arXiv subjects

Tobias Munk

Publications and source records attributed to Tobias Munk.

6 recordsLinked to original sources

arXiv2010

The Localization Transition of the Two-Dimensional Lorentz Model

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 density, the motion of the tracer becomes anomalous over many decades in time, which is rationalized in terms of an underlying percolation transition of the void space. In the vicinity of this critical density the dynamics follows the anomalous one up to a crossover time scale where the motion becomes either diffusive or localized. We analyze the scaling behavior of the time-dependent diffusion coefficient D(t) including corrections to scaling. Away from the critical density, D(t) exhibits universal hydrodynamic long-time tails both in the diffusive as well as in the localized phase.

cond-mat.soft↗

arXiv2009

Effective Perrin theory for the anisotropic diffusion of a strongly hindered rod

Slender rods in concentrated suspensions constitute strongly interacting systems with rich dynamics: transport slows down drastically and the anisotropy of the motion becomes arbitrarily large. We develop a mesoscopic description of the dynamics down to the length scale of the interparticle distance. Our theory is based on the exact solution of the Smoluchowski-Perrin equation; it is in quantitative agreement with extensive Brownian dynamics simulations in the dense regime. In particular, we show that the tube confinement is characterised by a power law decay of the intermediate scattering function with exponent 1/2.

cond-mat.soft↗

arXiv2008

Entangled Dynamics of a Stiff Polymer

Entangled networks of stiff biopolymers exhibit complex dynamic response, emerging from the topological constraints that neighboring filaments impose upon each other. We propose a class of reference models for entanglement dynamics of stiff polymers and provide a quantitative foundation of the tube concept for stiff polymers. For an infinitely thin needle exploring a planar course of point obstacles, we have performed large-scale computer simulations proving the conjectured scaling relations from the fast transverse equilibration to the slowest process of orientational relaxation. We determine the rotational diffusion coefficient of the tracer, its angular confinement, the tube diameter and the orientational correlation functions.

cond-mat.soft↗

arXiv2007

Critical dynamics of ballistic and Brownian particles in a heterogeneous environment

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 spans at least 5 decades in time. To extract the scaling function, one has to allow for the leading universal corrections to scaling. Our findings suggest that apparent power laws with varying exponents generically occur and dominate experimentally accessible time windows as soon as the heterogeneities cover a decade in length scale. We extract the divergent length scales, quantify the spatial heterogeneities in terms of the non-Gaussian parameter, and corroborate our results by a thorough finite-size analysis.

cond-mat.soft↗

arXiv2006

Dynamics of Semiflexible Polymers in a Flow Field

We present a novel method to investigate the dynamics of a single semiflexible polymer, subject to anisotropic friction in a viscous fluid. In contrast to previous approaches, we do not rely on a discrete bead-rod model, but introduce a suitable normal mode decomposition of a continuous space curve. By means of a perturbation expansion for stiff filaments we derive a closed set of coupled Langevin equations in mode space for the nonlinear dynamics in two dimensions, taking into account exactly the local constraint of inextensibility. The stochastic differential equations obtained this way are solved numerically, with parameters adjusted to describe the motion of actin filaments. As an example, we show results for the tumbling motion in shear flow.

q-bio.BM↗

arXiv2003

Transverse fluctuations of grafted polymers

We study the statistical mechanics of grafted polymers of arbitrary stiffness in a two-dimensional embedding space with Monte Carlo simulations. The probability distribution function of the free end is found to be highly anisotropic and non-Gaussian for typical semiflexible polymers. The reduced distribution in the transverse direction, a Gaussian in the stiff and flexible limits, shows a double peak structure at intermediate stiffnesses. We also explore the response to a transverse force applied at the polymer free end. We identify F-Actin as an ideal benchmark for the effects discussed.

physics.bio-ph↗