arXiv subjects

Felix Höfling

Publications and source records attributed to Felix Höfling.

50 records · Page 3Linked to original sources

arXiv2010

Anomalous transport of a tracer on percolating clusters

We investigate 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. The mean-square displacement displays anomalous transport, which extends to infinite times precisely at the critical obstacle density. The slowing down of the diffusion coefficient exhibits power-law behavior for densities close to the critical point and we show that the mean-square displacement fulfills a scaling hypothesis. Furthermore, we calculate the dynamic conductivity as response to an alternating electric field. Last, we discuss the non-gaussian parameter as an indicator for heterogeneous dynamics.

cond-mat.stat-mech↗

arXiv2010

Anomalous transport resolved in space and time by fluorescence correlation spectroscopy

A ubiquitous observation in crowded cell membranes is that molecular transport does not follow Fickian diffusion but exhibits subdiffusion. The microscopic origin of such a behaviour is not understood and highly debated. Here we discuss the spatio-temporal dynamics for two models of subdiffusion: fractional Brownian motion and hindered motion due to immobile obstacles. We show that the different microscopic mechanisms can be distinguished using fluorescence correlation spectroscopy (FCS) by systematic variation of the confocal detection area. We provide a theoretical framework for space-resolved FCS by generalising FCS theory beyond the common assumption of spatially Gaussian transport. We derive a master formula for the FCS autocorrelation function, from which it is evident that the beam waist of an FCS experiment is a similarly important parameter as the wavenumber of scattering experiments. These results lead to scaling properties of the FCS correlation for both models, which are tested by in silico experiments. Further, our scaling prediction is compatible with the FCS half-value times reported by Wawrezinieck et al. [Biophys. J. 89, 4029 (2005)] for in vivo experiments on a transmembrane protein.

cond-mat.soft↗

arXiv2010

Localization phenomena in models of ion-conducting glass formers

The mass transport in soft-sphere mixtures of small and big particles as well as in the disordered Lorentz gas (LG) model is studied using molecular dynamics (MD) computer simulations. The soft-sphere mixture shows anomalous small-particle diffusion signifying a localization transition separate from the big-particle glass transition. Switching off small-particle excluded volume constraints slows down the small-particle dynamics, as indicated by incoherent intermediate scattering functions. A comparison of logarithmic time derivatives of the mean-squared displacements reveals qualitative similarities between the localization transition in the soft-sphere mixture and its counterpart in the LG. Nevertheless, qualitative differences emphasize the need for further research elucidating the connection between both models.

cond-mat.stat-mech↗

arXiv2010

Space-resolved dynamics of a tracer in a disordered solid

The dynamics of a tracer particle in a glassy matrix of obstacles displays slow complex transport as the free volume approaches a critical value and the void space falls apart. We investigate the emerging subdiffusive motion of the test particle by extensive molecular dynamics simulations and characterize the spatio-temporal transport in terms of two-time correlation functions, including the time-dependent diffusion coefficient as well as the wavenumber-dependent intermediate scattering function. We rationalize our findings within the framework of critical phenomena and compare our data to a dynamic scaling theory.

cond-mat.stat-mech↗

arXiv2010

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

We show that for particles performing Brownian motion in a frozen array of scatterers long-time correlations emerge in the mean-square displacement. Defining the velocity autocorrelation function (VACF) via the second time-derivative of the mean-square displacement, power-law tails govern the long-time dynamics similar to the case of ballistic motion. The physical origin of the persistent memory is due to repeated encounters with the same obstacle which occurs naturally in Brownian dynamics without involving other scattering centers. This observation suggests that in this case the VACF exhibits these anomalies already at first order in the scattering density. Here we provide an analytic solution for the dynamics of a tracer for a dilute planar Lorentz gas and compare our results to computer simulations. Our result support the idea that quenched disorder provides a generic mechanism for persistent correlations irrespective of the microdynamics of the tracer particle.

cond-mat.stat-mech↗

arXiv2010

Development of anomalous diffusion among crowding proteins

In cell membranes, proteins and lipids diffuse in a highly crowded and heterogeneous landscape, where aggregates and dense domains of proteins or lipids obstruct the path of diffusing molecules. In general, hindered motion gives rise to anomalous transport, though the nature of the onset of this behavior is still under debate and difficult to investigate experimentally. Here, we present a systematic study where proteins bound to supported lipid membranes diffuse freely in two dimensions, but are increasingly hindered by the presence of other like proteins. In our model system, the surface coverage of the protein avidin on the lipid bilayer is well controlled by varying the concentration of biotinylated lipid anchors. Using fluorescence correlation spectroscopy (FCS), we measure the time correlation function over long times and convert it to the mean-square displacement of the diffusing proteins. Our approach allows for high precision data and a clear distinction between anomalous and normal diffusion. It enables us to investigate the onset of anomalous diffusion, which takes place when the area coverage of membrane proteins increases beyond approximately 5%. This transition region exhibits pronounced spatial heterogeneities. Increasing the packing fraction further, transport becomes more and more anomalous, manifested in a decrease of the exponent of subdiffusion.

cond-mat.soft↗

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

Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems

For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our derivation is based on a cluster-resolved scaling theory unifying the scaling of both the cluster size distribution and the dynamics of a random walker. We corroborate our theoretical approach by extensive simulations for a site percolating square lattice and numerically determine both the static and dynamic correction exponents.

cond-mat.stat-mech↗

arXiv2008

Enhanced Diffusion of a Needle in a Planar Course of Point Obstacles

The transport of an infinitely thin, hard rod in a random, dense array of point obstacles is investigated by molecular dynamics simulations. Our model mimics the sterically hindered dynamics in dense needle liquids. The center-of-mass diffusion exhibits a minimum, and transport becomes increasingly fast at higher densities. The diffusion coefficient diverges according to a power law in the density with an approximate exponent of 0.8. This observation is connected with a new divergent time scale, reflected in a zig-zag motion of the needle, a two-step decay of the velocity-autocorrelation function, and a negative plateau in the non-Gaussian parameter.

cond-mat.stat-mech↗

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↗

arXiv2007

Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model

The long-time behavior of transport coefficients in a model for spatially heterogeneous media in two and three dimensions is investigated by Molecular Dynamics simulations. The behavior of the velocity auto-correlation function is rationalized in terms of a competition of the critical relaxation due to the underlying percolation transition and the hydrodynamic power-law anomalies. In two dimensions and in the absence of a diffusive mode, another power law anomaly due to trapping is found with an exponent -3 instead of -2. Further, the logarithmic divergence of the Burnett coefficient is corroborated in the dilute limit; at finite density, however, it is dominated by stronger divergences.

cond-mat.soft↗

arXiv2006

Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation

The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation theory, an excellent matching of both the critical density and exponents is obtained. Upon exploiting a dynamic scaling Ansatz employing two divergent length scales we find data collapse for the mean-square displacements and identify the leading-order corrections to scaling. The non-Gaussian parameter is predicted to diverge at the transition.

cond-mat.soft↗