Combining Monte Carlo Simulations Research Articles

Integrated probabilistic analysis of nuclear power plant building damage due to an aircraft crash

In order to ensure that nuclear power plant buildings are reliable and safe in case of external loading, it is very important to evaluate uncertainties associated with loads, material properties, geometrical parameters, boundaries and other parameters. Therefore, a probability-based analysis was developed as the integration of deterministic and probabilistic methods using existing state-of-the-art software. The subject of this paper is the integrated analysis of building failure due to impact by a commercial aircraft. The Monte Carlo Simulation, First-Order Reliability and the combined Monte Carlo Simulation and Response Surface methods were used for the probabilistic analyses. During an aircraft crash, the dynamic impact loading is uncertain. Therefore a relation expressed by the probability of failure of impacted wall and loading function was determined. With failure defined as concrete cracking and rebar rupture, the failure probabilities of the impacted wall were calculated as a function of the peak impact load. The integrated deterministic and probabilistic analysis approach was applied to the Ignalina Nuclear Power Plant in Lithuania. The conclusions from this analysis was that a through-the-wall crack in the concrete element of a plant wall may occur with a probability of 0.0266, but the failure probability of the reinforcement bars is very small, that is, near zero. Thus, no perforation of the impacted wall by structures of the aircraft should occur. The importance of performing a probabilistic analysis of crash events is shown by comparing results to those obtained by a mean value deterministic approach.

Stochastic finite-element modelling and optimization for net-shape forging of three-dimensional aero-engine blades

The stochastic nature of the forging process is a key influencing factor for achievable dimensional and shape accuracy of forged aerofoil blades for aero-engine applications. In this article, a finite-element-based stochastic modelling and optimization method is presented for net-shape forging of three-dimensional (3D) aerofoil blades. A combined Monte Carlo simulation and response surface method as well as the first-order second-moment reliability method are developed to quantify the stochastic characteristics of forging errors due to uncertainties of process parameters and forging conditions. A two-step optimization approach is presented to minimize systematic errors using a direct compensation method and to reduce random variations through a variance control procedure. A 3D blade forging case study is presented to evaluate the stochastic characteristics of the dimensional errors of forged aerofoil blades in comparison with measurement data and to demonstrate much improved forging accuracy using the proposed stochastic optimization method. The results from the case study also suggest that the stochastic-based optimization method may be easily applied to other metal-forming processes.

Stochastic finite-element modelling and optimization for net-shape forging of three-dimensional aero-engine blades

The stochastic nature of the forging process is a key influencing factor for achievable dimensional and shape accuracy of forged aerofoil blades for aero-engine applications. In this article, a finite-element-based stochastic modelling and optimization method is presented for net-shape forging of three-dimensional (3D) aerofoil blades. A combined Monte Carlo simulation and response surface method as well as the first-order second-moment reliability method are developed to quantify the stochastic characteristics of forging errors due to uncertainties of process parameters and forging conditions. A two-step optimization approach is presented to minimize systematic errors using a direct compensation method and to reduce random variations through a variance control procedure. A 3D blade forging case study is presented to evaluate the stochastic characteristics of the dimensional errors of forged aerofoil blades in comparison with measurement data and to demonstrate much improved forging accuracy using the proposed stochastic optimization method. The results from the case study also suggest that the stochastic-based optimization method may be easily applied to other metal-forming processes.

Determination of the phase diagram from interatomic potentials: The iron–chromium case

Prior to applying any interatomic potential, it is important to know the stability of the different phases it describes. In the literature many methods to determine the phase diagram from an interatomic potential are described. Although for pure elements the procedure to obtain the thermodynamic functions is well established, for alloys it is not. In this work a method is developed to determine the phase diagram, i.e., solubility limits and spinodal gap, for the case of miscibility gaps. The method combines Monte Carlo simulations in the isobaric semi-grand canonical ensemble, full thermodynamic integration and Redlich–Kister expansions to parameterize the Gibbs free energy. Besides numerical inaccuracies, this method does not rely on any physical approximations to determine the phase diagram of a given interatomic potential. The method is applied to two different Fe–Cr potentials that are widely used in the literature. The resulting phase diagrams are discussed by comparing them to the experimental one and ones obtained in other works from the same potentials.

Theoretical Investigation of Grain Size Tuning during Prolonged Bias-Enhanced Nucleation

In this paper, the effects of prolonged bias-enhanced nucleation (“prolonged BEN”) on the growth mechanisms of diamond are investigated by molecular dynamics (MD) and combined MD-Metropolis Monte Carlo (MD-MMC) simulations. First, cumulative impacts of CxHy+ and Hx+ on an a-C:H/nanodiamond composite were simulated; second, nonconsecutive impacts of the dominant ions were simulated in order to understand the observed phenomena in more detail. As stated in the existing literature, the growth of diamond structures during prolonged BEN is a process that takes place below the surface of the growing film. The investigation of the penetration behavior of CxHy+ and Hx+ species shows that the carbon-containing ions remain trapped within this amorphous phase where they dominate mechanisms like precipitation of sp3 carbon clusters. The H+ ions, however, penetrate into the crystalline phase at high bias voltages (>100 V), destroying the perfect diamond structure. The experimentally measured reduction of grain sizes at high bias voltage, reported in the literature, might thus be related to penetrating H+ ions. Furthermore, the CxHy+ ions are found to be the most efficient sputtering agents, preventing the build up of defective material.

Experimental study of the response of CZT and CdTe detectors of various thicknesses in strong magnetic field

Abstract In this paper, we used a combined experimental and Monte Carlo simulation approach to investigate the detailed charge collection process within thick CdTe/CZT detectors operated inside a strong magnetic field. As one of the key objectives, we quantitatively assessed the effect of the Lorenz force on the migration of charge carriers inside the detector bulk. This information would allow an accurate modeling of the detector's response to gamma ray interactions and therefore help to compensate for the event-positioning error induced by the strong magnetic field. In this study, a pixilated ERPC detector with 350 μm square pixels was set on a non-magnetic gantry and operated inside a 3 T Siemens MRI scanner. Multiple studies, with similar geometries, were performed using the same detector setup with and without the presence of the magnetic field to investigate the effect on the charge collection behavior from the strong magnetic field. The experimental results were used to validate the Monte Carlo simulation package that models both photon transportation and charge collection process inside the detector.

Hybrid MC−DFT Method for Studying Multidimensional Entropic Forces

Entropic force has been a focus of many recent theoretical studies because of its fundamental importance in solution thermodynamics and its close relevance to a broad range of practical applications. Whereas previous investigations are mostly concerned with the potential energy as a one-dimensional function of the separation, here we propose a hybrid method for studying multidimensional systems by combining Monte Carlo simulation for the microscopic configurations of the solvent and the density functional theory for the free energy. We demonstrate that the hybrid method predicts the potential of mean force between a test particle and various concave objects in a hard-sphere solvent in excellent agreement with the results from alternative but more expensive computational methods. In particular, the hybrid method captures the entropic force between asymmetric particles and its dependence on the particle size and shape that underlies the "lock and key" interactions. Because the same molecular model is used for the theory and simulation, we expect that the hybrid method provides a new avenue to efficient computation of entropic forces in complex molecular systems.

Dealing with multi-factor uncertainty in electricity markets by combining Monte Carlo simulation with spatial interpolation techniques

Electricity markets are characterised by uncertainty that has an important influence on the behaviour of the agents. Demand, fuel costs, CO2 prices or hydro conditions are examples of sources of uncertainty. Electricity market models are useful tools to support agents’ decision-making process and, therefore should consider this uncertainty. Monte Carlo simulation is a common method to incorporate the uncertainty. However, Monte Carlo simulation requires a large number of realisations of the model, which usually entails huge computational time and effort. In this study, an efficient method to cope with this drawback is described, allowing one to obtain a large number of realisations reducing the computational time and effort. The method is based on a spatial interpolation technique. The obtained results confirm that the comparison between the intensive computation and the interpolation of realisations does not show relevant differences. Additionally, the computational time is significantly reduced.

Combining Monte Carlo Simulations and Options to Manage the Risk of Real Estate Portfolios

Combining Monte Carlo Simulations and Options to Manage the Risk of Real Estate Portfolios

Monte Carlo modeling of time-resolved fluorescence for depth-selective interrogation of layered tissue

Computational approaches for simulation of light–tissue interactions have provided extensive insight into biophotonic procedures for diagnosis and therapy. However, few studies have addressed simulation of time-resolved fluorescence (TRF) in tissue and none have combined Monte Carlo simulations with standard TRF processing algorithms to elucidate approaches for cancer detection in layered biological tissue. In this study, we investigate how illumination-collection parameters (e.g., collection angle and source–detector separation) influence the ability to measure fluorophore lifetime and tissue layer thickness. Decay curves are simulated with a Monte Carlo TRF light propagation model. Multi-exponential iterative deconvolution is used to determine lifetimes and fractional signal contributions. The ability to detect changes in mucosal thickness is optimized by probes that selectively interrogate regions superficial to the mucosal–submucosal boundary. Optimal accuracy in simultaneous determination of lifetimes in both layers is achieved when each layer contributes 40–60% of the signal. These results indicate that depth-selective approaches to TRF have the potential to enhance disease detection in layered biological tissue and that modeling can play an important role in probe design optimization.

Origin of ultrafast annihilation effect of martensite aging: Atomistic simulations

Martensite aging effects, e.g., martensitic stabilization and rubberlike behavior, have attracted considerable attention in the past decades. It is known that martensite aging effects can be quickly eliminated once the aged martensite is brought into the parent phase even for a very short time, i.e., the annihilating effect of martensite aging (AEMA). However, the underlying mechanism of AEMA remains unclear due to the lack of an effective tool to probe the atomic processes during AEMA. It is unclear (1) whether AEMA is caused by a mere diffusionless transformation into the parent phase or by a diffusional process in the parent phase and (2) why long-time aging in martensite can be so easily eliminated in the parent phase. In this paper we use combined molecular-dynamics and Monte Carlo simulations to show that the origin of AEMA is related to atomic diffusion in the parent phase, not merely the reverse phase transformation. The open structure in the B2 parent phase and high-temperature result in a significantly higher diffusivity of point defects in the parent phase compared with that in the martensite; this explains the ultrafast annihilation of martensite aging. We attribute the driving force of AEMA to the symmetry-conforming short-range ordering tendency of point defects.

Conformational Flexibility of Chitosan: A Molecular Modeling Study

Chitin and chitosan are naturally occurring polysaccharides composed of β-(1,4) linked N-acetylglucosamine units (GlcNAc) and, for chitosan, also glucosamine units (GlcN). In recent years, chitosan has attracted much interest because of its special physical and chemical properties related to drug delivery, wound healing, and tissue engineering. However, limited structural knowledge is available for chitosan because of its composition of the randomly mixed building blocks, GlcNAc and GlcN. In this study, we present exhaustive combined molecular dynamics and Monte Carlo simulations that unravel the conformational flexibility of the β-(1,4)-linkage in di-, tri-, and tetrasaccharide models of chitin and chitosan. The most flexible disaccharide unit was found to be GlcN-GlcNAc, populating four conformations. Furthermore, it is found that the conformational freedom of a glycosidic bond is independent of the flexibility of the neighboring linkages along the oligomer. The results are interpreted with respect to hydrogen bond formation and implications for polymer properties.

Energy transport analysis in ultrashort pulse laser ablation through combined molecular dynamics and Monte Carlo simulation

Mechanisms of energy transport during ultrashort laser pulses (USLPs) ablation are investigated in this paper. Nonequilibrium electron-transport, material ionization, as well as density change effects, are studied using atomistic models---the molecular dynamics (MD) and Monte Carlo (MC) methods, in addition to the previously studied laser absorption, heat conduction, and stress wave propagation. The target material is treated as consisting of two subsystems: valence-electron system and lattice system. MD method is applied to analyze the motion of atoms while MC method is applied for simulating electron dynamics and multiscattering events between particles. Early-time laser-energy absorption and redistribution as well as later-time material ablation and expansion processes are analyzed. This model is validated in terms of ablation depth, lattice/electron temperature distribution as well as evolution, and plume front velocity, through comparisons with experimental or theoretical results in literature. It is generally believed that the hydrodynamic motion of the ablated material is negligible for USLP but this study shows it is true only for its effect on laser-energy deposition. This study shows that the consideration of hydrodynamic expansion and fast density change in both electron and lattice systems is important for obtaining a reliable energy transport mechanism in the locally heated zone.

Novel MOF‐Membrane for Molecular Sieving Predicted by IR‐Diffusion Studies and Molecular Modeling

The predicted permeation selectivity of a binary gas mixture for a metal-organic framework ZIF-8 membrane was estimated from combined Grand Canonical Monte Carlo (GCMC) simulations and infrared microscopy (IRM) data and compared with permeation measurements on a ZIF-8 membrane. It is shown that membrane selectivity can be predicted and hence porous materials can be preselected for membrane applications thus saving time and effort in R&D.

Significance of higher moments for complete characterization of the travel time probability density function in heterogeneous porous media using the maximum entropy principle

The travel time formulation of advective transport in heterogeneous porous media is of interest both conceptually, e.g., for incorporating retention processes, and in applications where typically the travel time peak, early, and late arrivals of contaminants are of major concern in a regulatory or remediation context. Furthermore, the travel time moments are of interest for quantifying uncertainty in advective transport of tracers released from point sources in heterogeneous aquifers. In view of this interest, the travel time distribution has been studied in the literature; however, the link to the hydraulic conductivity statistics has been typically restricted to the first two moments. Here we investigate the influence of higher travel time moments on the travel time probability density function (pdf) in heterogeneous porous media combining Monte Carlo simulations with the maximum entropy principle. The Monte Carlo experimental pdf is obtained by the adaptive Fup Monte Carlo method (AFMCM) for advective transport characterized by a multi‐Gaussian structure with exponential covariance considering two injection modes (in‐flux and resident) and lnK variance up to 8. A maximum entropy (MaxEnt) algorithm based on Fup basis functions is used for the complete characterization of the travel time pdf. All travel time moments become linear with distance. Initial nonlinearity is found mainly for the resident injection mode, which exhibits a strong nonlinearity within first 5IY for high heterogeneity. For the resident injection mode, the form of variance and all higher moments changes from the familiar concave form predicted by the first‐order theory to a convex form; for the in‐flux mode, linearity is preserved even for high heterogeneity. The number of moments sufficient for a complete characterization of the travel time pdf mainly depends on the heterogeneity level. Mean and variance completely describe travel time pdf for low and mild heterogeneity, skewness is dominant for lnK variance around 4, while kurtosis and fifth moment are required for lnK variance higher than 4. Including skewness seems sufficient for describing the peak and late arrivals. Linearity of travel time moments enables the prediction of asymptotic behavior of the travel time pdf which in the limit converges to a symmetric distribution and Fickian transport. However, higher‐order travel time moments may be important for most practical purposes and in particular for advective transport in highly heterogeneous porous media for a long distance from the source.

FAST VALUATION OF FORWARD-STARTING BASKET DEFAULT SWAPS

A basket default swap (BDS) is a credit derivative with contingent payments that are triggered by a combination of default events of the reference entities. A forward-starting basket default swap (FBDS) is a BDS starting at a specified future time. Existing analytic or semi-analytic methods for pricing FBDS are time consuming due to the large number of possible default combinations before the BDS starts. This paper develops a fast approximation method for FBDS based on the conditional independence framework. The method converts the pricing of a FBDS to an equivalent BDS pricing problem and combines Monte Carlo simulation with an analytic approach to achieve an effective method. This hybrid method is a novel technique which can be viewed either as a means to accelerate the convergence of Monte Carlo simulation or as a way to estimate parameters in an analytic method that are difficult to compute directly. Numerical results demonstrate the accuracy and efficiency of the proposed hybrid method.

Study of the optical and magnetic properties of pyrimidine in water combining PCM and QM/MM methodologies

The solvent effects on the low-lying absorption spectrum and on the (15)N chemical shielding of pyrimidine in water are calculated using the combined and sequential Monte Carlo simulation and quantum mechanical calculations. Special attention is devoted to the solute polarization. This is included by an iterative procedure previously developed where the solute is electrostatically equilibrated with the solvent. In addition, we verify the simple yet unexplored alternative of combining the polarizable continuum model (PCM) and the hybrid QM/MM method. We use PCM to obtain the average solute polarization and include this in the MM part of the sequential QM/MM methodology, PCM-MM/QM. These procedures are compared and further used in the discrete and the explicit solvent models. The use of the PCM polarization implemented in the MM part seems to generate a very good description of the average solute polarization leading to very good results for the n-π* excitation energy and the (15)N nuclear chemical shield of pyrimidine in aqueous environment. The best results obtained here using the solute pyrimidine surrounded by 28 explicit water molecules embedded in the electrostatic field of the remaining 472 molecules give the statistically converged values for the low lying n-π* absorption transition in water of 36 900 ± 100 (PCM polarization) and 36 950 ± 100 cm(-1) (iterative polarization), in excellent agreement among one another and with the experimental value observed with a band maximum at 36 900 cm(-1). For the nuclear shielding (15)N the corresponding gas-water chemical shift obtained using the solute pyrimidine surrounded by 9 explicit water molecules embedded in the electrostatic field of the remaining 491 molecules give the statistically converged values of 24.4 ± 0.8 and 28.5 ± 0.8 ppm, compared with the inferred experimental value of 19 ± 2 ppm. Considering the simplicity of the PCM over the iterative polarization this is an important aspect and the computational savings point to the possibility of dealing with larger solute molecules. This PCM-MM/QM approach reconciles the simplicity of the PCM model with the reliability of the combined QM/MM approaches.

FRET Fluctuation Spectroscopy of Diffusing Biopolymers: Contributions of Conformational Dynamics and Translational Diffusion

The use of fluorescence correlation spectroscopy (FCS) to study conformational dynamics in diffusing biopolymers requires that the contributions to the signal due to translational diffusion are separated from those due to conformational dynamics. A simple approach that has been proposed to achieve this goal involves the analysis of fluctuations in fluorescence resonance energy transfer (FRET) efficiency. In this work, we investigate the applicability of this methodology by combining Monte Carlo simulations and experiments. Results show that diffusion does not contribute to the measured fluctuations in FRET efficiency in conditions where the relaxation time of the kinetic process is much shorter than the mean transit time of the molecules in the optical observation volume. However, in contrast to what has been suggested in previous work, the contributions of diffusion are otherwise significant. Neglecting the contributions of diffusion can potentially lead to an erroneous interpretation of the kinetic mechanisms. As an example, we demonstrate that the analysis of FRET fluctuations in terms of a purely kinetic model would generally lead to the conclusion that the system presents complex kinetic behavior even for an idealized two-state system.

Estimation of survival probability for a ship in beam seas using the safe basin

The purpose of this paper is to analyze the nonlinear ship roll motion equation and the main parameters that induce ship capsizing in beam seas, estimate the survival probability of a ferry in random seas and to find out a risk assessment method for the ship’s intact stability. A single degree of freedom (1-DOF) dynamic system of ship rolling in beam seas is investigated and the nonlinear differential equation is solved in the time domain by the fourth order Runge–Kutta algorithm. The survival probability of a ferry in beam seas is investigated using the theory of “safe basin”. The survival probability is calculated by estimating erosion of “safe basin” during ship rolling motion by Monte Carlo simulations. From the results it can be concluded that the survival probability of a ship in beam sea condition can be predicted by combining Monte Carlo simulations and the theory of “safe basin”.

Real option value and random jumps: application of a simulation model

This article studies how sensitive real option valuations are to incorrect assumptions about the stochastic process followed by the state variables. We design a valuation model which combines Monte Carlo simulation and dynamic programming and provides an appropriate framework to evaluate the effect of estimation errors on both the value of real options and their critical frontier. Although the model is flexible enough to value American-type options contingent on a wide range of stochastic processes, we focus on the analysis of the effect of stochastic jumps. We apply our model to the valuation of an investment in the car parts industry documented in previous literature. Our results clearly show that underestimating this type of jumps might lead to substantial misjudgements in a firm's decision-making processes. For instance, it may lead to profitable projects being rejected when jump diffusion is low, or negative expanded net present value projects being accepted.