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Journal articles on the topic 'Monte-Carlo numerical simulation'

Author: Grafiati

Published: 25 January 2025

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1

Takahashi, Akiyuki, Naoki Soneda, and Masanori Kikuchi. "Computer Simulation of Microstructure Evolution of Fe-Cu Alloy during Thermal Ageing." Key Engineering Materials 306-308 (March 2006): 917–22. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.917.

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This paper describes a computer simulation of thermal ageing process in Fe-Cu alloy. In order to perform accurate numerical simulation, firstly, we make numerical models of the diffusion and dissociation of Cu and Cu-vacancy clusters. This modeling was performed with kinetic lattice Monte Carlo method, which allows us to perform long-time simulation of vacancy diffusion in Fe-Cu dilute alloy. The model is input to the kinetic Monte Carlo method, and then, we performed the kinetic Monte Carlo simulation of the thermal ageing in the Fe-Cu alloy. The results of the KMC simulations tell us that the our new models describes well the rate and kinetics of the diffusion and dissociation of Cu and Cu-vacancy clusters, and works well in the kinetic Monte Carlo simulations. Finally, we discussed the further application of these numerical models.

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Li, Yuan Ying, and De Sheng Zhang. "Plane Truss Reliability Numerical Simulation Based on MATLAB." Applied Mechanics and Materials 256-259 (December 2012): 1091–96. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.1091.

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Based on the basic principles of structure reliability numerical analysis, the numerical simulation of the displacement and stress reliability of plane truss under vertical load was programmed with MATLAB. The failure probability of the most unfavorable structural vertical displacement and stress and reliable indicators were obtained through direct sampling Monte Carlo method, response surface method, response surface-Monte Carlo method and response surface-important sampling Monte Carlo method. It is found that calculation lasts longer since there are so many samples with Monte-Carlo method, higher accuracy and less calculation time can be achieved through response surface-Monte Carlo method and response surface-important sampling Monte Carlo method with fewer samples. The results of different numerical simulation calculations are almost identical and reliable, providing references to reliability analysis of complex structures.

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3

Price, Thomas E., and D. P. Story. "Monte Carlo Simulation of Numerical Integration." Journal of Statistical Computation and Simulation 23, no. 1-2 (December 1985): 97–112. http://dx.doi.org/10.1080/00949658508810860.

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4

Cheng, Minqi, and Jiasheng Guo. "Analysis of the Principle and Two Applications for Monte-Carlo Simulations." Highlights in Science, Engineering and Technology 88 (March 29, 2024): 136–41. http://dx.doi.org/10.54097/3dg18k50.

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As a matter of fact, stochastic process and sampling algorithms are widely used in the state-of-art numerical simulations. In order to evaluate the random effect, the means of Monte-Carlo simulations are widely adopted and used to obtain a convergence or trending results. With this in mind, this essay mainly talks about the two applications of Monte Carlo simulation and the impact of it toward the society and human race. To be specific, firstly, the origin of Monte-Carlo simulation was revealed and its history of development was elaborated. After that, the basic concept of Monte-Carlo analysis was formulated as well as the sampling process of it is done briefly. All those foreshadows were aimed at assisting the readers to obtain a basic idea of this simulating method and be able to comprehend the relatively sophisticated applications, including financial and computer science knowledge. Overall, these results shed light on guiding further exploration of Monte-Carlo simulations.

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Mo, Wen Hui. "Monte Carlo Simulation of Reliability for Gear." Advanced Materials Research 268-270 (July 2011): 42–45. http://dx.doi.org/10.4028/www.scientific.net/amr.268-270.42.

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Production errors, material properties and applied loads of the gear are stochastic .Considering the influence of these stochastic factors, reliability of gear is studied. The sensitivity analysis of random variable can reduce the number of random variables. Simulating random variables, a lot of samples are generated. Using the Monte Carlo simulation based on the sensitivity analysis, reliabilities of contacting fatigue strength and bending fatigue strength can be obtained. The Monte Carlo simulation approaches the accurate solution gradually with the increase of the number of simulations. The numerical example validates the proposed method.

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Caflisch, Russel E. "Monte Carlo and quasi-Monte Carlo methods." Acta Numerica 7 (January 1998): 1–49. http://dx.doi.org/10.1017/s0962492900002804.

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Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. The resulting quadrature method, called quasi-Monte Carlo, has a convergence rate of approximately O((logN)kN−1). For quasi-Monte Carlo, both theoretical error estimates and practical limitations are presented. Although the emphasis in this article is on integration, Monte Carlo simulation of rarefied gas dynamics is also discussed. In the limit of small mean free path (that is, the fluid dynamic limit), Monte Carlo loses its effectiveness because the collisional distance is much less than the fluid dynamic length scale. Computational examples are presented throughout the text to illustrate the theory. A number of open problems are described.

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7

Sheet, Abd Al Kareem I., and Nadia Adeel Saeed. "Monte Carlo Simulation and Applications." Journal of Kufa for Mathematics and Computer 1, no. 6 (December 30, 2012): 75–78. https://doi.org/10.31642/jokmc/2018/010608.

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The Monte Carlo simulation technique is one of the common computational tools used to imitate and follow up complex real life systems and their development with time. Variables of a disease problem were defined and the mathematical model for this problem was constructed. The numerical solution of this model was compared with the computational simulation of Â Markov Renewal Process of the type '' Birth and Death ''. We obvious from the results we obtained the efficiency of the Monte Carlo simulation technique and through out extended time periods episodes.Â

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MATUTTIS, HANS-GEORG, and NOBUYASU ITO. "NONEXISTENCE OF d-WAVE-SUPERCONDUCTIVITY IN THE QUANTUM MONTE CARLO SIMULATION OF THE HUBBARD MODEL." International Journal of Modern Physics C 16, no. 06 (June 2005): 857–66. http://dx.doi.org/10.1142/s0129183105007571.

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For the existence of d-wave-superconductivity in the Hubbard model, previous quantum Monte Carlo results by other authors, which showed a power law increase of the d-wave susceptibility, seem to contradict a recently published theorem. We show those quantum Monte Carlo calculations were numerically contaminated, analyze the numerical problem and propose a numerically more stable computing scheme.

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9

Zhang, Xiaobo, Zhenzhou Lu, Kai Cheng, and Yanping Wang. "A novel reliability sensitivity analysis method based on directional sampling and Monte Carlo simulation." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 234, no. 4 (February 12, 2020): 622–35. http://dx.doi.org/10.1177/1748006x19899504.

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Local reliability sensitivity and global reliability sensitivity are required in reliability-based design optimization, since they can provide rich information including variable importance ranking and gradient information. However, traditional Monte Carlo simulation is inefficient for engineering application. A novel numerical simulation method based on Monte Carlo simulation and directional sampling is proposed to simultaneously estimate local reliability sensitivity and global reliability sensitivity. By suitable transformation, local reliability sensitivity and global reliability sensitivity can be estimated simultaneously as by-products of reliability analysis for Monte Carlo simulation method. The key is how to efficiently classify Monte Carlo simulation samples into two categories: failure samples and safety samples. Directional sampling method, a classical reliability analysis method, is more efficient than Monte Carlo simulation for reliability analysis. A novel strategy based on nearest Euclidean distance is proposed to approximately screen out failure samples from Monte Carlo simulation samples using directional sampling samples. In the proposed method, local reliability sensitivity and global reliability sensitivity are by-products of reliability analysis using the directional sampling method. Different from existing methods, the proposed method does not introduce hypotheses and does not require additional gradient information. The advantages of the Monte Carlo simulation and directional sampling are well integrated in the proposed method. The accuracy and the efficiency of the proposed method for local reliability sensitivity and global reliability sensitivity are demonstrated by four numerical examples and two engineering examples including the headless rivet and the wing box structure.

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10

Casella, Bruno, and Gareth O. Roberts. "Exact Monte Carlo simulation of killed diffusions." Advances in Applied Probability 40, no. 1 (March 2008): 273–91. http://dx.doi.org/10.1239/aap/1208358896.

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We describe and implement a novel methodology for Monte Carlo simulation of one-dimensional killed diffusions. The proposed estimators represent an unbiased and efficient alternative to current Monte Carlo estimators based on discretization methods for the cases when the finite-dimensional distributions of the process are unknown. For barrier option pricing in finance, we design a suitable Monte Carlo algorithm both for the single barrier case and the double barrier case. Results from numerical investigations are in excellent agreement with the theoretical predictions.

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Casella, Bruno, and Gareth O. Roberts. "Exact Monte Carlo simulation of killed diffusions." Advances in Applied Probability 40, no. 01 (March 2008): 273–91. http://dx.doi.org/10.1017/s0001867800002470.

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We describe and implement a novel methodology for Monte Carlo simulation of one-dimensional killed diffusions. The proposed estimators represent an unbiased and efficient alternative to current Monte Carlo estimators based on discretization methods for the cases when the finite-dimensional distributions of the process are unknown. For barrier option pricing in finance, we design a suitable Monte Carlo algorithm both for the single barrier case and the double barrier case. Results from numerical investigations are in excellent agreement with the theoretical predictions.

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Mendoza, Alberto, Carlos Torres-Verdín, and Bill Preeg. "Linear iterative refinement method for the rapid simulation of borehole nuclear measurements: Part I — Vertical wells." GEOPHYSICS 75, no. 1 (January 2010): E9—E29. http://dx.doi.org/10.1190/1.3267877.

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As a result of its high numerical accuracy and versatility to include complex tool configurations and arbitrary spatial distributions of material properties, the Monte Carlo method is the foremost numerical technique used to simulate borehole nuclear measurements. Although recent advances in computer technology have considerably reduced the computer time required by Monte Carlo simulations of borehole nuclear measurements, the efficiency of the method is still not sufficient for estimation of layer-by-layer properties or combined quantitative interpretation with other borehole measurements. We develop and successfully test a new linear iterative refinement method to simulate nuclear borehole measurements accurately and rapidly. The approximation stems from Monte Carlo-derived geometric response factors, referred to as flux sensitivity functions (FSFs), for specific density and neutron-tool configurations. Our procedure first invokes the integral representation of Boltzmann’s transport equation to describe the detector response from the flux of particles emitted by the radioactive source. Subsequently, we use theMonte Carlo N-particle (MCNP) code to calculate the associated detector response function and the particle flux included in the integral form of Boltzmann’s equation. The linear iterative refinement method accounts for variations of the response functions attributable to local perturbations when numerically simulating neutron and density porosity logs. We quantify variations in the FSFs of neutron and density measurements from borehole environmental effects and spatial variations of formation properties. Simulations performed with the new approximations yield errors in the simulated value of density of less than [Formula: see text] with respect to Monte Carlo-simulated logs. Moreover, for the case of radial geometric factor of density, we observe a maximum shift of [Formula: see text] at 90% of the total sensitivity as a result of realistic variations of formation density. For radial variation of neutron properties (migration length), the maximum change in the radial length of investigation is [Formula: see text]. Neutron porosity values simulated with the new approximation differ by less than 10% from Monte Carlo simulations. The approximations enable the simulation of borehole nuclear measurements in seconds of CPU time compared to several hours with MCNP.

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Akintola, Samson Oluyomi. "A Scientific Computing Analysis of Financial Black-Scholes and Monte Carlo Differential Equation: An American Option." Current Journal of Applied Science and Technology 43, no. 7 (July 30, 2024): 181–97. http://dx.doi.org/10.9734/cjast/2024/v43i74415.

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This study presents a systematic computing analysis of financial models, precisely focusing on the Black-Scholes and Monte Carlo derivative equations, to evaluate American options. American selections are exercised at any time before expiration, posing unique challenges in financial modelling due to their complex early exercise features. The Black-Scholes formulation gives a foundational framework for choice pricing, utilizing partial derivative formulations to estimate the fair value of options under definite assumptions. Nevertheless, because of its restriction, Monte Carlo computations are taken to give a better simulation scheme to overcome the posed challenges by computing wider likely underlying price path assets. This study implements a computationa approach to compare the efficacy of the Black-Scholes formulation and Monte Carlo methods in selected American pricing. A numerical scheme for solving the Black-Scholes derivative systems and a variance reduction technique for enhancing the effectiveness of Monte Carlo simulations are adopted. Our analysisl reveals that while the Black-Scholes model provides a useful approximation, Monte Carlo simulations deliver more accurate and flexible results for American options, especially in scenarios with substantial volatility and early exercise potential. The outcomes underscore the importance of sophisticated numerical methods in financial engineering and highlight the trade-offs between analytical tractability and numerical precision.

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14

Zhao, Di, and Haiwu He. "DSMC: Fast direct simulation Monte Carlo solver for the Boltzmann equation by Multi-Chain Markov Chain and multicore programming." International Journal of Modeling, Simulation, and Scientific Computing 07, no. 02 (June 2016): 1650009. http://dx.doi.org/10.1142/s1793962316500094.

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Direct Simulation Monte Carlo (DSMC) solves the Boltzmann equation with large Knudsen number. The Boltzmann equation generally consists of three terms: the force term, the diffusion term and the collision term. While the first two terms of the Boltzmann equation can be discretized by numerical methods such as the finite volume method, the third term can be approximated by DSMC, and DSMC simulates the physical behaviors of gas molecules. However, because of the low sampling efficiency of Monte Carlo Simulation in DSMC, this part usually occupies large portion of computational costs to solve the Boltzmann equation. In this paper, by Markov Chain Monte Carlo (MCMC) and multicore programming, we develop Direct Simulation Multi-Chain Markov Chain Monte Carlo (DSMC3): a fast solver to calculate the numerical solution for the Boltzmann equation. Computational results show that DSMC3 is significantly faster than the conventional method DSMC.

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15

Kablukova, E. G., V. G. Oshlakov, and S. M. Prigarin. "Monte Carlo Simulation of Laser Navigation System Signals." Numerical Analysis and Applications 16, no. 3 (September 2023): 208–15. http://dx.doi.org/10.1134/s1995423923030023.

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16

Xie, Wei-Chau. "Monte Carlo Simulation of Moment Lyapunov Exponents." Journal of Applied Mechanics 72, no. 2 (March 1, 2005): 269–75. http://dx.doi.org/10.1115/1.1839592.

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A Monte Carlo simulation method for determining the pth moment Lyapunov exponents of stochastic systems, which governs the pth moment stability, is developed. Numerical results of two-dimensional systems under bounded noise and real noise excitations are presented to illustrate the approach.

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17

Hu, S. L. J., and M. Muin. "Dynamic Response Statistics of Linear System Under Morison-Type Wave Force." Journal of Offshore Mechanics and Arctic Engineering 112, no. 1 (February 1, 1990): 42–52. http://dx.doi.org/10.1115/1.2919834.

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The primary objective of this study is to establish the non-normal relationship between Morison-type random wave loading and structural response via repeated Monte Carlo simulations. A standardized equation of motion will be developed, such that the numerical results can apply to various structures and sea states, instead of a particular structure or sea state. The reliability of the Monte Carlo simulation technique will also be investigated, analytically and experimentally.

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18

Sari, Rina Filia, Rima Aprilia, Rina Widyasari, Afnaria Afnaria, Syech Suhaimi, and Chindy Aulia Putri. "SIMULASI PENGENDALIAN PERSEDIAAN ALAT TULIS KANTOR PADA DINAS PERKEBUNAN DAN PETERNAKAN PROVINSI SUMATERA UTARA DENGAN METODE MONTE CARLO." Jurnal Pengabdian Mitra Masyarakat 3, no. 2 (May 24, 2024): 89–95. http://dx.doi.org/10.30743/jurpammas.v3i2.9284.

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In a Government Agency, office stationery supplies are an absolute necessity. The provision of adequate office stationery will facilitate performance. This study aims to predict the demand for office stationery using Monte Carlo Simulation. Monte Carlo is a numerical analysis method that uses random number samples. The data used in this study are primary data in the form of the number of stock items and the number of requests for goods from January to December 2023. The accuracy result using the Monte Carlo method for Year 2024 is 91.78%. This shows that the Monte Carlo method simulation can be used to predict the demand for stationery for the following year.

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Hwang, Yunn Lin, and Thi Na Ta. "Uncertainty Analysis of CNC Machine Tools Based on Monte Carlo Method." Applied Mechanics and Materials 900 (July 2020): 9–13. http://dx.doi.org/10.4028/www.scientific.net/amm.900.9.

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The uncertainty of mechanical system performance is strongly influenced by the properties of system components such as mass, stiffness-damping coefficient, and friction coefficient. Based on computational simulations, the system performance under uncertainty conditions can be estimated. However, the nonlinear dynamic behavior of friction is difficult to simulate in numerical simulations, this research is therefore employed a smooth stick-slip friction force model instead of the Coulomb friction force model. Monte Carlo simulation (MCS) combined with multibody dynamic (MBD) simulation is proposed to evaluate the uncertainty characteristics of the system components and stick-slip friction force between two contacting bodies. Numerical simulations applied the proposed method were performed to consider the effects of uncertainty of friction coefficient on the machining accuracy of a three axes CNC (Computer Numerical Control) machine tool.

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20

FRANK, T. D. "EXACT SOLUTIONS AND MONTE CARLO SIMULATIONS OF SELF-CONSISTENT LANGEVIN EQUATIONS: A CASE STUDY FOR THE COLLECTIVE DYNAMICS OF STOCK PRICES." International Journal of Modern Physics B 21, no. 07 (March 20, 2007): 1099–112. http://dx.doi.org/10.1142/s0217979207036904.

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In a case study, the exact solution of a self-consistent Langevin equation associated with a nonlinear Fokker–Planck equation is derived. On the basis of this solution, a Monte Carlo simulation scheme for the Langevin equation is proposed. The case study addresses a generalized geometric Brownian walk that describes the collective dynamics of a large set of interacting stocks. Numerical results obtained from the Monte Carlo simulation are compared with analytical solutions derived from the nonlinear Fokker–Planck equation. The power of the Monte Carlo simulation is demonstrated for situations in which analytical solutions are not available.

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LAI, YONGZENG, and HAIXIANG YAO. "SIMULATION OF MULTI-ASSET OPTION GREEKS UNDER A SPECIAL LÉVY MODEL BY MALLIAVIN CALCULUS." ANZIAM Journal 57, no. 3 (January 2016): 280–98. http://dx.doi.org/10.1017/s1446181115000292.

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We discuss simulation of sensitivities or Greeks of multi-asset European style options under a special Lévy process model: that is, the subordinated Brownian motion model. The Malliavin calculus method combined with Monte Carlo and quasi-Monte Carlo methods is used in the simulations. Greeks are expressed in terms of the expectations of the option payoff functions multiplied by the weights involving Malliavin derivatives for multi-asset options. Numerical results show that the Malliavin calculus method is usually more efficient than the finite difference method for options with nonsmooth payoffs. The superiority of the former method over the latter is even more significant when both are combined with quasi-Monte Carlo methods.

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Omori, Toshiaki, Hiroshi Taniguchi, and Kazuhiko Kudo. "Monte Carlo simulation of indoor radiant environment." International Journal for Numerical Methods in Engineering 30, no. 4 (September 1990): 615–27. http://dx.doi.org/10.1002/nme.1620300405.

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23

Venkat, Rama, Bharat Reddy Pemmireddy, Ramprasad Vijayagopal, Hwa Cheng, and Rich Bresnahan. "Flux profile modeling: Monte Carlo simulation and numerical computation." Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures 22, no. 3 (2004): 1549. http://dx.doi.org/10.1116/1.1752912.

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24

Phantu, Suganya, Yupaporn Areepong, and Saowanit Sukparungsee. "Double Moving Average Control Chart for Time Series Data with Poisson INARCH(1)." WSEAS TRANSACTIONS ON BUSINESS AND ECONOMICS 21 (February 23, 2024): 694–707. http://dx.doi.org/10.37394/23207.2024.21.58.

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The objectives of this research are to find the explicit formulas of the average run length (ARL) of a double moving average (DMA) control chart for first-order integer-valued autoregressive conditional heteroscedasticity (INARCH1))) of Poisson count data. In addition, the numerical results obtained from the proposed explicit formulas are compared with those obtained from Monte Carlo simulations (MC) for the Poisson INARCH(1) counting process. An out-of-control ARL (ARL1) is the criteria for measuring the performance of control charts. The numerical results found that the values of both ARL0 and ARL1 obtained from explicit formulas agree with the numerical results obtained from the Monte Carlo simulation (MC), but the latter is very timeconsuming.

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25

Feng, Mingbin, and Jeremy Staum. "Green Simulation with Database Monte Carlo." ACM Transactions on Modeling and Computer Simulation 31, no. 1 (February 2021): 1–26. http://dx.doi.org/10.1145/3429336.

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In a setting in which experiments are performed repeatedly with the same simulation model, green simulation means reusing outputs from previous experiments to answer the question currently being asked of the model. In this article, we address the setting in which experiments are run to answer questions quickly, with a time limit providing a fixed computational budget, and then idle time is available for further experimentation before the next question is asked. The general strategy is database Monte Carlo for green simulation: the output of experiments is stored in a database and used to improve the computational efficiency of future experiments. In this article, the database provides a quasi-control variate, which reduces the variance of the estimated mean response in a future experiment that has a fixed computational budget. We propose a particular green simulation procedure using quasi-control variates, addressing practical issues such as experiment design, and analyze its theoretical properties. We show that, under some conditions, the variance of the estimated mean response in an experiment with a fixed computational budget drops to zero over a sequence of repeated experiments, as more and more idle time is invested in creating databases. Our numerical experiments on the procedure show that using idle time to create databases of simulation output provides variance reduction immediately, and that the variance reduction grows over time in a way that is consistent with the convergence analysis.

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Zakrad, Az-eddine, and Abdelaziz Nasroallah. "Estimation of steady-state quantities of an HMM with some rarely generated emissions." Monte Carlo Methods and Applications 28, no. 1 (February 15, 2022): 27–44. http://dx.doi.org/10.1515/mcma-2022-2103.

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Abstract We propose to apply the importance sampling and the antithetic variates statistical techniques to estimate steady-state quantities of an Hidden Markov chain (HMM) of which certain emissions are rarely generated. Compared to standard Monte Carlo simulation, the use of these techniques, allow a significant reduction in simulation time. Numerical Monte Carlo examples are studied to show the usefulness and efficiency of the proposed approach.

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Ding, Enyong, and Yun Huang. "Monte Carlo simulation of SATs in 2D." Communications in Nonlinear Science and Numerical Simulation 1, no. 1 (January 1996): 21–27. http://dx.doi.org/10.1016/s1007-5704(96)90019-2.

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Ariffin, Ahmad Kamal, M. R. M. Akramin, Syifaul Huzni, Shahrum Abdullah, and Mariyam Jameelah Ghazali. "Probabilistic Analysis of Cracked Structures With Uncertainty Parameters." Advanced Materials Research 33-37 (March 2008): 223–28. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.223.

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This paper presents a probabilistic approach for fracture mechanics analysis of cracked structures. The objective of this work is to calculate the rigidity of cracked structures based on failure probability. The methodology consists of cracked structures modelling, finite element analysis with adaptive mesh, sampling of cracked structure including uncertainties factors and probabilistic analysis using Monte Carlo method. Probabilistic analysis represents the priority of proceeding either suitable to repair the structures or it can be justified that the structures are still in safe condition. Therefore, the combination of finite element and probabilistic analysis represents the failure probability of the structures by operating the sampling of cracked structures process. The uncertainty of the crack size can produce a significant effect on the probability of failure, particularly for the crack size with large coefficient of variation. The probability of failure caused by uncertainties relates to loads and material properties of the structure are estimated using Monte Carlo simulation technique. Numerical example is presented to show that probabilistic analysis based on Monte Carlo simulation provides accurate estimates of failure probability. The comparisons of simulation result, analytical solution and relevant numerical results obtained from other previous works shows that the combination of finite element analysis and probabilistic analysis based on Monte Carlo simulation provides accurate estimation of failure probability.

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Cerf, N. J., and S. E. Koonin. "Monte Carlo simulation of quantum computation." Mathematics and Computers in Simulation 47, no. 2-5 (August 1998): 143–52. http://dx.doi.org/10.1016/s0378-4754(98)00099-8.

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Semerdjiev, Tz A., V. P. Jilkov, and D. S. Angelova. "Target tracking using Monte Carlo simulation." Mathematics and Computers in Simulation 47, no. 2-5 (August 1998): 441–47. http://dx.doi.org/10.1016/s0378-4754(98)00125-6.

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Lin, Guiyuan, Shiwo Deng, and Xiaoqun Wang. "An efficient quasi-Monte Carlo method with forced fixed detection for photon scatter simulation in CT." PLOS ONE 18, no. 8 (August 24, 2023): e0290266. http://dx.doi.org/10.1371/journal.pone.0290266.

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Detected scattered photons can cause cupping and streak artifacts, significantly degrading the quality of CT images. For fast and accurate estimation of scatter intensities resulting from photon interactions with a phantom, we first transform the path probability of photons interacting with the phantom into a high-dimensional integral. Secondly, we develope a new efficient algorithm called gQMCFFD, which combines graphics processing unit(GPU)-based quasi-Monte Carlo (QMC) with forced fixed detection to approximate this integral. QMC uses low discrepancy sequences for simulation and is deterministic versions of Monte Carlo. Numerical experiments show that the results are in excellent agreement and the efficiency improvement factors are 4 ∼ 46 times in all simulations by gQMCFFD with comparison to GPU-based Monte Carlo methods. And by combining gQMCFFD with sparse matrix method, the simulation time is reduced to 2 seconds in a single projection angle and the relative difference is 3.53%.

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Rioux-Lavoie, Damien, Ryusuke Sugimoto, Tümay Özdemir, Naoharu H. Shimada, Christopher Batty, Derek Nowrouzezahrai, and Toshiya Hachisuka. "A Monte Carlo Method for Fluid Simulation." ACM Transactions on Graphics 41, no. 6 (November 30, 2022): 1–16. http://dx.doi.org/10.1145/3550454.3555450.

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We present a novel Monte Carlo-based fluid simulation approach capable of pointwise and stochastic estimation of fluid motion. Drawing on the Feynman-Kac representation of the vorticity transport equation, we propose a recursive Monte Carlo estimator of the Biot-Savart law and extend it with a stream function formulation that allows us to treat free-slip boundary conditions using a Walk-on-Spheres algorithm. Inspired by the Monte Carlo literature in rendering, we design and compare variance reduction schemes suited to a fluid simulation context for the first time, show its applicability to complex boundary settings, and detail a simple and practical implementation with temporal grid caching. We validate the correctness of our approach via quantitative and qualitative evaluations - across a range of settings and domain geometries - and thoroughly explore its parameters' design space. Finally, we provide an in-depth discussion of several axes of future work building on this new numerical simulation modality.

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Kahane, Sylvian. "Backscattered Electrons Spectra and Angular Distributions: Simulations with EGS5." European Journal of Engineering Research and Science 3, no. 10 (October 26, 2018): 95–102. http://dx.doi.org/10.24018/ejers.2018.3.10.917.

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The purpose of the present study is to compare numerical Monte Carlo simulations of backscattering of electrons, mainly in the keV range, with available experimental data. The final goal is to assess the ability of the Monte Carlo code to predict viable results, in view of the complexity and difficulty of performing experimental measurements. A specific code for simulating electrons backscattering was developed, based on the EGS5 electron-photon transport routines. The code was parallelized very efficiently for a common memory configuration. Simulation results for the backscattering coefficient h, the energy spectrum dh/dq, and the angle dependent energy spectrum dh/dqdW were obtained. Comparing with experiments shows agreement from very good to fair, especially in regions of high q (energy) values. For low values of q there are not experimental results due to difficulties in measurements. Hence, the Monte Carlo program can provide good estimates, in the range of energies from tens of keV up to 100-200 keV.

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Kahane, Sylvian. "Backscattered Electrons Spectra and Angular Distributions: Simulations with EGS5." European Journal of Engineering and Technology Research 3, no. 10 (October 26, 2018): 95–102. http://dx.doi.org/10.24018/ejeng.2018.3.10.917.

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The purpose of the present study is to compare numerical Monte Carlo simulations of backscattering of electrons, mainly in the keV range, with available experimental data. The final goal is to assess the ability of the Monte Carlo code to predict viable results, in view of the complexity and difficulty of performing experimental measurements. A specific code for simulating electrons backscattering was developed, based on the EGS5 electron-photon transport routines. The code was parallelized very efficiently for a common memory configuration. Simulation results for the backscattering coefficient h, the energy spectrum dh/dq, and the angle dependent energy spectrum dh/dqdW were obtained. Comparing with experiments shows agreement from very good to fair, especially in regions of high q (energy) values. For low values of q there are not experimental results due to difficulties in measurements. Hence, the Monte Carlo program can provide good estimates, in the range of energies from tens of keV up to 100-200 keV.

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Lécot, Christian, and Faysal El Khettabi. "Quasi-Monte Carlo Simulation of Diffusion." Journal of Complexity 15, no. 3 (September 1999): 342–59. http://dx.doi.org/10.1006/jcom.1999.0509.

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Gill, Daniel F. "INLINE THERMAL AND XENON FEEDBACK ITERATIONS IN MONTE CARLO REACTOR CALCULATIONS." EPJ Web of Conferences 247 (2021): 04019. http://dx.doi.org/10.1051/epjconf/202124704019.

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In this work, we describe a method for converging nonlinear feedback during the convergence of the neutron fission source in a Monte Carlo reactor simulation. This approach involves updating feedback physics during discard batches in the Monte Carlo simulation rather than fully (or partially) converging the neutronics prior to the nonlinear update. This approach is demonstrated for a single PWR pin with thermal feedback and with both thermal and xenon feedback. Converging these feedbacks inline with the fission source is shown to have the benefit of reducing numerical instability by effectively underrelaxing the tallied quantities in the Monte Carlo simulation and improving computational performance by converging feedback within (or near to) the number of discard batches required to converge the fission source even without any feedback.

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de Raynal, Paul-Éric Chaudru, Gilles Pagès, and Clément Rey. "Numerical methods for Stochastic differential equations: two examples." ESAIM: Proceedings and Surveys 64 (2018): 65–77. http://dx.doi.org/10.1051/proc/201864065.

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The goal of this paper is to present a series of recent contributions arising in numerical probability. First we present a contribution to a recently introduced problem: stochastic differential equations with constraints in law, investigated through various theoretical and numerical viewpoints. Such a problem may appear as an extension of the famous Skorokhod problem. Then a generic method to approximate in a weak way the invariant distribution of an ergodic Feller process by a Langevin Monte Carlo simulation. It is an extension of a method originally developed for diffusions and based on the weighted empirical measure of an Euler scheme with decreasing step. Finally, we mention without details a recent development of a multilevel Langevin Monte Carlo simulation method for this type of problem.

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SETTAOUTI, A., and L. SETTAOUTI. "MONTE CARLO SIMULATION OF POSITIVE CORONA DISCHARGE IN NITROGEN." International Journal of Modern Physics C 21, no. 07 (July 2010): 943–54. http://dx.doi.org/10.1142/s0129183110015609.

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The corona discharge commonly occurs in many engineering devices and processes. Their application is still largely based on empirical knowledge; accordingly it is very important to predict the physical properties of corona discharge by the appropriate numerical method. To control corona discharge properly by understanding of corona discharge properties at different discharge stages, time-varying characteristics of discharge which are resulted from electron collision with the gas molecules should be investigated. A numerical study of a corona discharge in nitrogen in a point to plane geometry is presented. It is obtained by Monte Carlo method and concerns space-time evolution of electron and ion densities as well as electric field distributions along the discharge axis.

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Hazimah Wan Omar and Siti Nur Iqmal Ibrahim. "Pricing Writer-Extendable Call Options with Monte Carlo Simulation." Applied Mathematics and Computational Intelligence (AMCI) 13, No.1 (February 14, 2024): 128–35. http://dx.doi.org/10.58915/amci.v13ino.1.491.

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Writer-extendable option is an exotic option that can either be exercised at its initial maturity time, or be extended to a future maturity time. Within the Black-Scholes environment, this study aims to price writer-extendable call options using the Monte Carlo simulation technique, and compare the obtained prices with the closed-form pricing formula. Numerical examples are provided using the closed-form solutions and the Monte Carlo simulation via Euler scheme, which shows that the prices obtained via the latter are accurate.

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Huang, Zhi Qin, Xiao Hui Fan, and Gai Ling Zheng. "The Establishment of Mathematical Model of LED Based on Monte Carlo Method." Key Engineering Materials 480-481 (June 2011): 1571–76. http://dx.doi.org/10.4028/www.scientific.net/kem.480-481.1571.

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Monte Carlo (MC method) of the computer simulation of the traditional forms of light-emitting diode (LED) is used for modeling and simulation. MC method than the method of geometrical optics of the LED is more suitable for complex optical structure on a Computer. MC method, the more accurate numerical solutions can improve the efficiency of LED design that is an effective means of LED design. MC method is with a very clear and unique advantage in the establishment of LED structure model.This paper first introduces the research background and purpose of the LED, then Monte Carlo methods Are outlined, and finally, some mathematical models of LED are given based on Monte Carlo method

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Chen, Qingshan, and Ju Ming. "The Multilevel Monte Carlo Method for Simulations of Turbulent Flows." Monthly Weather Review 146, no. 9 (August 24, 2018): 2933–47. http://dx.doi.org/10.1175/mwr-d-18-0053.1.

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Abstract In this paper, the application of the multilevel Monte Carlo (MLMC) method to numerical simulations of turbulent flows with uncertain parameters is investigated. Several strategies for setting up the MLMC method are presented, and the advantages and disadvantages of each strategy are also discussed. A numerical experiment is carried out using an idealized model for the Antarctic Circumpolar Current (ACC) with uncertain, small-scale bottom topographic features. It is demonstrated that unlike the pointwise solutions, the averaged volume transports are correlated across grid resolutions, and the MLMC method can increase simulation efficiency without losing accuracy in uncertainty assessments.

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Peskin, Mark, and Christine Maziar. "MOMENTS: The Modular Monte Carlo Environment for Charge Transport Simulation, Overview and Applications." VLSI Design 8, no. 1-4 (January 1, 1998): 35–40. http://dx.doi.org/10.1155/1998/18794.

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We present MOMENTS, a newly developed software library lbr Monte Carlo simulation of semiconductor devices. This library uses object-oriented design principles to provide a flexible, extensible toolset that allows rapid development of a wide variety of Monte Carlo simulation applications. It allows concurrent simulation of multiple particle species (e.g. electrons and holes) with arbitrary user-defined interactions between species (e.g. generation – recombination and carrier – carrier scattering) in arbitrary geometries using either analytic or numerical bandstructure representations. The modular design allows virtually all simulation parameters to be freely varied across the simulation domain. MOMENTS also takes advantage of the parallelism inherent in the ensemble Monte Carlo approach, employing a scheme that can support a wide variety of parallel architectures with active load balancing. To demonstrate some of the library's capabilities, we also present preliminary results from a GaAs avalanche photodiode (APD) simulator based on MOMENTS.

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Li, Da Wei, Zhen Zhou Lu, and Zhang Chun Tang. "Local Monte Carlo Simulation for the Reliability Sensitivity Analysis." Advanced Materials Research 291-294 (July 2011): 2183–88. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.2183.

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An efficient numerical technique, namely the Local Monte Carlo Simulation method, is presented to assess the reliability sensitivity in this paper. Firstly some samples are obtained by the random sampling, then the local domain with a constant probability content corresponding to each sample point can be defined, finally the conditional reliability and reliability sensitivity corresponding to every local region can be calculated by using linear approximation of the limit state function. The reliability and reliability sensitivity can be estimated by the expectation of all the conditional reliability and reliability sensitivity. Three examples testify the applicability, validity and accuracy of the proposed method. The results computed by the Local Monte Carlo Simulation method and the Monte Carlo method are compared, which demonstrates that, without losing precision, the computational cost by the former method is much less than the later.

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Crevillén-García, D., and H. Power. "Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media." Royal Society Open Science 4, no. 8 (August 2017): 170203. http://dx.doi.org/10.1098/rsos.170203.

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In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log-Gaussian random field by using direct Karhunen–Loéve decompositions. The random terms in such expansions represent the coefficients in the equations. Numerical calculations demonstrating the effectiveness of each of the methods are presented. A comparison of the computational cost incurred by each of the methods for three different tolerances is provided. The accuracy of the approaches is quantified via the mean square error.

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du Plooy, Ryno, and Pierre J. Venter. "A Comparison of Artificial Neural Networks and Bootstrap Aggregating Ensembles in a Modern Financial Derivative Pricing Framework." Journal of Risk and Financial Management 14, no. 6 (June 7, 2021): 254. http://dx.doi.org/10.3390/jrfm14060254.

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In this paper, the pricing performances of two learning networks, namely an artificial neural network and a bootstrap aggregating ensemble network, were compared when pricing the Johannesburg Stock Exchange (JSE) Top 40 European call options in a modern option pricing framework using a constructed implied volatility surface. In addition to this, the numerical accuracy of the better performing network was compared to a Monte Carlo simulation in a separate numerical experiment. It was found that the bootstrap aggregating ensemble network outperformed the artificial neural network and produced price estimates within the error bounds of a Monte Carlo simulation when pricing derivatives in a multi-curve framework setting.

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Gu, Tianyu, and Yang Zhang. "Analysis of the Applications for Monte-Carlo Simulations in Real Estate Modeling, Radiation Therapy and Brachytherapy." Highlights in Science, Engineering and Technology 88 (March 29, 2024): 565–70. http://dx.doi.org/10.54097/c6agm649.

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Monte Carlo simulation is a frequently utilized modeling technique present in PMBOK, primarily in the quantitative risk analysis process of the risk management knowledge area. It serves as one of the fundamental tools for conducting quantitative risk analysis in a project. Monte Carlo simulation can estimate project schedule or cost, as well as assist in creating a schedule plan. This study will introduce the Monte Carlo simulation regarding its historical background, derivation process, algorithms, and significant role in the fields of economics and physics. The text uses clear, concise language with passive tone and avoids biased or ornamental language. Precise technical terms are utilized, with explanations for abbreviations. The structure creates a logical flow of information with causal connections between statements, adheres to conventional academic sections, and maintains regular formatting. Additionally, the text is free from grammatical errors and follows consistent citation and footnote style. Based on the analysis, the Monte Carlo simulation method efficiently resolves cash flow randomness and uncertainty related to project investment. Financial analysts and project decision makers can be relieved from taxing mathematical calculations, and the computer can conduct numerous numerical simulation experiments within a relatively short span of time, enhancing decision-making efficiency.

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Coraddu, Andrea, Massimo Figari, and Stefano Savio. "Numerical investigation on ship energy efficiency by Monte Carlo simulation." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 228, no. 3 (June 26, 2014): 220–34. http://dx.doi.org/10.1177/1475090214524184.

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Mak, Tak K., and Fassil Nebebe. "Numerical approximation of conditional asymptotic variances using Monte Carlo simulation." Computational Statistics 24, no. 2 (May 24, 2008): 333–44. http://dx.doi.org/10.1007/s00180-008-0121-0.

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Mo, Wen Hui. "Reliability Calculation and Perturbation Stochastic Finite Element." Applied Mechanics and Materials 155-156 (February 2012): 570–73. http://dx.doi.org/10.4028/www.scientific.net/amm.155-156.570.

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This paper proposes a method of calculating reliability using perturbation stochastic finite element. The mean and variance of the stress can be computed by the perturbation stochastic finite element. Computer program is used to generate samples of stress and strength. If the stress is greater than the strength, the structure will fail. The Monte Carlo simulation is proposed to compute structural reliability. Reliability calculation using the Monte Carlo simulation is developed. A numerical example demonstrates the proposed method is feasible.

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Sawicki, Bartosz, and Artur Krupa. "Stochastic Modeling of Electrical Field in Potato Tuber using Polynomial Chaos Expansion." ITM Web of Conferences 29 (2019): 01008. http://dx.doi.org/10.1051/itmconf/20192901008.

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The paper deals with numerical modeling of objects with a natural origin. The stochastic approach based on description using random variables allows processing such challenges. The Monte-Carlo methods are known a tool for simulations containing stochastic parameters however, they require significant computational power to obtain stable results. Authors compare Monte- Carlo with more advanced Polynomial Chaos Expansion (PCE) method. Both statistical tools have been applied for simulation of the electric field used in ohmic heating of potato tuber probes. Results indicate that PCE is remarkably faster, however, it simplifies some probabilistic features of the solution.

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