Lagrangian coherent structures in n-dimensional systems

Numerical simulations and experimental observations reveal that unsteady fluid systems can be divided into regions of qualitatively different dynamics. The key to understanding transport and stirring is to identify the dynamic boundaries between these almost-invariant regions. Recently, ridges in finite-time Lyapunov exponent fields have been used to define such hyperbolic, almost material, Lagrangian coherent structures in two-dimensional systems. The objective of this paper is to develop and apply a similar theory in higher dimensional spaces. While the separatrix nature of these structures is their most important property, a necessary condition is their almost material nature. This property is addressed in this paper. These results are applied to a model of Rayleigh-Bénard convection based on a three-dimensional extension of the model of Solomon and Gollub

Determining The Value-at-risk In The Shadow Of The Power Law: The Case Of The SP-500 Index

In extant financial market models, including the Black-Scholes’ contruct, the dramatic events of October 1987 and August 2007 are totally unexpected, because these models are based on the assumptions of ‘independent price fluctuations’ and the existence of some ‘fixed-point equilibrium’. This paper argues that the convolution of a generalized fractional Brownian motion (into an array in frequency or time domain) and their corresponding amplitude spectra describes the surface of the attractor driving the evolution of prices. This more realistic approach shows that the SP-500 Index is characterized by a high long term Hurst exponent and hence by a ‘black noise’ with a power spectrum proportional to f-b (b > 2). In that set up, the above dramatic events are expected and their frequencies are determined. The paper also constructs an exhaustive frequency-variation relationship which can be used as practical guide to assess the ‘value at risk’.Market Collapse; Fractional Brownian Motion; Fractal Attractors; Maximum Hausdorff Dimension of Markets and Affine Profiles; Hurst Exponent; Power Spectrum Exponent; Value at Risk

Chemical Evolution of Damped Ly alpha galaxies: The [S/Zn] abundance ratio at redshift z > 2

Relative elemental abundances, and in particular the alpha/Fe ratio, are an important diagnostic tool of the chemical evolution of damped Ly alpha systems (DLAs). The S/Zn ratio is not affected by differential dust depletion and is an excellent estimator of the alpha/Fe ratio. We report 6 new determinations of sulphur abundance in DLAs at zabs greater than or equal to 2 with already known zinc abundances. The combination with extant data from the literature provides a measure of the S/Zn abundance ratio for a total of 11 high redshift DLA systems. The observed [S/Zn] ratios do not show the characteristic [alpha/Fe] enhancement observed in metal-poor stars of the Milky Way at comparable level of metallicity ([Zn/H] ~ -1). The behaviour of DLAs data is consistent with a general trend of decreasing [S/Zn] ratio with increasing metallicity [Zn/H]. This would be the first evidence of the expected decrease of the alpha/Fe ratio in the course of chemical evolution of DLA systems. However, in contrast to what observed in our Galaxy, the alpha/iron-peak ratio seems to attain solar values when the metallicity is still low ([Zn/H] < -1) and to decrease below solar values at higher metallicities. The behaviour of the alpha/Fe ratio challenges the frequently adopted hypothesis that high redshift DLAs are progenitors of spiral galaxies and favours instead an origin in galaxies characterized by low star formation rates, in agreement with the results from imaging studies of low redshift DLAs, where the candidate DLA galaxies show a variety of morphological types including dwarfs and LSBs and only a minority of spirals.Comment: ApJ (accepted

Lagrange-Poincare field equations

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original problem with those of the reduced problem. The Kelvin-Noether theorem is formulated in this context. Applications to the isoperimetric problem, the Skyrme model for meson interaction, metamorphosis image dynamics, and molecular strands illustrate various aspects of the theory.Comment: Submitted to Journal of Geometry and Physics, 45 pages, 1 figur

Distributed computer system enhances productivity for SRB joint optimization

Initial calculations of a redesign of the solid rocket booster joint that failed during the shuttle tragedy showed that the design had a weight penalty associated with it. Optimization techniques were to be applied to determine if there was any way to reduce the weight while keeping the joint opening closed and limiting the stresses. To allow engineers to examine as many alternatives as possible, a system was developed consisting of existing software that coupled structural analysis with optimization which would execute on a network of computer workstations. To increase turnaround, this system took advantage of the parallelism offered by the finite difference technique of computing gradients to allow several workstations to contribute to the solution of the problem simultaneously. The resulting system reduced the amount of time to complete one optimization cycle from two hours to one-half hour with a potential of reducing it to 15 minutes. The current distributed system, which contains numerous extensions, requires one hour turnaround per optimization cycle. This would take four hours for the sequential system

Black hole-neutron star mergers: effects of the orientation of the black hole spin

The spin of black holes in black hole-neutron star (BHNS) binaries can have a strong influence on the merger dynamics and the postmerger state; a wide variety of spin magnitudes and orientations are expected to occur in nature. In this paper, we report the first simulations in full general relativity of BHNS mergers with misaligned black hole spin. We vary the spin magnitude from a/m=0 to a/m=0.9 for aligned cases, and we vary the misalignment angle from 0 to 80 degrees for a/m=0.5. We restrict our study to 3:1 mass ratio systems and use a simple Gamma-law equation of state. We find that the misalignment angle has a strong effect on the mass of the postmerger accretion disk, but only for angles greater than ~ 40 degrees. Although the disk mass varies significantly with spin magnitude and misalignment angle, we find that all disks have very similar lifetimes ~ 100ms. Their thermal and rotational profiles are also very similar. For a misaligned merger, the disk is tilted with respect to the final black hole's spin axis. This will cause the disk to precess, but on a timescale longer than the accretion time. In all cases, we find promising setups for gamma-ray burst production: the disks are hot, thick, and hyperaccreting, and a baryon-clear region exists above the black hole.Comment: 15 pages, 13 figure

Near-UV to near-IR disk-averaged Earth's reflectance spectra

We report 320 to 1020nm disk-averaged Earth reflectance spectra obtained from Moon's Earthshine observations with the EMMI spectrograph on the NTT at ESO La Silla (Chile). The spectral signatures of Earth atmosphere and ground vegetation are observed. A vegetation red-edge of up to 9% is observed on Europe and Africa and ~2% upon Pacific Ocean. The spectra also show that Earth is a blue planet when Rayleigh scattering dominates, or totally white when the cloud cover is large.Comment: Proceeding of an oral prensentation at the UAI No200 Colloquiu