Search results for "chaos"
showing 10 items of 106 documents
Lorenz–Haken instability in a laser with arbitrary mirrors reflectivity
2000
Abstract We study the Lorenz–Haken instability in a laser with arbitrary mirrors reflectivity R . In the limit of slow population difference we demonstrate that in order to observe the instability the reflectivity must exceed the critical value R c ≃0.5379, which coincides with that found recently for the multimode (Risken–Nummedal–Graham–Haken) instability. Several other differences with respect to the uniform field limit R →1 are presented.
Exact results for the homogeneous cooling state of an inelastic hard-sphere gas
1998
The infinite set of moments of the two-particle distribution function is found exactly for the uniform cooling state of a hard-sphere gas with inelastic collisions. Their form shows that velocity correlations cannot be neglected, and consequently the 'molecular chaos' hypothesis leading to the inelastic Boltzmann and Enskog kinetic equations must be questioned. © 1998 Cambridge University Press.
Condensation and thermalization of classsical optical waves in a waveguide
2011
http://pra.aps.org/; International audience; We consider the long-term evolution of a random nonlinear wave that propagates in a multimode optical waveguide. The optical wave exhibits a thermalization process characterized by an irreversible evolution toward an equilibrium state. The tails of the equilibrium distribution satisfy the property of energy equipartition among the modes of the waveguide. As a consequence of this thermalization, the optical field undergoes a process of classical wave condensation, which is characterized by a macroscopic occupation of the fundamental mode of the waveguide. Considering the nonlinear Schrödinger equation with a confining potential, we formulate a wav…
Texture Discrimination Using Hierarchical Complex Networks
2008
Texture analysis represents one of the main areas in image processing and computer vision. The current article describes how complex networks have been used in order to represent and characterized textures. More speci?cally, networks are derived from the texture images by expressing pixels as network nodes and similarities between pixels as network edges. Then, measurements such as the node degree, strengths and clustering coe?cient are used in order to quantify properties of the connectivity and topology of the analyzed networks. Because such properties are directly related to the structure of the respective texture images, they can be used as features for characterizing and classifying te…
Soliton Statistical Mechanics: Statistical Mechanics of the Quantum and Classical Integrable Models
1988
It is shown how the Bethe Ansatz (BA) analysis for the quantum statistical mechanics of the Nonlinear Schrodinger Model generalises to the other quantum integrable models and to the classical statistical mechanics of the classical integrable models. The bose-fermi equivalence of these models plays a fundamental role even at classical level. Two methods for calculating the quantum or classical free energies are developed: one generalises the BA method the other uses functional integral methods. The familiar classical action-angle variables of the integrable models developed for the real line R are used throughout, but the crucial importance of periodic boundary conditions is recognized and t…
Local softening of information geometric indicators of chaos in statistical modeling in the presence of quantum-like considerations
2013
In a previous paper (C. Cafaro et al., 2012), we compared an uncorrelated 3D Gaussian statistical model to an uncorrelated 2D Gaussian statistical model obtained from the former model by introducing a constraint that resembles the quantum mechanical canonical minimum uncertainty relation. Analysis was completed by way of the information geometry and the entropic dynamics of each system. This analysis revealed that the chaoticity of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE), is softened or weakened with respect to the chaoticity of the 3D Gaussian statistical model due to the accessibility of more information. In this companion work, we…
Unveiling two-dimensional discrete quantum walks dynamics via dispersion relations
2011
The discrete, or coined, quantum walk (QW) [1] is a process originally introduced as the quantum counterpart of the classical random walk (RW). In both cases there is a walker and a coin: at every time step the coin is tossed and the walker moves depending on the toss output. Unlike the RW, in the QW the walker and coin are quantum in nature what allows the coherent superpositions right/left and head/tail happen. This feature endows the QW with outstanding properties, such as making the standard deviation of the position of an initially localized walker grow linearly with time t, unlike the RW in which this growth goes as t1/2. This has strong consequences in algorithmics and is one of the …
A New Analysis of the Three-Body Problem
2022
In the recent papers [5, 18], respectively, the existence of motions where the perihelions afford periodic oscillations about certain equilibria and the onset of a topological horseshoe have been proved. Such results have been obtained using, as neighbouring integrable system, the so-called two-centre (or Euler) problem and a suitable canonical setting proposed in [16, 17]. Here we review such results.
Comment améliorer la prévision des ventes pour le marketing ? Les apports de la théorie du chaos
2013
National audience; La littérature en marketing constate un décalage entre les avancées réalisées par les chercheurs qui développent de nouvelles méthodes de prévision des ventes, et l'usage massif de méthodes traditionnelles reposant sur l'hypothèse de linéarité des processus analysés. Cette recherche expose la contribution poten¬tielle de la théorie du chaos à l'amélioration de la prévision des ventes. Une illustration de ces apports est proposée avec une application à la prévision des ventes de consoles de jeux vidéo au Japon. Les résultats mettent en évidence la capacité de la méthode proposée à détecter la présence de chaos dans la série et montrent la possibilité de préciser l'horizon …
Living and Not-living Matter: Complexity and Self-Organisation in Kauffman
2016
Which is the relation between the living and not-living matter? In this paper I’ll try to give this question an answer and to explore the underlying framework. I think that the theoretical biologist Stuart Kauffman develops an outstanding and interesting approach, which is formulated within the research field of the non-equilibrium chaotic systems dynamics, the theory of complexity and self-organization and the recent debate on the evolution. Therefore, my aim is to show the way in which Kauffman employs the concept of self-organization to build a not reductionist model that may account for the issues concerning the living and not-living matter by integrating physics with biology. In genera…