Analytical Study of the Julia Set of a Coupled Generalized Logistic Map

A coupled system of two generalized logistic maps is studied. In particular influence of the coupling to the behaviour of the Julia set in two dimensional complex space is analyzed both analytically and numerically. It is proved analytically that the Julia set disappears from the complex plane uniformly as a parameter interpolates from the chaotic phase to the integrable phase, if the coupling strength satisfies a certain condition.Comment: 30pages, 22figure

Complex Analysis of a Piece of Toda Lattice

We study a small piece of two dimensional Toda lattice as a complex dynamical system. In particular the Julia set, which appears when the piece is deformed, is shown analytically how it disappears as the system approaches to the integrable limit.Comment: 17 pages, LaTe

Simulation of premixed combustion with varying equivalence ratio in gas turbine combustor

RANS simulation of a gas turbine combustor with complex geometry is performed. The turbulence is modelled using a two-equation approach. The scalar mixing and combustion is modelled using a flamelet based approach for partially premixed combustion. In this approach transport equations to described scalar mixing and reacting fields and their statistical interactions are solved along with standard conservation equations. The boundary conditions are specified using measured values. The computed spatial variations of averaged temperature and dry mole fractions of various scalars, including CO and NOx, compared quite well with measured values. The results of this combustion model are compared to the eddy-dissipation-concept (EDC) model commonly used for gas turbine combustion calculation and this comparison showed that the results of partially premixed combustion model is improved considerably.This is the author accepted manuscript. The final version is available from the American Institute of Aeronautics and Astronautics via http://dx.doi.org/10.2514/1.B3551

Enrichment of r-process elements in dwarf spheroidal galaxies in chemo-dynamical evolution model

The rapid neutron-capture process (r-process) is a major process to synthesize elements heavier than iron, but the astrophysical site(s) of r-process is not identified yet. Neutron star mergers (NSMs) are suggested to be a major r-process site from nucleosynthesis studies. Previous chemical evolution studies however require unlikely short merger time of NSMs to reproduce the observed large star-to-star scatters in the abundance ratios of r-process elements relative to iron, [Eu/Fe], of extremely metal-poor stars in the Milky Way (MW) halo. This problem can be solved by considering chemical evolution in dwarf spheroidal galaxies (dSphs) which would be building blocks of the MW and have lower star formation efficiencies than the MW halo. We demonstrate that enrichment of r-process elements in dSphs by NSMs using an N-body/smoothed particle hydrodynamics code. Our high-resolution model reproduces the observed [Eu/Fe] by NSMs with a merger time of 100 Myr when the effect of metal mixing is taken into account. This is because metallicity is not correlated with time up to ~ 300 Myr from the start of the simulation due to low star formation efficiency in dSphs. We also confirm that this model is consistent with observed properties of dSphs such as radial profiles and metallicity distribution. The merger time and the Galactic rate of NSMs are suggested to be <~ 300 Myr and ~ $10^{-4}$ yr$^{-1}$, which are consistent with the values suggested by population synthesis and nucleosynthesis studies. This study supports that NSMs are the major astrophysical site of r-process.Comment: 16 pages, 16 figures, accepted for publication in Ap

Hyper-elliptic Nambu flow associated with integrable maps

We study hyper-elliptic Nambu flows associated with some $n$ dimensional maps and show that discrete integrable systems can be reproduced as flows of this class.Comment: 13 page