Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids

Combined Molecular Algorithms for the Generation, Equilibration and Topological Analysis of Entangled Polymers: Methodology and Performance

We review the methodology, algorithmic implementation and performance characteristics of a hierarchical modeling scheme for the generation, equilibration and topological analysis of polymer systems at various levels of molecular description: from atomistic polyethylene samples to random packings of freely-jointed chains of tangent hard spheres of uniform size. Our analysis focuses on hitherto less discussed algorithmic details of the implementation of both, the Monte Carlo (MC) procedure for the system generation and equilibration, and a postprocessing step, where we identify the underlying topological structure of the simulated systems in the form of primitive paths. In order to demonstrate our arguments, we study how molecular length and packing density (volume fraction) affect the performance of the MC scheme built around chain-connectivity altering moves. In parallel, we quantify the effect of finite system size, of polydispersity, and of the definition of the number of entanglements (and related entanglement molecular weight) on the results about the primitive path network. Along these lines we approve main concepts which had been previously proposed in the literature

Theoretical molecular rheology of branched polymers in simple and complex flows: the pom-pom model

The nonlinear rheological constitutive equation of a class of multiply branched polymers is derived using the tube model. The molecular architecture may be thought of as two q-arm stars connected by a polymeric ''crossbar.'' The dynamics lead to a novel integrodifferential equation which exhibits extreme strain hardening in extension and strain softening in shear. Calculations of flow through a contraction predict that the degree of long-chain branching controls the growth of corner vortices, in agreement with experiments on commercial branched polymers

A French Would-Be Settler on Lafayette\u27s Florida Township

Lewis A. Pellerin, thirty-seven years old, a native of Normandy, sailed up the Mississippi to New Orleans in late March 1833. After taking part in the July Revolution of 1830 in France, he had suffered severe financial losses and was emigrating, together with his wife and two children, to the New World in search of a better fortune

A Planning Model for Construction Minerals

The problem of allocating construction minerals is rarely considered by those who plan the destiny of our urban environment. The purpose of this research is: (1) to delineate in dollar terms the magnitude of the result of not planning for the consumption of construction minerals, and (2) to develop a computer simulation model which will provide planners with an indication of the effects of decisions. affecting these resources. Construction mineral aggregates (sand, gravel, and crushed stone) are among the earth's most plentiful, yet are rapidly being rendered inaccessible in those areas which need them most. They are characterized by a low intrinsic value, a high bulk, and a delivered price which is very sensitive to the transportation cost associated with moving them from the quarries to their points of demand, It is ironic that the cities which create the demands for mineral aggregates are, at the same time, preventing their extraction by being built over them or by legally limiting their use through zoning restrictions. The simulation model which has been developed enables the planner to investigate the effects of various zoning strategies. It allows him to investigate the results of limiting individual operations and to force the removal of material from a site before it is covered by urban development. It does not attempt to search for decisions which yield "optimal" solutions; rather it indicates the results, over a (simulated) time period, of various planning strategies, thus providing the planner with greater insight into the effects of the decisions that he alone can make.