10 research outputs found
Higher Order Variational Integrators: a polynomial approach
We reconsider the variational derivation of symplectic partitioned
Runge-Kutta schemes. Such type of variational integrators are of great
importance since they integrate mechanical systems with high order accuracy
while preserving the structural properties of these systems, like the
symplectic form, the evolution of the momentum maps or the energy behaviour.
Also they are easily applicable to optimal control problems based on mechanical
systems as proposed in Ober-Bl\"obaum et al. [2011].
Following the same approach, we develop a family of variational integrators
to which we refer as symplectic Galerkin schemes in contrast to symplectic
partitioned Runge-Kutta. These two families of integrators are, in principle
and by construction, different one from the other. Furthermore, the symplectic
Galerkin family can as easily be applied in optimal control problems, for which
Campos et al. [2012b] is a particular case.Comment: 12 pages, 1 table, 23rd Congress on Differential Equations and
Applications, CEDYA 201
First Stars. I. Evolution without mass loss
The first generation of stars was formed from primordial gas. Numerical
simulations suggest that the first stars were predominantly very massive, with
typical masses M > 100 Mo. These stars were responsible for the reionization of
the universe, the initial enrichment of the intergalactic medium with heavy
elements, and other cosmological consequences. In this work, we study the
structure of Zero Age Main Sequence stars for a wide mass and metallicity range
and the evolution of 100, 150, 200, 250 and 300 Mo galactic and pregalactic Pop
III very massive stars without mass loss, with metallicity Z=10E-6 and 10E-9,
respectively. Using a stellar evolution code, a system of 10 equations together
with boundary conditions are solved simultaneously. For the change of chemical
composition, which determines the evolution of a star, a diffusion treatment
for convection and semiconvection is used. A set of 30 nuclear reactions are
solved simultaneously with the stellar structure and evolution equations.
Several results on the main sequence, and during the hydrogen and helium
burning phases, are described. Low metallicity massive stars are hotter and
more compact and luminous than their metal enriched counterparts. Due to their
high temperatures, pregalactic stars activate sooner the triple alpha reaction
self-producing their own heavy elements. Both galactic and pregalactic stars
are radiation pressure dominated and evolve below the Eddington luminosity
limit with short lifetimes. The physical characteristics of the first stars
have an important influence in predictions of the ionizing photon yields from
the first luminous objects; also they develop large convective cores with
important helium core masses which are important for explosion calculations.Comment: 17 pages, 24 figures, 2 table