Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles
In this study, we investigate the behavior of free inertial active Brownian particles in the presence of thermal noise. While finding a closed-form solution for the joint distribution of positions, orientations, and velocities using the Fokker–Planck equation is generally challenging, we utilize a L...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ad1538 |
| _version_ | 1827396752902193152 |
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| author | Manish Patel Debasish Chaudhuri |
| author_facet | Manish Patel Debasish Chaudhuri |
| author_sort | Manish Patel |
| collection | DOAJ |
| description | In this study, we investigate the behavior of free inertial active Brownian particles in the presence of thermal noise. While finding a closed-form solution for the joint distribution of positions, orientations, and velocities using the Fokker–Planck equation is generally challenging, we utilize a Laplace transform method to obtain the exact temporal evolution of all dynamical moments in arbitrary dimensions. Our expressions in d dimensions reveal that inertia significantly impacts steady-state kinetic temperature and swim pressure while leaving the late-time diffusivity unchanged. Notably, as a function of activity and inertia, the steady-state velocity distribution exhibits a remarkable re-entrant crossover from ‘passive’ Gaussian to ‘active’ non-Gaussian behaviors. We construct a corresponding ‘phase diagram’ using the exact expression of the d -dimensional kurtosis. Our analytic expressions describe steady states and offer insights into time-dependent crossovers observed in moments of velocity and displacement. Our calculations can be extended to predict up to second-order moments for run-and-tumble particles and the active Ornstein–Uhlenbeck process (AOUP). Additionally, the kurtosis shows differences from AOUP. |
| first_indexed | 2024-03-08T18:56:50Z |
| format | Article |
| id | doaj.art-5ff23cd9e03c45f2a8827822c397eef6 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-08T18:56:50Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-5ff23cd9e03c45f2a8827822c397eef62023-12-28T11:18:49ZengIOP PublishingNew Journal of Physics1367-26302023-01-01251212304810.1088/1367-2630/ad1538Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particlesManish Patel0Debasish Chaudhuri1https://orcid.org/0000-0003-1759-125XInstitute of Physics , Sachivalaya Marg, Bhubaneswar 751005, India; Homi Bhabha National Institute , Anushaktinagar, Mumbai 400094, IndiaInstitute of Physics , Sachivalaya Marg, Bhubaneswar 751005, India; Homi Bhabha National Institute , Anushaktinagar, Mumbai 400094, IndiaIn this study, we investigate the behavior of free inertial active Brownian particles in the presence of thermal noise. While finding a closed-form solution for the joint distribution of positions, orientations, and velocities using the Fokker–Planck equation is generally challenging, we utilize a Laplace transform method to obtain the exact temporal evolution of all dynamical moments in arbitrary dimensions. Our expressions in d dimensions reveal that inertia significantly impacts steady-state kinetic temperature and swim pressure while leaving the late-time diffusivity unchanged. Notably, as a function of activity and inertia, the steady-state velocity distribution exhibits a remarkable re-entrant crossover from ‘passive’ Gaussian to ‘active’ non-Gaussian behaviors. We construct a corresponding ‘phase diagram’ using the exact expression of the d -dimensional kurtosis. Our analytic expressions describe steady states and offer insights into time-dependent crossovers observed in moments of velocity and displacement. Our calculations can be extended to predict up to second-order moments for run-and-tumble particles and the active Ornstein–Uhlenbeck process (AOUP). Additionally, the kurtosis shows differences from AOUP.https://doi.org/10.1088/1367-2630/ad1538active Brownian particlesinertial effectexact dynamical momentsre-entrant transitions |
| spellingShingle | Manish Patel Debasish Chaudhuri Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles New Journal of Physics active Brownian particles inertial effect exact dynamical moments re-entrant transitions |
| title | Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles |
| title_full | Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles |
| title_fullStr | Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles |
| title_full_unstemmed | Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles |
| title_short | Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles |
| title_sort | exact moments and re entrant transitions in the inertial dynamics of active brownian particles |
| topic | active Brownian particles inertial effect exact dynamical moments re-entrant transitions |
| url | https://doi.org/10.1088/1367-2630/ad1538 |
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