Numerical study of multitime scaling in a solid system undergoing phase separation

Hyperuniformity in phase ordering: the roles of activity, noise, and non-constant mobility

Hyperuniformity emerges generically in the coarsening regime of phase-separating fluids. Numerical studies of active and passive systems have shown that the structure factorS(q) behaves asqςforq → 0, with hyperuniformity exponentς = 4. For passive systems, this result was explained in 1991 by a qualitative scaling analysis of Tomita, exploiting isotropy at scales much larger than the coarsening length. Here we reconsider and extend Tomita's argument to address cases of active phase separation and of non-constant mobility, again findingς = 4. We further show that dynamical noise of varianceDcreates a transientς = 2 regime forq^≪q^∗∼Dt[1-(d+2)ν]/2, crossing over toς = 4 at largerq^. Here,νis the coarsening exponent for the domain sizeℓ, such thatℓ(t)∼tν, andq^∝qℓis the rescaled wavenumber. In diffusive coarseningν=1/3, so the rescaled crossover wavevectorq^∗vanishes at large times whend⩾2. The slowness of this decay suggests a natural explanation for experiments that observe a long-livedς = 2 scaling in phase-separatingactivefluids (where noise is typically large). Conversely, ind = 1, we demonstrate that with noise theς = 2 regime survives ast→∞, withq^∗∼D5/6. (The structure factor is not then determined by the zero-temperature fixed point.) We confirm our analytical predictions by numerical simulations of continuum theories for active and passive phase separation in the deterministic case and of Model B for the stochastic case. We also compare them with related findings for a system near an absorbing-state transition rather than undergoing phase separation. A central role is played throughout by the presence or absence of a conservation law for the centre of mass positionRof the order parameter field.

Collective behavior of passive and active circle swimming particle mixtures

We present a numerical study on a binary mixture of passive and circle swimming, self-propelling particles which interact via the Lennard-Jones (LJ) potential in two dimensions. Using Brownian Dynamics (BD) simulations, we present state diagrams using the control parameters such as attraction strength, angular velocity, self-propulsion velocity and composition. In a symmetric mixture, the system undergoes a transition from a mixed gel to a rotating passive cluster state and finally to a homogeneous fluid state as translational activity increases. The formation of the rotating cluster of passive particles surrounded by active and passive monomers is attributed to the combined effect of composition, activity and strength of attraction of the active particles. Different phases are characterized using radial distribution functions, bond order parameters, cluster fraction and probability distribution of local volume fractions. The present study addresses comprehensively the intricate role of activity, angular velocity, inter-particle interaction and compositional variation on the phase behavior. The predictions presented in the study can be experimentally realized in synthetic colloidal swimmers and motile bacterial suspensions.

Motility-Induced Microphase and Macrophase Separation in a Two-Dimensional Active Brownian Particle System

As a result of nonequilibrium forces, purely repulsive self-propelled particles undergo macrophase separation between a dense and a dilute phase. We present a thorough study of the ordering kinetics of such motility-induced phase separation (MIPS) in active Brownian particles in two dimensions, and we show that it is generically accompanied by microphase separation. The growth of the dense phase follows a law akin to the one of liquid-gas phase separation. However, it is made of a mosaic of hexatic microdomains whose size does not coarsen indefinitely, leaving behind a network of extended topological defects from which microscopic dilute bubbles arise. The characteristic length of these finite-size structures increases with activity, independently of the choice of initial conditions.

Initial correlation dependence of aging in phase separating solid binary mixtures and ordering ferromagnets

Following quenches of initial configurations having long range spatial correlations, prepared at the demixing critical point, to points inside the miscibility gap, we study aging phenomena in solid binary mixtures. Results on the decay of the two-time order-parameter autocorrelation functions, obtained from Monte Carlo simulations of the two-dimensional Ising model, with Kawasaki exchange kinetics, are analyzed via state-of-the art methods. The outcome is compared with that obtained for the ordering in uniaxial ferromagnets. For the latter, we have performed Monte Carlo simulations of the same model using the Glauber mechanism. For both types of systems we provide comparative discussion of our results with reference to those concerning quenches with configurations having no spatial correlation. We also discuss the role of structure on the decay of these correlations.

Ballistic aggregation in systems of inelastic particles: Cluster growth, structure, and aging

We study far-from-equilibrium dynamics in models of freely cooling granular gas and ballistically aggregating compact clusters. For both the cases, from event-driven molecular dynamics simulations, we have presented detailed results on structure and dynamics in space dimensions d=1 and 2. Via appropriate analyses it has been confirmed that the ballistic aggregation mechanism applies in d=1 granular gases as well. Aging phenomena for this mechanism, in both the dimensions, have been studied via the two-time density autocorrelation function. This quantity is demonstrated to exhibit scaling property similar to that in the standard phase transition kinetics. The corresponding functional forms have been quantified and the outcomes have been discussed in connection with the structural properties. Our results on aging establish a more complete equivalence between the granular gas and the ballistic aggregation models in d=1.

Role of initial state and final quench temperature on aging properties in phase-ordering kinetics

We study numerically the two-dimensional Ising model with nonconserved dynamics quenched from an initial equilibrium state at the temperature T_{i}≥T_{c} to a final temperature T_{f} below the critical one. By considering processes initiating both from a disordered state at infinite temperature T_{i}=∞ and from the critical configurations at T_{i}=T_{c} and spanning the range of final temperatures T_{f}∈[0,T_{c}[ we elucidate the role played by T_{i} and T_{f} on the aging properties and, in particular, on the behavior of the autocorrelation C and of the integrated response function χ. Our results show that for any choice of T_{f}, while the autocorrelation function exponent λ_{C} takes a markedly different value for T_{i}=∞ [λ_{C}(T_{i}=∞)≃5/4] or T_{i}=T_{c} [λ_{C}(T_{i}=T_{c})≃1/8] the response function exponents are unchanged. Supported by the outcome of the analytical solution of the solvable spherical model we interpret this fact as due to the different contributions provided to autocorrelation and response by the large-scale properties of the system. As changing T_{f} is considered, although this is expected to play no role in the large-scale and long-time properties of the system, we show important effects on the quantitative behavior of χ. In particular, data for quenches to T_{f}=0 are consistent with a value of the response function exponent λ_{χ}=1/2λ_{C}(T_{i}=∞)=5/8 different from the one [λ_{χ}∈(0.5-0.56)] found in a wealth of previous numerical determinations in quenches to finite final temperatures. This is interpreted as due to important preasymptotic corrections associated to T_{f}>0.

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.

Phase Separation Kinetics of Binary Systems: Effects of Hydrodynamic Interaction And Surfactants

Cell dynamics computer simulation method is used to investigate effects of hydro-dynamic interaction as well as effects of added surfactants on phase separation kinetics. In the former the obtained scattering structure function for 3-dimensional system reproduces the experimental results for polymer blends remarkably well. In the latter we display self-assembling process in two-dimensional system on computer.

Influence of thermal fluctuations on the geometry of interfaces of the quenched Ising model

We study the role of the quench temperature Tf in the phase-ordering kinetics of the Ising model with single spin flip in d=2,3 . Equilibrium interfaces are flat at Tf=0 , whereas at Tf>0 they are curved and rough (above the roughening temperature in d=3 ). We show, by means of scaling arguments and numerical simulations, that this geometrical difference is important for the phase-ordering kinetics as well. In particular, while the growth exponent z=2 of the size of domains L(t) approximately t 1/z is unaffected by Tf, other exponents related to the interface geometry take different values at Tf=0 or Tf>0 . For Tf>0 a crossover phenomenon is observed from an early stage where interfaces are still flat and the system behaves as at Tf=0 , to the asymptotic regime with curved interfaces characteristic of Tf>0 . Furthermore, it is shown that the roughening length, although subdominant with respect to L(t) , produces appreciable correction to scaling up to very long times in d=2 .

Coarsening of "clouds" and dynamic scaling in a far-from-equilibrium model system

A two-dimensional lattice gas of two species, driven in opposite directions by an external force, undergoes a jamming transition if the filling fraction is sufficiently high. Using Monte Carlo simulations, we investigate the growth of these jams (''clouds''), as the system approaches a nonequilibrium steady state from a disordered initial state. We monitor the dynamic structure factor S(k{x},k{y};t) and find that the k{x}=0 component exhibits dynamic scaling, of the form S(0,k{y};t)=t;{beta}S[over](k{y}t;{alpha}) . Over a significant range of times, we observe excellent data collapse with alpha=12 and beta=1 . The effects of varying filling fraction and driving force are discussed.

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.

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.

Morphological characterization of bicontinuous structures in polymer blends and microemulsions by the inverse-clipping method in the context of the clipped-random-wave model

A method is proposed to determine the spectral function of the clipped-random-wave (CRW) model directly from scattering data. The spectral function f(k) (k is a wave number) gives the distribution of the magnitude of wave vectors of the sinusoidal waves that describes the essential features of the two-phase morphology. The proposed method involves "inverse clipping" of a correlation function to obtain f(k) and does not require any a priori assumptions for f(k). A critical test of the applicability of the inverse-clipping method was carried out by using three-component bicontinuous microemulsions. The method was then used to determine f(k) of the bicontinuous structure of a phase-separating polymer blend. f(k) for the polymer blend turned out to be a multipeaked function, while f(k) for the microemulsions exhibits a single broad maximum representing periodicity of the morphology. These results indicate the presence of the long-range regularity in the morphology of the polymer blend. Three-dimensional (3D) morphology corresponding to the scattering data of the polymer blend was generated using the CRW model together with the multipeaked f(k). Interface curvatures of the 3D morphology calculated from f(k) were measured and compared with those experimentally determined directly from the laser scanning confocal microscopy in the same blend.