Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control parameter is varied bifurcations in the fixed points appear. We verified at the bifurcation point in both; the transcritical, pitchfork and period-doubling bifurcations, that the decay for the stationary point is characterized via a homogeneous function with three critical exponents depending on the nonlinearity of the mapping. Near the bifurcation the decay to the fixed point is exponential with a relaxation time given by a power law whose slope is independent of the nonlinearity. The formalism is general and can be extended to other dissipative mappings.

A dynamical phase transition from integrability to non-integrability for a family of 2-D Hamiltonian mappings whose angle, θ , diverges in the limit of vanishingly action, I, is characterised. The mappings are described by two parameters: (i) , controlling the transition from integrable ( = 0) to non-integrable ( = 0); and (ii) γ , denoting the power of the action in the equation which defines the angle. We prove the average action is scaling invariant with respect to either or n and obtain a scaling law for the three critical exponents.

h i g h l i g h t sA physical air-entraining method has been reported. The properties of high porosity cement-based foam materials have been investigated. Influence of water-cement ratio and HPMC on material properties has been analyzed. Pore structure formation mechanism has been clarified. a b s t r a c tHigh porosity cement-based foam materials were prepared through physical air-entraining method and the pore structure and the properties of materials were characterized. The results show that water-cement ratio and Hydroxypropyl Methyl Cellulose (HPMC) content have crucial influence on material properties. When the water-cement ratio was 0.9 and the content of HPMC was 0.4%, the cement-based foam material with the porosity of 94.33% and thermal conductivity value of 0.049 W/(m K) could be obtained. The formation mechanism of pore structure was analyzed that water-cement ratio and HPMC content affect the bubble film toughness which influence on material properties.