From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description
The generalized elastic model encompasses several linear stochastic models describing the dynamics of polymers, membranes, rough surfaces, and fluctuating interfaces. While usually defined in the overdamped case, in this paper we formally include the inertial term to account for the initial diffusiv...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-01-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/5/1/3 |
| _version_ | 1818245427636469760 |
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| author | Alessandro Taloni |
| author_facet | Alessandro Taloni |
| author_sort | Alessandro Taloni |
| collection | DOAJ |
| description | The generalized elastic model encompasses several linear stochastic models describing the dynamics of polymers, membranes, rough surfaces, and fluctuating interfaces. While usually defined in the overdamped case, in this paper we formally include the inertial term to account for the initial diffusive stages of the stochastic dynamics. We derive the generalized Langevin equation for a probe particle and we show that this equation reduces to the usual Langevin equation for Brownian motion, and to the fractional Langevin equation on the long-time limit. |
| first_indexed | 2024-12-12T14:32:45Z |
| format | Article |
| id | doaj.art-476bf170c1534f1388284c7bb48f2c5f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-12T14:32:45Z |
| publishDate | 2017-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-476bf170c1534f1388284c7bb48f2c5f2022-12-22T00:21:28ZengMDPI AGMathematics2227-73902017-01-0151310.3390/math5010003math5010003From the Underdamped Generalized Elastic Model to the Single Particle Langevin DescriptionAlessandro Taloni0Center for Complexity and Biosystems and Department of Physics, University of Milano, Via Celoria 16, 20133 Milano, ItalyThe generalized elastic model encompasses several linear stochastic models describing the dynamics of polymers, membranes, rough surfaces, and fluctuating interfaces. While usually defined in the overdamped case, in this paper we formally include the inertial term to account for the initial diffusive stages of the stochastic dynamics. We derive the generalized Langevin equation for a probe particle and we show that this equation reduces to the usual Langevin equation for Brownian motion, and to the fractional Langevin equation on the long-time limit.http://www.mdpi.com/2227-7390/5/1/3fractional calculusstochastic processesLangevin equation |
| spellingShingle | Alessandro Taloni From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description Mathematics fractional calculus stochastic processes Langevin equation |
| title | From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description |
| title_full | From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description |
| title_fullStr | From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description |
| title_full_unstemmed | From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description |
| title_short | From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description |
| title_sort | from the underdamped generalized elastic model to the single particle langevin description |
| topic | fractional calculus stochastic processes Langevin equation |
| url | http://www.mdpi.com/2227-7390/5/1/3 |
| work_keys_str_mv | AT alessandrotaloni fromtheunderdampedgeneralizedelasticmodeltothesingleparticlelangevindescription |