The macroscopic properties of high-performance bulk polymer composite materials derive from the properties of the microscopic building block component particles, the polymer matrix in which they are placed, and the state of particle dispersion. The rational design of new materials then requires the characterization of the polymer matrix and the individual particles, as well as an understanding of how particle properties change as a function of spatial dispersion and particle size polydispersity and shape fluctuations. This is a challenging scientific and technical problem, but in principle we can use computer simulations to systematically explore the multi-dimensional parameter space required for designing new composite materials and for characterizing the normally complex-shaped component particles. In the past, the calculation of the composite properties has normally been restricted to rather idealized descriptions of particle shape for mathematical expediency (e.g., ellipsoids or spheres) or the treatment involves the numerical solution of differential equations with complicated differential equations using boundary or finite element methods, both approaches having limitations in terms of adequacy of physical description, inherent computational uncertainties associated with finite element computations and the necessity of long computational times for even routine property calculations. To address this class of problems, we explore the use of a new computational approach, ZENO, a numerical path-integration computational approach that efficiently generates solutions to many transport properties of interest for composites where the particles can have essentially arbitrary shape and where no meshing of the particles is required. As specific illustrations of this perfectly parallel computational method, we calculate hydrodynamic properties of DNA-gold nanoparticle systems and the conductivity of carbon nanotubes composites problems that are currently under active experimental investigation at NIST.