Tracer diffusion on a crowded random Manhattan lattice
We study, by extensive numerical simulations, the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder— frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The l...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2020-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ab7bf1 |
| _version_ | 1797750316482953216 |
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| author | Carlos Mejía-Monasterio Sergei Nechaev Gleb Oshanin Oleg Vasilyev |
| author_facet | Carlos Mejía-Monasterio Sergei Nechaev Gleb Oshanin Oleg Vasilyev |
| author_sort | Carlos Mejía-Monasterio |
| collection | DOAJ |
| description | We study, by extensive numerical simulations, the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder— frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The latter perform lattice random walks, constrained by a single-occupancy condition of each lattice site, and are either insensitive to random flows (model A) or choose the jump directions as dictated by the local directionality of bonds of the random Manhattan lattice (model B). We focus on the TP disorder-averaged mean-squared displacement, (which shows a super-diffusive behaviour ∼ t ^4/3 , t being time, in all the cases studied here), on higher moments of the TP displacement, and on the probability distribution of the TP position X along the x -axis, for which we unveil a previously unknown behaviour. Indeed, our analysis evidences that in absence of the lattice gas particles the latter probability distribution has a Gaussian central part $\sim \exp (-{u}^{2})$ , where u = X / t ^2/3 , and exhibits slower-than-Gaussian tails $\sim \exp (-| u{| }^{4/3})$ for sufficiently large t and u . Numerical data convincingly demonstrate that in presence of a crowded environment the central Gaussian part and non-Gaussian tails of the distribution persist for both models. |
| first_indexed | 2024-03-12T16:30:57Z |
| format | Article |
| id | doaj.art-e715a005067b4fa89f81f682d52b6008 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:30:57Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
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| series | New Journal of Physics |
| spelling | doaj.art-e715a005067b4fa89f81f682d52b60082023-08-08T15:30:19ZengIOP PublishingNew Journal of Physics1367-26302020-01-0122303302410.1088/1367-2630/ab7bf1Tracer diffusion on a crowded random Manhattan latticeCarlos Mejía-Monasterio0Sergei Nechaev1Gleb Oshanin2https://orcid.org/0000-0001-8467-3226Oleg Vasilyev3School of Agricultural, Food and Biosystems Engineering, Technical University of Madrid , Av. Complutense s/n, E-28040 Madrid, SpainInterdisciplinary Scientific Center J.-V. Poncelet (UMI CNRS 2615), Bolshoy Vlasyevskiy Lane 11, 119002 Moscow, Russia; Lebedev Physical Institute RAS, 119991, Moscow, RussiaInterdisciplinary Scientific Center J.-V. Poncelet (UMI CNRS 2615), Bolshoy Vlasyevskiy Lane 11, 119002 Moscow, Russia; Sorbonne Université , CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), 4 Place Jussieu, F-75252 Paris Cedex 05, FranceMax-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569, Stuttgart, Germany; IV. Institut für Theoretische Physik, Universität Stuttgart , Pfaffenwaldring 57, D-70569 Stuttgart, GermanyWe study, by extensive numerical simulations, the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder— frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The latter perform lattice random walks, constrained by a single-occupancy condition of each lattice site, and are either insensitive to random flows (model A) or choose the jump directions as dictated by the local directionality of bonds of the random Manhattan lattice (model B). We focus on the TP disorder-averaged mean-squared displacement, (which shows a super-diffusive behaviour ∼ t ^4/3 , t being time, in all the cases studied here), on higher moments of the TP displacement, and on the probability distribution of the TP position X along the x -axis, for which we unveil a previously unknown behaviour. Indeed, our analysis evidences that in absence of the lattice gas particles the latter probability distribution has a Gaussian central part $\sim \exp (-{u}^{2})$ , where u = X / t ^2/3 , and exhibits slower-than-Gaussian tails $\sim \exp (-| u{| }^{4/3})$ for sufficiently large t and u . Numerical data convincingly demonstrate that in presence of a crowded environment the central Gaussian part and non-Gaussian tails of the distribution persist for both models.https://doi.org/10.1088/1367-2630/ab7bf1random Manhattan latticetracer diffusionhard-core lattice gassimple exclusion processquenched versus dynamical disorder |
| spellingShingle | Carlos Mejía-Monasterio Sergei Nechaev Gleb Oshanin Oleg Vasilyev Tracer diffusion on a crowded random Manhattan lattice New Journal of Physics random Manhattan lattice tracer diffusion hard-core lattice gas simple exclusion process quenched versus dynamical disorder |
| title | Tracer diffusion on a crowded random Manhattan lattice |
| title_full | Tracer diffusion on a crowded random Manhattan lattice |
| title_fullStr | Tracer diffusion on a crowded random Manhattan lattice |
| title_full_unstemmed | Tracer diffusion on a crowded random Manhattan lattice |
| title_short | Tracer diffusion on a crowded random Manhattan lattice |
| title_sort | tracer diffusion on a crowded random manhattan lattice |
| topic | random Manhattan lattice tracer diffusion hard-core lattice gas simple exclusion process quenched versus dynamical disorder |
| url | https://doi.org/10.1088/1367-2630/ab7bf1 |
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