Related papers: Spatial and Temporal Taylor's Law in 1-Dim Chaotic…
This paper tackles Hamiltonian chaos by means of elementary tools of Riemannian geometry. More precisely, a Hamiltonian flow is identified with a geodesic flow on configuration space-time endowed with a suitable metric due to Eisenhart.…
The dynamics of a passive scalar plume in a turbulent boundary layer is experimentally investigated via vertical turbulent transport time-series. Data are acquired in a rough-wall turbulent boundary layer that develops in a recirculating…
Space-time area laws play a fundamental role in modeling strongly interacting phenomena, such as in relativistic string models, QCD on the lattice, and in hadronization modeling. For the latter, an exact expression for relevant space-time…
We theoretically study the propagation of light in one-dimensional space- and time-dependent disorder. The disorder is described by a fluctuating permittivity $\epsilon(x,t)$ exhibiting short-range correlations in space and time, without…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a Coupled Map Lattice as an example. The optimal arrangement of the control sites is shown to depend…
Statistical mechanics harmonizes mechanical and thermodynamical quantities, via the notion of local thermodynamic equilibrium (LTE). In absence of external drivings, LTE becomes equilibrium tout court, and states are characterized by…
We obtain large deviations estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems (CLT) obtained by Nicol,…
In light of the emergence of big data, I have advocated and argued for a paradigm shift from Tobler's law to scaling law, from Euclidean geometry to fractal geometry, from Gaussian statistics to Paretian statistics, and - more importantly -…
Three-dimensional miscible Rayleigh--Taylor (RT) turbulence at small Atwood number and at Prandtl number one is investigated by means of high resolution direct numerical simulations of the Boussinesq equations. RT turbulence is a…
We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…
Temporal Equilibrium Logic (TEL) is a promising framework that extends the knowledge representation and reasoning capabilities of Answer Set Programming with temporal operators in the style of LTL. To our knowledge it is the first…
In incompressible and periodic statistically stationary turbulence, exchanges of turbulent energy across scales and space are characterised by very intense and intermittent spatio-temporal fluctuations around zero of the time-derivative…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence…
Except the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist, share a common property--the number of times each random variable appears in the matrix is (more…
Traffic prediction, an essential component for intelligent transportation systems, endeavours to use historical data to foresee future traffic features at specific locations. Although existing traffic prediction models often emphasize…
From the nonlinear (NL) Vlasov equation, a NL turbulence scattering term is found to describe the stochastic dissipation on the time scale longer than the turbulence correlation time. The evolution of the plasma distribution is determined…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 1. We deduce this behavior as a simple consequence of the statistical…