Classical and all-floating FETI methods for the simulation of arterial tissues

High-resolution and anatomically realistic computer models of biological soft tissues play a significant role in the understanding of the function of cardiovascular components in health and disease. However, the computational effort to handle fine grids to resolve the geometries as well as sophisticated tissue models is very challenging. One possibility to derive a strongly scalable parallel solution algorithm is to consider finite element tearing and interconnecting (FETI) methods. In this study we propose and investigate the application of FETI methods to simulate the elastic behavior of biological soft tissues. As one particular example we choose the artery which is - as most other biological tissues - characterized by anisotropic and nonlinear material properties. We compare two specific approaches of FETI methods, classical and all-floating, and investigate the numerical behavior of different preconditioning techniques. In comparison to classical FETI, the all-floating approach has not only advantages concerning the implementation but in many cases also concerning the convergence of the global iterative solution method. This behavior is illustrated with numerical examples. We present results of linear elastic simulations to show convergence rates, as expected from the theory, and results from the more sophisticated nonlinear case where we apply a well-known anisotropic model to the realistic geometry of an artery. Although the FETI methods have a great applicability on artery simulations we will also discuss some limitations concerning the dependence on material parameters.Comment: 29 page

Lie algebras generated by extremal elements

We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.Comment: 28 page

3D Bioprinted Sustained-Release Platform for Intravaginal Delivery of Probiotics

• Bacterial Vaginosis (BV) is the most prevalent vaginal infection, affecting 30% of reproductive age women in the United States and worldwide. • BV is characterized by a shift in the vaginal microbiome from a dominance of Lactobacilli to the overgrowth of vaginal pathogens (specifically Gardnerella vaginalis). • Some common complications include adverse pregnancy outcomes and increased risk for sexually transmitted diseases. • Current treatment primarily involves antibiotics, but this is ineffective due to high antibiotic resistance and BV recurrence rates of 50%. Thus, a more permanent cure is sought. • Lactobacilli probiotics are a promising alternative to antibiotics. They have shown success in reestablishing healthy flora, inhibiting pathogen growth, and reducing recurrence. • Probiotics have been administered both orally and intravaginally, but vaginal delivery is preferred. • Unfortunately, present vaginal dosage forms require frequent administration, thereby decreasing user adherence and efficacy. • Only one sustained release probiotic dosage form, in the form of pod intravaginal rings, has been published to date. However this design leads to discomfort and is susceptible to biofilm formation. • Therefore, an intravaginal probiotic delivery platform capable of sustained release and that offers women flexibility in dosage forms is necessary

Roughness gradient induced spontaneous motion of droplets on hydrophobic surfaces: A lattice Boltzmann study

The effect of a step wise change in the pillar density on the dynamics of droplets is investigated via three-dimensional lattice Boltzmann simulations. For the same pillar density gradient but different pillar arrangements, both motion over the gradient zone as well as complete arrest are observed. In the moving case, the droplet velocity scales approximately linearly with the texture gradient. A simple model is provided reproducing the observed linear behavior. The model also predicts a linear dependence of droplet velocity on surface tension. This prediction is clearly confirmed via our computer simulations for a wide range of surface tensions.Comment: 6 pages, 8 figure