Strong non-exponential relaxation and memory effects in a fluid with non-linear drag
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| Format: | Preprint |
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2021
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| author | Patrón, A. Sánchez-Rey, B. Prados, A. |
| author_facet | Patrón, A. Sánchez-Rey, B. Prados, A. |
| contents | We analyse the dynamical evolution of a fluid with non-linear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of non-linear Brownian motion, displays a really complex behaviour when quenched to low temperatures. Its glassy response is controlled by a long-lived non-equilibrium state, independent of the degree of non-linearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behaviour persists in the collisionless case, where the fluid is described by the non-linear Fokker-Planck equation. The observed response, which includes non-exponential, algebraic, relaxation and strong memory effects, presents scaling properties: the time evolution of the temperature -- for both relaxation and memory effects -- falls onto a master curve, regardless of the details of the experiment. To account for the observed behaviour in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation -- which considers not only the fourth cumulant but also the sixth one. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2107_12012 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Strong non-exponential relaxation and memory effects in a fluid with non-linear drag Patrón, A. Sánchez-Rey, B. Prados, A. Soft Condensed Matter Statistical Mechanics We analyse the dynamical evolution of a fluid with non-linear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of non-linear Brownian motion, displays a really complex behaviour when quenched to low temperatures. Its glassy response is controlled by a long-lived non-equilibrium state, independent of the degree of non-linearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behaviour persists in the collisionless case, where the fluid is described by the non-linear Fokker-Planck equation. The observed response, which includes non-exponential, algebraic, relaxation and strong memory effects, presents scaling properties: the time evolution of the temperature -- for both relaxation and memory effects -- falls onto a master curve, regardless of the details of the experiment. To account for the observed behaviour in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation -- which considers not only the fourth cumulant but also the sixth one. |
| title | Strong non-exponential relaxation and memory effects in a fluid with non-linear drag |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2107.12012 |