Patterns formation in ferrofluids and solid dissolutions using stochastic models with dissipative dynamics

A functional with interactions short-range and long-range low coarse-grained approximation is proposed. This functional satisfies models with dissipative dynamics A, B and the stochastic Swift-Hohenberg equation. Furthermore, terms associated with multiplicative noise source are added in these models. These models are solved numerically using the method known as fast Fourier transform. Results of the spatio-temporal dynamic show similarity with respect to patterns behaviour in ferrofluids phases subject to external fields (magnetic, electric and temperature), as well as with the nucleation and growth phenomena present in some solid dissolutions. As a result of the multiplicative noise effect over the dynamic, some microstructures formed by changing solid phase and composed by binary alloys of Pb-Sn, Fe-C and Cu-Ni, as well as a NiAl-Cr(Mo) eutectic composite material. The model A for active-particles with a non-potential term in form of quadratic gradient explain the formation of nanostructured particles of silver phosphate. With these models is shown that the underlying mechanisms in the patterns formation in all these systems depends of: (a) dissipative dynamics; (b) the short-range and long-range interactions and (c) the appropiate combination of quadratic and multiplicative noise terms.