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
Pulse wave velocity in the investigation of hypertension. The theory of the velocity of the transmission of the pulse through the circulation dates back to 1808 with the work of Thomas Young. The relationship between pulse wave velocity (PWV) and arterial wall stiffness can be derived from Newton's second law of motion (formula_1) applied to a small fluid element, where the force on the element equals the product of density (the mass per unit volume; formula_2) and the acceleration. The approach for calculating PWV is similar to the calculation of the speed of sound, formula_3, in a compressible fluid (e.g. air): formula_4, where