Monte Carlo

The evaluation of uncertainties according to the ""Guide to the Expression of Uncertainty in Measurement"" is presented in this study based on a novel Fuzzy-random-variables approach. Whereas the classically proposed methods like Monte Carlo techniques treat all uncertainties as having a random nature, the fuzzy technique distinguishes between aleatoric and epistemic uncertainties. The aleatoric components are modeled in a Monte Carlo framework, and the epistemic uncertainties were treated with fuzzy techniques. The applied procedure is outlined showing both the theory and a numerical example for the evaluation of uncertainties in an application for terrestrial laserscanning.

We present a continuous extension of the recent Monte Carlo entropic method for sampling a density of states restricted in dimensionless macroscopic parameters. The method performs a random walk through a two-dimensional macrostate space and provides complete ...

Lead-210 assay and dating are subject to several sources of error, including natural variation, the statistical nature of measuring radioactivity, and estimation of the supported fraction. These measurable errors are considered in calculating confidence intervals for 210Pb dates. Several sources of error, including the effect of blunders or misapplication of the mathematical model, are not included in the quantitative analysis.

A numerical strategy for the efficient estimation of set-valued failure probabilities, coupling Monte Carlo with optimization methods, is presented in this paper. The notion of uncertainty is generalized to include both aleatory and epistemic uncertainties, allowing to capture gaps of knowledge and scarcity of data. The proposed formulation of the generalized uncertainty model allows for sets of probability distribution functions, also known as credal sets, and sets of bounded variables. The developed Advanced Line Sampling method is combined with the generalized uncertainty model, in order to both speed up the reliability analysis, and provide a better estimate for the lower and upper bounds of the failure probability. The proposed strategy knocks down the computational barrier of computing interval failure probabilities, and reduces the cost of a robust reliability analysis by many orders of magnitude. The efficiency and applicability of the developed method is demonstrated via numerical examples. The solution strategy is integrated into the open-source software for uncertainty quantification and risk analysis OPENCOSSAN, allowing its application on large-scale engineering problems as well as broadening its spectrum of applications.

It is a well known fact that the neutron diffusion theory fails in the vicinity of strongly absorbing media, such as the control rods. This failure is much more pronounced in the PBMR because the location of control rods in the side reflector adds a directional dependence to the flux, and this complicates the problem further. Reactor control and safety can only be ensured if control rod worths are accurately predicted. In this work a thorough evaluation of different control rod models is performed by constructing an approximate two-dimensional (2D) model adopting the so-called grey curtain and this is compared to full 3D deterministic transport model. Both these models are compared to an explicit MCNP model. It is shown in this study that it is possible to have an accurate 2D model of control rods, utilizing appropriate equivalent cross sections and applying them to a control rod grey curtain. Further, this paper also shows that it is possible to obtain reasonably accurate control r...

We discuss two numerical techniques, based on the path integral approach described in a previous paper, for solving the stochastic equations underlying the financial markets: the path integral Monte Carlo, and the path integral deterministic evaluation. In particular, we apply the latter to some specific financial problems: the pricing of a European option, a zero-coupon bond, a caplet, an American option, and a Bermudan swaption.

In recent years, a variety of approaches to deriving sediment quality guidelines have been developed. One approach relies on establishing an empirical relationship between the concentration of a contaminant in sediment and the condition of some biological indicator, for example, combining measured sediment concentrations of contaminants combined with data on colocated benthic species to measure in situ community effects of contamination. Biological threshold concentrations derived in this manner are being considered or have already been adopted by some regulatory agencies as a means for deriving sediment guidelines (e.g., Canada's Provincial Sediment Quality Guidelines). In order to test the validity of this method, we constructed several Monte Carlo simulations to illustrate that the methodology used to develop these guidelines is flawed by the effects of sampling and statistical artifacts that emerge from undersampling a lognormal density function. As a case study, this paper will present the screening level concentration method used by the Ontario Ministry of the Environment (Toronto, ON, Canada) and provide the results of several probabilistic exercises highlighting these issues. We present a word of caution on the applicability of methods that rely exclusively on statistical and mathematical relationships between invertebrate data and sediment concentrations to derive sediment quality guidelines.

The results are presented for an experiment that compares the difference between a one- and two-step reaction setup using 1 GeV protons. The rates of production from an on-line isotope separator target containing UCx are measured for isotopes in the neutron mass region of Rb and Cs. Some details about the measured results and predictions by the Monte Carlo models are discussed. The effects of the delayed release on the extracted efficiency are generalized using analytical models for application to a wide range of nuclear decay lifetimes.