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We herein report a theoretical study of the geometrical structure of porousdust aggregates formed via ballistic cluster-cluster aggregation (BCCA). Wecalculated the gyration radius $R_{\rm gyr}$ and the graph-based geodesicradius $R_{\rm geo}$ as a function of the number of constituent particles $N$.We found that $R_{\rm gyr} / r_{0} \sim N^{0.531 \pm 0.011}$ and $R_{\rm geo} /r_{0} \sim N^{0.710 \pm 0.013}$, where $r_{0}$ is the radius of constituentparticles. Furthermore, we defined two constants that characterize thegeometrical structure of fractal aggregates: $D_{\rm f}$ and $\alpha$. Thedefinition of $D_{\rm f}$ and $\alpha$ are $N \sim {( R_{\rm gyr} / r_{0})}^{D_{\rm f}}$ and ${R_{\rm geo}} / {r_{0}} \sim {\left( {R_{\rm gyr}} /{r_{0}} \right)}^{\alpha}$, respectively. Our study revealed that $D_{\rm f}\simeq 1.88$ and $\alpha \simeq 1.34$ for the clusters of the BCCA.  In addition, we also studied the filling factor dependence of thermalconductivity of statically compressed fractal aggregates. From this study, wereveal that the thermal conductivity of statically compressed aggregates $k$ isgiven by $k \sim 2 k_{\rm mat} {( r_{\rm c} / r_{0} )} \phi^{(1 + \alpha) / (3- D_{\rm f})}$, where $k_{\rm mat}$ is the material thermal conductivity,$r_{\rm c}$ is the contact radius of constituent particles, and $\phi$ is thefilling factor of dust aggregates.

Geometrical structure and thermal conductivity of dust aggregates formed via ballistic cluster-cluster aggregation