Federico Corberi

Two-Scale Competition in Phase Separation with Shear

The behavior of a phase separating binary mixture in uniform shear flow is investigated by numerical simulations and in a renormalization group (RG) approach. Results show the simultaneous existence of domains of two characteristic scales. Stretching and cooperative ruptures of the network produce a rich interplay where the recurrent prevalence of thick and thin domains determines log-time periodic oscillations. A power law growth

Off-equilibrium generalization of the fluctuation dissipation theorem for Ising spins and measurement of the linear response function.

R(t) \sim t^{\alpha}

Fluctuation dissipation relations far from equilibrium

of the average domain size, with

Spinodal Decomposition of Binary Mixtures in Uniform Shear Flow

\alpha =4/3

Nonlinear response and fluctuation-dissipation relations

and

Ordering of the lamellar phase under a shear flow

\alpha = 1/3

Slow relaxation in the large-N model for phase ordering.

in the flow and shear direction respectively, is shown to be obeyed.

The effective temperature in the quenching of coarsening systems to and to below TC

We derive for Ising spins an off-equilibrium generalization of the fluctuation dissipation theorem, which is formally identical to the one previously obtained for soft spins with Langevin dynamics [L.F. Cugliandolo, J. Kurchan, and G. Parisi, J. Phys. I 4, 1641 (1994)]. The result is quite general and holds both for dynamics with conserved and nonconserved order parameters. On the basis of this fluctuation dissipation relation, we construct an efficient numerical algorithm for the computation of the linear response function without imposing the perturbing field, which is alternative to those of Chatelain [J. Phys. A 36, 10 739 (2003)] and Ricci-Tersenghi [Phys. Rev. E 68, 065104(R) (2003)]. As applications of the new algorithm, we present very accurate data for the linear response function of the Ising chain, with conserved and nonconserved order parameter dynamics, finding that in both cases the structure is the same with a very simple physical interpretation. We also compute the integrated response function of the two-dimensional Ising model, confirming that it obeys scaling chi (t, t(w)) approximately equal to t(-a)(w) f (t/t(w)) , with a =0.26+/-0.01 , as previously found with a different method.

Phase separation of binary mixtures in shear flow: A numerical study

In this paper we review some recent progress in the field of non-equilibrium linear response theory. We show how a generalization of the fluctuation dissipation theorem can be derived for Markov processes, and discuss the Cugliandolo–Kurchan fluctuation dissipation relation for ageing systems and the theorem by Franz et al relating static and dynamic properties. We than specialize to phase ordering systems, examining the scaling properties of the linear response function and how these are determined by the behaviour of topological defects. We discuss how the connection between statics and dynamics can be violated in these systems at the lower critical dimension or due to stochastic instability.

Interface fluctuations, bulk fluctuations, and dimensionality in the off-equilibrium response of coarsening systems.

Results are presented for the phase separation process of a binary mixture subject to an uniform shear flow quenched from a disordered to a homogeneous ordered phase. The kinetics of the process is described in the context of the time-dependent Ginzburg-Landau equation with an external velocity term. The one-loop approximation is used to study the evolution of the model. We show that the structure factor obeys a generalized dynamical scaling. The domains grow with different typical lengthscales