In which, [??] represents the velocity vector, p the pressure, [rho] the liquid density, [??] the shear stress tensor, [??] the gravitational acceleration, and [[??].sub.b] any

body force (per unit volume) acting on the fluid.

The styrenic material studied here was also modeled previously using a one-dimensional formulation with only the

body force present (6).

(1) [delta]u is displacement vector increment, t is time, [[rho].sub.t] is the mass density, [V.sub.t] is the volume bounded by the surface [a.sub.t], with the surface vector [a.sub.t] pointing outwards, [delta]S is the second Piola-Kirchhoff stress tensor increment, [sigma] is the Cauchy stress tensor at the beginning of the increment, [delta]F = grad [delta]u is the deformation gradient tensor increment and [delta][f.sub.b] is the resulting

body force increment.

body force (weight) is taken in the downward (-y) direction, and the term [q.sub.x] is zero.

where [Mathematical Expression Omitted] is the stress tensor and [Mathematical Expression Omitted] is the

body force. For isotropic linear elastic materials, the components of [Mathematical Expression Omitted] in Cartesian coordinates (13) are

Sgt Gerrard said: "We managed to force him to the ground by sheer

body force, but we still couldn't cuff him because he was too strong.

where [Mathematical Expression Omitted], [Mathematical Expression Omitted] are the

body force vector per unit mass and the acceleration vector, respectively.

ISLAMABAD -- The civic

body force behind encroachment operations breathed his last in the line of duty on Monday.

The smoothing length is h = [10.sup.-4] m, the distance between the walls is L = [10.sup.-3] m, the

body force is g = [10.sup.-3] m/[s.sup.2], and the imposed velocity is V = 2 x [10.sup.-4] m/s.

There are wide-ranging opportunities to optimize the tangential velocity -which would impact the magnitude of the

body force that inhibits mixing - by revising the geometry, and fuel injection strategy to avoid the very rich zone in the center; however, this is beyond the scope of the current work.

There are three forces acting on suspended particle such as buoyancy force, drag force and

body force. Their balance makes the nanoparticle stable.

where [F.sub.D] is the drag force, [F.sub.P] is the pressure gradient force, [F.sub.g] is the gravity force, and [F.sub.u] is the user-defined

body force.