76 research outputs found
Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow
We develop a theory to describe the reorientation phenomena in the lamellar
phase of block copolymer melt under reciprocating shear flow. We show that
similar to the steady-shear, the oscillating flow anisotropically suppresses
fluctuations and gives rise to the parallel-perpendicular orientation
transition. The experimentally observed high-frequency reverse transition is
explained in terms of interaction between the melt and the shear-cell walls.Comment: RevTex, 3 pages, 1 figure, submitted to PR
Influence of confinement on the orientational phase transitions in the lamellar phase of a block copolymer melt under shear flow
In this work we incorporate some real-system effects into the theory of
orientational phase transitions under shear flow (M. E. Cates and S. T. Milner,
Phys. Rev. Lett. v.62, p.1856 (1989) and G. H. Fredrickson, J. Rheol. v.38,
p.1045 (1994)). In particular, we study the influence of the shear-cell
boundaries on the orientation of the lamellar phase. We predict that at low
shear rates the parallel orientation appears to be stable. We show that there
is a critical value of the shear rate at which the parallel orientation loses
its stability and the perpendicular one appears immediately below the spinodal.
We associate this transition with a crossover from the fluctuation to the
mean-field behaviour. At lower temperatures the stability of the parallel
orientation is restored. We find that the region of stability of the
perpendicular orientation rapidly decreases as shear rate increases. This
behaviour might be misinterpreted as an additional perpendicular to parallel
transition recently discussed in literature.Comment: 25 pages, 4 figures, submitted to Phys. Rev.
Activity phase transition for constrained dynamics
We consider two cases of kinetically constrained models, namely East and
FA-1f models. The object of interest of our work is the activity A(t) defined
as the total number of configuration changes in the interval [0,t] for the
dynamics on a finite domain. It has been shown in [GJLPDW1,GJLPDW2] that the
large deviations of the activity exhibit a non-equilibirum phase transition in
the thermodynamic limit and that reducing the activity is more likely than
increasing it due to a blocking mechanism induced by the constraints. In this
paper, we study the finite size effects around this first order phase
transition and analyze the phase coexistence between the active and inactive
dynamical phases in dimension 1. In higher dimensions, we show that the finite
size effects are also determined by the dimension and the choice of boundary
conditions.Comment: 38 pages, 3 figure
Surface states in nearly modulated systems
A Landau model is used to study the phase behavior of the surface layer for
magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz
point marking the boundary between modulated and homogeneous bulk phases. The
model incorporates surface and bulk fields and includes a term in the free
energy proportional to the square of the second derivative of the order
parameter in addition to the usual term involving the square of the first
derivative. In the limit of vanishing bulk field, three distinct types of
surface ordering are possible: a wetting layer, a non-wet layer having a small
deviation from bulk order, and a different non-wet layer with a large deviation
from bulk order which decays non-monotonically as distance from the wall
increases. In particular the large deviation non-wet layer is a feature of
systems at the Lifshitz point and also those having only homogeneous bulk
phases.Comment: 6 pages, 7 figures, submitted to Phys. Rev.
Singularities in ternary mixtures of k-core percolation
Heterogeneous k-core percolation is an extension of a percolation model which
has interesting applications to the resilience of networks under random damage.
In this model, the notion of node robustness is local, instead of global as in
uniform k-core percolation. One of the advantages of k-core percolation models
is the validity of an analytical mathematical framework for a large class of
network topologies. We study ternary mixtures of node types in random networks
and show the presence of a new type of critical phenomenon. This scenario may
have useful applications in the stability of large scale infrastructures and
the description of glass-forming systems.Comment: To appear in Complex Networks, Studies in Computational Intelligence,
Proceedings of CompleNet 201
Ordering of the lamellar phase under a shear flow
The dynamics of a system quenched into a state with lamellar order and
subject to an uniform shear flow is solved in the large-N limit. The
description is based on the Brazovskii free-energy and the evolution follows a
convection-diffusion equation. Lamellae order preferentially with the normal
along the vorticity direction. Typical lengths grow as (with
logarithmic corrections) in the flow direction and logarithmically in the shear
direction. Dynamical scaling holds in the two-dimensional case while it is
violated in D=3
Dynamic charge density correlation function in weakly charged polyampholyte globules
We study solutions of statistically neutral polyampholyte chains containing a
large fraction of neutral monomers. It is known that, even if the quality of
the solvent with respect to the neutral monomers is good, a long chain will
collapse into a globule. For weakly charged chains, the interior of this
globule is semi-dilute. This paper considers mainly theta-solvents, and we
calculate the dynamic charge density correlation function g(k,t) in the
interior of the globules, using the quadratic approximation to the
Martin-Siggia-Rose generating functional. It is convenient to express the
results in terms of dimensionless space and time variables. Let R be the blob
size, and let T be the characteristic time scale at the blob level. Define the
dimensionless wave vector q = R k, and the dimensionless time s = t/T. We find
that for q<1, corresponding to length scales larger than the blob size, the
charge density fluctuations relax according to g(q,s) = q^2(1-s^(1/2)) at short
times s < 1, and according to g(q,s) = q^2 s^(-1/2) at intermediate times 1 < s
0.1, where
entanglements are unimportant.Comment: 12 pages RevTex, 1 figure ps, PACS 61.25.Hq, reason replacement:
Expression for dynamic corr. function g(k,t) in old version was incorrect
(though expression for Fourier transform g(k,w) was correct, so the major
part of the calculation remains.) Also major textual chang
Cutoff for the East process
The East process is a 1D kinetically constrained interacting particle system,
introduced in the physics literature in the early 90's to model liquid-glass
transitions. Spectral gap estimates of Aldous and Diaconis in 2002 imply that
its mixing time on sites has order . We complement that result and show
cutoff with an -window.
The main ingredient is an analysis of the front of the process (its rightmost
zero in the setup where zeros facilitate updates to their right). One expects
the front to advance as a biased random walk, whose normal fluctuations would
imply cutoff with an -window. The law of the process behind the
front plays a crucial role: Blondel showed that it converges to an invariant
measure , on which very little is known. Here we obtain quantitative
bounds on the speed of convergence to , finding that it is exponentially
fast. We then derive that the increments of the front behave as a stationary
mixing sequence of random variables, and a Stein-method based argument of
Bolthausen ('82) implies a CLT for the location of the front, yielding the
cutoff result.
Finally, we supplement these results by a study of analogous kinetically
constrained models on trees, again establishing cutoff, yet this time with an
-window.Comment: 33 pages, 2 figure
Density functional theory of phase coexistence in weakly polydisperse fluids
The recently proposed universal relations between the moments of the
polydispersity distributions of a phase-separated weakly polydisperse system
are analyzed in detail using the numerical results obtained by solving a simple
density functional theory of a polydisperse fluid. It is shown that universal
properties are the exception rather than the rule.Comment: 10 pages, 2 figures, to appear in PR
Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach
We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian
with a competing long-range repulsive term in the presence of an external
magnetic field. The model is analytically solved within the self consistent
Hartree approximation for two different initial conditions: disordered or zero
field cooled (ZFC), and fully magnetized or field cooled (FC). To test the
predictions of the approximation we develop a suitable numerical scheme to
ensure the isotropic nature of the interactions. Both the analytical approach
and the numerical simulations of two-dimensional finite systems confirm a
simple aging scenario at zero temperature and zero field. At zero temperature a
critical field is found below which the initial conditions are relevant
for the long time dynamics of the system. For a logarithmic growth of
modulated domains is found in the numerical simulations but this behavior is
not captured by the analytical approach which predicts a growth law at
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