1994 |
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| 2. | Barma, M; Ramaswamy, R Field–induced transport in random media Conference Non-Linearity and Breakdown in Soft Condensed Matter, Springer, Calcutta, India, 1994. Abstract | Links | BibTeX | Tags: Random Walk @conference{Barma1994, title = {Field–induced transport in random media}, author = {M Barma and R Ramaswamy}, url = {https://link.springer.com/chapter/10.1007/3-540-58652-0_45}, year = {1994}, date = {1994-01-01}, booktitle = {Non-Linearity and Breakdown in Soft Condensed Matter}, pages = {309-330}, publisher = {Springer}, address = {Calcutta, India}, abstract = {We review the problem of particle transport in random media in the presence of an external field. The random medium is modeled by the infinite cluster above the percolation threshold. The field imposes a preferred direction of motion along which diffusing particles (random walkers are more likely to move than against. Two kinds of traps occur – branches pointing in the direction of the field, and backbends, in which particles must move against the field. For noninteracting particles, the drift velocity is a nonmonotonic function of the biasing field, and the two kinds of traps make the current vanish above a threshold value of the bias. If there is hard-core repulsion between the particles, branches get filled up and eventually cease to be traps. Below the directed percolation threshold, transport is rate-limited by backbends, and the particle current flows predominantly along those paths on the percolation backbone on which the length of every backbend is bounded. The current is a nonmonotonic function of the biasing field. We also consider a different sort of interparticle interaction which leads to levels of particles equalising near backbend bottoms. The motion along a typical path is then described by ‘drop-push’ dynamics: between backbends, particles drop down, assisted by the field, and push those on the next backbend, possibly leading to a cascade of overflows. Drop-push dynamics has interesting connections with other lattice gas automata, and Monte Carlo simulations show that the model supports kinematic waves and exhibits interesting behaviour of time-dependent correlations.}, keywords = {Random Walk}, pubstate = {published}, tppubtype = {conference} } We review the problem of particle transport in random media in the presence of an external field. The random medium is modeled by the infinite cluster above the percolation threshold. The field imposes a preferred direction of motion along which diffusing particles (random walkers are more likely to move than against. Two kinds of traps occur – branches pointing in the direction of the field, and backbends, in which particles must move against the field. For noninteracting particles, the drift velocity is a nonmonotonic function of the biasing field, and the two kinds of traps make the current vanish above a threshold value of the bias. If there is hard-core repulsion between the particles, branches get filled up and eventually cease to be traps. Below the directed percolation threshold, transport is rate-limited by backbends, and the particle current flows predominantly along those paths on the percolation backbone on which the length of every backbend is bounded. The current is a nonmonotonic function of the biasing field. We also consider a different sort of interparticle interaction which leads to levels of particles equalising near backbend bottoms. The motion along a typical path is then described by ‘drop-push’ dynamics: between backbends, particles drop down, assisted by the field, and push those on the next backbend, possibly leading to a cascade of overflows. Drop-push dynamics has interesting connections with other lattice gas automata, and Monte Carlo simulations show that the model supports kinematic waves and exhibits interesting behaviour of time-dependent correlations. |
1987 |
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| 1. | Ramaswamy, R; Barma, M Transport in random networks in a field: Interacting particles Journal Article Journal of Physics A: Mathematical and General, 20 (10), pp. 2973–2987, 1987, ISSN: 03054470. Abstract | Links | BibTeX | Tags: Monte Carlo, Random Network, Random Walk, Transport @article{Ramaswamy1987, title = {Transport in random networks in a field: Interacting particles}, author = {R Ramaswamy and M Barma}, url = {https://ramramaswamy.org/papers/031.pdf}, doi = {10.1088/0305-4470/20/10/039}, issn = {03054470}, year = {1987}, date = {1987-01-01}, journal = {Journal of Physics A: Mathematical and General}, volume = {20}, number = {10}, pages = {2973–2987}, abstract = {Transport through a random medium in an external field is modelled by particles performing biased random walks on the infinite cluster above the percolation threshold. Steps are more likely in the direction of the field-say downward-than against. A particle is allowed to move only onto an empty site (particles interact via hard core exclusion). Branches that predominantly point downwards and backbends-backbone segments on which particles must move upwards-act as traps. The authors have studied the movement of interacting random walkers in branches and backbends by Monte Carlo simulations and also analytically. In the full network, the trap-limited current flows primarily through the part of the backbond composed of paths with the smallest backbends and its magnitude in high fields is estimated. Unlike in the absence of interactions, the drift velocity does not vanish in finite fields. However, it continues to show a non-monotonic dependence on the field over a sizeable range of density and percolation probability.}, keywords = {Monte Carlo, Random Network, Random Walk, Transport}, pubstate = {published}, tppubtype = {article} } Transport through a random medium in an external field is modelled by particles performing biased random walks on the infinite cluster above the percolation threshold. Steps are more likely in the direction of the field-say downward-than against. A particle is allowed to move only onto an empty site (particles interact via hard core exclusion). Branches that predominantly point downwards and backbends-backbone segments on which particles must move upwards-act as traps. The authors have studied the movement of interacting random walkers in branches and backbends by Monte Carlo simulations and also analytically. In the full network, the trap-limited current flows primarily through the part of the backbond composed of paths with the smallest backbends and its magnitude in high fields is estimated. Unlike in the absence of interactions, the drift velocity does not vanish in finite fields. However, it continues to show a non-monotonic dependence on the field over a sizeable range of density and percolation probability. |