36 research outputs found
Generalized Langevin equations for a driven tracer in dense soft colloids: construction and applications
We describe a tracer in a bath of soft Brownian colloids by a particle
coupled to the density field of the other bath particles. From the Dean
equation, we derive an exact equation for the evolution of the whole system,
and show that the density field evolution can be linearized in the limit of a
dense bath. This linearized Dean equation with a tracer taken apart is
validated by the reproduction of previous results on the mean-field liquid
structure and transport properties. Then, the tracer is submitted to an
external force and we compute the density profile around it, its mobility and
its diffusion coefficient. Our results exhibit effects such as bias enhanced
diffusion that are very similar to those observed in the opposite limit of a
hard core lattice gas, indicating the robustness of these effects. Our
predictions are successfully tested against molecular dynamics simulations.Comment: 21 pages, 7 figure
Scaling of the glassy dynamics of soft repulsive particles: a mode-coupling approach
We combine the hyper-netted chain approximation of liquid state theory with
the mode-coupling theory of the glass transition to analyze the structure and
dynamics of soft spheres interacting via harmonic repulsion. We determine the
locus of the fluid-glass dynamic transition in a temperature -- volume fraction
phase diagram. The zero-temperature (hard sphere) glass transition influences
the dynamics at finite temperatures in its vicinity. This directly implies a
form of dynamic scaling for both the average relaxation time and dynamic
susceptibilities quantifying dynamic heterogeneity. We discuss several
qualitative disagreements between theory and existing simulations at
equilibrium. Our theoretical results are, however, very similar to numerical
results for the driven athermal dynamics of repulsive spheres, suggesting that
`mean-field' mode-coupling approaches might be good starting points to describe
these nonequilibrium dynamics.Comment: 11 pages, 8 figure
Quantitative field theory of the glass transition
We develop a full microscopic replica field theory of the dynamical
transition in glasses. By studying the soft modes that appear at the dynamical
temperature we obtain an effective theory for the critical fluctuations. This
analysis leads to several results: we give expressions for the mean field
critical exponents, and we study analytically the critical behavior of a set of
four-points correlation functions from which we can extract the dynamical
correlation length. Finally, we can obtain a Ginzburg criterion that states the
range of validity of our analysis. We compute all these quantities within the
Hypernetted Chain Approximation (HNC) for the Gibbs free energy and we find
results that are consistent with numerical simulations.Comment: 6 pages, 2 figures + supplementary information -- a few minor errors
of the published version have been fixe
On the entropy of protein families
Proteins are essential components of living systems, capable of performing a
huge variety of tasks at the molecular level, such as recognition, signalling,
copy, transport, ... The protein sequences realizing a given function may
largely vary across organisms, giving rise to a protein family. Here, we
estimate the entropy of those families based on different approaches, including
Hidden Markov Models used for protein databases and inferred statistical models
reproducing the low-order (1-and 2-point) statistics of multi-sequence
alignments. We also compute the entropic cost, that is, the loss in entropy
resulting from a constraint acting on the protein, such as the fixation of one
particular amino-acid on a specific site, and relate this notion to the escape
probability of the HIV virus. The case of lattice proteins, for which the
entropy can be computed exactly, allows us to provide another illustration of
the concept of cost, due to the competition of different folds. The relevance
of the entropy in relation to directed evolution experiments is stressed.Comment: to appear in Journal of Statistical Physic
Static replica approach to critical correlations in glassy systems
We discuss the slow relaxation phenomenon in glassy systems by means of
replicas by constructing a static field theory approach to the problem. At the
mean field level we study how criticality in the four point correlation
functions arises because of the presence of soft modes and we derive an
effective replica field theory for these critical fluctuations. By using this
at the Gaussian level we obtain many physical quantities: the correlation
length, the exponent parameter that controls the Mode-Coupling dynamical
exponents for the two-point correlation functions, and the prefactor of the
critical part of the four point correlation functions. Moreover we perform a
one-loop computation in order to identify the region in which the mean field
Gaussian approximation is valid. The result is a Ginzburg criterion for the
glass transition. We define and compute in this way a proper Ginzburg number.
Finally, we present numerical values of all these quantities obtained from the
Hypernetted Chain approximation for the replicated liquid theory.Comment: 34 pages, 1 figure - to be published on J.Chem.Phys. for a special
issue on the Glass Transitio
Field theoretic formulation of a mode-coupling equation for colloids
The only available quantitative description of the slowing down of the
dynamics upon approaching the glass transition has been, so far, the
mode-coupling theory, developed in the 80's by G\"otze and collaborators. The
standard derivation of this theory does not result from a systematic expansion.
We present a field theoretic formulation that arrives at very similar
mode-coupling equation but which is based on a variational principle and on a
controlled expansion in a small dimensioneless parameter. Our approach applies
to such physical systems as colloids interacting via a mildly repulsive
potential. It can in principle, with moderate efforts, be extended to higher
orders and to multipoint correlation functions
Can the jamming transition be described using equilibrium statistical mechanics?
When materials such as foams or emulsions are compressed, they display solid
behaviour above the so-called `jamming' transition. Because compression is done
out-of-equilibrium in the absence of thermal fluctuations, jamming appears as a
new kind of a nonequilibrium phase transition. In this proceeding paper, we
suggest that tools from equilibrium statistical mechanics can in fact be used
to describe many specific features of the jamming transition. Our strategy is
to introduce thermal fluctuations and use statistical mechanics to describe the
complex phase behaviour of systems of soft repulsive particles, before sending
temperature to zero at the end of the calculation. We show that currently
available implementations of standard tools such as integral equations,
mode-coupling theory, or replica calculations all break down at low temperature
and large density, but we suggest that new analytical schemes can be developed
to provide a fully microscopic, quantitative description of the jamming
transition.Comment: 8 pages, 6 figs. Talk presented at Statphys24 (July 2010, Cairns,
Australia