In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) for a material element subjected to a space-and-time-dependent velocity field. The material derivative can serve as a link between Eulerian and Lagrangian descriptions of continuum deformation.
For example, in fluid dynamics, take the case that the velocity field under consideration is the flow velocity itself, and the quantity of interest is the temperature of the fluid. Then the material derivative describes the temperature evolution of a certain fluid parcel in time, as it is being moved along its pathline (trajectory) while following the fluid flow.
Read more about Material Derivative: Names, Definition, Development, Orthogonal Coordinates
Famous quotes containing the words material and/or derivative:
“Trying to love your children equally is a losing battle. Your children’s scorecards will never match your own. No matter how meticulously you measure and mete out your love and attention, and material gifts, it will never feel truly equal to your children. . . . Your children will need different things at different times, and true equality won’t really serve their different needs very well, anyway.”
—Marianne E. Neifert (20th century)
“When we say “science” we can either mean any manipulation of the inventive and organizing power of the human intellect: or we can mean such an extremely different thing as the religion of science the vulgarized derivative from this pure activity manipulated by a sort of priestcraft into a great religious and political weapon.”
—Wyndham Lewis (1882–1957)