Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper velocity
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,