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T. Franosch

Publications and source records attributed to T. Franosch.

17 recordsLinked to original sources
arXiv2024

Dimensional crossover via confinement in the lattice Lorentz gas

We consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a cylinder. We compute the velocity autocorrelation function and show that already in equilibrium the system exhibits a dimensional crossover from two- to one-dimensional as time progresses. A pulling force is switched on and we characterize analytically the stationary state in terms of the stationary velocity and diffusion coefficient. Stochastic simulations are used to discuss the range of validity of the analytic results. Our calculation, exact to first order in the obstacle density, holds for arbitrarily large forces and confinement size.

cond-mat.stat-mech↗
arXiv2024

Time-dependent dynamics in the confined lattice Lorentz gas

We study a lattice model describing the non-equilibrium dynamics emerging from the pulling of a tracer particle through a disordered medium occupied by randomly placed obstacles. The model is considered in a restricted geometry pertinent for the investigation of confinement-induced effects. We analytically derive exact results for the characteristic function of the moments valid to first order in the obstacle density. By calculating the velocity autocorrelation function and its long-time tail we find that already in equilibrium the system exhibits a dimensional crossover. This picture is further confirmed by the approach of the drift velocity to its terminal value attained in the non-equilibrium stationary state. At large times the diffusion coefficient is affected by both the driving and confinement in a way that we quantify analytically. The force-induced diffusion coefficient depends sensitively on the presence of confinement. The latter is able to modify qualitatively the non-analytic behavior in the force observed for the unbounded model. We then examine the fluctuations of the tracer particle along the driving force. We show that in the intermediate regime superdiffusive anomalous behavior persists even in the presence of confinement. Stochastic simulations are employed in order to test the validity of the analytic results, exact to first order in the obstacle density and valid for arbitrary force and confinement.

cond-mat.stat-mech↗
arXiv2019

Heterogeneities Shape Passive Intracellular Transport

A living cell's interior is one of the most complex and intrinsically dynamic systems, providing an elaborate interplay between cytosolic crowding and ATP-driven motion, which controls cellular functionality. Here, we investigated two distinct fundamental features of the merely passive, not-bio-motor shuttled material transport within the cytoplasm of Dictyostelium discoideum cells: the anomalous non-linear scaling of the mean-squared displacement of a 150nm-diameter particle and non-Gaussian distribution of increments. Relying on single-particle tracking data of 320,000 data points, we performed a systematic analysis of four possible origins for non-Gaussian transport: (1) sample-based variability, (2) rare occurring strong motion events, (3) ergodicity breaking/ageing, and (4) spatio-temporal heterogeneities of the intracellular medium. After excluding the first three reasons, we investigated the remaining hypothesis of a heterogeneous cytoplasm as cause for non-Gaussian transport. A novel fit model with randomly distributed diffusivities implementing medium heterogeneities suits the experimental data. Strikingly, the non-Gaussian feature is independent of the cytoskeleton condition and lag time. This reveals that efficiency and consistency of passive intracellular transport and the related anomalous scaling of the mean-squared displacement are regulated by cytoskeleton components, while cytoplasmic heterogeneities are responsible for the generic, non-Gaussian distribution of increments.

physics.bio-ph↗
arXiv2014

Multiple reentrant glass transitions in confined hard-sphere glasses

Glass forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of the order of a few particle diameters. For a moderately polydisperse, densely packed hard-sphere fluid confined between two smooth hard walls, we show via event-driven molecular dynamics simulations the emergence of a multiple reentrant glass transition scenario upon a variation of the wall separation. Using thermodynamic relations, this reentrant phenomenon is shown to persist also under constant chemical potential. This allows straightforward experimental investigation and opens the way to a variety of applications in micro- and nanotechnology, where channel dimensions are comparable to the size of the contained particles. The results are in-line with theoretical predictions obtained by a combination of density functional theory and the mode-coupling theory of the glass transition.

cond-mat.soft↗
arXiv2011

Molecular self-organization: Predicting the pattern diversity and lowest energy state of competing ordering motifs

Self-organized monolayers of highly flexible \Frechet dendrons were deposited on graphite surfaces by solution casting. Scanning tunneling microscopy (STM) reveals an unprecedented variety of patterns with up to seven stable hierarchical ordering motifs serving as a versatile model system. The essential molecular properties determined by molecular mechanics simulations are condensed to a coarse grained interaction site model of various chain configurations. In a Monte Carlo approach with random starting configurations the experimental pattern diversity can be reproduced in all facets of the local and global ordering. Based on an energy analysis of the Monte Carlo and molecular mechanics modeling the thermodynamically most stable pattern is predicted coinciding with the pattern, which dominates in the STM images after several hours or upon moderate heating.

cond-mat.mes-hall↗
arXiv2011

Long-Wavelength Anomalies in the Asymptotic Behavior of Mode-Coupling Theory

We discuss the dynamic behavior of a tagged particle close to a classical localization transition in the framework of the mode-coupling theory of the glass transition. Asymptotic results are derived for the order parameter as well as the dynamic correlation functions and the mean-squared displacement close to the transition. The influence of an infrared cutoff is discussed.

cond-mat.dis-nn↗
arXiv2006

Driven lattice gas of dimers coupled to a bulk reservoir

We investigate the non-equilibrium steady state of a one-dimensional (1D) lattice gas of dimers. The dynamics is described by a totally asymmetric exclusion process (TASEP) supplemented by attachment and detachment processes, mimicking chemical equilibrium of the 1D driven transport with the bulk reservoir. The steady-state phase diagram, current and density profiles are calculated using both a refined mean-field theory and extensive stochastic simulations. As a consequence of the on-off kinetics, a new phase coexistence region arises intervening between low and high density phases such that the discontinuous transition line of the TASEP splits into two continuous ones. The results of the mean-field theory and simulations are found to coincide. We show that the physical picture obtained in the corresponding lattice gas model with monomers is robust, in the sense that the phase diagram changes quantitatively, but the topology remains unaltered. The mechanism for phase separation is identified as generic for a wide class of driven 1D lattice gases.

cond-mat.stat-mech↗
arXiv2005

Melting of Colloidal Molecular Crystals on Triangular Lattices

The phase behavior of a two-dimensional colloidal system subject to a commensurate triangular potential is investigated. We consider the integer number of colloids in each potential minimum as rigid composite objects with effective discrete degrees of freedom. It is shown that there is a rich variety of phases including ``herring bone'' and ``Japanese 6 in 1'' phases. The ensuing phase diagram and phase transitions are analyzed analytically within variational mean-field theory and supplemented by Monte Carlo simulations. Consequences for experiments are discussed.

cond-mat.soft↗
arXiv2004

The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics

We discuss a new class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting non-conserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high an low density phases, two and three phase coexistence regions and a boundary independent ``Meissner'' phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert $W$-functions. It allows to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.

cond-mat.stat-mech↗
arXiv2003

Phase Coexistence in Driven One Dimensional Transport

We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte-Carlo simulations and we predict the phase diagram of this non-conserved dynamics in the thermodynamic limit.

cond-mat.stat-mech↗
arXiv2002

Light-Scattering by Longitudinal phonons in Molecular Supercooled Liquids I: Phenomenological Approach

We derive expressions for the intensity of the Brillouin polarized spectrum of a molecular liquid formed of axially symmetric molecules. These expressions take into account both the molecular dielectric anisotropy and the modulation of the local polarisability by density fluctuations. They also incorporate all the retardation effects which occur in such liquids. We show that the spectrum splits into a q-independent rotational contribution and q-dependent term, which reflects the propagation of longitudinal phonons. In the latter, the two light scattering mechanisms enter on an equal footing and generate three scattering channels. We study the influence of the two new channels and show that they may substantially modify the Brillouin line-shape when the relaxation time of the supercooled liquid and the phonon period are of the same order of magnitude.

cond-mat.stat-mech↗
arXiv2002

Light-Scattering by Longitudinal phonons in Supercooled Molecular Liquids II: Microscopic Derivation of the Phenomenological Equations

The constitutive equations for the orientational dynamics of a liquid formed of linear molecules are derived microscopically. The resulting generalised Langevin equations coincide with the phenomenological approach of Dreyfus et al. Formally exact expressions are given for the phenomenological coefficients and various constraints are shown to be consequences of this microscopic approach.

cond-mat.stat-mech↗
arXiv2002

Completely monotone solutions of the mode-coupling theory for mixtures

We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely monotone, i.e. they can exactly be written as superpositions of decaying exponentials only. This statement holds, no matter what further approximations are needed to calculate the theory's coupling parameters. The long-time limit of these functions fulfills a maximum property, and an iteration scheme for its numerical determination is given. We also show the existence of a unique solution to the equations of motion for which power series both for short times and small frequencies exist, the latter except at special points where ergodic-to-nonergodic transitions occur. These transitions are bifurcations that are proven to be of the cuspoid family.

cond-mat.soft↗
arXiv2000

Shear response of a smectic film stabilized by an external field

The response of a field-stabilized two-dimensional smectic to shear stress is discussed. Below a critical temperature the smectic film exhibits elastic response to an infinitesimal shear stress normal to the layering. At finite stresses free dislocations nucleate and relax the applied stress. The coupling of the dislocation current to the stress results in non-newtonian viscous flow. The flow profile in a channel geometry is shown to change qualitatively from a power-law dependence to a Poiseuille-like profile opon increasing the pressure head.

cond-mat.soft↗
arXiv2000

Light scattering spectra of supercooled molecular liquids

The light scattering spectra of molecular liquids are derived within a generalized hydrodynamics. The wave vector and scattering angle dependences are given in the most general case and the change of the spectral features from liquid to solidlike is discussed without phenomenological model assumptions for (general) dielectric systems without long-ranged order. Exact microscopic expressions are derived for the frequency-dependent transport kernels, generalized thermodynamic derivatives and the background spectra.

cond-mat.stat-mech↗
arXiv1998

Structure and structure relaxation

A discrete--dynamics model, which is specified solely in terms of the system's equilibrium structure, is defined for the density correlators of a simple fluid. This model yields results for the evolution of glassy dynamics which are identical with the ones obtained from the mode-coupling theory for ideal liquid--glass transitions. The decay of density fluctuations outside the transient regime is shown to be given by a superposition of Debye processes. The concept of structural relaxation is given a precise meaning. It is proven that the long-time part of the mode-coupling-theory solutions is structural relaxation, while the transient motion merely determines an overall time scale for the glassy dynamics.

cond-mat.dis-nn↗