Scale Dependence Of Fluctuations Research Articles

Joint assessment of density correlations and fluctuations for analysing spatial tree patterns.

Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology. Much effort has been made in the past decades to collect extensive and detailed information about the spatial distribution of tropical rainforests, as demonstrated, e.g. in the 50 ha tropical forest plot on Barro Colorado Island, Panama. These kinds of plots have been crucial to shed light on diverse qualitative features, emerging both at the single-species or the community level, like the spatial aggregation or clustering at short scales. Here, we build on the progress made in the study of the density correlation functions applied to biological systems, focusing on the importance of accurately defining the borders of the set of trees, and removing the induced biases. We also pinpoint the importance of combining the study of correlations with the scale dependence of fluctuations in density, which are linked to the well-known empirical Taylor’s power law. Density correlations and fluctuations, in conjunction, provide a unique opportunity to interpret the behaviours and, possibly, to allow comparisons between data and models. We also study such quantities in models of spatial patterns and, in particular, we find that a spatially explicit neutral model generates patterns with many qualitative features in common with the empirical ones.

Turbulence in simulated H ii regions

We investigate the scale dependence of fluctuations inside a realistic model of an evolving turbulent HII region and to what extent these may be studied observationally. We find that the multiple scales of energy injection from champagne flows and the photoionization of clumps and filaments leads to a flatter spectrum of fluctuations than would be expected from top-down turbulence driven at the largest scales. The traditional structure function approach to the observational study of velocity fluctuations is shown to be incapable of reliably determining the velocity power spectrum of our simulation. We find that a more promising approach is the Velocity Channel Analysis technique of Lazarian & Pogosyan (2000), which, despite being intrinsically limited by thermal broadening, can successfully recover the logarithmic slope of the velocity power spectrum to a precision of +-0.1 from high resolution optical emission line spectroscopy.

The energy dependence of pt angular correlations inferred from mean-pt fluctuation scale dependence in heavy ion collisions at the SPS and RHIC

We present the first study of the energy dependence of pt angular correlations inferred from event-wise mean transverse momentum ⟨pt⟩ fluctuations in heavy ion collisions. We compare our large-acceptance measurements at CM energies , 62.4, 130 and 200 GeV to SPS measurements at 12.3 and 17.3 GeV. pt angular correlation structure suggests that the principal source of pt correlations and fluctuations is minijets (minimum-bias parton fragments). We observe a dramatic increase in correlations and fluctuations from SPS to RHIC energies, increasing linearly with from the onset of observable jet-related ⟨pt⟩ fluctuations near 10 GeV.

Autocorrelations from fluctuation scale dependence by inversion

Fluctuations in nuclear collisions can be measured as a function of momentum-space binning scale over a scale interval bounded by detector two-track resolution and acceptance. Fluctuation scale dependence is related to two-particle correlations by a Fredholm integral equation. That equation can be inverted by standard numerical methods to yield an autocorrelation distribution on difference variables as a projection of the full two-particle distribution which retains most of the correlation information in a more compact form. Autocorrelation distributions are typically more easily interpreted in terms of physical mechanisms than fluctuation measurements.

The equivalence of fluctuation scale dependence and autocorrelations

We define optimal per-particle fluctuation and correlation measures, relate fluctuations and correlations through an integral equation and show how to invert that equation to obtain precise autocorrelations from fluctuation scale dependence. We test the precision of the inversion with Monte Carlo data and compare autocorrelations to conditional distributions conventionally used to study high-pt jet structure.

Off-equilibrium dynamics of the primordial perturbations in the inflationary universe: TheO(N)model

Using the $O(N)$ model as an example, we investigate the self-interaction effects of inflaton on the dynamics of the primordial perturbations. When taking interactions into account, it is essential to employ a self-consistent off-equilibrium formalism to study the evolution of the inflationary background field and its fluctuations with back-reaction effects. Within the Hartree factorization scheme, we show that the $O(N)$ model has at least two observable remains left behind by the off-equilibrium processes: the running spectral index of primordial density perturbations and the correlations between perturbation modes in phase space. We find that the running of the spectral index is fully determined by the rate of the energy transfer from the inflationary background field to its fluctuations via particle creation processes as well as the dynamics of the background field itself. Furthermore, the amplitude of the field fluctuations turns out to be scale dependent due to the off-equilibrium evolution. As a consequence, the scale dependence of fluctuations yields a correlation between the phase-space modes of energy density perturbations, while the one-point function of the fluctuations in each Hartree mode is still Gaussian. More importantly, the mode-mode correlation of the primordial perturbations depends upon the dynamics of the self-interaction as well as the initial conditions of the inflation. Hence, we propose that the running spectral index and the correlation between phase-space modes would be two observable fossils to probe the epoch of inflation, even beyond.

Fractal properties of inertial-range turbulence with implications for aircraft response

SummaryFractal geometry provides a method for modelling the scale dependence of fluctuations in atmospheric-turbulence velocity. In this paper the basic concepts are outlined and illustrated by a method of data analysis which, for a fractal process, displays measured probability distributions in scale-invariant form. To a first approximation the data exhibit statistical self-similarity, consistent with the classical theory of Kolmogorov. However, on more detailed analysis, the more intense fluctuations show systematic departures from self-similarity, consistent with recent theoretical estimates of the fractal dimension of the support of turbulence. Implications for aircraft gust response are discussed.