Hydrodynamic Processes in Massive Stars

The hydrodynamic processes operating within stellar interiors are far richer than represented by the best stellar evolution model available. Although it is now widely understood, through astrophysical simulation and relevant terrestrial experiment, that many of the basic assumptions which underlie our treatments of stellar evolution are flawed, we lack a suitable, comprehensive replacement. This is due to a deficiency in our fundamental understanding of the transport and mixing properties of a turbulent, reactive, magnetized plasma; a deficiency in knowledge which stems from the richness and variety of solutions which characterize the inherently non-linear set of governing equations. The exponential increase in availability of computing resources, however, is ushering in a new era of understanding complex hydrodynamic flows; and although this field is still in its formative stages, the sophistication already achieved is leading to a dramatic paradigm shift in how we model astrophysical fluid dynamics. We highlight here some recent results from a series of multi-dimensional stellar interior calculations which are part of a program designed to improve our one-dimensional treatment of massive star evolution and stellar evolution in general.Comment: 10 pages, 4 figures, IAUS 252 Conference Proceeding (Sanya) - "The Art of Modeling Stars in the 21st Century

Laplacian transfer across a rough interface: Numerical resolution in the conformal plane

We use a conformal mapping technique to study the Laplacian transfer across a rough interface. Natural Dirichlet or Von Neumann boundary condition are simply read by the conformal map. Mixed boundary condition, albeit being more complex can be efficiently treated in the conformal plane. We show in particular that an expansion of the potential on a basis of evanescent waves in the conformal plane allows to write a well-conditioned 1D linear system. These general principle are illustrated by numerical results on rough interfaces

Inverse monoids and immersions of 2-complexes

It is well known that under mild conditions on a connected topological space $\mathcal X$, connected covers of $\mathcal X$ may be classified via conjugacy classes of subgroups of the fundamental group of $\mathcal X$. In this paper, we extend these results to the study of immersions into 2-dimensional CW-complexes. An immersion $f : {\mathcal D} \rightarrow \mathcal C$ between CW-complexes is a cellular map such that each point $y \in {\mathcal D}$ has a neighborhood $U$ that is mapped homeomorphically onto $f(U)$ by $f$. In order to classify immersions into a 2-dimensional CW-complex $\mathcal C$, we need to replace the fundamental group of $\mathcal C$ by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex

Unsteady aerodynamic simulation of multiple bodies in relative motion: A prototype method

A prototype method for time-accurate simulation of multiple aerodynamic bodies in relative motion is presented. The method is general and features unsteady chimera domain decomposition techniques and an implicit approximately factored finite-difference procedure to solve the time-dependent thin-layer Navier-Stokes equations. The method is applied to a set of two- and three- dimensional test problems to establish spatial and temporal accuracy, quantify computational efficiency, and begin to test overall code robustness

Aerodynamic properties of fractal grains: Implications for the primordial solar nebula

Under conditions in the primordial solar nebula and dense interstellar clouds, small grains have low relative velocities. This is the condition for efficient sticking and formation of fractal aggregates. A calculation of the ratio of cross section, sigma, to number of primary particles, N, for fractal clusters yielded 1n sigma/N = 0.2635 + 0.5189N sup (-0.1748). This ratio decreases slowly with N and approaches a constant for large N. Under the usual assumption of collisions producing spherical compact, uniform density aggregates, sigma/N varies as N sup -1/3 and decreases rapidly. Fractal grains are therefore much more closely coupled to the gas than are compact aggregates. This has a significant effect on the aerodynamic behavior of aggregates and consequently on their evolution and that of the nebula

Spatial scaling in fracture propagation in dilute systems

The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence of the vacancy clusters in the network. For strong dilution, it has been shown earlier that there exists a characteristic time $t_c$ at which a dynamical transition occurs with a power law divergence (with the exponent $z$) of the average cluster size. Close to $t_c$, the growth of the clusters is scale-invariant in time and satisfies a dynamical scaling law. This paper shows that the cluster growth near $t_c$ also exhibits spatial scaling in addition to the temporal scaling. As fracture develops with time, the connectivity length $\xi$ of the clusters increses and diverges at $t_c$ as $\xi \sim (t_c-t)^{-\nu}$, with $\nu = 0.83 \pm 0.06$. As a result of the scale-invariant growth, the vacancy clusters attain a fractal structure at $t_c$ with an effective dimensionality $d_f \sim 1.85 \pm 0.05$. These values are independent (within the limit of statistical error) of the concentration (provided it is sufficiently high) with which the network is diluted to begin with. Moreover, the values are very different from the corresponding values in qualitatively similar phenomena suggesting a different universality class of the problem. The values of $\nu$ and $d_f$ supports the scaling relation $z=\nu d_f$ with the value of $z$ obtained before.Comment: A single ps file (6 figures included), 12 pages, to appear in Physica