We herein report a theoretical study of the geometrical structure of porous dust aggregates formed via ballistic cluster-cluster aggregation ( BCCA ) .
We calculated the gyration radius R _ { gyr } and the graph-based geodesic radius R _ { geo } as a function of the number of constituent particles N .
We found that R _ { gyr } / r _ { 0 } \sim N ^ { 0.531 \pm 0.011 } and R _ { geo } / r _ { 0 } \sim N ^ { 0.710 \pm 0.013 } , where r _ { 0 } is the radius of constituent particles .
Furthermore , we defined two constants that characterize the geometrical structure of fractal aggregates : D _ { f } and \alpha .
The definition of D _ { f } and \alpha are N \sim { ( R _ { gyr } / r _ { 0 } ) } ^ { D _ { f } } and { R _ { geo } } / { r _ { 0 } } \sim { \left ( { R _ { gyr } } / { r _ { 0 } } \right ) } ^ { \alpha } , respectively .
Our study revealed that D _ { 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 thermal conductivity of statically compressed fractal aggregates .
From this study , we reveal that the thermal conductivity of statically compressed aggregates k is given by k \sim 2 k _ { mat } { ( r _ { c } / r _ { 0 } ) } \phi ^ { ( 1 + \alpha ) / ( 3 - D _ { f } ) } , where k _ { mat } is the material thermal conductivity , r _ { c } is the contact radius of constituent particles , and \phi is the filling factor of dust aggregates .