2,839 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
Formation and Equilibrium Properties of Living Polymer Brushes
Polydisperse brushes obtained by reversible radical chain polymerization
reaction onto a solid substrate with surface-attached initiators, are studied
by means of an off-lattice Monte Carlo algorithm of living polymers (LP).
Various properties of such brushes, like the average chain length and the
conformational orientation of the polymers, or the force exerted by the brush
on the opposite container wall, reveal power-law dependence on the relevant
parameters. The observed molecular weight distribution (MWD) of the grafted LP
decays much more slowly than the corresponding LP bulk system due to the
gradient of the monomer density within the dense pseudo-brush which favors
longer chains. Both MWD and the density profiles of grafted polymers and chain
ends are well fitted by effective power laws whereby the different exponents
turn out to be mutually self-consistent for a pseudo-brush in the
strong-stretching regime.Comment: 33 pages, 11 figues, J.Chem. Phys. accepted Oct. 199
Dynamical Monte Carlo Study of Equilibrium Polymers : Static Properties
We report results of extensive Dynamical Monte Carlo investigations on
self-assembled Equilibrium Polymers (EP) without loops in good solvent. (This
is thought to provide a good model of giant surfactant micelles.) Using a novel
algorithm we are able to describe efficiently both static and dynamic
properties of systems in which the mean chain length \Lav is effectively
comparable to that of laboratory experiments (up to 5000 monomers, even at high
polymer densities). We sample up to scission energies of over
nearly three orders of magnitude in monomer density , and present a
detailed crossover study ranging from swollen EP chains in the dilute regime up
to dense molten systems. Confirming recent theoretical predictions, the
mean-chain length is found to scale as \Lav \propto \phi^\alpha \exp(\delta
E) where the exponents approach
and in the
dilute and semidilute limits respectively. The chain length distribution is
qualitatively well described in the dilute limit by the Schulz-Zimm
distribution \cN(s)\approx s^{\gamma-1} \exp(-s) where the scaling variable
is s=\gamma L/\Lav. The very large size of these simulations allows also an
accurate determination of the self-avoiding walk susceptibility exponent
. ....... Finite-size effects are discussed in
detail.Comment: 15 pages, 14 figures, LATE
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
Flow structure generated by perpendicular blade-vortex interaction and implications for helicopter noise prediction. Volume 1: Measurements
The perpendicular interaction of a streamwise vortex with an infinite span helicopter blade was modeled experimentally in incompressible flow. Three-component velocity and turbulence measurements were made using a sub-miniature four sensor hot-wire probe. Vortex core parameters (radius, peak tangential velocity, circulation, and centerline axial velocity deficit) were determined as functions of blade-vortex separation, streamwise position, blade angle of attack, vortex strength, and vortex size. The downstream development of the flow shows that the interaction of the vortex with the blade wake is the primary cause of the changes in the core parameters. The blade sheds negative vorticity into its wake as a result of the induced angle of attack generated by the passing vortex. Instability in the vortex core due to its interaction with this negative vorticity region appears to be the catalyst for the magnification of the size and intensity of the turbulent flowfield downstream of the interaction. In general, the core radius increases while peak tangential velocity decreases with the effect being greater for smaller separations. These effects are largely independent of blade angle of attack; and if these parameters are normalized on their undisturbed values, then the effects of the vortex strength appear much weaker. Two theoretical models were developed to aid in extending the results to other flow conditions. An empirical model was developed for core parameter prediction which has some rudimentary physical basis, implying usefulness beyond a simple curve fit. An inviscid flow model was also created to estimate the vorticity shed by the interaction blade, and to predict the early stages of its incorporation into the interacting vortex
Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies
It has been assumed until very recently that all long-range correlations are
screened in three-dimensional melts of linear homopolymers on distances beyond
the correlation length characterizing the decay of the density
fluctuations. Summarizing simulation results obtained by means of a variant of
the bond-fluctuation model with finite monomer excluded volume interactions and
topology violating local and global Monte Carlo moves, we show that due to an
interplay of the chain connectivity and the incompressibility constraint, both
static and dynamical correlations arise on distances . These
correlations are scale-free and, surprisingly, do not depend explicitly on the
compressibility of the solution. Both monodisperse and (essentially)
Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure
Inhomogeneous elastic response of silica glass
Using large scale molecular dynamics simulations we investigate the
properties of the {\em non-affine} displacement field induced by macroscopic
uniaxial deformation of amorphous silica,a strong glass according to Angell's
classification. We demonstrate the existence of a length scale
characterizing the correlations of this field (corresponding to a volume of
about 1000 atoms), and compare its structure to the one observed in a standard
fragile model glass. The "Boson-peak'' anomaly of the density of states can be
traced back in both cases to elastic inhomogeneities on wavelengths smaller
than , where classical continuum elasticity becomes simply unapplicable
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Studies of the nonlinear dynamics effects of APPLE-II type EPUs at the ALS
Elliptically Polarizing Undulators (EPUs) have become more and more popular at synchrotron radiation sources, providing full polarization control of the photon beam. The fields of the most commonly used APPLE-II type EPUs have a very fast, intrinsic field roll-off, creating significant non-linearities of the beam motion with in some cases large impact on the dynamic (momentum) aperture. In general, the nonlinear effects get stronger with longer periods and higher undulator magnetic fields. One of the planned future beamlines at the ALS (MERLIN) will use a quasiperiodic EPU with 9 cm period and maximum B fields of about 1.3 T. We will present simulation studies for the proposed shimming schemes for this future device to reduce the nonlinear effects to acceptable values, as well as experimental studies for the existing 5 cm period EPUs already installed in the ALS
Statistical Mechanics of Stress Transmission in Disordered Granular Arrays
We give a statistical-mechanical theory of stress transmission in disordered
arrays of rigid grains with perfect friction. Starting from the equations of
microscopic force and torque balance we derive the fundamental equations of
stress equilibrium. We illustrate the validity of our approach by solving the
stress distribution of a homogeneous and isotropic array.Comment: 4 pages, to be published in PR
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
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