quasi-Monte Carlo methods

We present a theoretical framework where any randomized quasi-Monte Carlo method can be viewed and analyzed as a parameterization method for parallel quasi-Monte Carlo. We present deterministic and stochastic error bounds when different processors of the computing environment run at different speeds. We implement two parameterization methods, both based on randomized quasi-Monte Carlo, and apply them to pricing digital options and collateralized mortgage obligations. Numerical results are used to compare the parameterization methods by their parallel performance as well as their Monte Carlo efficiency.

A new model calculation of the peak efficiency for HPGe detectors used in assays of radioactive waste drums

In this paper we present a new semi-empirical model calculation of the peak efficiency for unshielded HPGe detectors based on the virtual point detector and the attenuation factor concepts. The validity of the model calculation was checked by comparison with Monte Carlo efficiency values and experimental efficiencies determined for a HPGe detector type GEM 25P4 using a calibration drum. The discrepancy between experimental and calculated efficiencies is smaller than 10% in the energy range 122-1408 keV.

Assessment of the Replicate Compression Heuristic to Improve Efficiency of Urban Water Supply Headworks Optimization

Urban water supply headworks systems are usually designed to provide high security against drought. The best way to evaluate this security is to use Monte Carlo simulation which is computationally expensive. The advent of parallel computing technology in conjunction with genetic algorithms has made it practicable to optimize operation for drought security. Nonetheless, computation turnaround times remain long. This paper presents a simple heuristic called replicate compression to improve Monte Carlo efficiency. It exploits the well known concept of a critical period. In a high reliability system there should be few critical periods. Therefore, restricting simulation to such periods should bring about substantial savings in computational effort. It was found for problems where the objective function evaluation is only affected by what happens during critical periods, replicate compression provides an effective means for substantially reducing simulation effort. The case study involving a nine-reservoir urb...