Effective mass (solid-state physics) from both sides gives where is the th element of , is the th element of , and are the th and th elements of , respectively, and is the total energy of the particle according to the Planck–Einstein relation. The index is contracted by the use of Einstein notation (there is an implicit summation over ). Since Newton's second law uses the inertial mass (not the gravitational mass), we can identify the inverse of this mass in the equation above as the tensor This tensor expresses the change in group velocity due to a change in crystal momentum. Its
Peculiar velocity example, in surveys of type Ia supernovae, peculiar velocities have a significant influence on measurements out to redshifts around 0.5, leading to errors of several percent when calculating cosmological parameters. Peculiar velocities can also contain useful information about the universe. The connection between correlated peculiar velocities and mass distribution has been suggested as a tool for determining constraints for cosmological parameters using peculiar velocity surveys. Peculiar velocity Peculiar motion or peculiar velocity refers to the velocity of an object relative to a rest frame — usually a frame in which the average velocity of some objects is zero. In galactic