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:
“Mans characteristic privilege is that the bond he accepts is not physical but moral; that is, social. He is governed not by a material environment brutally imposed on him, but by a conscience superior to his own, the superiority of which he feels. Because the greater, better part of his existence transcends the body, he escapes the bodys yoke, but is subject to that of society.”
—Emile Durkheim (18581917)
“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 (18821957)