This implies that the balancing action of internal contact forces generates a " contact force density " or " Cauchy traction field"
4.
This allows the force density in each bond to depend on the stretches in all the bonds connected to its endpoints, in addition to its own stretch.
5.
Where "'f "'is the force density exerted by some outer field on the fluid, and " ? " is the Cauchy stress tensor.
6.
Body forces are represented by a body force density \ mathbf b ( \ mathbf x, t ) ( per unit of mass ), which is a frame-indifferent vector field.
7.
Although magnetic tension is referred to as a force, it is actually a pressure gradient ( Pa m " 1 ) which is also a force density ( N m " 3 ).
8.
Physically, the solution u to this two-point boundary value problem represents the shape taken by a string under the influence of a force such that at every point x between a and b the force density is f ( x ) \ mathbf { e } ( where \ mathbf { e } is a unit vector pointing vertically, while the endpoints of the string are on a horizontal line, see the picture on the right ).
9.
By virtue of the slenderness of the body, the force exerted on the fluid at the surface of the body may be approximated by a distribution of Stokeslets along the axis with force density \ boldsymbol { f } ( s ) per unit length . \ boldsymbol { f } is assumed to vary only over lengths much greater than a, and the fluid velocity at the surface adjacent to \ boldsymbol { X } ( s, t ) is well-approximated by \ partial \ boldsymbol { X } / \ partial t.
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