6,016 research outputs found
Predicting the self-assembly of a model colloidal crystal
We investigate the self-assembly (crystallisation) of particles with hard
cores and isotropic, square-well interactions, using a Monte Carlo scheme to
simulate overdamped Langevin dynamics. We measure correlation and response
functions during the early stages of assembly, and we analyse the results using
fluctuation-dissipation theorems, aiming to predict which systems will
self-assemble successfully and which will get stuck in disordered states. The
early-time correlation and response measurements are made before significant
crystallisation has taken place, indicating that dynamical measurements are
valuable in measuring a system's propensity for kinetic trapping
Geometrical interpretation of fluctuating hydrodynamics in diffusive systems
We discuss geometric formulations of hydrodynamic limits in diffusive
systems. Specifically, we describe a geometrical construction in the space of
density profiles --- the Wasserstein geometry --- which allows the
deterministic hydrodynamic evolution of the systems to be related to steepest
descent of the free energy, and show how this formulation can be related to
most probable paths of mesoscopic dissipative systems. The geometric viewpoint
is also linked to fluctuating hydrodynamics of these systems via a saddle point
argument.Comment: 19 page
Duality symmetries in driven one-dimensional hopping models
We consider some duality relations for models of non-interacting particles
hopping on disordered one-dimensional chains. In particular, we discuss
symmetries of bulk-driven barrier and trap models, and relations between
boundary-driven and equilibrium models with related energy landscapes. We
discuss the relationships between these duality relations and similar results
for interacting many-body systems.Comment: 11 pages, 3 fig
Large deviations and ensembles of trajectories in stochastic models
We consider ensembles of trajectories associated with large deviations of
time-integrated quantities in stochastic models. Motivated by proposals that
these ensembles are relevant for physical processes such as shearing and glassy
relaxation, we show how they can be generated directly using auxiliary
stochastic processes. We illustrate our results using the Glauber-Ising chain,
for which biased ensembles of trajectories can exhibit ferromagnetic ordering.
We discuss the relation between such biased ensembles and quantum phase
transitions.Comment: 14 pages, 1 fi
Evidence for a disordered critical point in a glass-forming liquid
Using computer simulations of an atomistic glass-forming liquid, we
investigate the fluctuations of the overlap between a fluid configuration and a
quenched reference system. We find that large fluctuations of the overlap
develop as temperature decreases, consistent with the existence of the random
critical point that is predicted by effective field theories. We discuss the
scaling of fluctuations near the presumed critical point, comparing the
observed behaviour with that of the random-field Ising model. We argue that
this critical point directly reveals the existence of an interfacial tension
between amorphous metastable states, a quantity relevant both for equilibrium
relaxation and for nonequilibrium melting of stable glass configurations.Comment: 4 figs, 5 page
Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories
We consider large deviations of the dynamical activity in the East model. We
bias this system to larger than average activity and investigate the structure
that emerges. To best characterise this structure, we exploit the fact that
there are effective interactions that would reproduce the same behaviour in an
equilibrium system. We combine numerical results with linear response theory
and variational estimates of these effective interactions, giving the first
insights into such interactions in a many-body system, across a wide range of
biases. The system exhibits a hierarchy of responses to the bias, remaining
quasi-equilibrated on short length scales, but deviating far from equilibrium
on large length scales. We discuss the connection between this hierarchy and
the hierarchical aging behaviour of the system.Comment: Revised version, 29 pages, 9 fig
Effective interactions and large deviations in stochastic processes
We discuss the relationships between large deviations in stochastic systems,
and "effective interactions" that induce particular rare events. We focus on
the nature of these effective interactions in physical systems with many
interacting degrees of freedom, which we illustrate by reviewing several recent
studies. We describe the connections between effective interactions, large
deviations at "level 2.5", and the theory of optimal control. Finally, we
discuss possible physical applications of variational results associated with
those theories.Comment: 12 page
Random pinning in glassy spin models with plaquette interactions
We use a random pinning procedure to study amorphous order in two glassy spin
models. On increasing the concentration of pinned spins at constant
temperature, we find a sharp crossover (but no thermodynamic phase transition)
from bulk relaxation to localisation in a single state. At low temperatures,
both models exhibit scaling behaviour. We discuss the growing length and time
scales associated with amorphous order, and the fraction of pinned spins
required to localize the system in a single state. These results, obtained for
finite dimensional interacting models, provide a theoretical scenario for the
effect of random pinning that differs qualitatively from previous approaches
based either on mean-field, mode-coupling, or renormalization group reatments.Comment: 15 pages, 9 fig
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