The FENE Dumbbell Model near Equilibrium

We study the global existence of smooth solutions near the equilibrium to a coupled microscopic-macroscopic FENE dumbbell model which arises from the kinetic theory of diluted solutions of polymeric liquids with noninteracting polymer chains.

A dumbbell model with five parameters describing nuclear fusion or fission

We propose a five-parameter dumbbell model to describe the fusion and fission processes of massive nuclei, where the collective variables are： distance ρ between center-of-mass of two fusing nuclei, neck parameter ν, asymmetry D, two deformation variables β1 and β2. The present model has macroscopic qualitative expression of polarization and nuclear collision of head to head, sphere to sphere, waist to waist and so on. The conception of ＂projectile eating target＂ based on open mouth and swallow is proposed to describe nuclear fusion process, and then our understanding of the probability of fusion and quasi-fission is in agreement with some previous work. The calculated fission barriers of a lot of compound nuclei are compared with the experimental data.

A Constitutive Model Describing Molecular Configuration Evolution and Transient Rheological Behavior of Entangled Polymer Solutions

Entanglement network is an important structural feature in concentrated polymer solutions and polymer melts,which has a great influe nee on the transie nt rheological behavior and molecular con figurati on evolution.However,the existi ng constitutive models have limitations in describi ng the influe nee of dyn amic entan glement behavior on molecular chain motion,resulti ng in inaccurate descriptions of the transient rheological behavior.Thus,a molecular con figuration evoluti on model for polymer solutions considering the dyn amic entanglement effect is proposed by introducing an intermolecular force that changes with the orientation of the molecular chain in this work.The intermolecular force is introduced by consider!ng the friction coefficient as anisotropic,and the orientation effect is considered by introducing an excluded volume depende nt an isotropic diffusi on.The proposed model can better describe the stress relaxation,stress growth,and dielectric an isotropy of polymer soluti ons compared with the an isotropy FENE model and FENE model.In addition,the in fluence of different model parameters on the transient and steady shear response of polymer soluti on is investigated,and the results show that the in fluence of volume loss on the fricti on anisotropy factor k0 in creases as the solution concen tration in creases.

Convergence of a Stochastic Method for the Modeling of Polymeric Fluids

We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the stochastic partial differential equations for shear flows. We establish the optimal rate of convergence. We also analyze the nature of the error by providing its leading order asymptotics.