His most notable contributions were in the field of computational condensed matter physics where he used molecular dynamics techniques to explore the properties of ion and cluster collisions with solid and liquid targets.
Tombrello developed a model for calculating the core excitation of electrons to account for inelastic energy loss in sputtering events.
The Shapiro-Tombrello model has been incorporated in the Kalypso molecular dynamics code[6] Shapiro also is known for the development together with Jonathan Melvin of the California Institute of Technology of one of the first "smart" remote sensing geophysical instruments.
Radon and environmental data obtained by the devices was periodically transmitted to a central computer at Caltech over telephone lines for analysis.
In 1999 Shapiro began publishing an online journal of commentary on issues in K through 12 and higher education, The Irascible Professor,[11] which includes articles by him and by guest commentators.