No abstract

The collapse and fragmentation of molecular cloud cores is examined numerically with unprecedentedly high spatial resolutions, using the publicly released code GADGET-2. As templates for the model clouds we use the ''standard isothermal test case'' in the variant calculated by Burkert & Bodenheimer in 1993 and the centrally condensed, Gaussian cloud advanced by Boss in 1991. A barotropic equation of state is used to mimic the nonisothermal collapse. We investigate both the sensitivity of fragmentation to thermal retardation and the level of resolution needed by smoothed particle hydrodynamics (SPH ) to achieve convergence to existing Jeans-resolved, finite-difference ( FD) calculations. We find that working with 0.6Y1.2 million particles, acceptably good convergence is achieved for the standard test model. In contrast, convergent results for the Gaussian-cloud model are achieved using from 5 to 10 million particles. If the isothermal collapse is prolonged to unrealistically high densities, the outcome of collapse for the Gaussian cloud is a central adiabatic core surrounded by dense trailing spiral arms, which in turn may fragment in the late evolution. If, on the other hand, the barotropic equation of state is adjusted to mimic the rise of temperature predicted by radiative transfer calculations, the outcome of collapse is a protostellar binary core. At least, during the early phases of collapse leading to formation of the first protostellar core, thermal retardation not only favors fragmentation but also results in an increased number of fragments, for the Gaussian cloud.

The joint influence of numerical parameters such as the number of particles N, the gravitational softening length ε and the time-step ∆t is investigated in the context of galaxy simulations. For isolated galaxy models we have performed a convergence study and estimated the numerical parameters ranges for which the relaxed models do not deviate significantly from its initial configuration. By fixing N, we calculate the range of the mean interparticle separation λ(r) along the disc radius. Uniformly spaced values of λ are used as ε in numerical tests of disc heating. We have found that in the simulations with N = 1 310 720 particles λ varies by a factor of 6, and the corresponding final Toomre's parameters Q change by only about 5 per cent. By decreasing N, the λ and Q ranges broaden. Large ε and small N cause an earlier bar formation. In addition, the numerical experiments indicate, that for a given set of parameters the disc heating is smaller with the Plummer softening than with the spline softening. For galaxy collision models we have studied the influence of the selected numerical parameters on the formation of tidally triggered bars in galactic discs and their properties, such as their dimensions, shape, amplitude and rotational velocity. Numerical simulations indicate that the properties of the formed bars strongly depend upon the selection of N and ε. Large values of the gravitational softening parameter and a small number of particles result in the rapid formation of a well defined, slowly rotating bar. On the other hand, small values of ε produce a small, rapidly rotating disc with tightly wound spiral arms, and subsequently a weak bar emerges. We have found that by increasing N, the bar properties converge and the effect of the softening parameter diminishes. Finally, in some cases short spiral arms are observed at the ends of the bar that change periodically from trailing to leading and vice-versa -the wiggle.

Angiogenesis is an important adaptation mechanism of the blood vessels to the changing requirements of the body during development, aging, and wound healing. Angiogenesis allows existing blood vessels to form new connections or to reabsorb existing ones. Blood vessels are composed of a layer of endothelial cells (ECs) covered by one or more layers of mural cells (smooth muscle cells or pericytes). We constructed a computational Boolean model of the molecular regulatory network involved in the control of angiogenesis. Our model includes the ANG/TIE, HIF, AMPK/mTOR, VEGF, IGF, FGF, PLCγ/Calcium, PI3K/AKT, NO, NOTCH, and WNT signaling pathways, as well as the mechanosensory components of the cytoskeleton. The dynamical behavior of our model recovers the patterns of molecular activation observed in Phalanx, Tip, and Stalk ECs. Furthermore, our model is able to describe the modulation of EC behavior due to extracellular micro-environments, as well as the effect due to loss- and gain-of-function mutations. These properties make our model a suitable platform for the understanding of the molecular mechanisms underlying some pathologies. For example, it is possible to follow the changes in the activation patterns caused by mutations that promote Tip EC behavior and inhibit Phalanx EC behavior, that lead to the conditions associated with retinal vascular disorders and tumor vascularization. Moreover, the model describes how mutations that promote Phalanx EC behavior are associated with the development of arteriovenous and venous malformations. These results suggest that the network model that we propose has the potential to be used in the study of how the modulation of the EC extracellular micro-environment may improve the outcome of vascular disease treatments.