Kinetics of ordering for correlated initial conditions

Automated characterization of spatial and dynamical heterogeneity in supercooled liquids via implementation of machine learning

A computational approach by an implementation of the principle component analysis (PCA) withK-means and Gaussian mixture (GM) clustering methods from machine learning algorithms to identify structural and dynamical heterogeneities of supercooled liquids is developed. In this method, a collection of the average weighted coordination numbers (WCNs‾) of particles calculated from particles' positions are used as an order parameter to build a low-dimensional representation of feature (structural) space forK-means clustering to sort the particles in the system into few meso-states using PCA. Nano-domains or aggregated clusters are also formed in configurational (real) space from a direct mapping using associated meso-states' particle identities with some misclassified interfacial particles. These classification uncertainties can be improved by a co-learning strategy which utilizes the probabilistic GM clustering and the information transfer between the structural space and configurational space iteratively until convergence. A final classification of meso-states in structural space and domains in configurational space are stable over long times and measured to have dynamical heterogeneities. Armed with such a classification protocol, various studies over the thermodynamic and dynamical properties of these domains indicate that the observed heterogeneity is the result of liquid-liquid phase separation after quenching to a supercooled state.

Perspectives on a Few Puzzles in Phase Transformations: When Should the Farthest Reach the Earliest?

We briefly review the facts concerning two important aspects of phase transitions, namely, critical and coarsening phenomena. A discussion of the universal features, highlighting the current challenges, is provided. Following this, we elaborate on a topic of much recent interest, viz., the Mpemba effect, a puzzle that found mention even in the works of Aristotle. After a description of the debated case of faster freezing of a hotter sample of liquid water, into ice, than a colder one, when quenched to the same subzero temperature, we discuss more modern interest. There one asks, should a hotter body of a material equilibrate faster than a colder one when quenched to a common lower temperature? Within this broad scenario, we focus on magnetic systems. A surprising observation of the effect during the para- to ferromagnetic transition, in a simple model system, viz., the nearest-neighbor Ising model, without any built-in frustration, is described. Some associated future directions are pointed out. A discussion is provided by considering the effect as a kinetic outcome in the background of critical phenomena. A picture is drawn by putting emphasis on the role of spatial correlations in the initial configurations alongside discussing the importance of frustration and metastability in evolution from one state to another. In connection with dynamical freezing, concerning metastability, we have introduced the complex Ginzburg-Landau equation that has relevance in phase transitions, chemical oscillations, and elsewhere. For this model and a few other cases also, we have described how a lack of order or correlation in certain parameters can lead to quicker evolution.

Aging exponents for nonequilibrium dynamics following quenches from critical points

Via Monte Carlo simulations we study nonequilibrium dynamics in the nearest-neighbor Ising model, following quenches to points inside the ordered region of the phase diagram. With the broad objective of quantifying the nonequilibrium universality classes corresponding to spatially correlated and uncorrelated initial configurations, in this paper we present results for the decay of the order-parameter autocorrelation function for quenches from the critical point. This autocorrelation is an important probe for the aging dynamics in far-from-equilibrium systems and typically exhibits power-law scaling. From the state-of-the-art analysis of the simulation results, we quantify the corresponding exponents (λ) for both conserved and nonconserved (order-parameter) dynamics of the model in space dimension d=3. Via structural analysis we demonstrate that the exponents satisfy a bound. We also revisit the d=2 case to obtain more accurate results. It appears that irrespective of the dimension, λ is approximately the same for both conserved and nonconserved dynamics.

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.

Exact results for curvature-driven coarsening in two dimensions

We consider the statistics of the areas enclosed by domain boundaries ("hulls") during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than A has, for large time t, the scaling form Nh(A,t)=2c/(A+lambdat), demonstrating the validity of dynamical scaling in this system, where c=1/8pisquare root 3 is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of A/lambdat. Identical forms are obtained for coarsening from a critical initial state, but with c replaced by c/2.

Universal aging properties at a disordered critical point

We investigate, analytically near the dimension d(uc) =4 and numerically in d=3 , the nonequilibrium relaxational dynamics of the randomly diluted Ising model at criticality. Using the exact renormalization-group method to one loop, we compute the two times t, t(w) correlation function and fluctuation dissipation ratio (FDR) for any Fourier mode of the order parameter, of finite wave vector q . In the large time separation limit, the FDR is found to reach a nontrivial value X(infinity) independently of (small) q and coincide with the FDR associated to the total magnetization obtained previously. Explicit calculations in real space show that the FDR associated to the local magnetization converges, in the asymptotic limit, to this same value X(infinity). Through a Monte Carlo simulation, we compute the autocorrelation function in three dimensions, for different values of the dilution fraction p at T(c) (p) . Taking properly into account the corrections to scaling, we find, according to the renormalization-group predictions, that the autocorrelation exponent lambda(c) is independent of p . The analysis is complemented by a study of the nonequilibrium critical dynamics following a quench from a completely ordered state.

Aging in the glass phase of a two-dimensional random periodic elastic system

Using the renormalization group method we investigate the nonequilibrium relaxation of the (Cardy-Ostlund) 2D random sine-Gordon model, which describes pinned arrays of lines. Its statics exhibit a marginal (theta = 0) glass phase for T < Tg described by a line of fixed points. We obtain the universal scaling functions for two-time dynamical response and correlations near Tg for various initial conditions, as well as the autocorrelation exponent. The fluctuation dissipation ratio is found to be nontrivial and continuously dependent on T.

Limits and regulations for mycotoxins in food and feed

Mycotoxins are natural contaminants whose presence in food- and feedstuffs cannot be completely avoided. Since several mycotoxins have been associated with and implicated in human and animal diseases there is a need to establish maximum levels, guidelines or action levels for them in some kinds of commodities. International and government authorities in many countries have been investing in mycotoxins research and initiating administrative actions for elaboration of legislation and implementing regulatory measures for the control of mycotoxins. Codex Alimentarius Commission is established international legislation on food and feed. In European Union specific limits and regulations for mycotoxins and other contaminants are constructed under the general Codex standards and based on proposal from European Commission. The legal basis for European Commission became available with the framework Council Regulation (EEC) No 315/93. In this paper, legislation regarding maximum levels for certain mycotoxins in food- and feedstuffs in European Community and other countries were reviewed and discussed.