Monte Carlo Perturbation Research Articles

Temperature perturbation method using on-the-fly treatment of the cross-sections in the resolved resonance region

A negative fuel temperature reactivity coefficient is an important reactor physical parameter that indicates the inherent reactor operating safety. However, existing Monte Carlo perturbation methods still cannot accurately and efficiently predict the derivative of the k-eigenvalue with respect to temperature. The main difficulty lies in calculating the derivatives of the microscopic cross-section with respect to the temperature. This paper presents a Temperature Perturbation Method (TPM) that incorporates on-the-fly cross-section treatment as well as the free gas model into the differential operator method to calculate derivatives of the k-eigenvalue with respect to fuel temperature. TPM was then used to predict the k-eigenvalue at various temperatures for the Mosteller pin model. The differences between TPM and the direct difference method are less than 3% within 3 times of standard deviation. The results indicate that TPM can accurately and efficiently estimate the derivatives of the k-eigenvalue with respect to the fuel temperature.

Exact Monte Carlo calculation method for K-eigenvalue change using perturbation source method

ABSTRACT The ‘perturbation source method’ (PSM) is a Monte Carlo perturbation method that calculates an exact k-eigenvalue change caused by cross-section changes. Although the PSM, which can consider the effect of fission source perturbation, was proposed long ago, it has garnered minimal interest as a Monte Carlo perturbation method. The applicability of the PSM has not been thoroughly elucidated hitherto. This study revisits the PSM and reviews the associated Monte Carlo algorithm. Some improvements have been made to improve the efficiency. The PSM is applied to some numerical tests that involve the replacement of a fuel material with light water, a density change in a water hole, an interface shift between a fuel and reflector, and an external boundary extension. The performance of the PSM for these tests is compared with that of another exact Monte Carlo perturbation method, which is the correlated sampling method. The PSM can yield an accurate k-eigenvalue change even for large cross-section changes such as the replacement of a material with another material. The PSM used in this study is the exact method except for the approximation related to the spatial discretization for fission source perturbation. Furthermore, it exhibits superiority in terms of accuracy and computational efficiency, particularly for large perturbations added in a small region.

A Polynomial Chaos-based Approach to Quantify Uncertainties of Correlated Renewable Energy Sources in Voltage Regulation

Renewable energy sources (RESs) and flexible loads have introduced significant uncertainties in the operation and control of power systems especially voltage regulation at the distribution system level. Assessing the impacts of uncertainties on power system behavior and response has become a key factor for modern power system operation and planning. Although several probabilistic methods have been used for quantifying uncertainties such as Monte Carlo simulation and perturbation techniques, they are computationally expensive and cannot be directly embedded in power system models. Also, the existence of more than one source of randomization requires complicated correlation models via intensive statistical approaches. To overcome the aforementioned challenges, this article proposes a generalized polynomial chaos (gPC) based approach to quantify the impacts of uncertainties resulting from RESs and load variations on voltage magnitudes of distribution systems through propagating uncertainties in the system under study. In the gPC, the behavior of each random variable is transformed into a series of orthogonal polynomials that can be easily evaluated. A correlation matrix is calculated and used to estimate the proper values of each RES. The proposed method is implemented on several systems including the IEEE 13-node, the IEEE 123-node, the 240-node, and the 8500-node distribution systems integrated with solar and wind energy sources at various locations. The results show that the proposed algorithm provides high efficiency and significant reduction in computation time in comparison with Monte Carlo simulation.

Stability Evaluation of the SDRE Technique based on Java in a CubeSat Attitude and Orbit Control Subsystem

In 2013, the STRaND (University of Surrey and Surrey Satellite Technology Ltd) and the PhoneSat (NASA) programs attracted the attention of the aerospace community applying commercial off-the-shelf smartphones in CubeSats. Both programs deployed CubeSats using smartphones based on Google's Android, in which application development is mainly based on Java programming language. Some of these CubeSats had actuators, e.g., STRaND-1 had three reaction wheels mounted in an orthogonal configuration to provide three-axis control, whereas PhoneSat 2.0 beta had magnetorquers to de-tumble the spacecraft. Taking into account a CubeSat that runs Android operating system (based on a smartphone), it is natural to evaluate the attitude and orbit control subsystem (AOCS) based on Java. Elsewhere, we shown State-Dependent Riccati Equation (SDRE) is a feasible non-linear control technique that can be applied in such CubeSats using Java. Moreover, we shown, through simulation using a Monte Carlo perturbation model, SDRE provides better performance than the PID controller, a linear control technique. In this paper, we tackle the next fundamental problem: stability. We evaluate stability from two perspectives: (1) parametric uncertainty of the inertia tensor and (2) a Monte Carlo perturbation model based on a uniform attitude probability distribution. Through the combination of these two perspectives, we grasp the stability properties of SDRE in a broader sense. In order to handle the uncertainty appropriately, we combine SDRE with H∞. The Nanosatellite Constellation for Environmental Data Collection (CONASAT), a CubeSat from the Brazilian National Institute for Space Research (INPE), provided the nominal parameters for the simulations. The initial results of the simulations shown that the SDRE controller is stable to ± 20% uncertainty in the inertia tensor for attitudes uniformly distributed and angular velocity up to 0.15 radians/second.

Monte Carlo perturbation calculation for geometry change in fixed source problems with the perturbation source method

The perturbation source method (PSM), which is a Monte Carlo perturbation calculation method, is applied to geometry changes in fixed-source neutron transport problems. In PSM, perturbation particles that represent the flux difference due to the changes in geometry are explicitly tracked within the perturbed system. A perturbation calculation for geometry change can be performed by replacing the material in a perturbed region with the material that occupies the adjoining region beyond the geometry change. The efficiency of the PSM can be enhanced by adding a pseudo-scattering cross section to the perturbed region. For geometry changes where the perturbed region is small, PSM exhibits excellent performance compared to the two independent runs before and after the perturbation if optimized pseudo-scattering cross sections are used. This method can also be applied to perturbation due to an external boundary change. Although the correlated sampling method (CS) is another available Monte Carlo method for geometry change, PSM largely outperforms CS in terms of computational efficiency for the numerical examples tested in this study.

Potentiality of carbon nanotube to encapsulate some alkylating agent anticancer drugs: a molecular simulation study

Encapsulation of chlorambucil, cyclophosphamide, and melphalan with (9,9) carbon nanotube was investigated in aqueous solution. The structures were modeled in gas phase applying density functional calculations. Then, solvation free energies and association free energies of considered structures in water were studied by Monte Carlo simulation and perturbation method. Outcomes of gas phase study revealed that all three drugs can encapsulate into carbon nanotube. Monte Carlo simulation results showed that electrostatic interactions play a crucial role in the intermolecular energies after encapsulation in aqueous media. It is found that among three drugs, solvation free energy of chlorambucil was increased after encapsulation. Moreover, solvation of carbon nanotube was enhanced after encapsulation of drugs which improve the pharmaceutical applications. Calculated association free energies indicated that chlorambucil–carbon nanotube was the only stable encapsulated drug in aqueous solution.

Monte Carlo simulated beam quality and perturbation correction factors for ionization chambers in monoenergetic proton beams.

Beam quality correction factors provided in current codes of practice for proton beams are approximated using the water-to-air mass stopping power ratio and by assuming the proton beam quality related perturbation correction factors to be unity. The aim of this work is to use Monte Carlo simulations to calculate energy dependent beam quality and perturbation correction factors for a set of nine ionization chambers in proton beams. The Monte Carlo code EGSnrc was used to determine the ratio of the absorbed dose to water and the absorbed dose to the sensitive air volume of ionization chambers related to the reference photon beam quality (60 Co). For proton beams, the quantity was simulated with GATE/Geant4 for five monoenergetic beam energies between 70 MeV and 250MeV. The perturbation correction factors for the air cavity, chamber wall, chamber stem, central electrode, and displacement effect in proton radiation were investigated separately. Additionally, the correction factors of cylindrical chambers were investigated with and without consideration of the effective point of measurement. The perturbation factors were shown to deviate from unity for the investigated chambers, contradicting the assumptions made in dosimetry protocols. The beam quality correction factors for both plane-parallel and cylindrical chambers positioned with the effective point of measurement at the measurement depth were constant within 0.8%. An increase of the beam quality correction factors determined for cylindrical ionization chambers placed with their reference point at the measurement depth with decreasing energy is attributed to the displacement perturbation correction factors , which were up to 1.045±0.1% for the lowest energy and 1.005±0.1% for the highest energy investigated. Besides , the largest perturbation was found for the chamber wall where the smallest determined was 0.981±0.3%. Beam quality correction factors applied in dosimetry with cylindrical chambers in monoenergetic proton beams strongly depend on the positioning method used. We found perturbation correction factors different from unity. Consequently, the approximation of ionization chamber perturbations in proton beams by the respective water-to-air mass stopping power ratio shall be revised.

Uncertainty quantification and sensitivity studies on Thorium-fueled reactors

This paper shows how Total Monte Carlo (TMC) method and Perturbation Theory (PT) can be applied to quantify uncertainty due to nuclear data on reactor static calculations of integral parameters such as keff and βeff. This work focuses on thorium fueled reactors and it aims to rank different cross sections uncertainty regarding criticality calculations. The consistency of the two methods are first studied. The cross sections set used for the TMC method is computed to build adequate correlation matrices. Those matrices are then multiplied by the sensitivity coefficients obtained thanks to the PT to obtain global uncertainties that are compared to the ones calculated by the TMC method. Results in good agreement allow us to use correlation matrix from the state of the art nuclear data library (JEFF 3-3) that provide insight of uncertainty on keff and βeff for thorium fueled Pressurized Water Reactors. Finally, maximum uncertainties on cross sections are estimated to reach a target uncertainty on integral parameters. It is shown that a strong reduction of the current uncertainty is needed and consequently, new measurements and evaluations have to be performed.

Monte Carlo simulations and perturbation theory for highly correlated fluids: The Lennard-Jones core softened potential case

The growing interest in anomalous thermodynamic properties of isotropic fluids has been followed by several attempts to implement an accurate and simple theoretical description of these phenomena. Here, we have performed an extensive Monte Carlo exploration of the thermodynamic properties and vapor-liquid equilibrium of the Lennard-Jones core softened potential with variable Gaussian tail strengths λ spanning fluids with short range attraction and long range repulsion to those with short range repulsion and long range attraction. The results have been compared with the theoretical framework provided by the Barker and Henderson perturbation theory evaluated at longer ranges than those usually employed in the literature. The correlation in close shells particles is also incorporated in an empirical way. The agreement between the theoretical approach and the simulation results are in quantitative agreement in most cases, but worsens when the Gaussian tail is deep enough to provoke substantial modifications in the fluid structure. These structured radial distribution functions differ from those of typical atomic fluids in the liquid state and are mainly responsible of the inaccuracy of the perturbative approach for quantitative purposes. Despite this drawback, we have successfully applied the theoretical treatment for predicting anomalies in fluid models that are in agreement with those reported in the literature. These results open the door for a wide use of perturbative treatments for predicting fluid anomalies if care is taken of the range of the perturbative approach and of the particle correlation within neighboring shells.

Dynamic load identification of stochastic structures based on unscented transformation

In view of some unknown parameters in structures, which are described by the Gaussian distribution model in this paper, a new dynamic load identification method for stochastic structures is proposed based on unscented transformation (UT). Firstly, the convolution equation for solving structural response is discretized, and the sampling points, namely, sigma points of stochastic parameters are calculated according to the unscented transformation. Then, when the stochastic parameters take each sigma point, the dynamic load is calculated by the direct inversion method combined with the regularization method. Finally, the mean value and standard deviation of the identified load are obtained, and the coefficient of variation and the upper and low bounds of the identified load are defined. The result of an example shows that compared with the Monte Carlo simulation (MCS) and perturbation method (PM), the proposed method has higher computational efficiency and accuracy.

Information and Inequality

This paper studies wealth inequality in a Blanchard/Yaari model with idiosyncratic investment returns. Its key innovation is to assume that individuals can buy information. Information reduces uncertainty about the unknown mean investment return. Reduced estimation risk encourages investment in higher yielding risky assets. As a result, endogenous information acquisition amplifies wealth inequality. Wealthy individuals buy more information, which leads them to invest a higher share of their wealth in higher yielding assets, which then makes them even wealthier. The model's empirical implications are studied using Monte Carlo simulations and perturbation approximations. An empirically plausible decrease in information costs can explain about two-thirds of the observed increase in the top 1% wealth share.

State-dependent Riccati equation controller using Java in remote sensing CubeSats

STRaND and PhoneSat programs have attracted the attention of the aerospace community by applying, in CubeSats, commercial off-the-shelf smartphones based on Google’s Android. In Android, the development commonly applies Java hence this language is a natural candidate for the attitude and orbit control subsystem (AOCS). Moreover, such AOCS can be designed with success by linear control theory; however, the linearized models are not able to represent all the effects of the nonlinear terms present in the dynamics. Therefore, nonlinear control techniques can yield better performance. An example is the Nano-Satellite Constellation for Environmental Data Collection, used as the reference in this work, a set of remote sensing CubeSats from the Brazilian National Institute for Space Research, in which the AOCS must stabilize the satellite in three-axes. We present the investigation of a state-dependent Riccati equation (SDRE) controller, a nonlinear controller, based on attitude errors given by quaternions. The investigation uses Java, accordingly, it can run on an Android operating system in a CubeSat, and it has low cost. Two controllers (linear and SDRE) were evaluated using a Monte Carlo perturbation model. The initial results show that the SDRE controller provides better performance.

Time-resolved early-photon scheme for high-resolution fluorescence molecular tomography with perturbation Monte Carlo modeling: Experimental validations using a multichannel TCSPC system

In near-infrared fluorescence molecular tomography (FMT), high turbidity of biological tissue exerts severe adversity to image reconstruction. In contrast to highly diffusive photons, early-photons preserve a significant amount of spatial information, and thereby considerably improve image quality by reducing ill-posedness in inversion processes. However, light propagation of early-photons is hard to be accurately modeled by the mathematically simple diffusion equation (DE), and the rich information in the time-resolved (TR) measurements has not been effectively utilized in reconstruction with the traditional single-gate (SG) data type. In order to take an advantage of the early-photons in time-domain FMT for in-vivo imaging of small animals, we have proposed an early-photon FMT based on a perturbation Monte-Carlo (pMC) modeling and an overlap-delaying TR data type. In this method, the fluorescence Jacobians are generated by the pMC-based forward calculations with calibration by measured instrumental response function for each source-detector pair, and the measured time-of-flight distributions of excitation and emission light are averaged over time-gates for enhancing the noise robustness. The proposed early-photon FMT based on TR-pMC has been verified by phantom experiments, demonstrating improved image qualities, such as the spatial resolution, gray-scale resolution, quantitativeness, and peak signal-to-noise ratio when compared with the early-photon FMT based on TR-DE and SG-pMC.

Variational methods and speed-up of Monte Carlo perturbation computations for optimal design in nuclear systems

Seeking optimal material distribution in a nuclear system to maximize a response function of interest has been a subject of considerable interest in nuclear engineering. Examples are the optimal fuel distribution in a nuclear reactor core to achieve uniform burnup using minimum critical mass and the use of composite materials with an optimal mix of constituent elements in detection systems and radiation shielding. For such studies, variational methods have been found to be useful but, they have been used for standalone analyses often restricted to idealized models, while more elaborate design studies have required computationally expensive Monte Carlo simulations ill-suited to iterative schemes for optimization. Such an inherent disadvantage of Monte Carlo methods changed with the development of perturbation algorithms but, their efficiency is still dependent on the reference configuration for which a hit-and-trial approach is often used. In the first illustrative example, this paper explores the computational speedup for a bare cylindrical reactor core, achievable by using a variational result to enhance the computational efficiency of Monte Carlo design optimization simulation. In the second example, the effect of non-uniform material density in a fixed-source problem, applicable to optimal moderator and radiation shielding, is presented. While applications of this work are numerous, the objective of this paper is to present preliminary variational results as inputs to elaborate stochastic optimization by Monte Carlo simulation for large and realistic systems.

Monte Carlo perturbation methods using “virtual density” theory for calculating reactivity due to geometry change

The “virtual density” theory in the field of neutronics is a method to quantify reactivity of a reactor core due to geometry changes by altering the material density or nuclear cross section instead of explicitly changing the geometry. The Monte Carlo perturbation methods—differential-operator sampling (DOS) and correlated sampling (CS)—can efficiently yield accurate small reactivity for cross section changes. However, Monte Carlo perturbation methods have weakness in their inability to deal with geometry changes. This study incorporates the virtual-density theory into the Monte Carlo perturbation methods. When an entire core expands or swells uniformly, keff of the perturbed core can be calculated by simply changing the material density without changing the geometry. Regarding uniform expansion or swelling, conventional Monte Carlo perturbation methods—where cross sections change proportionally to the material density—can predict the altered keff. According to the virtual-density theory, keff perturbed due to a uniform anisotropic expansion or swelling can be predicted by stretching or shrinking the mean free path of neutrons in only one direction without changing the geometry. A new Monte Carlo algorithm is developed to incorporate the path length-stretching or -shrinking in only one direction into a random-walk process in a Monte Carlo keff-eigenvalue calculation. The new Monte Carlo algorithm provides accurate keff values for uniform anisotropic expansion and swelling regardless of the perturbation degree. New formulations of the Monte Carlo perturbation methods are derived to predict the change in keff due to a uniform anisotropic expansion or swelling. Both Monte Carlo perturbation methods can accurately and efficiently predict changes in keff for a small uniform anisotropic expansion or swelling.

Improvement of fission source distribution by correlated sampling method in Monte Carlo perturbation calculations

ABSTRACT To increase the accuracy of Monte Carlo perturbation calculations, the main issue is to estimate the variations of fission source distribution in perturbed systems. For estimating the difference between effective multiplication factors in unperturbed and perturbed systems, this study proposes combining the fission matrix method and the correlated sampling method, and applying the weight window technique for stabilizing the weight fluctuation of fission sources in perturbed systems. By applying the proposed method to the Smart and User-frIendly Monte Carlo Particle Transport Code (SUIT) Monte Carlo code, perturbation calculations are carried out for GODIVA and for simplified STACY problems. The results thus estimated show good agreement compared with those of reference calculations, demonstrating that the proposed method can effectively estimate variations of fission source distribution in perturbed systems for improving the accuracy of Monte Carlo correlated sampling method, especially for large variations.

Two dimensional fluid with one site-site associating point. Monte Carlo, integral equation and thermodynamic perturbation theory study

In this paper we propose a model for the two dimensional fluid with one site-site associating point. We studied its structural and thermodynamic properties by the Monte Carlo computer simulations, the site-site integral equation theory (RISM), the Wertheim's thermodynamic perturbation theory (TPT) and the Wertheim's integral equation theory (WIET) for associative liquids. The model can have arbitrary position of the associating point from the center of particles. All particles have Lennard-Jones core while interactions between associating points are modeled as Gaussian like potential where the interaction depends only on the distance between sites. The methods were used to study the thermodynamic and structural properties as a function of the position of associating point, temperature and density. The accuracy of the analytic theories were checked by comparing the theoretical results with the corresponding Monte Carlo ones. The theories are quite accurate for cases when the associating point is on the surface and only dimers can be formed. In this case, the theories correctly predict the pair correlation functions of the model, internal energy, ratios of free and bonded particles and chemical potential. This is no longer true when associating point is away from the surface of particles and the higher clusters are formed.

A new approach to the stabilization and convergence acceleration in coupled Monte Carlo–CFD calculations: The Newton method via Monte Carlo perturbation theory

Abstract This paper proposes the adoption of Monte Carlo perturbation theory to approximate the Jacobian matrix of coupled neutronics/thermal-hydraulics problems. The projected Jacobian is obtained from the eigenvalue decomposition of the fission matrix, and it is adopted to solve the coupled problem via the Newton method. This avoids numerical differentiations commonly adopted in Jacobian-free Newton–Krylov methods that tend to become expensive and inaccurate in the presence of Monte Carlo statistical errors in the residual. The proposed approach is presented and preliminarily demonstrated for a simple two-dimensional pressurized water reactor case study.

Improvement and performance evaluation of the perturbation source method for an exact Monte Carlo perturbation calculation in fixed source problems

This paper presents improvement and performance evaluation of the “perturbation source method”, which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an “on-the-fly” technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section.

Modeling Ignition Probability for Stratified Flows

High-energy short-duration spark igniters are common in combustion devices where the discharge often occurs in a nonfueled region. This requires convection between where the spark kernel is created and where combustion can begin. Here, a reduced-order model is developed to study an ignition kernel in conditions similar to a gas turbine combustor. The kernel is generated in air and entrains ambient fluid into the reactor to model such observed fluid dynamics in a parallel set of experiments. Continuous dilution with cold reactants and endothermic fuel decomposition reactions are shown to compete with heat release in the entraining kernel. Simulation results also reveal a pressure influence on the kernel’s initial energy density and entrainment that can exceed the direct dependence of the reaction rates. A Monte Carlo perturbation approach is directly input to simulations, resulting in ignition probabilities that are directly comparable to experimental results. A computationally efficient support vector machine is trained in multiple ways with simulation results and used to quickly classify ignition success. Including the statistical variation of input parameters, the simulated ignition probabilities match the experimental results, indicating the capability of this approach for predicting ignition probability in non-premixed combustors.