Large Fluctuations and Dynamic Phase Transition in a System of Self-Propelled Particles.

We study the statistics, in stationary conditions, of the work W_{τ} done by the active force in different systems of self-propelled particles in a time τ. We show the existence of a critical value W_{τ}^{†} such that fluctuations with W_{τ}>W_{τ}^{†} correspond to configurations where interaction between particles plays a minor role whereas those with W_{τ}

Complex phase ordering of the one-dimensional Heisenberg model with conserved order parameter.

We study the phase-ordering kinetics of the one-dimensional Heisenberg model with conserved order parameter by means of scaling arguments and numerical simulations. We find a rich dynamical pattern with a regime characterized by two distinct growing lengths. Spins are found to be coplanar over regions of a typical size LV(t), while inside these regions smooth rotations associated to a smaller length LC(t) are observed. Two different and coexisting ordering mechanisms are associated to these lengths, leading to different growth laws LV(t) approximately t1/3 and LC(t) approximately t1/4 violating dynamical scaling.

Phase-ordering kinetics on graphs.

We study numerically the phase-ordering kinetics following a temperature quench of the Ising model with single spin-flip dynamics on a class of graphs, including geometrical fractals and random fractals, such as the percolation cluster. For each structure we discuss the scaling properties and compute the dynamical exponents. We show that the exponent a_{chi} for the integrated response function, at variance with all the other exponents, is independent of temperature and of the presence of pinning. This universal character suggests a strict relation between a_{chi} and the topological properties of the networks, in analogy to what is observed on regular lattices.

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 nonmonotonous relaxation of the time correlator is also found.

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. Lamellas order preferentially with the normal along the vorticity direction. Typical lengths grow as gamma t(5/4) (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.

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

The relationship between statics and dynamics proposed by Franz, Mezard, Parisi, and Peliti (FMPP) for slowly relaxing systems [Phys. Rev. Lett. 81, 1758 (1998)] is investigated in the framework of nondisordered coarsening systems. Separating the bulk from interface response we find that for statics to be retrievable from dynamics the interface contribution must be asymptotically negligible. How fast this happens depends on dimensionality. There exists a critical dimensionality above that the interface response vanishes like the interface density and below that it vanishes more slowly. At d=1 the interface response does not vanish leading to the violation of the FMPP scheme. This behavior is explained in terms of the competition between curvature-driven and field-driven interface motion.

Slow dynamics and aging in a constrained diffusion model.

We carry out a complete analysis of the schematic diffusive model recently introduced for the description of supercooled liquids and glassy systems above the glass temperature. The model is described by a trivial equilibrium measure and the presence of kinetics constraints is mimicked through a rapidly decreasing mobility at high particle density. The governing equation describing a sudden quench process is investigated analytically in a mean field approach and by means of numerical simulations. For deep quenches a long lasting off-equilibrium dynamics is observed in dense systems before equilibration is achieved, where time translational invariance lacks and the system ages. The kinetics is slow in this time domain since the average particle diffusivity D decreases in time, as opposed to the standard diffusion case of a constant D, that is recovered only in equilibrium. The autocorrelation function decays slower than an exponential, falling in mean field as an enhanced power law. The linear response function is computed and the modalities of the break-down of the fluctuation dissipation theorem are analytically investigated, showing that an effective temperature can be defined which slowly approaches the bath temperature from above.

Off-equilibrium response function in the one-dimensional random-field Ising model.

A thorough numerical investigation of the slow dynamics in the d=1 random-field Ising model in the limit of an infinite ferromagnetic coupling is presented in this paper. Crossovers from the preasymptotic pure regime to the asymptotic Sinai regime are investigated for the average domain size, the autocorrelation function, and staggered magnetization. By switching on an additional small random field at the time t(w) the linear off-equilibrium response function is obtained, which displays as well the crossover from the nontrivial behavior of the d=1 pure Ising model to the asymptotic behavior where it vanishes identically.

Crossover in growth law and violation of superuniversality in the random-field Ising model.

We study the nonconserved phase-ordering dynamics of the d=2,3 random-field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three dimensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, we find the exponent in the preasymptotic power law to be disorder dependent, rather than being that of the pure system. Furthermore, we find that the autocorrelation function does not display superuniversal behavior. This restores consistency with previous results for the d=1 system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random-bond Ising model.

Aging dynamics and the topology of inhomogenous networks.

We study phase ordering on networks and we establish a relation between the exponent a(x) of the aging part of the integrated auto-response function and the topology of the underlying structures. We show that a(x) > 0 in full generality on networks which are above the lower critical dimension d(L), i.e., where the corresponding statistical model has a phase transition at finite temperature. For discrete symmetry models on finite ramified structures with T(c) = 0, which are at the lower critical dimension d(L), we show that a(x) is expected to vanish. We provide numerical results for the physically interesting case of the 2 - d percolation cluster at or above the percolation threshold, i.e., at or above d(L), and for other networks, showing that the value of a(x) changes according to our hypothesis. For O(N) models we find that the same picture holds in the large-N limit and that a(x) only depends on the spectral dimension of the network.

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

The phase-separation kinetics of binary fluids in shear flow is studied numerically in the framework of the continuum convection-diffusion equation based on a Ginzburg-Landau free energy. Simulations are carried out for different temperatures both in d=2 and 3. Our results confirm the qualitative picture put forward by the large-N limit equations studied by Corberi et al. [Phys. Rev. Lett. 81, 3852 (1998)]. In particular, the structure factor is characterized by the presence of four peaks whose relative oscillations give rise to a periodic modulation of the behavior of the rheological indicators and of the average domains sizes. This peculiar pattern of the structure factor corresponds to the presence of domains with two characteristic thicknesses, whose relative abundance changes with time.

Structure and rheology of binary mixtures in shear flow

Results are presented for the phase separation process of a binary mixture subject to a 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 large-n approximation is used to study the evolution of the model in the presence of a stationary flow and in the case of an oscillating shear. For stationary flow we show that the structure factor obeys a generalized dynamical scaling. The domains grow with different typical length scales Rx and R( perpendicular), respectively, in the flow direction and perpendicularly to it. In the scaling regime R( perpendicular) approximately t(alpha( perpendicular)) and Rx approximately gammat(alpha(x)) (with logarithmic corrections), gamma being the shear rate, with alpha(x)=5/4 and alpha( perpendicular)=1/4. The excess viscosity Deltaeta after reaching a maximum relaxes to zero as gamma(-2)t(-3/2). Deltaeta and other observables exhibit logarithmic-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and breakup of domains occur cyclically. In the case of an oscillating shear a crossover phenomenon is observed: Initially the evolution is characterized by the same growth exponents as for a stationary flow. For longer times the phase-separating structure cannot align with the oscillating drift and a different regime is entered with an isotropic growth and the same exponents as in the case without shear.