QDPDQualified Domestic Production Deduction (tax term)
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Given the forces [f.sub.1i] acting on particles at time t, the fundamental QDPD cycle, repeated for as many timesteps as are in a simulation, is
In the basic QDPD (MD) cycle above, the [r.sub.2]s may belong to particles which have moved out of the simulation box, such as particles in the periodic image of cell 21 represented by the dashed box 21' in Fig.
Hence the [r.sub.3] coordinates make sure that particles are assigned to one of the cells in the QDPD simulation box (i.e., particles are kept within the QDPD simulation box running from (-[L.sub.x]/2, -[L.sub.y]/2,-[L.sub.z]/2) to ([L.sub.x]/2,[L.sub.y]/2,[L.sub.z]/2) in [r.sub.3] space).
In treating edge cells, a "ghost" layer of cells is added to the QDPD simulation box.
Because QDPD in its present form is being used to study the steady-shear viscosity of a suspension of solid inclusions in a Newtonian fluid, there is a shear boundary condition at the topmost layer of the QDPD simulation box, implemented with the Lees-Edwards boundary conditions [9] (pp.
QDPD was originally written in Fortran 77 as a serial program.
This extra communication step is necessary in the QDPD method since the interparticle force calculation involves the use of a random number for thermal effects and momentum conservation requires that the same random number be used in the equal and opposite force calculation.
The MD (or QDPD) cell is divided into a number of "subcells" and the linked list structure lists the molecules or atoms belonging to each subcell.
In the case of QDPD, the parallelization using the above replicated data has been the workhorse for some time now.
Sims and Nicos Martys, Simulation of Sheared Suspensions with a Parallel Implementation of QDPD, to be published (2002).
Second, the QDPD technique is being applied to suspensions, so there are two types of particles: "free" particles and particles belonging to solid inclusions such as ellipsoids.
6, Kirk Kern of SGI for the 64 processor SGI runs cited in the QDPD section (Sec.