This work presents a Monte Carlo computational approach for solving the spatially homo-geneous nonlinear Boltzmann equation through a modified “particle-in-cells” model. Building upon theBelotserkovski-Yanitski and Kac models, the paper introduces a stochastic simulation scheme that synthe-sizes the principle of splitting operators with branching Markov processes. The method constructs unbiasedestimators with small variance to compute molecular velocities and particle distributions, providing highernumerical accuracy and physical realism compared to traditional linear models. The developed algorithmenables efficient simulation of rarefied gas dynamics and demonstrates stable results across varying particledensities. Computational experiments, including shock wave structure modeling, show that this approachachieves improved convergence and fidelity in approximating spatially heterogeneous Boltzmann behavior.
| Mualliflar | Rasulov, Abdujabar, Raimova, Gulnora, Rakhmatov, Makhmadrasul |
|---|---|
| Jurnal | Ўзбекистон Миллий университети хабарлари |
| Nashriyot | Ўзбекистон Миллий университети |
| ISSN | 2181-7324, 3093-8996 |
| Nashr sanasi | 2026-10-07 |
| Jild | 2 |
| Son | 2.3 |
| Betlar | 184-189 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-10-08 |
Spatially Homogeneous Boltzmann equation, Particle-in-Cell Model, Branching Markov pro- cess, Monte Carlo Method, Unbiased Estimator, Conjugated Computational Schemes
| APA | Rasulov, Abdujabar, Raimova, Gulnora, & Rakhmatov, Makhmadrasul (2026). Monte Carlo method for the Spatially Homogenous Boltzmann equation. Ўзбекистон Миллий университети хабарлари, 2(2.3), 184-189. https://journals.nuu.uz/index.php/actanuuz/article/view/15279 |
|---|---|
| GOST (OAK) | Rasulov, Abdujabar, Raimova, Gulnora, Rakhmatov, Makhmadrasul Monte Carlo method for the Spatially Homogenous Boltzmann equation // Ўзбекистон Миллий университети хабарлари. – 2026. – T. 2, № 2.3. – P. 184-189. |
| MLA | Rasulov, Abdujabar, Raimova, Gulnora, and Rakhmatov, Makhmadrasul. “Monte Carlo method for the Spatially Homogenous Boltzmann equation.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 184-189, 2026. https://journals.nuu.uz/index.php/actanuuz/article/view/15279 |
| Chicago | Rasulov, Abdujabar, Raimova, Gulnora, and Rakhmatov, Makhmadrasul. “Monte Carlo method for the Spatially Homogenous Boltzmann equation.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 184-189 (2026). https://journals.nuu.uz/index.php/actanuuz/article/view/15279 |
| Harvard | Rasulov, Abdujabar, Raimova, Gulnora, and Rakhmatov, Makhmadrasul (2026) ‘Monte Carlo method for the Spatially Homogenous Boltzmann equation’, Ўзбекистон Миллий университети хабарлари, 2(2.3), 184-189. https://journals.nuu.uz/index.php/actanuuz/article/view/15279 |
| BibTeX | @article{rasulovabdujabar2026,
title = {Monte Carlo method for the Spatially Homogenous Boltzmann equation},
author = {Rasulov, Abdujabar and Raimova, Gulnora and Rakhmatov, Makhmadrasul},
journal = {Ўзбекистон Миллий университети хабарлари},
year = {2026},
volume = {2},
number = {2.3},
pages = {184-189},
url = {https://journals.nuu.uz/index.php/actanuuz/article/view/15279}
} |
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