a two-dimensional single particle finite element model was used to examine the effects of particle fragmental pattern on the average molecular weights, polymerization rate and particle overheating in heterogeneous ziegler-natta olefin polymerization. a two-site catalyst kinetic mechanism was employed together with a dynamic two-dimensional molecular species in diffusion-reaction equation. the i...

a two-dimensional (2d) single particle model for the copolymerization of propylene-ethylene with heterogeneous ziegler-natta catalyst is developed. the model accounts for the effects of the initial shape of the catalyst and carck/ pore patterns on the copolymer composition, polymerization rate and the average molecular weight properties. the spherical and oblate ellipsoidal shapes of catalyst p...

the markowitz’s optimization problem is considered as a standard quadratic programming problem that has exact mathematical solutions. considering real world limits and conditions, the portfolio optimization problem is a mixed quadratic and integer programming problem for which efficient algorithms do not exist. therefore, the use of meta-heuristic methods such as neural networks and evolutionar...

the angle of repose of soil particles is an important factor for determining critical shear stress for initiation of soil particles motion during the erosion process. there are different methods for measuring the angle of particle repose and the result of each method is somewhat different from those of the others. sliding and fixed-base piling methods are the two most common methods in the lite...

one of the most important advantages of particle simulation as compared to fluid simulation is the capacity for working with and tracing particles. in particle simulations, the test particle method is usually used to get some idea of the behavior of plasma or other substances. in this method, first, a small number of particles are injected into the frame of static electromagnetic fields. then, ...

Many of the computer vision algorithms have been posed in various forms of differential equations, derived from minimization of specific energy functionals, and the finite element representation and computation have become the de facto numerical strategies for solving these problems. However, for cases where domain mappings between numerical iterations or image frames involve large geometrical ...