Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality

We discuss the role played by the Lyapunov exponents in the dynamics of Zhang's model of Self-Organized Criticality. We show that a large part of the spectrum (slowest modes) is associated with the energy transpor in the lattice. In particular, we give bounds on the first negative Lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time. We then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites. We use a finite size scaling ansatz for the Lyapunov spectrum and relate the scaling exponent to the scaling of quantities like avalanche size, duration, density of active sites, etc ...Comment: 33 pages, 6 figures, 1 table (to appear

Nonlinear time-series analysis of Hyperion's lightcurves

Hyperion is a satellite of Saturn that was predicted to remain in a chaotic rotational state. This was confirmed to some extent by Voyager 2 and Cassini series of images and some ground-based photometric observations. The aim of this aticle is to explore conditions for potential observations to meet in order to estimate a maximal Lyapunov Exponent (mLE), which being positive is an indicator of chaos and allows to characterise it quantitatively. Lightcurves existing in literature as well as numerical simulations are examined using standard tools of theory of chaos. It is found that existing datasets are too short and undersampled to detect a positive mLE, although its presence is not rejected. Analysis of simulated lightcurves leads to an assertion that observations from one site should be performed over a year-long period to detect a positive mLE, if present, in a reliable way. Another approach would be to use 2---3 telescopes spread over the world to have observations distributed more uniformly. This may be achieved without disrupting other observational projects being conducted. The necessity of time-series to be stationary is highly stressed.Comment: 34 pages, 12 figures, 4 tables; v2 after referee report; matches the version accepted in Astrophysics and Space Scienc

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved

Methanol-Mediated Formation of an Iridium(III) NHC/Azolato Chelate Complex: An Experimental and Theoretical Study

One equivalent of methanol-d4 reacts with the iridium(III)-carbonato-NHC complex [Ir(Cp*)(NHC-theo)(O2CO)] [1] containing an N-heterocyclic carbene ligand with an N-tethered C8-iodotheophylline group (NHC-theo) to form the iridium(III) chelate complex [Ir(Cp*)(theophyllinato^NHC)I] [2] that bears a theophyllinato^NHC chelate ligand, an iodo ligand, and the pentamethylcyclopentadienyl ligand (Cp*). The methanol-d4 solvent is oxidized to formaldehyde-d2 that was identified by a detailed LC–MS study using the 2,4-dinitrophenylhydrazine (DNPH) method. A plausible rearrangement involving the unusual oxidative addition of the C8–I bond of the theophylline group to an iridium(III) center to give a seven-coordinate iridium(V) intermediate is supported by density functional theory calculations

Methanol-Mediated Formation of an Iridium(III) NHC/Azolato Chelate Complex: An Experimental and Theoretical Study

One equivalent of methanol-d4 reacts with the iridium(III)-carbonato-NHC complex [Ir(Cp*)(NHC-theo)(O2CO)] [1] containing an N-heterocyclic carbene ligand with an N-tethered C8-iodotheophylline group (NHC-theo) to form the iridium(III) chelate complex [Ir(Cp*)(theophyllinato^NHC)I] [2] that bears a theophyllinato^NHC chelate ligand, an iodo ligand, and the pentamethylcyclopentadienyl ligand (Cp*). The methanol-d4 solvent is oxidized to formaldehyde-d2 that was identified by a detailed LC–MS study using the 2,4-dinitrophenylhydrazine (DNPH) method. A plausible rearrangement involving the unusual oxidative addition of the C8–I bond of the theophylline group to an iridium(III) center to give a seven-coordinate iridium(V) intermediate is supported by density functional theory calculations

Experimental test of spatial updating models for monkey eye-head gaze shifts

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