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The Monte Carlo Method
Abstract
We shall present here the motivation and a general description of a method dealing with a class of problems in mathematical physics. The method is, essentially, a statistical approach to the study of differential equations, or more generally, of integro-differential equations that occur in various branches of the natural sciences.
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“Frequently, the study of thermodynamical properties and observables, such as adsorption isotherms, Henry constants, heats of adsorption, is carried out via Monte Carlo simulations, which are based on statistical mechanics.344−346”
From Zeolites in Adsorption Processes: State of the Art and Future Prospects (2022) · cites this paper as [344]
In the citing paper
“Because bootstrapping of standard errors of the indirect effects was not possible with Lavaan, con fi dence intervals (95%) for indirect effects in the multiple imputed datasets were estimated using the Monte Carlo sampling method (Metropolis & Ulam, 1949).”
From Mindfulness, Self-compassion, and Psychological Wellbeing as Correlates of Paternal Bonding in Pregnancy. (2025) · cites this paper as Metropolis & Ulam, 1949
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Dauchet, J., Cornet, J.-F., Gros, F., Roudet, M., & Dussap, C.-G. (2016) · Advances in Chemical Engineering · doi:10.1016/bs.ache.2015.11.003 · Cited by 28
Typing Exercises as Interactive Worked Examples for Deliberate Practice in CS Courses
Gaweda, A. M., Lynch, C. F., Seamon, N., Silva de Oliveira, G., & Deliwa, A. (2020) · Proceedings of the Twenty-Second Australasian Computing Education Conference · doi:10.1145/3373165.3373177 · Cited by 21
“For example, to implement the Monte Carlo algorithm [34] for”
MethodModular large language model agents for multi-task computational materials science
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“The continuum simulation agent executes advanced materials science simulations, integrating two key modeling techniques: Cellular Automata (CA) 51,52 for phase transformations and Monte Carlo Annealing (MCA) 50,53 for microstructural evolution during annealing.”
The Game of Bridge: A Challenge for ILP
Legras, S., Rouveirol, C., & Ventos, V. (2018) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-99960-9_5 · Cited by 7
de Waal, N., Nyklíček, I., van der Gucht, K., Pop, V. J. M., & Boekhorst, M. G. B. M. (2025) · Journal of Child and Family Studies · doi:10.1007/s10826-024-02968-y · Cited by 1
“%) for indirect effects in the multiple imputed datasets were estimated using the Monte Carlo sampling method (Metropolis & Ulam, 1949).”
Binder (1997) · doi:10.1002/(sici)1099-0488(19970115)35:1
Metadata
- Authors
- Metropolis, N., & Ulam, S.
- Affiliations
- Los Alamos National Laboratory (US)
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1949-09
- Volume
- 44
- Issue
- 247
- Pages
- 335-341
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2051203581
- Cited by
- 6,474
- References
- 0
- Citations by year
- 2026: 368 · 2025: 419 · 2024: 327 · 2023: 345 · 2022: 333 · 2021: 343 · 2020: 318 · 2019: 304 · 2018: 270 · 2017: 252 · 2016: 258 · 2015: 249 · 2014: 254 · 2013: 283 · 2012: 262
- FWCI
- 8.97
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Mathematics › Numerical Analysis › Mathematical Approximation and Integration
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- Monte Carlo methods, integro-differential equations, mathematical physics, numerical solution of partial differential equations
- MeSH terms
- Biometry, Humans, Monte Carlo Method, Statistics as Topic
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