Patent ID: 7266469

Claim:
A method for determining a rate of change of orientation of a plurality of fibers disposed in a fluid, the method comprising: (a) determining a first tensor indicative of the rate of change of orientation of the plurality of fibers in the fluid in a predetermined region due to rigid body rotation of the plurality of fibers and the fluid; (b) determining a second tensor indicative of the rate of change of orientation of the plurality of fibers in the fluid in the predetermined region due to deformation of the plurality of fibers and the fluid in the predetermined region, utilizing a first scalar value that reduces the rate of change or orientation of the plurality of fibers due to deformation of the plurality of fibers and the fluid; (c) determining a third tensor indicative of a total rate of change of orientation of the plurality of fibers based on the first and second tensors, wherein the third tensor is an objective tensor; and (d) storing the third tensor in a memory device; wherein at least one of said first, second and third tensors is determined utilizing a vorticity tensor associated with the fluid and the plurality of fibers and an orientation tensor associated with the plurality of fibers.