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Journal articles on the topic 'Monte Carlo simulation method'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 January 2023

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1

Takahashi, Akihiko, and Nakahiro Yoshida. "Monte Carlo Simulation with Asymptotic Method." JOURNAL OF THE JAPAN STATISTICAL SOCIETY 35, no. 2 (2005): 171–203. http://dx.doi.org/10.14490/jjss.35.171.

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2

Alexander, Francis J., and Alejandro L. Garcia. "The Direct Simulation Monte Carlo Method." Computers in Physics 11, no. 6 (1997): 588. http://dx.doi.org/10.1063/1.168619.

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3

Rota, Gian-Carlo. "Simulation and the Monte-Carlo method." Advances in Mathematics 60, no. 1 (April 1986): 123. http://dx.doi.org/10.1016/0001-8708(86)90009-5.

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4

Date, Hiroyuki. "2. Monte Carlo Method and Simulation." Japanese Journal of Radiological Technology 70, no. 7 (2014): 705–14. http://dx.doi.org/10.6009/jjrt.2014_jsrt_70.7.705.

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5

Giles, Michael B. "Multilevel Monte Carlo methods." Acta Numerica 24 (April 27, 2015): 259–328. http://dx.doi.org/10.1017/s096249291500001x.

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Monte Carlo methods are a very general and useful approach for the estimation of expectations arising from stochastic simulation. However, they can be computationally expensive, particularly when the cost of generating individual stochastic samples is very high, as in the case of stochastic PDEs. Multilevel Monte Carlo is a recently developed approach which greatly reduces the computational cost by performing most simulations with low accuracy at a correspondingly low cost, with relatively few simulations being performed at high accuracy and a high cost.In this article, we review the ideas behind the multilevel Monte Carlo method, and various recent generalizations and extensions, and discuss a number of applications which illustrate the flexibility and generality of the approach and the challenges in developing more efficient implementations with a faster rate of convergence of the multilevel correction variance.

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6

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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7

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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8

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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9

Gelman, Andrew. "Method of Moments Using Monte Carlo Simulation." Journal of Computational and Graphical Statistics 4, no. 1 (March 1995): 36. http://dx.doi.org/10.2307/1390626.

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10

Gelman, Andrew. "Method of Moments Using Monte Carlo Simulation." Journal of Computational and Graphical Statistics 4, no. 1 (March 1995): 36–54. http://dx.doi.org/10.1080/10618600.1995.10474664.

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11

Papadopoulos, Christos E., and Hoi Yeung. "Uncertainty estimation and Monte Carlo simulation method." Flow Measurement and Instrumentation 12, no. 4 (August 2001): 291–98. http://dx.doi.org/10.1016/s0955-5986(01)00015-2.

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12

Gadallah, Mohamed H. "An alternative to Monte Carlo simulation method." International Journal of Experimental Design and Process Optimisation 2, no. 2 (2011): 93. http://dx.doi.org/10.1504/ijedpo.2011.040261.

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13

Erfanian, Hamid Reza, Seyed Jaliledin Ghaznavi Bidgoli, and Parvin Shakibaei. "The pricing of spread option using simulation." International Journal of Applied Mathematical Research 6, no. 4 (October 19, 2017): 121. http://dx.doi.org/10.14419/ijamr.v6i4.7914.

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Monte Carlo simulation is one of the most common and popular method of options pricing. The advantages of this method are being easy to use, suitable for all kinds of standard and exotic options and also are suitable for higher dimensional problems. But on the other hand Monte Carlo variance convergence rate is which due to that it will have relatively slow convergence rate to answer the problems, as to achieve accuracy when it has been d-dimensions, complexity is . For this purpose, several methods are provided in quasi Monte Carlo simulation to increase variance convergence rate as variance reduction techniques, so far. One of the latest presented methods is multilevel Monte Carlo that is introduced by Giles in 2008. This method not only reduces the complexity of computing amount in use of Euler discretization scheme and the amount in use of Milstein discretization scheme, but also has the ability to combine with other variance reduction techniques. In this paper, using Multilevel Monte Carlo method by taking Milstein discretization scheme, pricing spread option and compared complexity of computing with standard Monte Carlo method. The results of Multilevel Monte Carlo method in pricing spread options are better than standard Monte Carlo simulation.

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14

Rashki, Mohsen. "The soft Monte Carlo method." Applied Mathematical Modelling 94 (June 2021): 558–75. http://dx.doi.org/10.1016/j.apm.2021.01.022.

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15

Meshkov, S. V. "Simulation by the Monte Carlo method in statistical physics." Uspekhi Fizicheskih Nauk 159, no. 9 (1989): 187. http://dx.doi.org/10.3367/ufnr.0159.198909i.0187.

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16

Liou, William W., and Yichuan Fang. "Forced Couette flow simulations using direct simulation Monte Carlo method." Physics of Fluids 16, no. 12 (December 2004): 4211–20. http://dx.doi.org/10.1063/1.1801092.

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17

Mengyu Jia, Mengyu Jia, Shanshan Cui Shanshan Cui, Xueying Chen Xueying Chen, Ming Liu Ming Liu, Xiaoqing Zhou Xiaoqing Zhou, Huijuan Zhao Huijuan Zhao, and Feng Gao Feng Gao. "Image reconstruction method for laminar optical tomography with only a single Monte-Carlo simulation." Chinese Optics Letters 12, no. 3 (2014): 031702–31706. http://dx.doi.org/10.3788/col201412.031702.

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18

SWENDSEN, ROBERT H., BRIAN DIGGS, JIAN-SHENG WANG, SHING-TE LI, CHRISTOPHER GENOVESE, and JOSEPH B. KADANE. "TRANSITION MATRIX MONTE CARLO." International Journal of Modern Physics C 10, no. 08 (December 1999): 1563–69. http://dx.doi.org/10.1142/s0129183199001340.

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Although histogram methods have been extremely effective for analyzing data from Monte Carlo simulations, they do have certain limitations, including the range over which they are valid and the difficulties of combining data from independent simulations. In this paper, we describe a complementary approach to extracting information from Monte Carlo simulations that uses the matrix of transition probabilities. Combining the Transition Matrix with an N-fold way simulation technique produces an extremely flexible and efficient approach to rather general Monte Carlo simulations.

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19

PREVE, NIKOLAOS P., and EMMANUEL N. PROTONOTARIOS. "MONTE CARLO SIMULATION ON COMPUTATIONAL FINANCE FOR GRID COMPUTING." International Journal of Modeling, Simulation, and Scientific Computing 03, no. 03 (May 17, 2012): 1250010. http://dx.doi.org/10.1142/s1793962312500109.

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Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in simulating complex systems. Because of their reliance on repeated computation of random or pseudo-random numbers, these methods are most suited to calculation by a computer and tend to be used when it is infeasible or impossible to compute an exact result with a deterministic algorithm. In finance, Monte Carlo simulation method is used to calculate the value of companies, to evaluate economic investments and financial derivatives. On the other hand, Grid Computing applies heterogeneous computer resources of many geographically disperse computers in a network in order to solve a single problem that requires a great number of computer processing cycles or access to large amounts of data. In this paper, we have developed a simulation based on Monte Carlo method which is applied on grid computing in order to predict through complex calculations the future trends in stock prices.

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20

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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21

NARITA, YUICHIRO. "Monte Carlo Simulation in Medical Engineering Field : Part 1. Basic of Monte Carlo Method." Japanese Journal of Radiological Technology 56, no. 9 (2000): 1145–52. http://dx.doi.org/10.6009/jjrt.kj00001357293.

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22

Huang, Zhao Dong, Wen Bing Chang, Yi Yong Xiao, and Rui Liu. "An Extended Monte Carlo Method on Simulating the Development Cost Uncertainties of Aircraft." Advanced Materials Research 118-120 (June 2010): 810–14. http://dx.doi.org/10.4028/www.scientific.net/amr.118-120.810.

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Monte Carlo Simulation is a general method for evaluating a deterministic model by iteratively generating inputs so as to get the natural distribution of outputs, which has often been employed for risk analysis of development cost estimation under uncertain environment. However, the traditional way of implementing Monte Carlo Simulation on cost risk analysis is always based on deterministic Cost Estimation Relation (CER) model and does not take the uncertainty of history cost data used to build CER into account, which will considerably affect the cost risk analysis. In this paper, we extend Monte Carlo Simulation model to make its simulating process cover the stage of building model so that not only the inputs are iteratively generated but also the model is iteratively rebuilt. An example is carried out to compare the extended model to the traditional one on analyzing aircraft development cost risk, which shows that the risk distribution gotten by Extended Monte Carlo Simulation is considerably different to that gotten by traditional one.

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23

Li, Jian Yong, Guang Xiang Yuan, Yu Min Zhang, and Zhi Quan Huang. "Simulation of Rock Fractures by Monte Carlo Method." Advanced Materials Research 1061-1062 (December 2014): 605–8. http://dx.doi.org/10.4028/www.scientific.net/amr.1061-1062.605.

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Discontinuities have an important influence on deformation and failure of rock mass in practical engineering. It is one of the key issues in modern rock mechanics to investigate geometric characteristics of joints and fractures inside the rock mass such as shape, size, location and direction etc. Based on the deep analysis of the above geometric properties, it is proposed that the stochastic fractures in the rock mass can be simulated with the random numbers generated by the Monte Carlo method. The related algorithm is designed and implemented. The correctness and effectiveness of the algorithm is verified with an example of a project. This will lay a solid foundation to further study the cutting problems of discontinuous rock block systems.

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24

YAMAGUCHI, Tomiko, Hideyuki IKEDA, and Kazumasa NISHIO. "Simulation of Grain Refinement using Monte Carlo Method." JOURNAL OF THE JAPAN WELDING SOCIETY 81, no. 2 (2012): 90–95. http://dx.doi.org/10.2207/jjws.81.90.

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25

Song, Cui Ying, and Chuan Dong Li. "Simulation of Ising Model by Monte Carlo Method." Advanced Materials Research 936 (June 2014): 2271–75. http://dx.doi.org/10.4028/www.scientific.net/amr.936.2271.

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Simulating Ising model to calculate magnetization intensity by Monte Carlo method. The Ising model was introduced simply, sampled importantly, and calculated with programming. It shows the dependency relationship between the magnetization intensity and the size of dot-square line in different temperatures for Ising model. It cans edulcorate the approximation of analytic method by computer simulating. It obtains a method to appraise a model right or wrong by comparing the model and the experimental data.

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26

Lo, Ming-Chung, Chien-Yu Pan, and Jong-Shinn Wu. "On an Axisymmetric Direct Simulation Monte Carlo Method." International Journal of Computational Fluid Dynamics 35, no. 5 (May 28, 2021): 373–87. http://dx.doi.org/10.1080/10618562.2021.1955867.

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27

Hong, Andrew, and Aaron Morris. "Novel direct simulation Monte Carlo method for spherocylinders." Powder Technology 399 (February 2022): 117085. http://dx.doi.org/10.1016/j.powtec.2021.117085.

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28

Sharipov, Felix. "Direct Simulation Monte Carlo Method Applied to Aerothermodynamics." Journal of the Brazilian Society of Mechanical Sciences 23, no. 4 (2001): 441–52. http://dx.doi.org/10.1590/s0100-73862001000400005.

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29

Marzjarani, Morteza. "Simulation and the Monte Carlo Method (3rd ed.)." Technometrics 61, no. 3 (July 3, 2019): 427–28. http://dx.doi.org/10.1080/00401706.2019.1629745.

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30

Ota, Masahiro, Hiroyoshi Taniguchi, and Masanori Aritomi. "Parallel Processings for Direct Simulation Monte Carlo Method." Transactions of the Japan Society of Mechanical Engineers Series B 61, no. 582 (1995): 496–502. http://dx.doi.org/10.1299/kikaib.61.496.

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31

Montanero, José María, and Andrés Santos. "Monte Carlo simulation method for the Enskog equation." Physical Review E 54, no. 1 (July 1, 1996): 438–44. http://dx.doi.org/10.1103/physreve.54.438.

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32

Sandvik, Anders W., and Juhani Kurkijärvi. "Quantum Monte Carlo simulation method for spin systems." Physical Review B 43, no. 7 (March 1, 1991): 5950–61. http://dx.doi.org/10.1103/physrevb.43.5950.

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33

Karabulut, Hasan, and Huriye Arıman Karabulut. "Stochastic theory of direct simulation Monte Carlo method." Theoretical Chemistry Accounts 122, no. 5-6 (March 6, 2009): 227–43. http://dx.doi.org/10.1007/s00214-009-0533-0.

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34

Haarhoff, J., and E. H. Mathews. "A Monte Carlo method for thermal building simulation." Energy and Buildings 38, no. 12 (December 2006): 1395–99. http://dx.doi.org/10.1016/j.enbuild.2006.01.009.

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35

Vats, Dootika. "Simulation and the Monte Carlo Method, 3rd ed." Journal of the American Statistical Association 114, no. 527 (July 3, 2019): 1425. http://dx.doi.org/10.1080/01621459.2019.1662243.

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36

Ikegawa, Masato, and Junichi Kobayashi. "Deposition Profile Simulation Using the Direct Simulation Monte Carlo Method." Journal of The Electrochemical Society 136, no. 10 (October 1, 1989): 2982–86. http://dx.doi.org/10.1149/1.2096387.

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37

Ikegawa, Masato, and Jun'ichi Kobayashi. "Semiconductor Deposition Profile Simulation Using Direct Simulation Monte Carlo Method." Transactions of the Japan Society of Mechanical Engineers Series B 59, no. 567 (1993): 3365–72. http://dx.doi.org/10.1299/kikaib.59.3365.

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38

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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39

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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40

de Groot, Paul F. M., Albertus H. Bril, Frans J. T. Floris, and A. Ewan Campbell. "Monte Carlo simulation of wells." GEOPHYSICS 61, no. 3 (May 1996): 631–38. http://dx.doi.org/10.1190/1.1443992.

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We present a method to simulate wells, i.e., 1-D stratigraphic profiles with attached physical properties but without spatial information, using a combination of geological knowledge and Monte Carlo statistics. The simulated data is intended to be used in seismic lateral prediction studies. Our algorithm simulates correlated stochastic variables one by one. There are two major advantages in this approach above the conventional way in which all correlated stochastic vectors are drawn simultaneously. The first advantage is that we can steer the algorithm with rules based on geological reasoning. The second advantage is that we can include hard constraints for each of the stochastic variables. If a simulated value does not satisfy these constraints, it can simply be drawn again. The input to the simulation algorithm consists of geological rules, probability density functions, correlations, and hard constraints for the stochastic variables. The variables are attached to the entities of a generic integration framework, which consists of acoustic‐stratigraphic units organized at three scale levels. The simulation algorithm constructs individual wells by selecting entities from the framework. The order in which the entities occur, and the thickness of each entity, is determined by a combination of random draws and specified geological rules. Acoustic properties and optional user‐defined physical properties are attached to the simulated layers by random draws. The acoustic properties are parameterized by top and bottom sonic and density values. The algorithm is capable of simulating acoustic hydrocarbon effects. The algorithm is demonstrated with a simulated example, describing the stratigraphic and physical variations in an oil field with a fluvial‐deltaic labyrinth type reservoir.

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41

Zheng, Qi, Wei Shen, Xuesong Li, Tengfei Hao, Qingming He, Jie Li, and Zhouyu Liu. "A HYBRID MONTE-CARLO-DETERMINISTIC METHOD FOR AP1000 EX-CORE DETECTOR RESPONSE SIMULATION." EPJ Web of Conferences 247 (2021): 05003. http://dx.doi.org/10.1051/epjconf/202124705003.

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The ex-core detector-response calculation is a typical deep-penetration problem, which is challenging for the Monte Carlo method. The response of the ex-core detector is an important parameter for the safe operation of the nuclear power plants. Meanwhile, evaluation of the ex-core detector response during each step of fuel-loading is used to guide the fuel-loading sequence. The response can also be used to reconstruct core-power distribution for online monitoring of long-term power. The detector used for the ex-core response is the source-range detector which is sensitive to thermal neutrons. For a Monte Carlo shielding calculation of the above detector response, the thermal flux under 0.625eV is needed, which is too small to be tallied by traditional Monte Carlo simulations. In practice, the tally results are close to zero in the detector region under direct Monte Carlo calculation. Even if the number of particles is increased to a significant amount, the statistical variance is still very large. The high variance along with a significant calculation time leads to a small Figure Of Merit (FOM). In order to solve this problem and to improve the tally efficiency of the ex-core detector response, a hybrid Monte-Carlo-deterministic method is employed in this study, and an in-house hybrid Monte-Carlo-deterministic particle transport code, NECP-MCX, is developed in this paper. The method takes the space-energy-dependent adjoint fluxes to generate importance parameters for the mesh-based weight window in the Monte Carlo calculation. Simultaneously, the mesh-based source biasing is performed with the consistent importance parameters to make the starting weight of neutrons matching with the survival weight of the weight windows. As the mesh used in the hybrid Monte-Carlo-deterministic method is superimposed, the mesh of the weight window will not be affected by the complex geometry model. The adjoint flux is obtained by the efficient SN method with the multi-group cross-section data. The whole toolset is convenient to use with single set of the modelling data for both Monte Carlo and deterministic simulations. Compared with the direct Monte Carlo simulation, the hybrid Monte-Carlo-deterministic method has a higher efficiency for a typical deep-penetration problem such as the AP1000 ex-core detector-response simulation.

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42

Ben Seghier, Mohamed el Amine, Mourad Bettayeb, José Correia, Abílio De Jesus, and Rui Calçada. "Structural reliability of corroded pipeline using the so-called Separable Monte Carlo method." Journal of Strain Analysis for Engineering Design 53, no. 8 (June 22, 2018): 730–37. http://dx.doi.org/10.1177/0309324718782632.

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The evaluation of the failure probability of corroded pipelines is an important calculation to quantify the risk assessment and integrity of pipelines. Traditional Monte Carlo simulation method has been widely used to solve this type of problems, where it generates a very large number of simulations and takes longer time in computing. In this study, enhanced computational method called Separable Monte Carlo is employed to evaluate the time-dependent reliability of pipeline segments containing active corrosion defects, where a practical example was used. The results show that the Separable Monte Carlo simulation method not only minimizes the computational cost strongly but also improves the calculation precision.

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43

Zhou, Kun. "Monte Carlo simulation for soot dynamics." Thermal Science 16, no. 5 (2012): 1391–94. http://dx.doi.org/10.2298/tsci1205391z.

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A new Monte Carlo method termed Comb-like frame Monte Carlo is developed to simulate the soot dynamics. Detailed stochastic error analysis is provided. Comb-like frame Monte Carlo is coupled with the gas phase solver Chemkin II to simulate soot formation in a 1-D premixed burner stabilized flame. The simulated soot number density, volume fraction, and particle size distribution all agree well with the measurement available in literature. The origin of the bimodal distribution of particle size distribution is revealed with quantitative proof.

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44

Valihrach, Jakub, and Petr Konečný. "Exit Condition for Probabilistic Assessment Using Monte Carlo Method." Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series 10, no. 1 (January 1, 2010): 1–9. http://dx.doi.org/10.2478/v10160-010-0014-3.

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Exit Condition for Probabilistic Assessment Using Monte Carlo Method This paper introduces a condition used to exit a probabilistic assessment using the Monte Carlo simulation, and to evaluate it with regard to the relationship between the computed estimate of the probability of failure and the target design probability. The estimation of probability of failure is treated as a random variable, considering its variance that is dependent on the number of performed Monte Carlo simulation steps. After theoretical derivation of the decision condition, it is tested numerically with regard to its accuracy and computational efficiency. The condition is suitable for optimization design using the Monte Carlo method.

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45

HUKUSHIMA, KOJI, HAJIME TAKAYAMA, and KOJI NEMOTO. "APPLICATION OF AN EXTENDED ENSEMBLE METHOD TO SPIN GLASSES." International Journal of Modern Physics C 07, no. 03 (June 1996): 337–44. http://dx.doi.org/10.1142/s0129183196000272.

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An efficient Monte Carlo algorithm for simulating hardly-relaxing systems is proposed. By using this algorithm the three-dimensional ± J Ising spin glass model is studied. The result shows that reasonable values of the critical temperature and of the critical exponents can be obtained within Monte Carlo steps much shorter than the observation time a conventional simulation usually requires.

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46

Pažický, Martin. "Stock Price Simulation Using Bootstrap and Monte Carlo." Scientific Annals of Economics and Business 64, no. 2 (June 27, 2017): 155–70. http://dx.doi.org/10.1515/saeb-2017-0010.

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Abstract In this paper, an attempt is made to assessment and comparison of bootstrap experiment and Monte Carlo experiment for stock price simulation. Since the stock price evolution in the future is extremely important for the investors, there is the attempt to find the best method how to determine the future stock price of BNP Paribas′ bank. The aim of the paper is define the value of the European and Asian option on BNP Paribas′ stock at the maturity date. There are employed four different methods for the simulation. First method is bootstrap experiment with homoscedastic error term, second method is blocked bootstrap experiment with heteroscedastic error term, third method is Monte Carlo simulation with heteroscedastic error term and the last method is Monte Carlo simulation with homoscedastic error term. In the last method there is necessary to model the volatility using econometric GARCH model. The main purpose of the paper is to compare the mentioned methods and select the most reliable. The difference between classical European option and exotic Asian option based on the experiment results is the next aim of tis paper.

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Apriliana Sari W., Indah, Boy Isma P., and Rudi Nurdiansyah. "Forecasting Sales of Hex Nut Using Trend Linier Line (TLL) Methode and Monte Carlo Simulation in PT. KMS East Java." Tibuana 5, no. 01 (January 31, 2022): 8–12. http://dx.doi.org/10.36456/tibuana.5.01.4542.8-12.

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This study presenting the result of forecasting sales of Hex Nuts between the Trend Linear Line (TLL) method and Monte Carlo Simulation. To determine the appropriate method, the Mean Average Percentage Error (MAPE) is used to evaluate theerror rate. We find that the Monte Carlo simulation outperforms the TTL method, where the MAPE value of the Monte Carlo simulation is 7,61%. Based on the result, the Monte Carlo simulation is the appropriate method to forecast the sales rate of Hex Nuts in the PT. KMS.

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TSUTSUI, Shingo, and Keiichi FUTAGI. "The Application Example of Direct Simulation Monte Carlo Method to Turbo-molecular Pump." Journal of the Vacuum Society of Japan 58, no. 7 (2015): 253–56. http://dx.doi.org/10.3131/jvsj2.58.253.

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RATNASARI, DEWA AYU AGUNG PUTRI, KOMANG DHARMAWAN, and DESAK PUTU EKA NILAKUSMAWATI. "PENENTUAN NILAI KONTRAK OPSI TIPE BINARY PADA KOMODITS KAKAO MENGGUNAKAN METODE QUASI MONTE CARLO DENGAN BARISAN BILANGAN ACAK FAURE." E-Jurnal Matematika 6, no. 4 (November 28, 2017): 214. http://dx.doi.org/10.24843/mtk.2017.v06.i04.p168.

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Contract options are the most important part of an investment strategy. An option is a contract that entitles the owner or holder to sell an asset on a designated maturity date. A binary or asset-or-nothing option is an option in which the option holder will perform or not the option. There are many methods used in determining the option contract value, one of this is the Monte Carlo Quasi method of the Faure random. The purpose of this study is to determine the value of binary type option contract using the Quasi Monte Carlo method of the Faure random and compare with the Monte Carlo method. The results of this study indicate that the option contract calculated by the Monte Carlo Quasi method results in a more fair value. Monte Carlo method simulation 10.000 generate standard error is 0.9316 and the option convergence at 18.9144. While Quasi Monte Carlo simulation 3000 generate standard error is 0.09091 and the option convergence at 18.8203. This show the Quasi Monte Carlo method reaches a faster convergent of Monte Carlo method.

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Sherniyozov, A. A., and Sh D. Payziyev. "Simulating optical processes: Monte Carlo photon tracing method." «Узбекский физический журнал» 24, no. 3 (September 11, 2022): 157–62. http://dx.doi.org/10.52304/.v24i3.357.

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In search of high accuracy and convenient implementation, computational optics uses several modeling techniques such as Maxwell’s equations-based methods, ray-tracing method, Fourier optics methods and many others. Each with its advantages, disadvantages, and applicability caveats. In this paper, we describe Monte Carlo photon tracing as a simulation technique for computational optics. The validity of the main assumptions in the simulation method is demonstrated with examples, and limitations of method’s applicability are discussed.

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