Wing Kam Liu* and Wei Chen, Northwestern University ... - SAMSI

More on the Theory: Motion Assumptions
Microstructural Kinematics
l*
*
( ( ), , Φ) ≡ ( ( ),0, Φ ) + ∫ ∂α ( ( ), , Φ)
0
x� p ξ l x� p ξ x� p ξ α dα
Beginning from the fundamental theorem of calculus on the second argument…
Meaning of the first term
�x(p(ξ),0,Φ)
Local (intrinsic) point behavior
Meaning of the second term
l*
∫ ∂ x� α ( p( ξ), α, Φ)
dα
0
Corrected influence at p due to
the inhomogeneous neighborhood
x
p