New universality class for gelation in a system with particle breakup

We introduce a model of coagulation with single-particle breakoff, described by the kernels $K_{\mathrm{ij}}=ij$ and $F_{\mathrm{ij}}=\alpha \mathrm{}\left(\right(j+1\mathrm{})\mathrm{}{\delta }_{i1\mathrm{}}+(i+1\mathrm{}\left)\mathrm{}{\delta }_{j1\mathrm{}}\right)$. For $\alpha$ above a critical value ${\alpha }_c$, the system either gels or reaches a steady-state size distribution, depending upon initial conditions. Below ${\alpha }_c$, gelation always occurs. At $\alpha ={\alpha }_c$, the scaling exponent $\tau$, which describes the large-size behavior of the steady-state size distribution, is frac72; rather than the usual value frac52;, indicating that this process belongs to a new universality class of gelation.