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
Dispersive mass transfer is caused by random molecular motions (i.e. Brownian motion) and is a microscopic phenomenon. Dispersion is often more significant than diffusion in convection-diffusion problems. The dispersion coefficient is frequently modeled as the product of the fluid velocity, "U", and some characteristic length scale, "α": Dispersive mass transfer Dispersive mass transfer, in fluid dynamics, is the spreading of mass from highly concentrated areas to less concentrated areas. It is one form of mass transfer. Dispersive mass flux is analogous to diffusion, and it can also be described using Fick's first law: where c is mass concentration of the species being dispersed,