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Journal articles on the topic 'Monte Carlo propagation'

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Author: Grafiati

Published: 14 March 2023

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1

Yanping Chen, Yanping Chen, Xiong Ma Xiong Ma, Xiaoling Wang Xiaoling Wang, and Shaojie Wang Shaojie Wang. "Near-infrared photon propagation in complex knee by Monte-Carlo modeling." Chinese Optics Letters 12, s2 (2014): S21701–321704. http://dx.doi.org/10.3788/col201412.s21701.

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2

Park, Ho Jin, Hyung Jin Shim, and Chang Hyo Kim. "Uncertainty Propagation in Monte Carlo Depletion Analysis." Nuclear Science and Engineering 167, no. 3 (March 2011): 196–208. http://dx.doi.org/10.13182/nse09-106.

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3

Rochman, D., W. Zwermann, S. C. van der Marck, A. J. Koning, H. Sjöstrand, P. Helgesson, and B. Krzykacz-Hausmann. "Efficient Use of Monte Carlo: Uncertainty Propagation." Nuclear Science and Engineering 177, no. 3 (July 2014): 337–49. http://dx.doi.org/10.13182/nse13-32.

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4

Gelman, Andrew, and Aki Vehtari. "Comment: Consensus Monte Carlo using expectation propagation." Brazilian Journal of Probability and Statistics 31, no. 4 (November 2017): 692–96. http://dx.doi.org/10.1214/17-bjps365a.

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5

Rochman, D., S. C. van der Marck, A. J. Koning, H. Sjöstrand, and W. Zwermann. "Uncertainty Propagation with Fast Monte Carlo Techniques." Nuclear Data Sheets 118 (April 2014): 367–69. http://dx.doi.org/10.1016/j.nds.2014.04.082.

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6

Skilling, John. "Galilean and Hamiltonian Monte Carlo." Proceedings 33, no. 1 (December 5, 2019): 19. http://dx.doi.org/10.3390/proceedings2019033019.

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Galilean Monte Carlo (GMC) allows exploration in a big space along systematic trajectories, thus evading the square-root inefficiency of independent steps. Galilean Monte Carlo has greater generality and power than its historical precursor Hamiltonian Monte Carlo because it discards second-order propagation under forces in favour of elementary force-free motion. Nested sampling (for which GMC was originally designed) has similar dominance over simulated annealing, which loses power by imposing an unnecessary thermal blurring over energy.

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7

Newell, Quentin, and Charlotta Sanders. "Stochastic Uncertainty Propagation in Monte Carlo Depletion Calculations." Nuclear Science and Engineering 179, no. 3 (March 2015): 253–63. http://dx.doi.org/10.13182/nse13-44.

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8

Rochman, D., A. J. Koning, S. C. van der Marck, A. Hogenbirk, and C. M. Sciolla. "Nuclear data uncertainty propagation: Perturbation vs. Monte Carlo." Annals of Nuclear Energy 38, no. 5 (May 2011): 942–52. http://dx.doi.org/10.1016/j.anucene.2011.01.026.

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9

Gunzburger, M. D., R. E. Hiromoto, and M. O. Mundt. "Analysis of a Monte Carlo boundary propagation method." Computers & Mathematics with Applications 31, no. 6 (March 1996): 61–70. http://dx.doi.org/10.1016/0898-1221(96)00006-5.

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10

Cabellos, Oscar, and Luca Fiorito. "Examples of Monte Carlo techniques applied for nuclear data uncertainty propagation." EPJ Web of Conferences 211 (2019): 07008. http://dx.doi.org/10.1051/epjconf/201921107008.

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The aim of this work is to review different Monte Carlo techniques used to propagate nuclear data uncertainties. Firstly, we introduced Monte Carlo technique applied for Uncertainty Quantification studies in safety calculations of large scale systems. As an example, the impact of nuclear data uncertainty of JEFF-3.3 235U, 238U and 239Pu is demonstrated for the main design parameters of a typical 3-loop PWR Westinghouse unit. Secondly, the Bayesian Monte Carlo technique for data adjustment is presented. An example for 235U adjustment using criticality and shielding integral benchmarks shows the importance of performing joint adjustment based on different set of integral benchmarks.

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11

Pakyuz-Charrier, Evren, Mark Jessell, Jérémie Giraud, Mark Lindsay, and Vitaliy Ogarko. "Topological analysis in Monte Carlo simulation for uncertainty propagation." Solid Earth 10, no. 5 (October 10, 2019): 1663–84. http://dx.doi.org/10.5194/se-10-1663-2019.

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Abstract. This paper proposes and demonstrates improvements for the Monte Carlo simulation for uncertainty propagation (MCUP) method. MCUP is a type of Bayesian Monte Carlo method aimed at input data uncertainty propagation in implicit 3-D geological modeling. In the Monte Carlo process, a series of statistically plausible models is built from the input dataset of which uncertainty is to be propagated to a final probabilistic geological model or uncertainty index model. Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUP. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets' variability and plausible model's variability. Non-linearity is shown to mainly arise from the effect of the geometrical rule set on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces topological heterogeneity and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUP is introduced. Boolean topological signatures recording lithological unit adjacency are used as n-dimensional points to be considered individually or clustered using the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data. Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the probabilistic geological models and uncertainty index models. Highlights. Monte Carlo uncertainty propagation (MCUP) methods often produce topologically distinct plausible models. Plausible models can be differentiated using topological signatures. Topologically similar probabilistic geological models may be obtained through topological signature clustering.

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12

Wang, Lin, Shenghan Ren, and Xueli Chen. "Comparative evaluations of the Monte Carlo-based light propagation simulation packages for optical imaging." Journal of Innovative Optical Health Sciences 11, no. 01 (November 20, 2017): 1750017. http://dx.doi.org/10.1142/s1793545817500171.

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Monte Carlo simulation of light propagation in turbid medium has been studied for years. A number of software packages have been developed to handle with such issue. However, it is hard to compare these simulation packages, especially for tissues with complex heterogeneous structures. Here, we first designed a group of mesh datasets generated by Iso2Mesh software, and used them to cross-validate the accuracy and to evaluate the performance of four Monte Carlo-based simulation packages, including Monte Carlo model of steady-state light transport in multi-layered tissues (MCML), tetrahedron-based inhomogeneous Monte Carlo optical simulator (TIMOS), Molecular Optical Simulation Environment (MOSE), and Mesh-based Monte Carlo (MMC). The performance of each package was evaluated based on the designed mesh datasets. The merits and demerits of each package were also discussed. Comparative results showed that the TIMOS package provided the best performance, which proved to be a reliable, efficient, and stable MC simulation package for users.

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13

Rochman, D., A. J. Koning, S. C. van der Marck, A. Hogenbirk, and D. van Veen. "Nuclear Data Uncertainty Propagation: Total Monte Carlo vs. Covariances." Journal of the Korean Physical Society 59, no. 2(3) (August 12, 2011): 1236–41. http://dx.doi.org/10.3938/jkps.59.1236.

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14

Key, H., E. R. Davies, P. C. Jackson, and P. N. T. Wells. "Monte Carlo modelling of light propagation in breast tissue." Physics in Medicine and Biology 36, no. 5 (May 1, 1991): 591–602. http://dx.doi.org/10.1088/0031-9155/36/5/003.

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15

Aloisio, Roberto, Denise Boncioli, Armando di Matteo, Aurelio F. Grillo, Sergio Petrera, and Francesco Salamida. "SimProp v2r4: Monte Carlo simulation code for UHECR propagation." Journal of Cosmology and Astroparticle Physics 2017, no. 11 (November 8, 2017): 009. http://dx.doi.org/10.1088/1475-7516/2017/11/009.

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16

Danforth, Amanda L., and Lyle N. Long. "Acoustic propagation using the direct simulation Monte Carlo method." Journal of the Acoustical Society of America 114, no. 4 (October 2003): 2356–57. http://dx.doi.org/10.1121/1.4776795.

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17

Tamura, Shin-ichiro. "Quasidiffusive propagation of phonons in silicon: Monte Carlo calculations." Physical Review B 48, no. 18 (November 1, 1993): 13502–7. http://dx.doi.org/10.1103/physrevb.48.13502.

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18

Vinckenbosch, Laura, Céline Lacaux, Samy Tindel, Magalie Thomassin, and Tiphaine Obara. "Monte Carlo methods for light propagation in biological tissues." Mathematical Biosciences 269 (November 2015): 48–60. http://dx.doi.org/10.1016/j.mbs.2015.08.017.

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19

Ganchenkova, Maria G., and Vladimir A. Borodin. "Monte-Carlo simulation of crack propagation in polycrystalline materials." Materials Science and Engineering: A 387-389 (December 2004): 372–76. http://dx.doi.org/10.1016/j.msea.2003.12.088.

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20

Albert, Daniel R. "Monte Carlo Uncertainty Propagation with the NIST Uncertainty Machine." Journal of Chemical Education 97, no. 5 (April 15, 2020): 1491–94. http://dx.doi.org/10.1021/acs.jchemed.0c00096.

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21

TAKEDA, Toshikazu, Naoki HIROKAWA, and Tomohiro NODA. "Estimation of Error Propagation in Monte-Carlo Burnup Calculations." Journal of Nuclear Science and Technology 36, no. 9 (September 1999): 738–45. http://dx.doi.org/10.1080/18811248.1999.9726262.

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22

Qin, Jun. "Computational analysis and Monte Carlo simulation of wave propagation." International Journal of Computational Biology and Drug Design 8, no. 2 (2015): 159. http://dx.doi.org/10.1504/ijcbdd.2015.071122.

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23

Döpking, Sandra, and Sebastian Matera. "Error propagation in first-principles kinetic Monte Carlo simulation." Chemical Physics Letters 674 (April 2017): 28–32. http://dx.doi.org/10.1016/j.cplett.2017.02.043.

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24

M, Lajili. "Improvement of Calculations for Turbulent Premixed Flame Characteristics Determination using PDF Monte Carlo Simulation." Petroleum & Petrochemical Engineering Journal 5, no. 1 (2021): 1–8. http://dx.doi.org/10.23880/ppej-16000256.

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This study aims at simulating turbulent premixed flame in a constant-pressure vessel (P = 1 atm) where the turbulence is supposed to be homogeneous and isotropic. The mixture of gas is composed by iso-octane-air. The realized CFD were based on Lagrange approach in Monte Carlo simulations. We focused on calculations of; flame radii R F , the flame propagation velocity S t , flame-brush thick ness  t an d flammability limit. During the study, influencing crucial parameters such as, the equivalence ratio  and the turbulence intensity u’ were considered. Results show that the equivalence ratio enhances the flame propagation when passing from lean to stoichiometric flames. Also, the turbulence intensity yields a notable growth for the flame characteristics mentioned above. Moreover, we noticed that the flammability limit is strongly depending of the turbulence intensity and the equivalence ratio. More precisely, we remarked that the minimum ignition energy (MIE) was situated quite smaller than the stoichiometric condition. But, it increased with the turbulence intensity.

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25

Kachelrieß, M., and J. Tjemsland. "On the origin and the detection of characteristic axion wiggles in photon spectra." Journal of Cosmology and Astroparticle Physics 2022, no. 01 (January 1, 2022): 025. http://dx.doi.org/10.1088/1475-7516/2022/01/025.

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Abstract Photons propagating in an external magnetic field may oscillate into axions or axion-like particles (ALPs). Such oscillations will lead to characteristic features in the energy spectrum of high-energy photons from astrophysical sources that can be used to probe the existence of ALPs. In this work, we revisit the signatures of these oscillations and stress the importance of a proper treatment of turbulent magnetic fields. We implement axions into ELMAG, a standard tool for modelling in a Monte Carlo framework the propagation of gamma-rays in the Universe, complementing thereby the usual description of photon-axion oscillations with a Monte Carlo treatment of high-energy photon propagation and interactions. We also propose an alternative method of detecting axions through the discrete power spectrum using as observable the energy dependence of wiggles in the photon spectra.

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26

Laureau, Axel, Vincent Lamirand, Dimitri Rochman, and Andreas Pautz. "Uncertainty propagation based on correlated sampling technique for nuclear data applications." EPJ Nuclear Sciences & Technologies 6 (2020): 8. http://dx.doi.org/10.1051/epjn/2020003.

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A correlated sampling technique has been implemented to estimate the impact of cross section modifications on the neutron transport and in Monte Carlo simulations in one single calculation. This implementation has been coupled to a Total Monte Carlo approach which consists in propagating nuclear data uncertainties with random cross section files. The TMC-CS (Total Monte Carlo with Correlated Sampling) approach offers an interesting speed-up of the associated computation time. This methodology is detailed in this paper, together with two application cases to validate and illustrate the gain provided by this technique: the highly enriched uranium/iron metal core reflected by a stainless-steel reflector HMI-001 benchmark, and the PETALE experimental programme in the CROCUS zero-power light water reactor.

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27

Cramer, S. N. "Forward-Adjoint Monte Carlo Coupling with No Statistical Error Propagation." Nuclear Science and Engineering 124, no. 3 (November 1996): 398–416. http://dx.doi.org/10.13182/nse96-a17919.

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28

Jean, Cyrille De Saint, Gilles Noguere, Benoit Habert, and Bertrand Iooss. "A Monte Carlo Approach to Nuclear Model Parameter Uncertainties Propagation." Nuclear Science and Engineering 161, no. 3 (March 2009): 363–70. http://dx.doi.org/10.13182/nse161-363.

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29

Periyasamy, Vijitha, and Manojit Pramanik. "Advances in Monte Carlo Simulation for Light Propagation in Tissue." IEEE Reviews in Biomedical Engineering 10 (2017): 122–35. http://dx.doi.org/10.1109/rbme.2017.2739801.

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30

Bilenca, A., A. Desjardins, B. E. Bouma, and G. J. Tearney. "Multicanonical Monte-Carlo simulations of light propagation in biological media." Optics Express 13, no. 24 (2005): 9822. http://dx.doi.org/10.1364/opex.13.009822.

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31

Tautz, R. C., J. Bolte, and A. Shalchi. "Monte Carlo simulations of intensity profiles for energetic particle propagation." Astronomy & Astrophysics 586 (February 2016): A118. http://dx.doi.org/10.1051/0004-6361/201527255.

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32

Díez, C. J., O. Cabellos, D. Rochman, A. J. Koning, and J. S. Martínez. "Monte Carlo uncertainty propagation approaches in ADS burn-up calculations." Annals of Nuclear Energy 54 (April 2013): 27–35. http://dx.doi.org/10.1016/j.anucene.2012.10.033.

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33

KAWAI, Masayoshi, and Yoshihisa HAYASHIDA. "Energy-Space Dependent Error Propagation in Monte Carlo Coupling Calculation." Journal of Nuclear Science and Technology 23, no. 8 (August 1986): 673–80. http://dx.doi.org/10.1080/18811248.1986.9735040.

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34

Hamada, Michael. "Coupling Bayesian Inference and Monte Carlo Methods in Error Propagation." Quality Engineering 14, no. 2 (February 2, 2002): 293–99. http://dx.doi.org/10.1081/qen-100108686.

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35

Al- Barwani, H. H., and A. Purnama. "Simple Monte Carlo Cellular Models for Surface Evolution." Sultan Qaboos University Journal for Science [SQUJS] 5 (December 1, 2000): 77. http://dx.doi.org/10.24200/squjs.vol5iss0pp77-84.

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Monte Carlo cellular simulations are described for some simple surface evolution models. Surface growth is simulated by adding new cells to the surface. The bonding of a new cell arriving to a site on the surface depends on the number of cells present around that site; new cells are more likely to stick at sites with the fewest missing surrounding cells. Applications are given for simulating the propagation of a flame front and the formation of surface landforms; and the (anisotropic) growth of a crystal, where the surface may grow more rapidly in one direction than others.

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36

Aloisio, Roberto. "COMPUTATIONAL SCHEMES FOR THE PROPAGATION OF ULTRA HIGH ENERGY COSMIC RAYS." Acta Polytechnica 53, A (December 18, 2013): 703–6. http://dx.doi.org/10.14311/ap.2013.53.0703.

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We discuss the problem of ultra high energy particles propagation in astrophysical backgrounds. We present two different computational schemes based on kinetic and Monte Carlo approaches. The kinetic approach is an analytical computation scheme based on the hypothesis of continuos energy losses while the Monte Carlo scheme takes into account also the stochastic nature of particle interactions. These schemes, which give quite reliable results, enable the computation of fluxes keeping track of the different primary and secondary components, providing a fast and useful workbench for studying Ultra High Energy Cosmic Rays.

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37

Koch, K. R. "Bayesian statistics and Monte Carlo methods." Journal of Geodetic Science 8, no. 1 (February 1, 2018): 18–29. http://dx.doi.org/10.1515/jogs-2018-0003.

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Abstract The Bayesian approach allows an intuitive way to derive the methods of statistics. Probability is defined as a measure of the plausibility of statements or propositions. Three rules are sufficient to obtain the laws of probability. If the statements refer to the numerical values of variables, the so-called random variables, univariate and multivariate distributions follow. They lead to the point estimation by which unknown quantities, i.e. unknown parameters, are computed from measurements. The unknown parameters are random variables, they are fixed quantities in traditional statistics which is not founded on Bayes’ theorem. Bayesian statistics therefore recommends itself for Monte Carlo methods, which generate random variates from given distributions. Monte Carlo methods, of course, can also be applied in traditional statistics. The unknown parameters, are introduced as functions of the measurements, and the Monte Carlo methods give the covariance matrix and the expectation of these functions. A confidence region is derived where the unknown parameters are situated with a given probability. Following a method of traditional statistics, hypotheses are tested by determining whether a value for an unknown parameter lies inside or outside the confidence region. The error propagation of a random vector by the Monte Carlo methods is presented as an application. If the random vector results from a nonlinearly transformed vector, its covariance matrix and its expectation follow from the Monte Carlo estimate. This saves a considerable amount of derivatives to be computed, and errors of the linearization are avoided. The Monte Carlo method is therefore efficient. If the functions of the measurements are given by a sum of two or more random vectors with different multivariate distributions, the resulting distribution is generally not known. TheMonte Carlo methods are then needed to obtain the covariance matrix and the expectation of the sum.

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38

Beskos, Alexandros, Dan O. Crisan, Ajay Jasra, and Nick Whiteley. "Error Bounds and Normalising Constants for Sequential Monte Carlo Samplers in High Dimensions." Advances in Applied Probability 46, no. 01 (March 2014): 279–306. http://dx.doi.org/10.1017/s0001867800007047.

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In this paper we develop a collection of results associated to the analysis of the sequential Monte Carlo (SMC) samplers algorithm, in the context of high-dimensional independent and identically distributed target probabilities. The SMC samplers algorithm can be designed to sample from a single probability distribution, using Monte Carlo to approximate expectations with respect to this law. Given a target density inddimensions our results are concerned withd→ ∞, while the number of Monte Carlo samples,N, remains fixed. We deduce an explicit bound on the Monte-Carlo error for estimates derived using the SMC sampler and the exact asymptotic relative-error of the estimate of the normalising constant associated to the target. We also establish marginal propagation of chaos properties of the algorithm. These results are deduced when the cost of the algorithm isO(Nd2).

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39

Laureau, Axel, Vincent Lamirand, Dimitri Rochman, and Andreas Pautz. "Total Monte Carlo acceleration for the PETALE experimental programme in the CROCUS reactor." EPJ Web of Conferences 211 (2019): 03002. http://dx.doi.org/10.1051/epjconf/201921103002.

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The Bayesian Monte Carlo technics requires individual evaluations of random cross section files based on a Total Monte Carlo propagation. This article discusses the use of a Correlated Sampling acceleration applied to TMC calculations for experiments where a brute force technics is too expensive. An e_cient estimation of the reaction rate uncertainties in small dosimeters is obtained, together with the inter-dosimeter correlation associated to the cross section uncertainties.

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40

Zhang, Li Quan. "The Atmospheric Propagation Simulation Characteristic of the Solar Blind Ultraviolet Light." Applied Mechanics and Materials 229-231 (November 2012): 2623–28. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.2623.

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In this paper, by using Monte Carlo method to study the Solar blind area in the near-Earth atmosphere ultraviolet non-line-of-sight propagation characteristics, and the use of Point to the probability method establish a rapid Monte Carlo model, this model can effectively simulate UV with complex boundary near Earth atmosphere system response function. Comparing with the single-scatter model it shows that, this model has higher accuracy and boundary processing ability. Simulation of obstacle on ultraviolet signal distribution effects, it shows that the UV signal has strong detouring ability. Different elevation on the UV signal propagation is analyzed, the simulation results are consistent with experimental results.

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41

Li, Jin Hai, Ru Song Tong, and Suo Sheng Cao. "Analysis of Uncertainty in Standard Metal Tank Volume Verification with Monte Carlo Method." Advanced Materials Research 712-715 (June 2013): 1974–78. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.1974.

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The uncertainty in standard metal tank volume value verification is evaluated by using Monte Carlo Method. For second standard metal tank, verification is conducted with volume comparison method. A mathematical model of second standard metal tank volume measurement is established by using first standard metal tank to measure second standard metal tank. An analog simulation is conducted for verification value by using Monte Carlo simulation method, and hence the uncertainty in volume verification is obtained. Through comparison between evaluation result and traditional uncertainty propagation evaluation method, the result indicates that the difference cannot be ignored and the evaluation result by using Monte Carlo Simulation Method is more reliable.

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42

Tang, Yi Nan, Xiao Ping Xie, and Wei Zhao. "Performances of Non-Line-of-Sight Ultraviolet Multi-Scatter Propagation for Noncoplanar Geometries." Advanced Materials Research 571 (September 2012): 214–18. http://dx.doi.org/10.4028/www.scientific.net/amr.571.214.

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A multi-scatter propagation model based on Monte Carlo method is presented. This model can be applied to all the geometries, including coplanar or noncoplanar scenario. The mathematical description of this model is deduced. We obtain the spatial positions of photon with three Cartesian coordinates after each propagation step and the received judgment conditions. Employing a photon tracing technique, Monte Carlo simulation is performed to investigate the signal impulse response and the path loss. The results indicate that, when the off-axis angle increases, the amplitude of the impulse response decreases, while the path loss increases. In addition, it is observed that the pulse width increases with the off-axis angle.

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43

Zhang, Qiao Fu, Xiao Qing Hu, Yan Jie Zhu, and Ye Li. "Statistical Analysis of the Magnetic Resonance Transmit Radiofrequency Field by the Saturated Turbo FLASH Method." Applied Mechanics and Materials 734 (February 2015): 572–76. http://dx.doi.org/10.4028/www.scientific.net/amm.734.572.

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The error propagation theory and Monte Carlo simulations were employed to quantitatively evaluate the robustness of the saturated Turbo FLASH (Fast Low Angle SHot, satTFL) method. The uncertainty and probability density function (PDF) of the satTFL were derived. An out-of-phase method was introduced to correct flip angles larger than 90 degrees. Monte Carlo simulations were implemented to estimate the impact of Gaussian white noises in the image domain and thus the sensitivity could be visualized for different flip angles and signal to noise ratios (SNRs). The uncertainty, Monte Carlo simulations and experiments show that the satTFL is more precise for flip angles around 90 degrees.

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44

Beskos, Alexandros, Dan O. Crisan, Ajay Jasra, and Nick Whiteley. "Error Bounds and Normalising Constants for Sequential Monte Carlo Samplers in High Dimensions." Advances in Applied Probability 46, no. 1 (March 2014): 279–306. http://dx.doi.org/10.1239/aap/1396360114.

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In this paper we develop a collection of results associated to the analysis of the sequential Monte Carlo (SMC) samplers algorithm, in the context of high-dimensional independent and identically distributed target probabilities. The SMC samplers algorithm can be designed to sample from a single probability distribution, using Monte Carlo to approximate expectations with respect to this law. Given a target density in d dimensions our results are concerned with d → ∞, while the number of Monte Carlo samples, N, remains fixed. We deduce an explicit bound on the Monte-Carlo error for estimates derived using the SMC sampler and the exact asymptotic relative -error of the estimate of the normalising constant associated to the target. We also establish marginal propagation of chaos properties of the algorithm. These results are deduced when the cost of the algorithm is O(Nd2).

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45

Kurdyaeva, Tamara, and Andreas Milias-Argeitis. "Uncertainty propagation for deterministic models of biochemical networks using moment equations and the extended Kalman filter." Journal of The Royal Society Interface 18, no. 181 (August 2021): 20210331. http://dx.doi.org/10.1098/rsif.2021.0331.

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Differential equation models of biochemical networks are frequently associated with a large degree of uncertainty in parameters and/or initial conditions. However, estimating the impact of this uncertainty on model predictions via Monte Carlo simulation is computationally demanding. A more efficient approach could be to track a system of low-order statistical moments of the state. Unfortunately, when the underlying model is nonlinear, the system of moment equations is infinite-dimensional and cannot be solved without a moment closure approximation which may introduce bias in the moment dynamics. Here, we present a new method to study the time evolution of the desired moments for nonlinear systems with polynomial rate laws. Our approach is based on solving a system of low-order moment equations by substituting the higher-order moments with Monte Carlo-based estimates from a small number of simulations, and using an extended Kalman filter to counteract Monte Carlo noise. Our algorithm provides more accurate and robust results compared to traditional Monte Carlo and moment closure techniques, and we expect that it will be widely useful for the quantification of uncertainty in biochemical model predictions.

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46

Poëtte, Gaël. "Efficient uncertainty propagation for photonics: Combining Implicit Semi-analog Monte Carlo (ISMC) and Monte Carlo generalised Polynomial Chaos (MC-gPC)." Journal of Computational Physics 450 (February 2022): 110807. http://dx.doi.org/10.1016/j.jcp.2021.110807.

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47

Ounjutturaporn, Pornpawit, Ramil Kesvarakul, Pipitanon Poonsawat, and Khompee Limpadapun. "Comparison of GUM and Monte Carlo Methods for the Measurement Uncertainty Circular Runout Error of Shafts." International Journal of Engineering and Technology 14, no. 3 (August 2022): 38–42. http://dx.doi.org/10.7763/ijet.2022.v14.1199.

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Measurement uncertainty is one of the most important concepts. The ISO IEC 17025:2005 standard: describes harmonized policies and procedures for testing and calibration laboratories. Guide to the expression of uncertainty in measurement (GUM) is a direct uncertainty analysis method, which calculates the combined standard uncertainty and expanded uncertainty by law of propagation of uncertainty. Monte Carlo Method (MCM) as presented by the (GUM S1) involves the propagation of the distributions of the input sources of uncertainty by using a model to provide the distribution of the output. By random sampling, the probability density function of the input quantities. In this paper, present measurement uncertainty to circular runout error. By use shaft standard with a diameter of 32 mm., length 100 mm. From the experiment results, Comparison of GUM and MCM showed no differences. The cases the estimated uncertainty using the GUM approach slightly overestimated the results obtained with the MCM. However, the use of numerical methods such MCM as a valuable alternative to the GUM approach. The practical use of MCM it has proven to be a fundamental tool, being able to address more complex measurement problems that were limited by the GUM approximations.

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Viganò, Davide, Adriano Annovazzi, and Filippo Maggi. "Monte Carlo Uncertainty Quantification Using Quasi-1D SRM Ballistic Model." International Journal of Aerospace Engineering 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/3765796.

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Compactness, reliability, readiness, and construction simplicity of solid rocket motors make them very appealing for commercial launcher missions and embarked systems. Solid propulsion grants high thrust-to-weight ratio, high volumetric specific impulse, and a Technology Readiness Level of 9. However, solid rocket systems are missing any throttling capability at run-time, since pressure-time evolution is defined at the design phase. This lack of mission flexibility makes their missions sensitive to deviations of performance from nominal behavior. For this reason, the reliability of predictions and reproducibility of performances represent a primary goal in this field. This paper presents an analysis of SRM performance uncertainties throughout the implementation of a quasi-1D numerical model of motor internal ballistics based on Shapiro’s equations. The code is coupled with a Monte Carlo algorithm to evaluate statistics and propagation of some peculiar uncertainties from design data to rocker performance parameters. The model has been set for the reproduction of a small-scale rocket motor, discussing a set of parametric investigations on uncertainty propagation across the ballistic model.

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YUN, TIANLIANG, WEI LI, XIAOYU JIANG, and HUI MA. "MONTE CARLO SIMULATION OF POLARIZED LIGHT SCATTERING IN TISSUES." Journal of Innovative Optical Health Sciences 02, no. 02 (April 2009): 131–35. http://dx.doi.org/10.1142/s1793545809000504.

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We investigate the propagation of polarized light in fibrous tissues such as muscle and skin. The myofibrils and collagen fibers are approximated as long cylinders and the tissue phantom is composed of spherical and cylindrical structures. We apply Monte Carlo method based on this phantom to simulate and analyze polarization imaging process of muscle. The good agreement between the simulation results and the experimental results validate the assumption of the phantom composition. This paper also presents how to describe the fiber orientation distribution and tissue anisotropy according to three parameters derived from the polarization imaging.

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Wang Xiaofang, 王晓芳, 张. 新. Zhang Xin, 张继真 Zhang Jizhen, and 王灵杰 Wang Lingjie. "Ultraviolet Light Atmospheric Scattering Propagation Model Based on Monte Carlo Method." Laser & Optoelectronics Progress 54, no. 11 (2017): 110102. http://dx.doi.org/10.3788/lop54.110102.

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