The localization transition of the two-dimensional Lorentz model

Bauer, Teresa; Höfling, Felix; Munk, Tobias; Frey, Erwin; Franosch, Thomas

doi:10.1140/epjst/e2010-01313-1

Cited by 62 publications

(103 citation statements)

References 54 publications

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“…Recent theoretical and simulation studies for a two-dimensional Lorentz model suggested that even though the non-universality of the transport exponent µ − β might originate from a sufficiently strong power-law singularity of the transition rate distribution between pores in three dimensions, narrow gaps responsible for the singularity would not be relevant in two dimensions and the transport exponent for lattices should be recovered. 18,19,21,23 We cannot conclusively determine whether the exponent µ-β is universal, but our analysis suggests this is the case if the system is ergodic. In order to investigate whether the transport exponent µ − β is universal, we estimate the transition rate (W) between two pores and its distribution (ρ(W )).…”

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confidence: 73%

Effect of Polydispersity on Diffusion in Random Obstacle Matrices

et al. 2012

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confidence: 73%

Effect of Polydispersity on Diffusion in Random Obstacle Matrices

et al. 2012

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“…This probably results from the completely different transport mechanism in our model and mechanisms proposed in continuous models (represented by the Lorentz model or by the DMD model) and in models based on a lattice. 33 The presence of a very high value of the exponent m can explain why the exponent a determined in experiments is considerably lower than 0.6-0.7. Thus, the scenario based on the DLL model can be closer to reality than other models, especially in membranes or cells.…”

Section: Discussionmentioning

confidence: 99%

“…This value is located between F c ¼ 0.22 found by Sung and Yethiraj 40 and the value F c ¼ 0.356 obtained by Bauer and coworkers using the Lorentz gas model. 33 …”

Section: Dynamic Behavior Near the Critical Point: The Percolationmentioning

confidence: 99%

“…16 Theoretical treatment of the motion of objects in a crowded environment also results in a subdiffusive behavior. [32][33][34][35][36][37] One should remember that similar motion could be achieved by the inuence of a geometrical connement or forces. Computer simulations showed that this subdiffusive motion in the matrix of immobile obstacles has been characterized by the exponent a located in a narrow range between 0.697 (at the percolation threshold) and 1 (ref.…”

Section: Introductionmentioning

confidence: 99%

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Simulation of diffusion in a crowded environment

Polanowski

Sikorski

2014

Soft Matter

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We performed extensive and systematic simulation studies of two-dimensional fluid motion in a complex crowded environment. In contrast to other studies we focused on cooperative phenomena that occurred if the motion of particles takes place in a dense crowded system, which can be considered as a crude model of a cellular membrane. Our main goal was to answer the following question: how do the fluid molecules move in an environment with a complex structure, taking into account the fact that motions of fluid molecules are highly correlated. The dynamic lattice liquid (DLL) model, which can work at the highest fluid density, was employed. Within the frame of the DLL model we considered cooperative motion of fluid particles in an environment that contained static obstacles. The dynamic properties of the system as a function of the concentration of obstacles were studied. The subdiffusive motion of particles was found in the crowded system. The influence of hydrodynamics on the motion was investigated via analysis of the displacement in closed cooperative loops. The simulation and the analysis emphasize the influence of the movement correlation between moving particles and obstacles.

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“…All this is thoroughly reviewed in ref. [48]. We will now be more quantitative to be able to compare with the ABPs.…”

Section: Mean Squared Displacementmentioning

confidence: 99%

Active Brownian particles moving in a random Lorentz gas

2017

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Abstract. Biological microswimmers often inhabit a porous or crowded environment such as soil. In order to understand how such a complex environment influences their spreading, we numerically study noninteracting active Brownian particles (ABPs) in a two-dimensional random Lorentz gas. Close to the percolation transition in the Lorentz gas, they perform the same subdiffusive motion as ballistic and diffusive particles. However, due to their persistent motion they reach their long-time dynamics faster than passive particles and also show superdiffusive motion at intermediate times. While above the critical obstacle density η c the ABPs are trapped, their long-time diffusion below ηc is strongly influenced by the propulsion speed v 0. With increasing v0, ABPs are stuck at the obstacles for longer times. Thus, for large propulsion speed, the long-time diffusion constant decreases more strongly in a denser obstacle environment than for passive particles. This agrees with the behavior of an effective swimming velocity and persistence time, which we extract from the velocity autocorrelation function.

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The localization transition of the two-dimensional Lorentz model

Cited by 62 publications

References 54 publications

Effect of Polydispersity on Diffusion in Random Obstacle Matrices

Effect of Polydispersity on Diffusion in Random Obstacle Matrices

Simulation of diffusion in a crowded environment

Active Brownian particles moving in a random Lorentz gas

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