Influence of gravity on surface melting

A chemical network system for use in the study of reaction cascades is described by the nonlinear rate equation, in which (x) is derived from the –G/x of Taylor's expansion of the order parameterx of the thermodynamic potential, Gibbs' functionG(T,P,x), at about the critical pointC(T_C,P_C) of the control variables (parameters)T andP. The behavior of the system around the stable pointx=0 is analyzed only with the sign ofk₁(T, P), becausek₂(T, P) is always positive. The system is not closed and is affected by physical and chemical changes in the neighbor systems. WhenT andP fluctuate () through the changes andk₁ passes zero, the system in the steady state becomes instable andk₁ jumps at the reaction threshold. Then, the products are formed at the number of moleculesx=(|k₁|/k₂)^1/2. To describe such a transition,k₁ giving theG curvature atx=0 is represented phenomenologically by an approximate function, tanh(G/RT), for a metastable state with a relatively smallk₁(>0). The reaction takes place in a cascade in accordance with a cubic state equation obtained from tanh(G/RT), which describes a jump of the reaction energy G at the reaction threshold.