818 research outputs found
Viscosity critical behaviour at the gel point in a 3d lattice model
Within a recently introduced model based on the bond-fluctuation dynamics we
study the viscoelastic behaviour of a polymer solution at the gelation
threshold. We here present the results of the numerical simulation of the model
on a cubic lattice: the percolation transition, the diffusion properties and
the time autocorrelation functions have been studied. From both the diffusion
coefficients and the relaxation times critical behaviour a critical exponent k
for the viscosity coefficient has been extracted: the two results are
comparable within the errors and are in close agreement with the Rouse model
prediction and with some experimental results. In the critical region below the
transition threshold the time autocorrelation functions show a long time tail
which is well fitted by a stretched exponential decay.Comment: 14 pag., RevTex, 9 figure
Static and dynamic heterogeneities in irreversible gels and colloidal gelation
We compare the slow dynamics of irreversible gels, colloidal gels, glasses
and spin glasses by analyzing the behavior of the so called non-linear
dynamical susceptibility, a quantity usually introduced to quantitatively
characterize the dynamical heterogeneities. In glasses this quantity typically
grows with the time, reaches a maximum and then decreases at large time, due to
the transient nature of dynamical heterogeneities and to the absence of a
diverging static correlation length. We have recently shown that in
irreversible gels the dynamical susceptibility is instead an increasing
function of the time, as in the case of spin glasses, and tends asymptotically
to the mean cluster size. On the basis of molecular dynamics simulations, we
here show that in colloidal gelation where clusters are not permanent, at very
low temperature and volume fractions, i.e. when the lifetime of the bonds is
much larger than the structural relaxation time, the non-linear susceptibility
has a behavior similar to the one of the irreversible gel, followed, at higher
volume fractions, by a crossover towards the behavior of glass forming liquids.Comment: 9 pages, 3 figure
Dynamical Correlation Length and Relaxation Processes in a Glass Former
We investigate the relaxation process and the dynamical heterogeneities of
the kinetically constrained Kob--Anderson lattice glass model, and show that
these are characterized by different timescales. The dynamics is well described
within the diffusing defect paradigm, which suggest to relate the relaxation
process to a reverse--percolation transition. This allows for a geometrical
interpretation of the relaxation process, and of the different timescales
Number of spanning clusters at the high-dimensional percolation thresholds
A scaling theory is used to derive the dependence of the average number
of spanning clusters at threshold on the lattice size L. This number should
become independent of L for dimensions d<6, and vary as log L at d=6. The
predictions for d>6 depend on the boundary conditions, and the results there
may vary between L^{d-6} and L^0. While simulations in six dimensions are
consistent with this prediction (after including corrections of order loglog
L), in five dimensions the average number of spanning clusters still increases
as log L even up to L = 201. However, the histogram P(k) of the spanning
cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L,
indicating that for sufficiently large L the average will approach a finite
value: a fit of the 5D multiplicity data with a constant plus a simple linear
correction to scaling reproduces the data very well. Numerical simulations for
d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review
Complex viscosity behavior and cluster formation in attractive colloidal systems
The increase of the viscosity, which is observed in attractive colloidal
systems by varying the temperature or the volume fraction, can be related to
the formation of structures due to particle aggregation. In particular we have
studied the non trivial dependence of the viscosity from the temperature and
the volume fraction in the copolymer-micellar system L64. The comparison of the
experimental data with the results of numerical simulations in a simple model
for gelation phenomena suggests that this intriguing behavior can be explained
in terms of cluster formation and that this picture can be quite generally
extended to other attractive colloidal systems.Comment: 5 pages, 4 figure
Granular dynamics in compaction and stress relaxation
Elastic and dissipative properties of granular assemblies under uniaxial
compression are studied both experimentally and by numerical simulations.
Following a novel compaction procedure at varying oscillatory pressures, the
stress response to a step-strain reveals an exponential relaxation followed by
a slow logarithmic decay. Simulations indicate that the latter arises from the
coupling between damping and collective grain motion predominantly through
sliding. We characterize an analogous "glass transition" for packed grains,
below which the system shows aging in time-dependent sliding correlation
functions.Comment: 5 pages, 5 figure
Percolation and cluster Monte Carlo dynamics for spin models
A general scheme for devising efficient cluster dynamics proposed in a
previous letter [Phys.Rev.Lett. 72, 1541 (1994)] is extensively discussed. In
particular the strong connection among equilibrium properties of clusters and
dynamic properties as the correlation time for magnetization is emphasized. The
general scheme is applied to a number of frustrated spin model and the results
discussed.Comment: 17 pages LaTeX + 16 figures; will appear in Phys. Rev.
Heterogeneous slow dynamics in a two dimensional doped classical antiferromagnet
We introduce a lattice model for a classical doped two dimensional
antiferromagnet which has no quenched disorder, yet displays slow dynamics
similar to those observed in supercooled liquids. We calculate two-time spatial
and spin correlations via Monte Carlo simulations and find that for
sufficiently low temperatures, there is anomalous diffusion and
stretched-exponential relaxation of spin correlations. The relaxation times
associated with spin correlations and diffusion both diverge at low
temperatures in a sub-Arrhenius fashion if the fit is done over a large
temperature-window or an Arrhenius fashion if only low temperatures are
considered. We find evidence of spatially heterogeneous dynamics, in which
vacancies created by changes in occupation facilitate spin flips on
neighbouring sites. We find violations of the Stokes-Einstein relation and
Debye-Stokes-Einstein relation and show that the probability distributions of
local spatial correlations indicate fast and slow populations of sites, and
local spin correlations indicate a wide distribution of relaxation times,
similar to observ ations in other glassy systems with and without quenched
disorder.Comment: 12 pages, 17 figures, corrected erroneous figure, and improved
quality of manuscript, updated reference
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