arXiv subjects

Klaus Kroy

Publications and source records attributed to Klaus Kroy.

At least 55 records · Page 3Linked to original sources

arXiv2014

Persistence-Length Renormalization of Polymers in a Crowded Environment of Hard Disks

The most conspicuous property of a semiflexible polymer is its persistence length, defined as the decay length of tangent correlations along its contour. Using an efficient stochastic growth algorithm to sample polymers embedded in a quenched two-dimensional hard-disk fluid, we find apparent wormlike chain statistics with a renormalized persistence length. We identify a universal form of the disorder renormalization that suggests itself as a quantitative measure of molecular crowding.

cond-mat.soft↗

arXiv2014

Non-Isothermal Fluctuation-Dissipation Relations and Brownian Thermometry

The classical theory of Brownian motion rests on fundamental laws of statistical mechanics, such as the equipartition theorem and the fluctuation-dissipation theorem, which are not applicable in non-isothermal situations. We derive the generalized fluctuation-dissipation relations and Langevin equations governing such non-isothermal Brownian motion, including explicit results for the frequency-dependent noise temperature and Brownian thermometry far from equilibrium.

cond-mat.stat-mech↗

arXiv2012

A two-species continuum model for aeolian sand transport

Starting from the physics on the grain scale, we develop a simple continuum description of aeolian sand transport. Beyond popular mean-field models, but without sacrificing their computational efficiency, it accounts for both dominant grain populations, hopping (or "saltating") and creeping (or "reptating") grains. The predicted stationary sand transport rate is in excellent agreement with wind tunnel experiments simulating wind conditions ranging from the onset of saltation to storms. Our closed set of equations thus provides an analytically tractable, numerically precise, and computationally efficient starting point for applications addressing a wealth of phenomena from dune formation to dust emission.

cond-mat.soft↗

arXiv2012

A minimal model for the inelastic mechanics of biopolymer networks and cells

Live cells have ambiguous mechanical properties. They were often described as either elastic solids or viscoelastic fluids and have recently been classified as soft glassy materials characterized by weak power-law rheology. Nonlinear rheological measurements have moreover revealed a pronounced inelastic response indicative of a competition between stiffening and softening. It is an intriguing question whether these observations can be explained from the material properties of much simpler in-vitro reconstituted networks of biopolymers that serve as reduced model systems for the cytoskeleton. Here, we explore the mechanism behind the inelastic response of cells and biopolymer networks, theoretically. Our analysis is based on the model of the inelastic glassy wormlike chain that accounts for the nonlinear polymer dynamics and transient crosslinking in biopolymer networks. It explains how inelastic and kinematic-hardening type behavior naturally emerges from the antagonistic mechanisms of viscoelastic stress-stiffening due to the polymers and inelastic fluidization due to bond breaking. It also suggests a simple set of schematic constitutive equations which faithfully reproduce the rich inelastic phenomenology of biopolymer networks and cells.

cond-mat.soft↗

arXiv2012

Rotational hot Brownian motion

We establish an effective Markov theory for the rotational Brownian motion of hot nanobeads and nanorods. Compact analytical expressions for the effective temperature and friction are derived from the fluctuating hydrodynamic equations of motion. They are verified by comparison with recent measurements and with GPU powered parallel molecular dynamics simulations over a wide temperature range. This provides unique insights into the physics of hot Brownian motion and an excellent starting point for further experimental tests and applications involving laser-heated nanobeads, nanorods and Janus particles.

cond-mat.soft↗

arXiv2011

Tube width fluctuations of entangled stiff polymers

The tube-like cages of stiff polymers in entangled solutions have been shown to exhibit characteristic spatial heterogeneities. We explain these observations by a systematic theory generalizing previous work by D. Morse (Phys. Rev. E 63:031502, 2001). With a local version of the binary collision approximation (BCA), the distribution of confinement strengths is calculated, and the magnitude and the distribution function of tube radius fluctuations are predicted. Our main result is a unique scaling function for the tube radius distribution, in good agreement with experimental and simulation data.

cond-mat.soft↗

arXiv2011

Monomer dynamics of a wormlike chain

We derive the stochastic equations of motion for a tracer that is tightly attached to a semiflexible polymer and confined or agitated by an externally controlled potential. The generalised Langevin equation, the power spectrum, and the mean-square displacement for the tracer dynamics are explicitly constructed from the microscopic equations of motion for a weakly bending wormlike chain by a systematic coarse-graining procedure. Our accurate analytical expressions should provide a convenient starting point for further theoretical developments and for the analysis of various single-molecule experiments and of protein shape fluctuations.

cond-mat.soft↗

arXiv2010

Weakly nonlinear rheology of transiently crosslinked biopolymer gels

Recent experimental investigations have revealed a non-Maxwellian absorption pattern in the rheological spectra of actin gels, which was interpreted in terms of transient bonds. Here we examine the consequences of reversible crosslinking on the apparent linear spectra of biopolymer solutions theoretically. For a schematic model consisting of a reversibly crosslinked power-law fluid we obtain a simple analytical prediction for the position of the absorption peak, which is backed up by a numerical evaluation of the inelastic glassy wormlike chain model. This establishes bond breaking as a nonlinear non-equilibrium effect that can already be significant for very small driving amplitudes. Our results may be useful for inferring binding affinities and reaction rates of biochemical crosslinkers from rheological measurements of {\it in-vitro} reconstituted cytoskeletal gels.

cond-mat.soft↗

arXiv2010

Hot Brownian Motion

We derive the generalized Markovian description for the non-equilibrium Brownian motion of a heated particle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nano-particles and provide a practical rational basis for emerging photothermal technologies.

cond-mat.stat-mech↗

arXiv2010

Inelastic mechanics of sticky biopolymer networks

We propose a physical model for the nonlinear inelastic mechanics of sticky biopolymer networks with potential applications to inelastic cell mechanics. It consists in a minimal extension of the glassy wormlike chain (GWLC) model, which has recently been highly successful as a quantitative mathematical description of the viscoelastic properties of biopolymer networks and cells. To extend its scope to nonequilibrium situations, where the thermodynamic state variables may evolve dynamically, the GWLC is furnished with an explicit representation of the kinetics of breaking and reforming sticky bonds. In spite of its simplicity the model exhibits many experimentally established non-trivial features such as power-law rheology, stress stiffening, fluidization, and cyclic softening effects.

cond-mat.soft↗

arXiv2008

A unit-cell approach to the nonlinear rheology of biopolymer solutions

We propose a nonlinear extension of the standard tube model for semidilute solutions of freely-sliding semiflexible polymers. Non-affine filament deformations at the entanglement scale, the renormalisation of direct interactions by thermal fluctuations, and the geometry of large deformations are systematically taken into account. The stiffening response predicted for athermal solutions of stiff rods is found to be thermally suppressed. Instead, we obtain a broad linear response regime, supporting the interpretation of shear stiffening at finite frequencies in polymerised actin solutions as indicative of coupling to longitudinal modes. We observe a destabilizing effect of large strains (about 100%), suggesting shear banding as a plausible explanation for the widely observed catastrophic collapse of in-vitro biopolymer solutions, usually attributed to network damage. In combination with friction-type interactions, our analysis provides an analytically tractable framework to address the nonlinear viscoplasticity of biological tissue on a molecular basis.

cond-mat.soft↗

arXiv2006

Tension dynamics in semiflexible polymers. Part I: Coarse-grained equations of motion

Based on the wormlike chain model, a coarse-grained description of the nonlinear dynamics of a weakly bending semiflexible polymer is developed. By means of a multiple scale perturbation analysis, a length-scale separation inherent to the weakly-bending limit is exploited to reveal the deterministic nature of the spatio-temporal relaxation of the backbone tension and to deduce the corresponding coarse-grained equation of motion. From this partial integro-differential equation, some detailed analytical predictions for the non-linear response of a weakly bending polymer are derived in an accompanying paper (Part II, cond-mat/0609638).

cond-mat.soft↗

arXiv2006

Tension dynamics in semiflexible polymers. Part II: Scaling solutions and applications

In Part I of this contribution, a systematic coarse-grained description of the dynamics of a weakly-bending semiflexible polymer was developed. Here, we discuss analytical solutions of the established deterministic partial integro-differential equation for the spatio-temporal relaxation of the backbone tension. For prototypal experimental situations, such as the sudden application or release of a strong external pulling force, it is demonstrated that the tensile dynamics reflects the self-affine conformational fluctuation spectrum in a variety of intermediate asymptotic power laws. Detailed and explicit analytical predictions for the tension propagation and relaxation and corresponding results for common observables, such as the end-to-end distance, are obtained.

cond-mat.soft↗

arXiv2005

Propagation and Relaxation of Tension in Stiff Polymers

We present a unified theory for the longitudinal dynamic response of a stiff polymer in solution to various external perturbations (mechanical excitations, hydrodynamic flows, electrical fields, temperature quenches ...) that can be represented as sudden changes of ambient/boundary conditions. The theory relies on a comprehensive analysis of the non--equilibrium propagation and relaxation of backbone stresses in a wormlike chain. We recover and substantially extend previous results based on heuristic arguments. Intriguing new experimental implications are pointed out.

cond-mat.soft↗

arXiv2005

Brownian motion: a paradigm of soft matter and biological physics

This is a pedagogical introduction to Brownian motion on the occasion of the 100th anniversary of Einstein's 1905 paper on the subject. After briefly reviewing Einstein's work in its contemporary context, we pursue some lines of further developments and applications in soft condensed matter and biology. Over the last century Brownian motion became promoted from an odd curiosity of marginal scientific interest to a guiding theme pervading all of the modern (live) sciences.

cond-mat.soft↗

arXiv2005

On the shape of barchan dunes

Barchans are crescent-shaped sand dunes forming in aride regions with unidirectional wind and limited sand supply. We report analytical and numerical results for dune shapes under different environmental conditions as obtained from the so-called `minimal model' of aeolian sand dunes. The profiles of longitudinal vertical slices (i.e. along the wind direction) are analyzed as a function of wind speed and sand supply. Shape transitions can be induced by changes of mass, wind speed and sand supply. Within a minimal extension of the model to the transverse direction the scale-invariant profile of transverse vertical cuts can be derived analytically.

cond-mat.soft↗

arXiv2004

Comment on "Relevant Length Scale of Barchan Dunes"

In a recent experimental breakthrough, Hersen et al. [1] demonstrated that by changing the agitating medium from air to water, one can obtain, on laboratory scale, dunes that are downsized copies of desert dunes, thereby overcoming a major obstacle for their systematic study. Here we argue in two steps (i),(ii) that an alternative data analysis leads to some conclusions that are qualitatively and quantitatively different from Hersen et al.'s but justify their similarity hypothesis on different grounds. [1] P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. 89 (2002) 264301

cond-mat.soft↗

arXiv2004

Overdamped Stress Relaxation in Buckled Rods

We present a comprehensive theoretical analysis of the stress relaxation in a multiply but weakly buckled incompressible rod in a viscous solvent. In the bulk two interesting regimes of generic self--similar intermediate asymptotics are distinguished, which give rise to two classes of approximate and exact power--law solutions, respectively. For the case of open boundary conditions the corresponding non--trivial boundary--layer scenarios are derived by a multiple--scale perturbation (``adiabatic'') method. Our results compare well with -- and provide the theoretical explanation for -- previous results from numerical simulations, and they suggest new directions for further fruitful numerical and experimental investigations.

cond-mat.soft↗