On the motion of a convex body interacting with a perfect gas in the mean-field approximation
We consider a convex body in R^3, moving along the x-axis, immersed in an infinitely extended perfect gas in the mean-field approximation. We assume that the gas particles interact with the body by means of elastic collisions. Giving to the body an initial velocity V_0, we prove that, for |V_0| sm...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2007-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2007(2)/123-145.pdf |
| _version_ | 1818022295379116032 |
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| author | G. Cavallaro |
| author_facet | G. Cavallaro |
| author_sort | G. Cavallaro |
| collection | DOAJ |
| description | We consider a convex body in R^3, moving along the x-axis, immersed in an infinitely extended perfect gas in the mean-field approximation. We assume that
the gas particles interact with the body by means of elastic collisions. Giving to the body an initial velocity V_0, we prove that, for |V_0| small enough, |V (t)| ≈ C t^{−5} for large t, being C a positive constant depending on the medium and on the shape of the obstacle. The power law approach to the equilibrium V = 0, instead of the exponential one (typical in viscous friction problems), is due to the long memory effect of the recollisions. This paper completes the analysis made in previous papers (see [7] and [8]), in which for simplicity the body was assumed to be a disk. |
| first_indexed | 2024-04-14T08:30:31Z |
| format | Article |
| id | doaj.art-d7aad61545c04b8da1a425ebaaaafe49 |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-04-14T08:30:31Z |
| publishDate | 2007-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-d7aad61545c04b8da1a425ebaaaafe492022-12-22T02:03:56ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502007-01-01272123145On the motion of a convex body interacting with a perfect gas in the mean-field approximationG. Cavallaro0Università di Roma La SapienzaWe consider a convex body in R^3, moving along the x-axis, immersed in an infinitely extended perfect gas in the mean-field approximation. We assume that the gas particles interact with the body by means of elastic collisions. Giving to the body an initial velocity V_0, we prove that, for |V_0| small enough, |V (t)| ≈ C t^{−5} for large t, being C a positive constant depending on the medium and on the shape of the obstacle. The power law approach to the equilibrium V = 0, instead of the exponential one (typical in viscous friction problems), is due to the long memory effect of the recollisions. This paper completes the analysis made in previous papers (see [7] and [8]), in which for simplicity the body was assumed to be a disk.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2007(2)/123-145.pdfviscous frictionmicroscopic dynamicsdynamics with memory |
| spellingShingle | G. Cavallaro On the motion of a convex body interacting with a perfect gas in the mean-field approximation Rendiconti di Matematica e delle Sue Applicazioni viscous friction microscopic dynamics dynamics with memory |
| title | On the motion of a convex body interacting with a perfect gas in the mean-field approximation |
| title_full | On the motion of a convex body interacting with a perfect gas in the mean-field approximation |
| title_fullStr | On the motion of a convex body interacting with a perfect gas in the mean-field approximation |
| title_full_unstemmed | On the motion of a convex body interacting with a perfect gas in the mean-field approximation |
| title_short | On the motion of a convex body interacting with a perfect gas in the mean-field approximation |
| title_sort | on the motion of a convex body interacting with a perfect gas in the mean field approximation |
| topic | viscous friction microscopic dynamics dynamics with memory |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2007(2)/123-145.pdf |
| work_keys_str_mv | AT gcavallaro onthemotionofaconvexbodyinteractingwithaperfectgasinthemeanfieldapproximation |