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

Hot Electrons and Cold Photons: Galaxy Clusters and the Sunyaev-Zel'dovich Effect

The hot gas in clusters of galaxies emits thermal bremsstrahlung emission that can be probed directly through measurements in the X-ray band with satellites like ROSAT and ASCA. Another probe of this gas comes from its effect on the cosmic microwave background radiation (CMBR): the hot cluster electrons inverse Compton scatter the CMBR photons and thereby distort the background radiation from its blackbody spectral form. In the last few years, the development of sensitive new instruments for measuring this distortion, called the Sunyaev-Zel'dovich (SZ) effect, has sparked a revolution in the field. Current radio interferometric arrays can now detect and map the SZ effect in even distant (z ~ 1) clusters. It is well known that one of the purposes of conducting such measurements is to determine the Hubble constant. In this review I report on the progress that has been made in this area, quote the current best estimate of Ho from the SZ effect of 8 galaxy clusters (44 - 64 km/s/Mpc +/- 17%), discuss important systematic uncertainties, and highlight what else has been learned about galaxy clusters from these investigations.Comment: 4 pages, including 2 postscript figs, LaTeX. To appear in the proceedings of IAU Symposium 188 "The Hot Universe" (held August 26-30, 1997, Kyoto, Japan

Refining Finite-Time Lyapunov Exponent Ridges and the Challenges of Classifying Them

While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model. (C) 2015 AIP Publishing LLC.ONR N000141210665Center for Nonlinear Dynamic

Vineyard and winery indicators of 'Shiraz' must fermentation behaviour

Nitrogen supply and rootstock have important consequences for the composition and quantity of nitrogenous compounds in the must, both of which impact on fermentation rate and wine quality. In the Sunraysia district (SE Australia), musts prepared from 'Shiraz' grapes from vines grafted onto three rootstocks and supplied with five different nitrogen (N) regimes were fermented to dryness. Leaf N at flowering and veraison, and berry and juice total N at harvest was influenced by N supply, but the juice total assimilable amino N pool was less sensitive. Consumption rate of soluble solids during fermentation was strongly and positively linearly related to %N in the petioles at veraison. The relationship described could be the basis of a tool to provide oenologists with timely data before harvest and receival on likely fermentation behaviour of specific parcels of grapes, and provide viticulturalists with another recognisable developmental stage to assess the efficacy of vineyard N management strategies within a season.

Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues

State of the art research and treatment of biological tissues require accurate and efficient methods for describing their mechanical properties. Indeed, micromechanics motivated approaches provide a systematic method for elevating relevant data from the microscopic level to the macroscopic one. In this work the mechanical responses of hyperelastic tissues with one and two families of collagen fibers are analyzed by application of a new variational estimate accounting for their histology and the behaviors of their constituents. The resulting, close form expressions, are used to determine the overall response of the wall of a healthy human coronary artery. To demonstrate the accuracy of the proposed method these predictions are compared with corresponding 3-D finite element simulations of a periodic unit cell of the tissue with two families of fibers. Throughout, the analytical predictions for the highly nonlinear and anisotropic tissue are in agreement with the numerical simulations

Simulating the Impact of Glassy Carbon Foam Electrodes on the Performance of Sodium Iodine Batteries

This publication examines the influences of glassy carbon foam electrodes on the overall battery performance of secondary sodium iodine batteries. The battery combines a molten sodium anode and an iodine-based cathode with NaSICON serving as a ceramic separator. The battery system works at 100 °C and is suitable for stationary energy storage. A long cycle life and good resource utilization are major concerns for establishing the proposed battery system. This paper employs a spatially resolved simulation approach to investigate the effects of foam electrodes of different porosities and cell sizes on the charging and discharging behavior. The spatially resolved model reflects species and mass transport as well as electrochemical processes and reactions in the positive half cell. An open-pored glassy carbon foam cathode structure shows an improved utilizable capacity compared to a simpler two-dimensional electrode. Parameter studies of foam porosity and specific surface area indicate that porosity is the crucial parameter for achievable depth of discharge. We conclude that glassy carbon open-pored foam of preferably high porosity is a suitable material for cathode electrodes in sodium iodine batteries

Limits on Arcminute Scale Cosmic Microwave Background Anisotropy with the BIMA Array

We have used the Berkeley-Illinois-Maryland-Association (BIMA) millimeter array outfitted with sensitive cm-wave receivers to search for Cosmic Microwave Background (CMB) anisotropies on arcminute scales. The interferometer was placed in a compact configuration which produces high brightness sensitivity, while providing discrimination against point sources. Operating at a frequency of 28.5 GHz, the FWHM primary beam of the instrument is 6.6 arcminutes. We have made sensitive images of seven fields, five of which where chosen specifically to have low IR dust contrast and be free of bright radio sources. Additional observations with the Owens Valley Radio Observatory (OVRO) millimeter array were used to assist in the location and removal of radio point sources. Applying a Bayesian analysis to the raw visibility data, we place limits on CMB anisotropy flat-band power Q_flat = 5.6 (+3.0 -5.6) uK and Q_flat < 14.1 uK at 68% and 95% confidence. The sensitivity of this experiment to flat band power peaks at a multipole of l = 5470, which corresponds to an angular scale of approximately 2 arcminutes. The most likely value of Q_flat is similar to the level of the expected secondary anisotropies.Comment: 15 pages, 5 figures, LaTex, aas2pp4.sty, ApJ submitte

Cosmological Parameter Extraction from the First Season of Observations with DASI

The Degree Angular Scale Interferometer (\dasi) has measured the power spectrum of the Cosmic Microwave Background anisotropy over the range of spherical harmonic multipoles 100<l<900. We compare this data, in combination with the COBE-DMR results, to a seven dimensional grid of adiabatic CDM models. Adopting the priors h>0.45 and 0.0<=tau_c<=0.4, we find that the total density of the Universe Omega_tot=1.04+/-0.06, and the spectral index of the initial scalar fluctuations n_s=1.01+0.08-0.06, in accordance with the predictions of inflationary theory. In addition we find that the physical density of baryons Omega_b.h^2=0.022+0.004-0.003, and the physical density of cold dark matter Omega_cdm.h^2=0.14+/-0.04. This value of Omega_b.h^2 is consistent with that derived from measurements of the primordial abundance ratios of the light elements combined with big bang nucleosynthesis theory. Using the result of the HST Key Project h=0.72+/-0.08 we find that Omega_t=1.00+/-0.04, the matter density Omega_m=0.40+/-0.15, and the vacuum energy density Omega_lambda=0.60+/-0.15. (All 68% confidence limits.)Comment: 7 pages, 4 figures, minor changes in response to referee comment