4,839 research outputs found
Mixmaster chaos
The significant discussion about the possible chaotic behavior of the
mixmaster cosmological model due to Cornish and Levin [J.N. Cornish and J.J.
Levin, Phys. Rev. Lett. 78 (1997) 998; Phys. Rev. D 55 (1997) 7489] is
revisited. We improve their method by correcting nontrivial oversights that
make their work inconclusive to precisely confirm their result: ``The mixmaster
universe is indeed chaotic''.Comment: 9 pages, 4 figure
Fractal and Multifractal Analysis of the Rise of Oxygen in Earth's Early Atmosphere
The rise of oxygen in Earth's atmosphere that occurred 2.4 to 2.2 billion
years ago is known as the Earth's Great Oxidation, and its impact on the
development of life on Earth has been profound. Thereafter, the increase in
Earth's oxygen level persisted, though at a more gradual pace. The proposed
underlying mathematical models for these processes are based on physical
parameters whose values are currently not well-established owing to
uncertainties in geological and biological data. In this paper, a previously
developed model of Earth's atmosphere is modified by adding different strengths
of noise to account for the parameters' uncertainties. The effects of the noise
on the time variations of oxygen, carbon and methane for the early Earth are
investigated by using fractal and multifractal analysis. We show that the time
variations following the Great Oxidation cannot properly be described by a
single fractal dimension because they exhibit multifractal characteristics. The
obtained results demonstrate that the time series as obtained exhibit
multifractality caused by long-range time correlations.Comment: 20 pages, 3 figures, 3 tables; Chaos, Solitons & Fractals (in press
- …