Related papers: Chaos and scaling in daily river flow
Understanding how annual peak flow, $Q_p$, relates to upstream basin area, $A$, and their scaling have been one of the challenges in surface hydrology. Although a power-law scaling relationship (i.e., $Q_p \propto A^\alpha$) has been widely…
In this paper we analyze the transport of passive tracers by deterministic stationary incompressible flows which can be decomposed over an infinite number of spatial scales without separation between them. It appears that a low order…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
This work deals with bifurcation and the chaotic behavior in one dimensional chains of small particles. We consider two distinct possibilities, one where the particles are modeled by a fourth-order potential which was already studied. We…
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering…
Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…
A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution…
In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…
Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of…
Scaling of turbulent wall-bounded flows is revealed in the gradient structures, for each of the Reynolds stress components. Within the dissipation structure, an asymmetrical order exists, that we can deploy to unify the scaling and…
The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method.…
Based on theoretical argument and experimental evidence, we conjecture that structure functions of turbulent times series exhibit log-periodic modulations decorating their power law dependence. In order to provide ironclad experimental…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
Statistical properties of circulation encode relevant information about the multi-scale structure of turbulent cascades. Recent massive computational efforts have posed challenging theoretical issues, as the dependence of circulation…
As a streak of dye is advected by a chaotic flow, it stretches and folds and becomes indistinguishable from a one-dimensional idealized material line. The variation along a material line of the total stretching experienced by fluid elements…
The hierarchy of channel networks in landscapes displays features that are characteristic of non-equilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial…
Recently, a concept of deterministic and stochastic turbulence has been introduced based on experiments with a boundary layer. In these experiments, the flow was driven with controlled random perturbation; in addition, natural ambient noise…
We study the chaotic behavior of the ``GOY'' shell model by measuring the variation of the maximal Lyapunov exponent with the parameter $\epsilon$ which determines the nature of the second invariant (the generalized ``helicity'' invariant).…
We study the formation of chaos and strange attractors in the order parameter space of a system of two coupled, non-resonantly driven exciton-polariton condensates. The typical scenario of bifurcations experienced by the system with…
We report on our theoretical and numerical results concerning the transport mechanisms in the asteroid belt. We first derive a simple kinetic model of chaotic diffusion and show how it gives rise to some simple correlations (but not laws)…