Symmetric factorization of the conformation tensor in viscoelastic fluid models

The positive definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.Comment: 7 pages, 5 figure

Ensemble Dynamics and Bred Vectors

We introduce the new concept of an EBV to assess the sensitivity of model outputs to changes in initial conditions for weather forecasting. The new algorithm, which we call the "Ensemble Bred Vector" or EBV, is based on collective dynamics in essential ways. By construction, the EBV algorithm produces one or more dominant vectors. We investigate the performance of EBV, comparing it to the BV algorithm as well as the finite-time Lyapunov Vectors. We give a theoretical justification to the observed fact that the vectors produced by BV, EBV, and the finite-time Lyapunov vectors are similar for small amplitudes. Numerical comparisons of BV and EBV for the 3-equation Lorenz model and for a forced, dissipative partial differential equation of Cahn-Hilliard type that arises in modeling the thermohaline circulation, demonstrate that the EBV yields a size-ordered description of the perturbation field, and is more robust than the BV in the higher nonlinear regime. The EBV yields insight into the fractal structure of the Lorenz attractor, and of the inertial manifold for the Cahn-Hilliard-type partial differential equation.Comment: Submitted to Monthly Weather Revie

Subcutaneous NPH Insulin for Severe Hypertriglyceridemia in a Pregnant Patient with Type V Hyperlipoproteinemia: a Case Report

An increase in triglyceride levels in familial hyperlipidemia during pregnancy has been reported. Severe hypertriglyceridemia can lead to complications such as acute pancreatitis, preeclampsia, maternal and fetal complications. Because of the teratogenic effects associated with fibrate therapy in pregnancy, alternative treatment strategies such as insulin as a rapid and potent activator of lipoprotein lipase are required during pregnancy. We report a case of hypertriglyceridemia in a 33-year-old pregnant woman in whom treatment with merely single one time administration of Neutral Protamine Hagedorn insulin was accompanied by a reduction in the serum triglyceride level; to the best of our knowledge, this has never been reported in the literature. Her triglyceride level was 3616 mg/dL before insulin treatment and 1246 mg/dL after insulin treatment. Although this regimen was used safely and effectively in our patient, comprehensive studies are required to evaluate the effectiveness and safety of subcutaneously intermediate-acting Neutral Protamine Hagedorn insulin for the treatment of severe hypertriglyceridemia in non-diabetic pregnant women