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Onboard ships, fire is one of the most dangerous events that can occur. For both military and commercial ships, fire risks are the most worrying; for this reason they have an important impact on the design of the vessel. The intumescent coatings react when heated or in contact with a living flame, and a multi-layered insulating structure grows up, protecting the underlying structure. In this concern, the aim of the paper is to evaluate the intumescent capacity of different composite coatings coupling synergistically modeling and experimental tests. In particular, the experiments have been carried out on a new paint formulation, developed by Colorificio Atria S.r.l., in which the active components are ammonium polyphosphate or pentaerythritol. The specimens were exposed to a gas-torch flame for about 70 s. The degree of thermal insulation of the coating was monitored by means of a thermocouple placed on the back of the sample. In order to get insights into the intumescent mechanism, experimental data was compared with the results of a mathematical model and a good agreement is detected. Furthermore, a predictive model on the swelling rate is addressed. The results highlight that all coatings exhibit a clear intumescent and barrier capacity. The best results were observed for coating enhanced with NH4PO3 where a regular and thick, porous char was formed during exposure to direct flame.

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We have theoretically investigated the phenomenon of Eckhaus instability of stationary patterns arising in hyperbolic reaction–diffusion models on large finite domains, in both supercritical and subcritical regime. Adopting multiple-scale weakly-nonlinear analysis, we have deduced the cubic and cubic–quintic real Ginzburg–Landau equations ruling the evolution of pattern amplitude close to criticality. Starting from these envelope equations, we have provided the explicit expressions of the most relevant dynamical features characterizing primary and secondary quantized branches of any order: stationary amplitude, existence and stability thresholds and linear growth rate. Particular emphasis is given on the subcritical regime, where cubic and cubic–quintic Ginzburg–Landau equations predict qualitatively different dynamical pictures. As an illustrative example, we have compared the above-mentioned analytical predictions to numerical simulations carried out on the hyperbolic modified Klausmeier model, a conceptual tool used to describe the generation of stationary vegetation stripes over flat arid environments. Our analysis has also allowed to elucidate the role played by inertia during the transient regime, where an unstable patterned state evolves towards a more favorable stable configuration through sequences of phase-slips. In particular, we have inspected the functional dependence of time and location at which wavelength adjustment takes place as well as the possibility to control these quantities, independently of each other.