Time-power series study of the triplet annihilation model and other cooperative growth models

We obtain the exact beginning coefficients in time-power series for several cooperative one-dimensional lattice growth models that include growth, diffusion and death processes. The model we use as our standard is the triplet annihilation model of Dickman. The series are obtained through eighth order. For those cases where growth follows a power law in the time we use standard techniques for studying critical phenomena to extract the appropriate exponents. For those cases where growth goes through a maximum, the series give reliable information only up to the maximum and do not describe well the ultimate decay to zero density.