12,037 research outputs found
Microrheological Characterisation of Anisotropic Materials
We describe the measurement of anisotropic viscoelastic moduli in complex
soft materials, such as biopolymer gels, via video particle tracking
microrheology of colloid tracer particles. The use of a correlation tensor to
find the axes of maximum anisotropy, and hence the mechanical director, is
described. The moduli of an aligned DNA gel are reported, as a test of the
technique; this may have implications for high DNA concentrations in vivo. We
also discuss the errors in microrheological measurement, and describe the use
of frequency space filtering to improve displacement resolution, and hence
probe these typically high modulus materials.Comment: 5 pages, 5 figures. Replaced after refereeing/ improvement. Main
results are the same. The final, published version of the paper is here
http://link.aps.org/abstract/PRE/v73/e03190
Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction
The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys.,
90 (1) : 463-473, 1989] to account for the influence of fluctuations in
hydrodynamic interactions in Rouse chains, is adapted here to derive a new
mean-field approximation for the FENE spring force. This "FENE-PG" force law
approximately accounts for spring-force fluctuations, which are neglected in
the widely used FENE-P approximation. The Gaussian Approximation for
hydrodynamic interactions is combined with the FENE-P and FENE-PG spring force
approximations to obtain approximate models for finitely-extensible bead-spring
chains with hydrodynamic interactions. The closed set of ODE's governing the
evolution of the second-moments of the configurational probability distribution
in the approximate models are used to generate predictions of rheological
properties in steady and unsteady shear and uniaxial extensional flows, which
are found to be in good agreement with the exact results obtained with Brownian
dynamics simulations. In particular, predictions of coil-stretch hysteresis are
in quantitative agreement with simulations' results. Additional simplifying
diagonalization-of-normal-modes assumptions are found to lead to considerable
savings in computation time, without significant loss in accuracy.Comment: 26 pages, 17 figures, 2 tables, 75 numbered equations, 1 appendix
with 10 numbered equations Submitted to J. Chem. Phys. on 6 February 200
Two-dimensional turbulence of dilute polymer solutions
We investigate theoretically and numerically the effect of polymer additives
on two-dimensional turbulence by means of a viscoelastic model. We provide
compelling evidence that at vanishingly small concentrations, such that the
polymers are passively transported, the probability distribution of polymer
elongation has a power law tail: its slope is related to the statistics of
finite-time Lyapunov exponents of the flow, in quantitative agreement with
theoretical predictions. We show that at finite concentrations and sufficiently
large elasticity the polymers react on the flow with manifold consequences:
velocity fluctuations are drastically depleted, as observed in soap film
experiments; the velocity statistics becomes strongly intermittent; the
distribution of finite-time Lyapunov exponents shifts to lower values,
signalling the reduction of Lagrangian chaos.Comment: 4 pages, 5 figure
Supersymmetry solution for finitely extensible dumbbell model
Exact relaxation times and eigenfunctions for a simple mechanical model of
polymer dynamics are obtained using supersymmetry methods of quantum mechanics.
The model includes the finite extensibility of the molecule and does not make
use of the self-consistently averaging approximation. The finite extensibility
reduces the relaxation times when compared to a linear force. The linear
viscoelastic behaviour is obtained in the form of the ``generalized Maxwell
model''. Using these results, a numerical integration scheme is proposed in the
presence of a given flow kinematics.Comment: 5 pages, 2 figure
Evaluating the Applicability of the Fokker-Planck Equation in Polymer Translocation: A Brownian Dynamics Study
Brownian dynamics (BD) simulations are used to study the translocation
dynamics of a coarse-grained polymer through a cylindrical nanopore. We
consider the case of short polymers, with a polymer length, N, in the range
N=21-61. The rate of translocation is controlled by a tunable friction
coefficient, gamma_{0p}, for monomers inside the nanopore. In the case of
unforced translocation, the mean translocation time scales with polymer length
N as ~ (N-N_p)^alpha, where N_p is the average number of monomers in the
nanopore. The exponent approaches the value alpha=2 when the pore friction is
sufficiently high, in accord with the prediction for the case of the
quasi-static regime where pore friction dominates. In the case of forced
translocation, the polymer chain is stretched and compressed on the cis and
trans sides, respectively, for low gamma_{0p}. However, the chain approaches
conformational quasi-equilibrium for sufficiently large gamma_{0p}. In this
limit the observed scaling of with driving force and chain length
supports the FP prediction that is proportional to N/f_d for sufficiently
strong driving force. Monte Carlo simulations are used to calculate
translocation free energy functions for the system. The free energies are used
with the Fokker-Planck equation to calculate translocation time distributions.
At sufficiently high gamma_{0p}, the predicted distributions are in excellent
agreement with those calculated from the BD simulations. Thus, the FP equation
provides a valid description of translocation dynamics for sufficiently high
pore friction for the range of polymer lengths considered here. Increasing N
will require a corresponding increase in pore friction to maintain the validity
of the FP approach. Outside the regime of low N and high pore friction, the
polymer is out of equilibrium, and the FP approach is not valid.Comment: 13 pages, 11 figure
Lattice-Boltzmann Method for Non-Newtonian Fluid Flows
We study an ad hoc extension of the Lattice-Boltzmann method that allows the
simulation of non-Newtonian fluids described by generalized Newtonian models.
We extensively test the accuracy of the method for the case of shear-thinning
and shear-thickening truncated power-law fluids in the parallel plate geometry,
and show that the relative error compared to analytical solutions decays
approximately linear with the lattice resolution. Finally, we also tested the
method in the reentrant-flow geometry, in which the shear-rate is no-longer a
scalar and the presence of two singular points requires high accuracy in order
to obtain satisfactory resolution in the local stress near these points. In
this geometry, we also found excellent agreement with the solutions obtained by
standard finite-element methods, and the agreement improves with higher lattice
resolution
Anomalous lateral diffusion in a viscous membrane surrounded by viscoelastic media
We investigate the lateral dynamics in a purely viscous lipid membrane
surrounded by viscoelastic media such as polymeric solutions. We first obtain
the generalized frequency-dependent mobility tensor and focus on the case when
the solvent is sandwiched by hard walls. Due to the viscoelasticity of the
solvent, the mean square displacement of a disk embedded in the membrane
exhibits an anomalous diffusion. An useful relation which connects the mean
square displacement and the solvent modulus is provided. We also calculate the
cross-correlation of the particle displacements which can be applied for
two-particle tracking experiments.Comment: 6 pages, 2 figure
Models of granular ratchets
We study a general model of granular Brownian ratchet consisting of an
asymmetric object moving on a line and surrounded by a two-dimensional granular
gas, which in turn is coupled to an external random driving force. We discuss
the two resulting Boltzmann equations describing the gas and the object in the
dilute limit and obtain a closed system for the first few moments of the system
velocity distributions. Predictions for the net ratchet drift, the variance of
its velocity fluctuations and the transition rates in the Markovian limit, are
compared to numerical simulations and a fair agreement is observed.Comment: 15 pages, 4 figures, to be published on Journal of Statistical
Mechanics: Theory and Experiment
Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems
We introduce a systematic classification method for the analogs of phase
transitions in finite systems. This completely general analysis, which is
applicable to any physical system and extends towards the thermodynamic limit,
is based on the microcanonical entropy and its energetic derivative, the
inverse caloric temperature. Inflection points of this quantity signal
cooperative activity and thus serve as distinct indicators of transitions. We
demonstrate the power of this method through application to the long-standing
problem of liquid-solid transitions in elastic, flexible homopolymers.Comment: 4 pages, 3 figure
Non-linear rheology of active particle suspensions: Insights from an analytical approach
We consider active suspensions in the isotropic phase subjected to a shear
flow. Using a set of extended hydrodynamic equations we derive a variety of
{\em analytical} expressions for rheological quantities such as shear viscosity
and normal stress differences. In agreement to full-blown numerical
calculations and experiments we find a shear thickening or -thinning behaviour
depending on whether the particles are contractile or extensile. Moreover, our
analytical approach predicts that the normal stress differences can change
their sign in contrast to passive suspensions.Comment: 11 pages, 10 figures, appear in PR
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