2,058 research outputs found
Asymptotics from scaling for nonlinear wave equations
We present a scaling technique which transforms the evolution problem for a
nonlinear wave equation with small initial data to a linear wave equation with
a distributional source. The exact solution of the latter uniformly
approximates the late-time behavior of solutions of the nonlinear problem in
timelike and null directions.Comment: 14 pages; minor changes (notation, typos
Linear and nonlinear tails II: exact decay rates in spherical symmetry
We derive the exact late-time asymptotics for small spherically symmetric
solutions of nonlinear wave equations with a potential. The dominant tail is
shown to result from the competition between linear and nonlinear effects.Comment: 17 pages, 3 figures, 2 table
Surface-mediated attraction between colloids
We investigate the equilibrium properties of a colloidal solution in contact
with a soft interface. As a result of symmetry breaking, surface effects are
generally prevailing in confined colloidal systems. In this Letter, particular
emphasis is given to surface fluctuations and their consequences on the local
(re)organization of the suspension. It is shown that particles experience a
significant effective interaction in the vicinity of the interface. This
potential of mean force is always attractive, with range controlled by the
surface correlation length. We suggest that, under some circumstances,
surface-induced attraction may have a strong influence on the local particle
distribution
Helical Tubes in Crowded Environments
When placed in a crowded environment, a semi-flexible tube is forced to fold
so as to make a more compact shape. One compact shape that often arises in
nature is the tight helix, especially when the tube thickness is of comparable
size to the tube length. In this paper we use an excluded volume effect to
model the effects of crowding. This gives us a measure of compactness for
configurations of the tube, which we use to look at structures of the
semi-flexible tube that minimize the excluded volume. We focus most of our
attention on the helix and which helical geometries are most compact. We found
that helices of specific pitch to radius ratio 2.512 to be optimally compact.
This is the same geometry that minimizes the global curvature of the curve
defining the tube. We further investigate the effects of adding a bending
energy or multiple tubes to begin to explore the more complete space of
possible geometries a tube could form.Comment: 10 page
Discrete elastic model for stretching-induced flagellar polymorphs
Force-induced reversible transformations between coiled and normal polymorphs
of bacterial flagella have been observed in recent optical-tweezer experiment.
We introduce a discrete elastic rod model with two competing helical states
governed by a fluctuating spin-like variable that represents the underlying
conformational states of flagellin monomers. Using hybrid Brownian dynamics
Monte-Carlo simulations, we show that a helix undergoes shape transitions
dominated by domain wall nucleation and motion in response to externally
applied uniaxial tension. A scaling argument for the critical force is
presented in good agreement with experimental and simulation results.
Stretching rate-dependent elasticity including a buckling instability are
found, also consistent with the experiment
Microscopic theory of solvent mediated long range forces: influence of wetting
We show that a general density functional approach for calculating the force
between two big particles immersed in a solvent of smaller ones can describe
systems that exhibit fluid-fluid phase separation: the theory captures effects
of strong adsorption (wetting) and of critical fluctuations in the solvent. We
illustrate the approach for the Gaussian core model, a simple model of a
polymer mixture in solution and find extremely attractive, long ranged solvent
mediated potentials between the big particles for state points lying close to
the binodal, on the side where the solvent is poor in the species which is
favoured by the big particles.Comment: 7 pages, 3 figures, submitted to Europhysics Letter
Adhesion of surfaces via particle adsorption: Exact results for a lattice of fluid columns
We present here exact results for a one-dimensional gas, or fluid, of
hard-sphere particles with attractive boundaries. The particles, which can
exchange with a bulk reservoir, mediate an interaction between the boundaries.
A two-dimensional lattice of such one-dimensional gas `columns' represents a
discrete approximation of a three-dimensional gas of particles between two
surfaces. The effective particle-mediated interaction potential of the
boundaries, or surfaces, is calculated from the grand-canonical partition
function of the one-dimensional gas of particles, which is an extension of the
well-studied Tonks gas. The effective interaction potential exhibits two
minima. The first minimum at boundary contact reflects depletion interactions,
while the second minimum at separations close to the particle diameter results
from a single adsorbed particle that crosslinks the two boundaries. The second
minimum is the global minimum for sufficiently large binding energies of the
particles. Interestingly, the effective adhesion energy corresponding to this
minimum is maximal at intermediate concentrations of the particles.Comment: to appear in Journal of Statistical Mechanics: Theory and Experimen
Entropic Interactions in Suspensions of Semi-Flexible Rods: Short-Range Effects of Flexibility
We compute the entropic interactions between two colloidal spheres immersed
in a dilute suspension of semi-flexible rods. Our model treats the
semi-flexible rod as a bent rod at fixed angle, set by the rod contour and
persistence lengths. The entropic forces arising from this additional
rotational degree of freedom are captured quantitatively by the model, and
account for observations at short range in a recent experiment. Global fits to
the interaction potential data suggest the persistence length of fd-virus is
about two to three times smaller than the commonly used value of .Comment: 4 pages, 5 figures, submitted to PRE rapid communication
Wall-Fluid and Liquid-Gas Interfaces of Model Colloid-Polymer Mixtures by Simulation and Theory
We perform a study of the interfacial properties of a model suspension of
hard sphere colloids with diameter and non-adsorbing ideal polymer
coils with diameter . For the mixture in contact with a planar hard
wall, we obtain from simulations the wall-fluid interfacial free energy,
, for size ratios and 1, using
thermodynamic integration, and study the (excess) adsorption of colloids,
, and of polymers, , at the hard wall. The interfacial
tension of the free liquid-gas interface, , is obtained following
three different routes in simulations: i) from studying the system size
dependence of the interfacial width according to the predictions of capillary
wave theory, ii) from the probability distribution of the colloid density at
coexistence in the grand canonical ensemble, and iii) for statepoints where the
colloidal liquid wets the wall completely, from Young's equation relating
to the difference of wall-liquid and wall-gas interfacial
tensions, . In addition, we calculate , and using density functional theory and a scaled particle
theory based on free volume theory. Good agreement is found between the
simulation results and those from density functional theory, while the results
from scaled particle theory quantitatively deviate but reproduce some essential
features. Simulation results for obtained from the three
different routes are all in good agreement. Density functional theory predicts
with good accuracy for high polymer reservoir packing fractions,
but yields deviations from the simulation results close to the critical point.Comment: 23 pages, 10 figures, REVTEX. Fig 5a changed. Final versio
Critical behavior in colloid-polymer mixtures: theory and simulation
We extensively investigated the critical behavior of mixtures of colloids and
polymers via the two-component Asakura-Oosawa model and its reduction to a
one-component colloidal fluid using accurate theoretical and simulation
techniques. In particular the theoretical approach, hierarchical reference
theory [Adv. Phys. 44, 211 (1995)], incorporates realistically the effects of
long-range fluctuations on phase separation giving exponents which differ
strongly from their mean-field values, and are in good agreement with those of
the three-dimensional Ising model. Computer simulations combined with
finite-size scaling analysis confirm the Ising universality and the accuracy of
the theory, although some discrepancy in the location of the critical point
between one-component and full-mixture description remains. To assess the limit
of the pair-interaction description, we compare one-component and two-component
results.Comment: 15 pages, 10 figures. Submitted to Phys. Rev.
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