31 research outputs found
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
Approach for Computation of Lyapunov Characteristic Exponents of Low Dimensional Continuous Dynamical Systems
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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