3,364 research outputs found
Distance dependence of angular correlations in dense polymer solutions
Angular correlations in dense solutions and melts of flexible polymer chains
are investigated with respect to the distance between the bonds by
comparing quantitative predictions of perturbation calculations with numerical
data obtained by Monte Carlo simulation of the bond-fluctuation model. We
consider both monodisperse systems and grand-canonical (Flory-distributed)
equilibrium polymers. Density effects are discussed as well as finite chain
length corrections. The intrachain bond-bond correlation function is
shown to decay as for \xi \ll r \ll \r^* with being
the screening length of the density fluctuations and a novel
length scale increasing slowly with (mean) chain length .Comment: 17 pages, 5 figures, accepted for publication at Macromolecule
Contact forces in regular 3D granular pile
We present exact results for the contact forces in a three dimensional static
piling of identical, stiff and frictionless spheres. The pile studied is a
pyramid of equilateral triangular base (``stack of cannonballs'') with a FCC
(face centered cubic) structure. We show in particular that, as for the two
dimensional case, the pressure on the base of such a pile is uniform.Comment: 10 pages, 5 figure
Note: Scale-free center-of-mass displacement correlations in polymer films without topological constraints and momentum conservation
We present here computational work on the center-of-mass displacements in
thin polymer films of finite width without topological constraints and without
momentum conservation obtained using a well-known lattice Monte Carlo algorithm
with chain lengths ranging up to N=8192. Computing directly the center-of-mass
displacement correlation function C_N(t) allows to make manifest the existence
of scale-free colored forces acting on a reference chain. As suggested by the
scaling arguments put forward in a recent work on three-dimensional melts, we
obtain a negative algebraic decay C_N(t) \sim -1/(Nt) for times t << T_N with
T_N being the chain relaxation time. This implies a logarithmic correction to
the related center-of-mass mean square-displacement h_N(t) as has been checked
directly
Computational confirmation of scaling predictions for equilibrium polymers
We report the results of extensive Dynamic Monte Carlo simulations of systems
of self-assembled Equilibrium Polymers without rings in good solvent.
Confirming recent theoretical predictions, the mean-chain length is found to
scale as \Lav = \Lstar (\phi/\phistar)^\alpha \propto \phi^\alpha \exp(\delta
E) with exponents and in the dilute and
semi-dilute limits respectively. The average size of the micelles, as measured
by the end-to-end distance and the radius of gyration, follows a very similar
crossover scaling to that of conventional quenched polymer chains. In the
semi-dilute regime, the chain size distribution is found to be exponential,
crossing over to a Schultz-Zimm type distribution in the dilute limit. The very
large size of our simulations (which involve mean chain lengths up to 5000,
even at high polymer densities) allows also an accurate determination of the
self-avoiding walk susceptibility exponent .Comment: 6 pages, 4 figures, LATE
Characterization of local dynamics and mobilities in polymer melts - a simulation study
The local dynamical features of a PEO melt studied by MD simulations are
compared to two model chain systems, namely the well-known Rouse model as well
as the semiflexible chain model (SFCM) that additionally incorporates chain
stiffness. Apart from the analysis of rather general quantities such as the
mean square displacement (MSD), we present a new statistical method to extract
the local bead mobility from the simulation data on the basis of the Langevin
equation, thus providing a complementary approach to the classical Rouse-mode
analysis. This allows us to check the validity of the Langevin equation and, as
a consequence, the Rouse model. Moreover, the new method has a broad range of
applications for the analysis of the dynamics of more complex polymeric systems
like comb-branched polymers or polymer blends.Comment: 6 pages, 5 figure
Development of Stresses in Cohesionless Poured Sand
The pressure distribution beneath a conical sandpile, created by pouring sand
from a point source onto a rough rigid support, shows a pronounced minimum
below the apex (`the dip'). Recent work of the authors has attempted to explain
this phenomenon by invoking local rules for stress propagation that depend on
the local geometry, and hence on the construction history, of the medium. We
discuss the fundamental difference between such approaches, which lead to
hyperbolic differential equations, and elastoplastic models, for which the
equations are elliptic within any elastic zones present .... This displacement
field appears to be either ill-defined, or defined relative to a reference
state whose physical existence is in doubt. Insofar as their predictions depend
on physical factors unknown and outside experimental control, such
elastoplastic models predict that the observations should be intrinsically
irreproducible .... Our hyperbolic models are based instead on a physical
picture of the material, in which (a) the load is supported by a skeletal
network of force chains ("stress paths") whose geometry depends on construction
history; (b) this network is `fragile' or marginally stable, in a sense that we
define. .... We point out that our hyperbolic models can nonetheless be
reconciled with elastoplastic ideas by taking the limit of an extremely
anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps.
Philosophical Transactions A, Royal Society, submitted 02/9
On two intrinsic length scales in polymer physics: topological constraints vs. entanglement length
The interplay of topological constraints, excluded volume interactions,
persistence length and dynamical entanglement length in solutions and melts of
linear chains and ring polymers is investigated by means of kinetic Monte Carlo
simulations of a three dimensional lattice model. In unknotted and
unconcatenated rings, topological constraints manifest themselves in the static
properties above a typical length scale ( being
the volume fraction, the mean bond length).
Although one might expect that the same topological length will play a role
in the dynamics of entangled polymers, we show that this is not the case.
Instead, a different intrinsic length de, which scales like excluded volume
blob size , governs the scaling of the dynamical properties of both linear
chains and rings.Comment: 7 pages. 4 figure
Elastic medium confined in a column versus the Janssen experiment
We compute the stresses in an elastic medium confined in a vertical column,
when the material is at the Coulomb threshold everywhere at the walls.
Simulations are performed in 2 dimensions using a spring lattice, and in 3
dimensions, using Finite Element Method. The results are compared to the
Janssen model and to experimental results for a granular material. The
necessity to consider elastic anisotropy to render qualitatively the
experimental findings is discussed
Stress Transmission through Three-Dimensional Ordered Granular Arrays
We measure the local contact forces at both the top and bottom boundaries of
three-dimensional face-centered-cubic and hexagonal-close-packed granular
crystals in response to an external force applied to a small area at the top
surface. Depending on the crystal structure, we find markedly different results
which can be understood in terms of force balance considerations in the
specific geometry of the crystal. Small amounts of disorder are found to create
additional structure at both the top and bottom surfaces.Comment: 9 pages including 9 figures (many in color) submitted to PR
Models of stress fluctuations in granular media
We investigate in detail two models describing how stresses propagate and
fluctuate in granular media. The first one is a scalar model where only the
vertical component of the stress tensor is considered. In the continuum limit,
this model is equivalent to a diffusion equation (where the r\^ole of time is
played by the vertical coordinate) plus a randomly varying convection term. We
calculate the response and correlation function of this model, and discuss
several properties, in particular related to the stress distribution function.
We then turn to the tensorial model, where the basic starting point is a wave
equation which, in the absence of disorder, leads to a ray-like propagation of
stress. In the presence of disorder, the rays acquire a diffusive width and the
angle of propagation is shifted. A striking feature is that the response
function becomes negative, which suggests that the contact network is
mechanically unstable to very weak perturbations. The stress correlation
function reveals characteristic features related to the ray-like propagation,
which are absent in the scalar description. Our analytical calculations are
confirmed and extended by a numerical analysis of the stochastic wave equation.Comment: 32 pages, latex, 18 figures and 6 diagram
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