Related papers: Extensive Chaos in the Lorenz-96 Model
Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…
We study the phase-space organization of the planar elastic pendulum as a function of its two dimensionless control parameters: the reduced energy $R$ and the squared frequency ratio $\mu$. By randomly sampling the isoenergetic volume to…
We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function…
General theoretic approach to classical Loschmidt echoes in chaotic systems with many degrees of freedom is developed. For perturbations which affect essentially all degrees of freedom we find a doubly exponential decay with the rate…
In 1996, Edward Lorenz introduced a system of ordinary differential equations that describes a single scalar quantity as it evolves on a circular array of sites, undergoing forcing, dissipation, and rotation invariant advection. Lorenz…
This work is inspired by a recent study of a two-dimensional stochastic fragmentation model. We show that the configurational entropy of this model exhibits log-periodic oscillations as a function of the sample size, by exploiting an exact…
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…
Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between…
in the last decade, studies of chaotic system are more often used for classical choatic system than for quantum chaotic system, there are many ways of observing the chaotic system such us analyzing the frequency with Fourier transform or…
We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We…
The predictability of weather and climate is strongly state-dependent: special and extremely relevant atmospheric states like blockings are associated with anomalous instability. Indeed, typically, the instability of a chaotic dynamical…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
Trees are key roughness elements in urban environments, shaping airflow, microclimates, and pollutant dispersion. Yet the aerodynamic drag of complex tree-like structures at high Reynolds numbers remains poorly characterized compared with…
We study the distribution of maxima (Extreme Value Statistics) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…
The correlation properties of a random system of densely packed disks, obeying a power-law size distribution, are analyzed in reciprocal space in the thermodynamic limit. This limit assumes that the total number of disks increases…
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…
The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here we present a variety of invariant measures for quantifying chaotic dynamics in relativity by exploiting the coordinate…
Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size.…
We study the Loschmidt echo F(t) for a class of dynamical systems showing critical chaos. Using a kicked rotor with singular potential as a prototype model, we found that the classical echo shows a gap (initial drop) 1-F_g where F_g scales…