DOI

1

BOOLEAN DELAY EQUATIONS ON NETWORKS IN ECONOMICS AND THE GEOSCIENCES - Coluzzi, Barbara and Ghil, Michael and Hallegatte, Stephane and Weisbuch, Gerard

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 21, 3511-3548 (2011)

Abstract : We study damage propagation in networks, with an emphasis on production-chain models. The models are formulated as systems of Boolean delay equations. This formalism helps take into account the complexity of the interactions between firms; it turns out to be well adapted to investigating propagation of an initial damage due to a climatic or other natural disaster. We consider in detail the effects of distinct delays and forcing, which represent external intervention to prevent economic collapse. We also account for the possible presence of randomness in the links and the delays. The paper concentrates on two different network structures, periodic and random, respectively; their study allows one to understand the effects of multiple, concurrent production paths, and the role played by the network topology in damage propagation. Applications to the recent network modeling of climate variability are discussed.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 21, 3511-3548 (2011)

Abstract : We study damage propagation in networks, with an emphasis on production-chain models. The models are formulated as systems of Boolean delay equations. This formalism helps take into account the complexity of the interactions between firms; it turns out to be well adapted to investigating propagation of an initial damage due to a climatic or other natural disaster. We consider in detail the effects of distinct delays and forcing, which represent external intervention to prevent economic collapse. We also account for the possible presence of randomness in the links and the delays. The paper concentrates on two different network structures, periodic and random, respectively; their study allows one to understand the effects of multiple, concurrent production paths, and the role played by the network topology in damage propagation. Applications to the recent network modeling of climate variability are discussed.

DOI

2

ANALYTICAL AND NUMERICAL ELEMENTS OF A SUPERSOLID MODEL - Rica, Sergio

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 19, 2783-2800 (2009)

Abstract : In this article, the main properties of a model of supersolid in the frame of a Gross-Pitaevskii equation is reviewed. It was developed mainly by the author with Pomeau, Josserand and Sepulveda. Emphasis is placed on the numerical details and tools that are absent in our previous publications and maybe useful for authors who are eventually interested in the model. The model exhibits superfluid properties like nonclassical moment of inertia at T = 0K, quantized vortices and persistent currents without the presence of defects, moreover, only a transient flow is allowed by defects, akin to plastic flow in ordinary solids.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 19, 2783-2800 (2009)

Abstract : In this article, the main properties of a model of supersolid in the frame of a Gross-Pitaevskii equation is reviewed. It was developed mainly by the author with Pomeau, Josserand and Sepulveda. Emphasis is placed on the numerical details and tools that are absent in our previous publications and maybe useful for authors who are eventually interested in the model. The model exhibits superfluid properties like nonclassical moment of inertia at T = 0K, quantized vortices and persistent currents without the presence of defects, moreover, only a transient flow is allowed by defects, akin to plastic flow in ordinary solids.

DOI

3

LOCAL DYNAMICS OF DEFECTS IN PARAMETRICALLY EXCITED WAVES - Falcon, Claudio and Fauve, Stephan

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 19, 3553-3559 (2009)

Abstract : We present an experimental study on the local dynamics of parametrically excited waves at an air-water interface when defects are present in the wave pattern. The probability density function (PDF) of the local wave amplitude displays an exponential part for values close to the average amplitude and decreases sharply to zero for large amplitudes. The power spectral density (PSD) of the local amplitude fluctuations shows a power-law behavior over one decade which we relate to a regime of defect-mediated turbulence.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 19, 3553-3559 (2009)

Abstract : We present an experimental study on the local dynamics of parametrically excited waves at an air-water interface when defects are present in the wave pattern. The probability density function (PDF) of the local wave amplitude displays an exponential part for values close to the average amplitude and decreases sharply to zero for large amplitudes. The power spectral density (PSD) of the local amplitude fluctuations shows a power-law behavior over one decade which we relate to a regime of defect-mediated turbulence.

DOI

4

GENERATION AND CHARACTERIZATION OF ABSOLUTE EQUILIBRIUM OF COMPRESSIBLE FLOWS - Krstulovic, Giorgio and Cartes, Carlos and Brachet, Marc and Tirapegui, Enrique

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 19, 3445-3459 (2009)

Abstract : A short review is given of recent papers on the relaxation to (incompressible) absolute equilibrium. A new algorithm to construct absolute equilibrium of spectrally truncated compressible flows is described. The algorithm uses stochastic processes based on the Clebsch representation of the velocity field to generate density and velocity fields that follow by construction the absolute equilibrium stationary probability. The new method is shown to reproduce the well-known Gaussian results in the incompressible limit. The irrotational compressible absolute equilibrium case is characterized and the distribution is shown to be non-Gaussian. The high-temperature compressible spectra are found not to obey k(2) scaling. Finally, oscillating behavior in constant-pressure variable-temperature relaxation is obtained, suggesting the presence of second sound.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 19, 3445-3459 (2009)

Abstract : A short review is given of recent papers on the relaxation to (incompressible) absolute equilibrium. A new algorithm to construct absolute equilibrium of spectrally truncated compressible flows is described. The algorithm uses stochastic processes based on the Clebsch representation of the velocity field to generate density and velocity fields that follow by construction the absolute equilibrium stationary probability. The new method is shown to reproduce the well-known Gaussian results in the incompressible limit. The irrotational compressible absolute equilibrium case is characterized and the distribution is shown to be non-Gaussian. The high-temperature compressible spectra are found not to obey k(2) scaling. Finally, oscillating behavior in constant-pressure variable-temperature relaxation is obtained, suggesting the presence of second sound.

DOI

5

Sparsely synchronized neuronal oscillations - Brunel, Nicolas and Hakim, Vincent

CHAOS 18, (2008)

Abstract : We discuss here the properties of fast global oscillations that emerge in networks of neurons firing irregularly at a low rate. We first provide a simple introduction to these sparsely synchronized oscillations, then show how they can be studied analytically in the simple setting of rate models and leaky integrate- and- fire neurons, and finally describe how various neurophysiological features can be incorporated in this framework. We end by a comparison of experimental data and theoretical results. (C) 2008 American Institute of Physics.

CHAOS 18, (2008)

Abstract : We discuss here the properties of fast global oscillations that emerge in networks of neurons firing irregularly at a low rate. We first provide a simple introduction to these sparsely synchronized oscillations, then show how they can be studied analytically in the simple setting of rate models and leaky integrate- and- fire neurons, and finally describe how various neurophysiological features can be incorporated in this framework. We end by a comparison of experimental data and theoretical results. (C) 2008 American Institute of Physics.

DOI

6

Optical solitons as quantum objects - Pomeau, Yves and Le Berre, Martine

CHAOS 17, (2007)

Abstract : The intensity of classical bright solitons propagating in linearly coupled identical fibers can be distributed either in a stable symmetric state at strong coupling or in a stable asymmetric state if the coupling is small enough. In the first case, if the initial state is not the equilibrium state, the intensity may switch periodically from fiber to fiber, while in the second case the asymmetrical state remains forever, with most of its energy in either fiber. The latter situation makes a state of propagation with two exactly reciprocal realizations. In the quantum case, such a situation does not exist as an eigenstate because of the quantum tunneling between the two fibers. Such a tunneling is a purely quantum phenomenon without counterpart in the classical theory. We estimate the rate of tunneling by quantizing a simplified dynamics derived from the original Lagrangian equations with test functions. This tunneling could be within reach of the experiments, particularly if the quantum coherence of the soliton can be maintained over a sufficient amount of time. (c) 2007 American Institute of Physics.

CHAOS 17, (2007)

Abstract : The intensity of classical bright solitons propagating in linearly coupled identical fibers can be distributed either in a stable symmetric state at strong coupling or in a stable asymmetric state if the coupling is small enough. In the first case, if the initial state is not the equilibrium state, the intensity may switch periodically from fiber to fiber, while in the second case the asymmetrical state remains forever, with most of its energy in either fiber. The latter situation makes a state of propagation with two exactly reciprocal realizations. In the quantum case, such a situation does not exist as an eigenstate because of the quantum tunneling between the two fibers. Such a tunneling is a purely quantum phenomenon without counterpart in the classical theory. We estimate the rate of tunneling by quantizing a simplified dynamics derived from the original Lagrangian equations with test functions. This tunneling could be within reach of the experiments, particularly if the quantum coherence of the soliton can be maintained over a sufficient amount of time. (c) 2007 American Institute of Physics.