157 research outputs found

### Glassy behavior of a homopolymer from molecular dynamics simulations

We study at- and out-of-equilibrium dynamics of a single homopolymer chain at
low temperature using molecular dynamics simulations. The main quantities of
interest are the average root mean square displacement of the monomers below
the theta point, and the structure factor, as a function of time. The
observation of these quantities show a close resemblance to those measured in
structural glasses and suggest that the polymer chain in its low temperature
phase is in a glassy phase, with its dynamics dominated by traps. In
equilibrium, at low temperature, we observe the trapping of the monomers and a
slowing down of the overall motion of the polymer as well as non-exponential
relaxation of the structure factor. In out-of-equilibrium, at low temperatures,
we compute the two-time quantities and observe breaking of ergodicity in a
range of waiting times, with the onset of aging.Comment: 11 pages, 4 figure

### Anomalous dynamical light scattering in soft glassy gels

We compute the dynamical structure factor S(q,tau) of an elastic medium where
force dipoles appear at random in space and in time, due to `micro-collapses'
of the structure. Various regimes are found, depending on the wave vector q and
the collapse time. In an early time regime, the logarithm of the structure
factor behaves as (q tau)^{3/2}, as predicted by Cipelletti et al. [1] using
heuristic arguments. However, in an intermediate time regime we rather obtain a
q tau)^{5/4} behaviour. Finally, the asymptotic long time regime is found to
behave as q^{3/2} tau. We also give a plausible scenario for aging, in terms of
a strain dependent energy barrier for micro-collapses. The relaxation time is
found to grow with the age t_w, quasi-exponentially at first, and then as
t_w^{4/5} with logarithmic corrections.Comment: 15 pages, 1 .eps figure. Submitted to EPJ-

### Glassy effects in the swelling/collapse dynamics of homogeneous polymers

We investigate, using numerical simulations and analytical arguments, a
simple one dimensional model for the swelling or the collapse of a closed
polymer chain of size N, representing the dynamical evolution of a polymer in a
\Theta-solvent that is rapidly changed into a good solvent (swelling) or a bad
solvent (collapse). In the case of swelling, the density profile for
intermediate times is parabolic and expands in space as t^{1/3}, as predicted
by a Flory-like continuum theory. The dynamics slows down after a time \propto
N^2 when the chain becomes stretched, and the polymer gets stuck in metastable
`zig-zag' configurations, from which it escapes through thermal activation. The
size of the polymer in the final stages is found to grow as \sqrt{\ln t}. In
the case of collapse, the chain very quickly (after a time of order unity)
breaks up into clusters of monomers (`pearls'). The evolution of the chain then
proceeds through a slow growth of the size of these metastable clusters, again
evolving as the logarithm of time. We enumerate the total number of metastable
states as a function of the extension of the chain, and deduce from this
computation that the radius of the chain should decrease as 1/\ln(\ln t). We
compute the total number of metastable states with a given value of the energy,
and find that the complexity is non zero for arbitrary low energies. We also
obtain the distribution of cluster sizes, that we compare to simple
`cut-in-two' coalescence models. Finally, we determine the aging properties of
the dynamical structure. The subaging behaviour that we find is attributed to
the tail of the distribution at small cluster sizes, corresponding to
anomalously `fast' clusters (as compared to the average). We argue that this
mechanism for subaging might hold in other slowly coarsening systems.Comment: 35 pages, 12 .ps figures. Submitted to EPJ

### Investigation of $q$-dependent dynamical heterogeneity in a colloidal gel by x-ray photon correlation spectroscopy

We use time-resolved X-Photon Correlation Spectroscopy to investigate the
slow dynamics of colloidal gels made of moderately attractive carbon black
particles. We show that the slow dynamics is temporally heterogeneous and
quantify its fluctuations by measuring the variance $\chi$ of the instantaneous
intensity correlation function. The amplitude of dynamical fluctuations has a
non-monotonic dependence on scattering vector $q$, in stark contrast with
recent experiments on strongly attractive colloidal gels [Duri and Cipelletti,
\textit{Europhys. Lett.} \textbf{76}, 972 (2006)]. We propose a simple scaling
argument for the $q$-dependence of fluctuations in glassy systems that
rationalizes these findings.Comment: Final version published in PR

### Correlated percolation models of structured habitat in ecology

Percolation offers acknowledged models of random media when the relevant
medium characteristics can be described as a binary feature. However, when
considering habitat modeling in ecology, a natural constraint comes from
nearest-neighbor correlations between the suitable/unsuitable states of the
spatial units forming the habitat. Such constraints are also relevant in the
physics of aggregation where underlying processes may lead to a form of
correlated percolation. However, in ecology, the processes leading to habitat
correlations are in general not known or very complex. As proposed by Hiebeler
[Ecology {\bf 81}, 1629 (2000)], these correlations can be captured in a
lattice model by an observable aggregation parameter $q$, supplementing the
density $p$ of suitable sites. We investigate this model as an instance of
correlated percolation. We analyze the phase diagram of the percolation
transition and compute the cluster size distribution, the pair-connectedness
function $C(r)$ and the correlation function $g(r)$. We find that while $g(r)$
displays a power-law decrease associated with long-range correlations in a wide
domain of parameter values, critical properties are compatible with the
universality class of uncorrelated percolation. We contrast the correlation
structures obtained respectively for the correlated percolation model and for
the Ising model, and show that the diversity of habitat configurations
generated by the Hiebeler model is richer than the archetypal Ising model. We
also find that emergent structural properties are peculiar to the implemented
algorithm, leading to questioning the notion of a well-defined model of
aggregated habitat. We conclude that the choice of model and algorithm have
strong consequences on what insights ecological studies can get using such
models of species habitat

### Spatial correlations in the relaxation of the Kob-Andersen model

We describe spatio-temporal correlations and heterogeneities in a kinetically
constrained glassy model, the Kob-Andersen model. The kinetic constraints of
the model alone induce the existence of dynamic correlation lengths, that
increase as the density $\rho$ increases, in a way compatible with a
double-exponential law. We characterize in detail the trapping time correlation
length, the cooperativity length, and the distribution of persistent clusters
of particles. This last quantity is related to the typical size of blocked
clusters that slow down the dynamics for a given density.Comment: 7 pages, 6 figures, published version (title has changed

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