# Critical dynamics of ballistic and Brownian particles in a heterogeneous environment.

@article{Hfling2007CriticalDO, title={Critical dynamics of ballistic and Brownian particles in a heterogeneous environment.}, author={Felix H{\"o}fling and Tobias Munk and Erwin Frey and Thomas Franosch}, journal={The Journal of chemical physics}, year={2007}, volume={128 16}, pages={ 164517 } }

The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed large-scale computer simulations, demonstrating that universality holds at long times in the immediate vicinity of the transition. The scaling function describing the crossover from anomalous transport to diffusive motion is found to vary extremely slowly and…

## 54 Citations

### The localization transition of the two-dimensional Lorentz model

- Physics
- 2010

Abstract.
We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle…

### Confined diffusion in a random Lorentz gas environment.

- PhysicsPhysical review. E
- 2020

The diffusive behavior of biased Brownian particles in a two dimensional confined geometry filled with the freezing obstacles is studied and a relation between η and f is found which provides an estimate of the minimum η up to a critical scaling parameter f_{c} beyond which the Fick-Jacobs description is invalid.

### Persistent memory for a Brownian walker in a random array of obstacles

- PhysicsChemical Physics
- 2010

### Crowding of Interacting Fluid Particles in Porous Media through Molecular Dynamics: Breakdown of Universality for Soft Interactions.

- PhysicsPhysical review letters
- 2018

The soft interactions are responsible for the breakdown of the universality of the dynamics of the Lorentz model scenario, as the system exhibits a transition from a diffusive to a localized state, but the transition is strongly rounded.

### Anomalous transport of a tracer on percolating clusters

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2011

The dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster shows anomalous transport, which extends to infinite times precisely at the critical obstacle density.

### Brownian motion of a self-propelled particle

- MathematicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2011

Comparing the dynamics of real and artificial microswimmers, like bacteria or catalytically driven Janus particles, to the analytical expressions reveals whether their motion is Brownian or not.

### Brownian motion of a self-propelled particle.

- Mathematics
- 2011

Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented…

### Dynamic arrest in model porous media—intermediate scattering functions

- Physics
- 2012

Heterogeneous media constitute random disordered environments where transport is drastically hindered. Employing extensive molecular dynamics simulations, we investigate the spatio-temporal dynamics…

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

- Physics
- 2017

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…

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