We review recent progress in the understanding of phase transitions and critical phenomena, obtained by means of numerical simulations of the early dynamic evolution of systems prepared at well-specified initial conditions. This field has seen exhaustive scientific research during the last decade, when the renormalization-group (RG) theoretical results obtained at the end of the 1980s were applied to the interpretation of dynamic Monte Carlo simulation results. While the original RG theory is restricted to critical phenomena under equilibrium conditions, numerical simulations have been applied to the study of far-from-equilibrium systems and irreversible phase transitions, the investigation of the behaviour of spinodal points close to first-order phase transitions and the understanding of the early-time evolution of self-organized criticality (SOC) systems when released far form the SOC regime. The present review intends to provide a comprehensive overview of recent applications in those fields, which can give the flavour of the main ideas, methods and results, and to discuss the directions for further studies. All of these numerical results pose new and interesting theoretical challenges that remain as open questions to be addressed by new research in the coming years.

The visible light induced cationic polymerization of epoxides can be achieved by means of multiwalled carbon nanotubes (MWCNTs), which act as visible light photoinitiators via a radical-induced cationic photopolymerization process. When MWCNTs are irradiated with longer wavelengths (above 400 nm), they generate carbon radicals, by means of hydrogen abstraction from the epoxy monomer; these radicals are oxidized in the presence of iodonium salt to a carbocation that is sufficiently reactive to start the cationic ring-opening polymerization of an epoxy monomer. These mechanisms have been supported by electron paramagnetic resonance analysis.

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Extensive Monte Carlo simulations are employed in order to study the dynamic critical behaviour of the one-dimensional Ising magnet, with algebraically decaying long-range interactions of the form 1 r d+σ , with σ = 0.75. The critical temperature, as well as the critical exponents, are evaluated from the power-law behaviour of suitable physical observables when the system is quenched from uncorrelated states, corresponding to infinite temperature, to the critical point. These results are compared with those obtained from the dynamic evolution of the system when it is suddenly annealed at the critical point from the ordered state. Also, the critical temperature in the infinite interaction limit is obtained by means of a finite-range scaling analysis of data measured with different truncated-interaction range. All the estimated static critical exponents (γ/ν, β/ν, and 1/ν ) are in good agreement with Renormalization Group (RG) results and previously reported numerical data obtained under equilibrium conditions. On the other hand, the dynamic exponent of the initial increase of the magnetization (θ) was close to RG predictions. However, the dynamic exponent z of the time correlation length is slightly different than the RG results likely due to the fact that either it may depend on the specific dynamics used or because the two-loop expansion used in the RG analysis may be insufficient.