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

Non-isothermal fluctuating hydrodynamics and Brownian motion

The classical theory of Brownian dynamics follows from coarse-graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally non-isothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the non-isothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions.Comment: 9 page

Modelling a Dune Field

We present a model to describe the collective motion of barchan dunes in a field. Our model is able to reproduce the observation that a typical dune stays confined within a stripe. We also obtain some of the pattern structures which ressemble those observed from aerial photos which we do analyse and compare with the specific field of La\^ayounne.Comment: 15 pages, 13 figure

Dynamic Light Scattering from Semidilute Actin Solutions: A Study of Hydrodynamic Screening, Filament Bending Stiffness and the Effect of Tropomyosin/Troponin-Binding

Quasi-elastic light scattering (QELS) is applied to investigate the effect of the tropomyosin/troponin complex (Tm/Tn) on the stiffness of actin filaments. The importance of hydrodynamic screening in semidilute solutions is demonstrated. A new concentration dependent expression for the dynamic structure factor $g(\bm k,t)$ of semiflexible polymers in semidilute solutions is used to analyze the experimental QELS data. A concentration independent value for the bending modulus $\kappa$ is thus obtained. It increases by 50\% as a consequence of Tm/Tn binding in a 7:1:1 molar ratio of actin/Tm/Tn. In addition a new expression for the initial slope of the dynamic structure factor of a semiflexible polymer is used to determine the effective hydrodynamic diameter of the actin filament. Our results confirm the general relevance of the concept of (intrinsic) semiflexibility to polymer dynamics.Comment: 9 pages, RevTeX, 9 figures, all uuencoded gzipe

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.Comment: 4 pages, 3 figure

Longitudinal Response of Confined Semiflexible Polymers

The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, e.g., in nano-fluidic devices or in polymeric networks or solutions, these polymers are effectively confined in a channel- or tube-like geometry. By means of heuristic scaling laws and rigorous analytical theory, we analyze the tension dynamics of confined semiflexible polymers for various generic experimental setups. It turns out that in contrast to the well-known linear response, the influence of confinement on the non-linear dynamics can largely be described as that of an effective prestress. We also study the free relaxation of an initially confined chain, finding a surprising superlinear t^(9/8) growth law for the change in end-to-end distance at short times.Comment: 18 pages, 1 figur

Microrheology probes length scale dependent rheology

We exploit the power of microrheology to measure the viscoelasticity of entangled F-actin solutions at different length scales from 1 to 100 mu m over a wide frequency range. We compare the behavior of single probe-particle motion to that of the correlated motion of two particles. By varying the average length of the filaments, we identify fluctuations that dissipate diffusively over the filament length. These provide an important relaxation mechanism of the elasticity between 0.1 and 30 rad/sec

The Glassy Wormlike Chain

We introduce a new model for the dynamics of a wormlike chain in an environment that gives rise to a rough free energy landscape, which we baptise the glassy wormlike chain. It is obtained from the common wormlike chain by an exponential stretching of the relaxation spectrum of its long-wavelength eigenmodes, controlled by a single stretching parameter. Predictions for pertinent observables such as the dynamic structure factor and the microrheological susceptibility exhibit the characteristics of soft glassy rheology and compare favourably with experimental data for reconstituted cytoskeletal networks and live cells. We speculate about the possible microscopic origin of the stretching, implications for the nonlinear rheology, and the potential physiological significance of our results.Comment: 12 pages, 8 figures. Minor correction

Generalised Einstein Relation for Hot Brownian Motion

The Brownian motion of a hot nanoparticle is described by an effective Markov theory based on fluctuating hydrodynamics. Its predictions are scrutinized over a wide temperature range using large-scale molecular dynamics simulations of a hot nanoparticle in a Lennard-Jones fluid. The particle positions and momenta are found to be Boltzmann distributed according to distinct effective temperatures $T_\mathrm{HBM}$ and $T_\mathrm{k}$ . For $T_\mathrm{HBM}$ we derive a formally exact theoretical prediction and establish a generalised Einstein relation that links it to directly measurable quantities