Nature Of Long-range Correlations Research Articles

A continuous transition from chaotic bursting to chaotic spiking in a glow discharge plasma and its associated long range correlation to anti correlation behaviour

An experimental investigation on the self-excited spiky oscillations in a glow discharge plasma device is presented. The system showed a continuous transition from chaotic bursting to chaotic spiking states with the increase in the applied discharge voltage at a particular pressure. Below a threshold discharge voltage, the system exhibits a fixed point dynamical behaviour and with the increase in the discharge voltage bursting type oscillations appear which are identified as “fold/fold circle” type. The occurrence of the relaxation type spiky oscillations is attributed to the formation and disruption of anode double layer. The burst phases occurred intermittently and the frequency of their occurrence increased with increase in the discharge voltage and finally the oscillation turned into spiking behaviour. The intermittent oscillations manifested the scaling law of the average laminar phase with respect to the change in the discharge voltage. The scaling law of the intermittent oscillations was similar to type III intermittency. During the transition, the system changes its behaviour from long range correlation to long range anti correlation. Detrended fluctuation analysis technique has been used to identify the nature of long range correlations. We found that bursting oscillations show scale invariant, long-range correlation behaviour whereas spiking oscillations show scale invariant, long range anti correlation behaviour.

Culturomics meets random fractal theory: insights into long-range correlations of social and natural phenomena over the past two centuries

Culturomics was recently introduced as the application of high-throughput data collection and analysis to the study of human culture. Here, we make use of these data by investigating fluctuations in yearly usage frequencies of specific words that describe social and natural phenomena, as derived from books that were published over the course of the past two centuries. We show that the determination of the Hurst parameter by means of fractal analysis provides fundamental insights into the nature of long-range correlations contained in the culturomic trajectories, and by doing so offers new interpretations as to what might be the main driving forces behind the examined phenomena. Quite remarkably, we find that social and natural phenomena are governed by fundamentally different processes. While natural phenomena have properties that are typical for processes with persistent long-range correlations, social phenomena are better described as non-stationary, on–off intermittent or Lévy walk processes.

Theory of binary boson solutions

The theory of binary boson solutions is derived by an extension of the paired-phonon analysis previously applied to liquid 4He. The results include expressions for an approximate ground state energy and wavefunction. the latter is composed of a product of a Jastrow factor and the correlation function employed in a correlated basis. The excited state energies are expressed in terms of a two-branch excitation spectrum, which is the generalization of the Bijl-Feynman excitation spectrum to a two-component system. A powerful variational principle satisfied by the optimum ground state solution of the paired-phonon analysis is derived. Techniques are discussed for calculating an interaction function which is necessary to obtain the optimum ground state. Finally, we speculate about the nature of long-range correlations in the results based upon the quantization of density fluctuations and the previous results of the paired-phonon analysis of liquid 4He.