Anomalous transport of a tracer on percolating clusters

Spanner, Markus; Höfling, Felix; Schröder‐Turk, Gerd E.; Mecke, Klaus; Franosch, Thomas

doi:10.1088/0953-8984/23/23/234120

Cited by 29 publications

(55 citation statements)

References 57 publications

(104 reference statements)

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“…μ∞ [62] as the transition is approached, corroborating furthermore the exponent relation for the conductivity exponent. Similarly, the scaling hypothesis, equation (5), has been tested by superimposing simulation data t −2/dw δr 2 ∞ (t, ) versus rescaled times t/t ξ .…”

Section: Mean-square Displacement and Diffusionsupporting

confidence: 78%

“…Particles confined to the infinite cluster will eventually display Gaussian transport on length scales larger than the correlation length ξ with corresponding crossover time t ξ ∼ ξ dw . Therefore for obstacle densities below the percolation threshold α (t → ∞) = 0, while directly at the transition a non-trivial finite value for α (∞) 2 (t → ∞) is found [62]. The situation is rather different once all-cluster averages are considered.…”

Section: Non-gaussian Parametermentioning

confidence: 92%

“…Simulation data of ballistic tracers in the 3D Lorentz model [61,62] are displayed in Figure 2 and show anomalous transport for the mean-square displacement at the critical obstacle density over more than 6 decades in time. μ∞ [62] as the transition is approached, corroborating furthermore the exponent relation for the conductivity exponent.…”

Section: Mean-square Displacement and Diffusionmentioning

confidence: 99%

“…Similarly, the scaling hypothesis, equation (5), has been tested by superimposing simulation data t −2/dw δr 2 ∞ (t, ) versus rescaled times t/t ξ . It appears that convergence to the scaling law is significantly slower [51,54,62] than for the exponents emphasizing that scaling behavior is a more stringent condition on the dynamics than power-law behavior. However, the corrections to scaling are anticipated to be again universal and a considerably better data collapse is achieved by incorporating these corrections in terms of the known exponent for the corrections of the cluster-size distribution [62,64].…”

Section: Mean-square Displacement and Diffusionmentioning

confidence: 99%

“…The scaling hypothesis for the mean-square displacement, equation (5), translates to each of these cases and has been tested, e.g. to discuss the crossover in the frequency-dependent linear response from dispersive to Ohmic transport [61,62].…”

Section: Mean-square Displacement and Diffusionmentioning

confidence: 99%

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Complex dynamics induced by strong confinement – From tracer diffusion in strongly heterogeneous media to glassy relaxation of dense fluids in narrow slits

Mandal

Spanner-Denzer

Leitmann

et al. 2017

Eur. Phys. J. Spec. Top.

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Abstract. We provide an overview of recent advances of the complex dynamics of particles in strong confinements. The first paradigm is the Lorentz model where tracers explore a quenched disordered host structure. Such systems naturally occur as limiting cases of binary glassforming systems if the dynamics of one component is much faster than the other. For a certain critical density of the host structure the tracers undergo a localization transition which constitutes a critical phenomenon. A series of predictions in the vicinity of the transition have been elaborated and tested versus computer simulations. Analytical progress is achieved for small obstacle densities. The second paradigm is a dense strongly interacting liquid confined to a narrow slab. Then the glass transition depends nonmonotonically on the separation of the plates due to an interplay of local packing and layering. Very small slab widths allow to address certain features of the statics and dynamics analytically.

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Section: Mean-square Displacement and Diffusionsupporting

confidence: 78%

Section: Non-gaussian Parametermentioning

confidence: 92%

Section: Mean-square Displacement and Diffusionmentioning

confidence: 99%

Section: Mean-square Displacement and Diffusionmentioning

confidence: 99%

Section: Mean-square Displacement and Diffusionmentioning

confidence: 99%

See 3 more Smart Citations

Complex dynamics induced by strong confinement – From tracer diffusion in strongly heterogeneous media to glassy relaxation of dense fluids in narrow slits

Mandal

Spanner-Denzer

Leitmann

et al. 2017

Eur. Phys. J. Spec. Top.

Self Cite

View full text Add to dashboard Cite

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Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

Soula

Caré

Beslon

et al. 2013

Biophysical Journal

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Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.

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Subdiffusive Dynamics Lead to Depleted Particle Densities near Cellular Borders

Holmes

2019

Biophysical Journal

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It has long been known that the complex cellular environment leads to anomalous motion of intracellular particles. At a gross level, this is characterized by mean-squared displacements that deviate from the standard linear profile. Statistical analysis of particle trajectories has helped further elucidate how different characteristics of the cellular environment can introduce different types of anomalousness. A significant majority of this literature has, however, focused on characterizing the properties of trajectories that do not interact with cell borders (e.g., cell membrane or nucleus). Numerous biological processes ranging from protein activation to exocytosis, however, require particles to be near a membrane. This study investigates the consequences of a canonical type of subdiffusive motion, fractional Brownian motion, and its physical analog, generalized Langevin equation dynamics, on the spatial localization of particles near reflecting boundaries. Results show that this type of subdiffusive motion leads to the formation of significant zones of depleted particle density near boundaries and that this effect is independent of the specific model details encoding those dynamics. Rather, these depletion layers are a natural and robust consequence of the anticorrelated nature of motion increments that is at the core of fractional Brownian motion (or alternatively generalized Langevin equation) dynamics. If such depletion zones are present, it would be of profound importance given the wide array of signaling and transport processes that occur near membranes. If not, that would suggest our understanding of this type of anomalous motion may be flawed. Either way, this result points to the need to further investigate the consequences of anomalous particle motions near cell borders from both theoretical and experimental perspectives.

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Anomalous transport of a tracer on percolating clusters

Cited by 29 publications

References 57 publications

Complex dynamics induced by strong confinement – From tracer diffusion in strongly heterogeneous media to glassy relaxation of dense fluids in narrow slits

Complex dynamics induced by strong confinement – From tracer diffusion in strongly heterogeneous media to glassy relaxation of dense fluids in narrow slits

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

Subdiffusive Dynamics Lead to Depleted Particle Densities near Cellular Borders

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