Statistical mechanics derivation of hydrodynamic boundary conditions: the diffusion equation

Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic structure in a microscopic relaxation kernel connected to the frequency dependent penetration length familiar for diffusive processes, and leads to a microscopic definition of the position where the hydrodynamic boundary condition has to be applied. Corrections to the hydrodynamic limit are obtained and we derive general amplitudes of spatially and temporally long ranged states in the considered diffusive system.Comment: 15 pages; slightly revised and shortened version; J. Phys.: Condens. Matter in prin

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

Brownian Molecules Formed by Delayed Harmonic Interactions

A time-delayed response of individual living organisms to information exchanged within flocks or swarms leads to the emergence of complex collective behaviors. A recent experimental setup by (Khadka et al 2018 Nat. Commun. 9 3864), employing synthetic microswimmers, allows to emulate and study such behavior in a controlled way, in the lab. Motivated by these experiments, we study a system of N Brownian particles interacting via a retarded harmonic interaction. For $N \leq 3$ , we characterize its collective behavior analytically, by solving the pertinent stochastic delay-differential equations, and for $N>3$ by Brownian dynamics simulations. The particles form molecule-like non-equilibrium structures which become unstable with increasing number of particles, delay time, and interaction strength. We evaluate the entropy and information fluxes maintaining these structures and, to quantitatively characterize their stability, develop an approximate time-dependent transition-state theory to characterize transitions between different isomers of the molecules. For completeness, we include a comprehensive discussion of the analytical solution procedure for systems of linear stochastic delay differential equations in finite dimension, and new results for covariance and time-correlation matrices.Comment: 36 pages, 26 figures, current version: further improvements and one correctio

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

In part I O. Hallatschek , preceding paper, Phys. Rev. E 75, 031905 (2007)] 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 spatiotemporal 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

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.Comment: Major revision (8 pages, 5 figures