25 research outputs found
Two-point microrheology and the electrostatic analogy
The recent experiments of Crocker et al. suggest that microrheological
measurements obtained from the correlated fluctuations of widely-separatedprobe
particles determine the rheological properties of soft, complex materials more
accurately than do the more traditional particle autocorrelations. This
presents an interesting problem in viscoelastic dynamics. We develop an
important, simplifing analogy between the present viscoelastic problem and
classical electrostatics. Using this analogy and direct calculation we analyze
both the one and two particle correlations in a viscoelastic medium in order to
explain this observation
Correlation effects and the high-frequency spin susceptibility of an electron liquid: Exact limits
Spin correlations in an interacting electron liquid are studied in the
high-frequency limit and in both two and three dimensions. The third-moment sum
rule is evaluated and used to derive exact limiting forms (at both long- and
short-wavelengths) for the spin-antisymmetric local-field factor, . In two dimensions is found to diverge as at long wavelengths,
and the spin-antisymmetric exchange-correlation kernel of time-dependent spin
density functional theory diverges as in both two and three dimensions.
These signal a failure of the local-density approximation, one that can be
redressed by alternative approaches.Comment: 5 page
Fluctuating Elastic Rings: Statics and Dynamics
We study the effects of thermal fluctuations on elastic rings. Analytical
expressions are derived for correlation functions of Euler angles, mean square
distance between points on the ring contour, radius of gyration, and
probability distribution of writhe fluctuations. Since fluctuation amplitudes
diverge in the limit of vanishing twist rigidity, twist elasticity is essential
for the description of fluctuating rings. We find a crossover from a small
scale regime in which the filament behaves as a straight rod, to a large scale
regime in which spontaneous curvature is important and twist rigidity affects
the spatial configurations of the ring. The fluctuation-dissipation relation
between correlation functions of Euler angles and response functions, is used
to study the deformation of the ring by external forces. The effects of inertia
and dissipation on the relaxation of temporal correlations of writhe
fluctuations, are analyzed using Langevin dynamics.Comment: 43 pages, 9 Figure
Statistical mechanics of triangulated ribbons
We use computer simulations and scaling arguments to investigate statistical
and structural properties of a semiflexible ribbon composed of isosceles
triangles. We study two different models, one where the bending energy is
calculated from the angles between the normal vectors of adjacent triangles,
the second where the edges are viewed as semiflexible polymers so that the
bending energy is related to the angles between the tangent vectors of
next-nearest neighbor triangles. The first model can be solved exactly whereas
the second is more involved. It was recently introduced by Liverpool and
Golestanian Phys.Rev.Lett. 80, 405 (1998), Phys.Rev.E 62, 5488 (2000) as a
model for double-stranded biopolymers such as DNA. Comparing observables such
as the autocorrelation functions of the tangent vectors and the bond-director
field, the probability distribution functions of the end-to-end distance, and
the mean squared twist we confirm the existence of local twist correlation, but
find no indications for other predicted features such as twist-stretch
coupling, kinks, or oscillations in the autocorrelation function of the
bond-director field.Comment: 10 pages, 13 figures. submitted to PRE, revised versio
The response function of a sphere in a viscoelastic two-fluid medium
In order to address basic questions of importance to microrheology, we study
the dynamics of a rigid sphere embedded in a model viscoelastic medium
consisting of an elastic network permeated by a viscous fluid. We calculate the
complete response of a single bead in this medium to an external force and
compare the result to the commonly-accepted, generalized Stokes-Einstein
relation (GSER). We find that our response function is well approximated by the
GSER only within a particular frequency range determined by the material
parameters of both the bead and the network. We then discuss the relevance of
this result to recent experiments. Finally we discuss the approximations made
in our solution of the response function by comparing our results to the exact
solution for the response function of a bead in a viscous (Newtonian) fluid.Comment: 12 pages, 2 figure
Depinning of semiflexible polymers in (1+1) dimensions
We present a theoretical analysis of a simple model of the depinning of an
anchored semiflexible polymer from a fixed planar substrate in (1+1)
dimensions. We consider a polymer with a discrete sequence of pinning sites
along its contour. Using the scaling properties of the conformational
distribution function in the stiff limit and applying the necklace model of
phase transitions in quasi-one-dimensional systems, we obtain a melting
criterion in terms of the persistence length, the spacing between pinning
sites, a microscopic effective length which characterizes a bond, and the bond
energy. The limitations of this and other similar approaches are also
discussed. In the case of force-induced unbinding, it is shown that the bending
rigidity favors the unbinding through a ``lever-arm effect''
Critical dynamics at the percolation threshold
SIGLEAvailable from British Library Document Supply Centre- DSC:D66517/86 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
THE PAIR POTENTIAL APPROACH FOR INTERFACES : FUNDAMENTAL PROBLEMS AND PRACTICAL SOLUTIONS
A fundamental problem in the use of a central pair-force model for defect problems is that it omits three-body and higher terms which are necessarily present in real systems. Electronic fluctuation effects are also usually omitted. While these can be small in the simple metals, they are significant in noble and transition metals, as shown by a simple real space argument. To gauge the importance of their effects in interface problems, the structure of a simple Σ 5 twist boundary is examined, with the atoms described by both pair- and three-center interactions and as a function of the relative strength of the two
Stretching and buckling of polymerized membranes: a Monte Carlo study
We study polymerized (elastic) membranes fluctuating under constrained boundary conditions. We show that the low-temperature, "flat" phase is not described by the classical theory of elasticity. Thermal fluctuations induce important modifications to mechanical laws such as Hooke's law. We study the approach to the buckled state of membranes, verify the finite-size scaling relations and measure related critical exponents. In the presence of thermal fluctuations the buckled state is qualitatively different from its classical counterpart