We studied coupled systems of the Fokker–Planck equation and the Navier–Stokes equation modeling the Hookean and the finitely extensible nonlinear elastic (FENE)-type polymeric flows. We proved the continuous embedding and compact embedding theorems in weighted spaces that naturally arise from related entropy estimates. These embedding estimates are shown to be sharp. For the Hookean polymeric ...

We consider a polymeric fluid model, consisting of the incompressible Navier-Stokes equations coupled to a non-symmetric Fokker-Planck equation. First, steady states and exponential convergence to them in relative entropy are proved for the linear Fokker-Planck equation in the Hookean case. The FENE model is also addressed proving the existence of stationary states and the convergence towards t...

A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and F...

In this paper we will discuss several issues related to the moment-closure approximation of multiscale models for viscoelastic polymeric fluids. These moment-closure approaches are based on special ansatz for the probability density function (PDF) in the finite extensible nonlinear elastic (FENE) dumbbell micro-macro models which consists of the coupled incompressible Navier-Stokes equations an...

We prove global well-posedness for the microscopic FENE model under a sharp boundary requirement. The well-posedness of the FENE model that consists of the incompressible Navier-Stokes equation and the Fokker-Planck equation has been studied intensively, mostly with the natural flux boundary condition. Recently it was illustrated by C. Liu and H. Liu [2008, SIAM J. Appl. Math., 68(5):1304–1315]...

Senile plaques (SPs) and neurofibrillary tangles (NFTs) are hallmark pathologies accompanying the neurodegeneration involved in Alzheimer's disease (AD), for which beta-amyloid (Abeta) peptide is a major constituent of SPs. Our laboratories previously developed the hydrophobic, fluorescent molecular-imaging probe 2-(1-(6-[(2-[(18)F]fluoroethyl)(methyl)amino]-2-naphthyl)ethylidene)malononitrile ...

We have implemented the log-conformation method for two-dimensional viscoelastic flow in COMSOL, a commercial high-level finite element package. The code is verified for an Oldroyd-B fluid flowing past a confined cylinder. We are also able to describe the well-known bistability of the viscoelastic flow in a crossslot geometry for a FENE-CR fluid, and we describe the changes required for perform...

Fengycin, a lipopeptidic antibiotic, is synthesized nonribosomally by five fengycin synthetases (FenC, FenD, FenE, FenA, and FenB) in Bacillus subtilis F29-3. This work demonstrates that these fengycin synthetases interlock to form a chain, which coils into a 14.5-nm structure. In this chain, fengycin synthetases are linked in the order FenC-FenD-FenE-FenA-FenB by interactions between the C-ter...

We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elon...

System parameters and steady-state convergence criteria For purposes of this work, a mesh size of was used. Steady state equilibrium was determined using the less stringent of the two error criteria as defined below: \* MERGEFORMAT (1) \* MERGEFORMAT (2) The time step used was determined using the maximum value of the FENE force relative to the spatial discretization and rounded for convenience...