The effect of shear on persistence in coarsening systems

We analytically study the effect of a uniform shear flow on the persistence properties of coarsening systems. The study is carried out within the anisotropic Ohta-Jasnow-Kawasaki (OJK) approximation for a system with nonconserved scalar order parameter. We find that the persistence exponent theta has a non-trivial value: theta = 0.5034... in space dimension d=3, and theta = 0.2406... for d=2, the latter being exactly twice the value found for the unsheared system in d=1. We also find that the autocorrelation exponent lambda is affected by shear in d=3 but not in d=2.Comment: 6 page

Facilitated spin models: recent and new results

Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from its equilibrium distribution only if the surrounding configuration fulfills a simple local constraint which \emph{does not involve} the chosen variable itself. Such simple models are quite popular in the glass community since they display some of the peculiar features of glassy dynamics, in particular they can undergo a dynamical arrest reminiscent of the liquid/glass transitiom. Due to the fact that the jumps rates of the Markov process can be zero, the whole analysis of the long time behavior becomes quite delicate and, until recently, KCSM have escaped a rigorous analysis with the notable exception of the East model. In these notes we will mainly review several recent mathematical results which, besides being applicable to a wide class of KCSM, have contributed to settle some debated questions arising in numerical simulations made by physicists. We will also provide some interesting new extensions. In particular we will show how to deal with interacting models reversible w.r.t. to a high temperature Gibbs measure and we will provide a detailed analysis of the so called one spin facilitated model on a general connected graph.Comment: 30 pages, 3 figure

Evidence of a Critical time in Constrained Kinetic Ising models

We study the relaxational dynamics of the one-spin facilitated Ising model introduced by Fredrickson and Andersen. We show the existence of a critical time which separates an initial regime in which the relaxation is exponentially fast and aging is absent from a regime in which relaxation becomes slow and aging effects are present. The presence of this fast exponential process and its associated critical time is in agreement with some recent experimental results on fragile glasses.Comment: 20 Pages + 7 Figures, Revte

Three-phase coexistence with sequence partitioning in symmetric random block copolymers

We inquire about the possible coexistence of macroscopic and microstructured phases in random Q-block copolymers built of incompatible monomer types A and B with equal average concentrations. In our microscopic model, one block comprises M identical monomers. The block-type sequence distribution is Markovian and characterized by the correlation \lambda. Upon increasing the incompatibility \chi\ (by decreasing temperature) in the disordered state, the known ordered phases form: for \lambda\ > \lambda_c, two coexisting macroscopic A- and B-rich phases, for \lambda\ < \lambda_c, a microstructured (lamellar) phase with wave number k(\lambda). In addition, we find a fourth region in the \lambda-\chi\ plane where these three phases coexist, with different, non-Markovian sequence distributions (fractionation). Fractionation is revealed by our analytically derived multiphase free energy, which explicitly accounts for the exchange of individual sequences between the coexisting phases. The three-phase region is reached, either, from the macroscopic phases, via a third lamellar phase that is rich in alternating sequences, or, starting from the lamellar state, via two additional homogeneous, homopolymer-enriched phases. These incipient phases emerge with zero volume fraction. The four regions of the phase diagram meet in a multicritical point (\lambda_c, \chi_c), at which A-B segregation vanishes. The analytical method, which for the lamellar phase assumes weak segregation, thus proves reliable particularly in the vicinity of (\lambda_c, \chi_c). For random triblock copolymers, Q=3, we find the character of this point and the critical exponents to change substantially with the number M of monomers per block. The results for Q=3 in the continuous-chain limit M -> \infty are compared to numerical self-consistent field theory (SCFT), which is accurate at larger segregation.Comment: 24 pages, 19 figures, version published in PRE, main changes: Sec. IIIA, Fig. 14, Discussio

Stability of Quasicrystals Composed of Soft Isotropic Particles

Quasicrystals whose building blocks are of mesoscopic rather than atomic scale have recently been discovered in several soft-matter systems. Contrary to metallurgic quasicrystals whose source of stability remains a question of great debate to this day, we argue that the stability of certain soft-matter quasicrystals can be directly explained by examining a coarse-grained free energy for a system of soft isotropic particles. We show, both theoretically and numerically, that the stability can be attributed to the existence of two natural length scales in the pair potential, combined with effective three-body interactions arising from entropy. Our newly gained understanding of the stability of soft quasicrystals allows us to point at their region of stability in the phase diagram, and thereby may help control the self-assembly of quasicrystals and a variety of other desired structures in future experimental realizations.Comment: Revised abstract, more detailed explanations, and better images of the numerical minimization of the free energ

Shear Alignment and Instability of Smectic Phases

We consider the shear flow of well-aligned one-component smectic phases, such as thermotropic smectics and lamellar diblock copolymers, below the critical region. We show that, as a result of thermal fluctuations of the layers, parallel ($c$) alignment is generically unstable and perpendicular ($a$) alignment is stable against long-wavelength undulations. We also find, surprisingly, that both $a$ and $c$ are stable for a narrow window of values for the anisotropic viscosity.Comment: To appear in PRL. Revtex, 1 figure

Reactions at polymer interfaces: A Monte Carlo Simulation

Reactions at a strongly segregated interface of a symmetric binary polymer blend are investigated via Monte Carlo simulations. End functionalized homopolymers of different species interact at the interface instantaneously and irreversibly to form diblock copolymers. The simulations, in the framework of the bond fluctuation model, determine the time dependence of the copolymer production in the initial and intermediate time regime for small reactant concentration $\rho_0 R_g^3=0.163 ... 0.0406$. The results are compared to recent theories and simulation data of a simple reaction diffusion model. For the reactant concentration accessible in the simulation, no linear growth of the copolymer density is found in the initial regime, and a $\sqrt{t}$-law is observed in the intermediate stage.Comment: to appear in Macromolecule

Global Stationary Phase and the Sign Problem

We present a computational strategy for reducing the sign problem in the evaluation of high dimensional integrals with non-positive definite weights. The method involves stochastic sampling with a positive semidefinite weight that is adaptively and optimally determined during the course of a simulation. The optimal criterion, which follows from a variational principle for analytic actions S(z), is a global stationary phase condition that the average gradient of the phase Im(S) along the sampling path vanishes. Numerical results are presented from simulations of a model adapted from statistical field theories of classical fluids.Comment: 9 pages, 3 figures, submitted for publicatio

Steady State of microemulsions in shear flow

Steady-state properties of microemulsions in shear flow are studied in the context of a Ginzburg-Landau free-energy approach. Explicit expressions are given for the structure factor and the time correlation function at the one loop level of approximation. Our results predict a four-peak pattern for the structure factor, implying the simultaneous presence of interfaces aligned with two different orientations. Due to the peculiar interface structure a non-monotonous relaxation of the time correlator is also found.Comment: 5 pages, 3 figure