Probability Density Function Of Fluctuations Research Articles

A Comparative Analysis of Scale-invariant Phenomena in Repeating Fast Radio Bursts and Glitching Pulsars

The recent discoveries of a remarkable glitch/antiglitch accompanied by fast radio burst (FRB)-like bursts from the Galactic magnetar SGR J1935+2154 have revealed the physical connection between the two. In this work, we study the statistical properties of radio bursts from the hyperactive repeating source FRB 20201124A and of glitches from the pulsar PSR B1737–30. For FRB 20201124A, we confirm that the probability density functions of fluctuations of energy, peak flux, duration, and waiting time well follow the Tsallis q-Gaussian distribution. The derived q values from q-Gaussian distribution keep approximately steady for different temporal interval scales, which indicates that there is a common scale-invariant structure in repeating FRBs. Similar scale-invariant properties can be found in PSR B1737–30's glitches, implying an underlying association between the origins of repeating FRBs and pulsar glitches. These statistical features can be well understood within the same physical framework of self-organized criticality systems.

Statistical similarity between soft gamma repeaters and repeating fast radio bursts

ABSTRACT We study the statistical properties of the soft gamma repeater SGR 1935+2154. We find that the cumulative distributions of duration, waiting time, fluence, and flux can be well fitted by bent power law. In addition, the probability density functions of fluctuations of duration, waiting time, fluence, and flux well follow the Tsallis q-Gaussian distribution. The q values keep steady for different temporal scale intervals, indicating a scale-invariant structure of the bursts. Those features are very similar to the property of the repeating fast radio burst FRB 121102, indicating the underlying association between the origins of soft gamma repeaters and repeating fast radio bursts.

Small air ion statistics near the earth's surface

The development of an atmospheric electricity-monitoring network stimulates research into the relationship between the global electrical circuit and environmental conditions. Small air ions in the lower atmosphere are the main carriers of the conduction current and, at the same time, are themselves carried by atmospheric turbulence. However, it is not clear to what extent the statistics of fluctuations in the concentration of small ions in the electrode layer adjacent to the earth's surface bears the features of scalar turbulence. Based on field experiment data, the probability density functions of fluctuations of both the concentration of small ions and temperature are found to be non-Gaussian and approximated by a stable distribution model with the index of stability α in the range from 1.1 to 1.96. Observations have demonstrated that statistics of temperature fluctuations is more intermittent, compared to height-dependent statistics of fluctuations of the concentration of small ions. It is found that the autocorrelation function and second-order structure function have different behavior for the concentration of small ions and temperature in the time range 1–50 s.

Scale-invariance in the repeating fast radio burst 121102

Abstract The statistical properties of the repeating fast radio burst FRB 121102 are investigated. We find that the cumulative distributions of fluence, flux density, total energy and waiting time can be well fitted by the bent power law. In addition, the probability density functions of fluctuations of fluence, flux density and total energy well follow the Tsallis q-Gaussian distribution. The q values keep steady around q ∼ 2 for different scale intervals, indicating a scale-invariant structure of the bursts. The statistical properties of FRB 121102 are very similar to that of the soft gamma repeater SGR J1550-5418. The underlying physical implications need to be further investigated.

Scale-invariance in soft gamma repeaters**Supported by National Natural Science Foundation of China (11375203, 11675182, 11690022, 11603005), and Fundamental Research Funds for Central Universities (106112016CDJCR301206)

The statistical properties of the soft gamma repeater SGR J1550–5418 are investigated carefully. We find that the cumulative distributions of fluence, peak flux and duration can be well fitted by a bent power law, while the cumulative distribution of waiting time follows a simple power law. In particular, the probability density functions of fluctuations of fluence, peak flux, and duration have a sharp peak and fat tails, which can be well fitted by a q-Gaussian function. The q values keep approximately steady for different scale intervals, indicating a scale-invariant structure of soft gamma repeaters. Those results support that the origin of soft gamma repeaters is crustquakes of neutron stars with extremely strong magnetic fields.

Singular Boundaries in the Forward Chapman-Kolmogorov Differential Equation

The forward Chapman-Kolmogorov differential equation is used to model the time evolution of the Probability Density Function of fluctuations. This equation may be restricted to either Master, Fokker-Planck or Liouville equations. A derivation of the Liouville equation with possible singular boundary conditions has already been presented in a previous publication (Valino and Hierro in Phys. Rev. E 67:046310, 2003). In this paper, that derivation is extended to the full Chapman-Kolmogorov differential equation.

The Signature of Evolving Turbulence in Quiet Solar Wind as Seen byUlysses

Solar wind fluctuations, such as magnetic field or velocity, show power-law power spectra suggestive both of an inertial range of intermittent turbulence (with ~–5/3 exponent), and at lower frequencies, of fluctuations of coronal origin (with ~–1 exponent). The Ulysses spacecraft spent many months in the quiet fast solar wind above the Sun's polar coronal holes in a highly ordered magnetic field. We use statistical analysis methods such as the generalized structure function (GSF) and extended self-similarity (ESS) to quantify the scaling of the moments of the probability density function of fluctuations in the magnetic field. The GSFs give power law scaling in the f−1 range of the form ⟨|y(t + τ) − y(t)|m⟩∼ τζ (m), but ESS is required to reveal scaling in the inertial range, which is of the form ⟨|y(t + τ) − y(t|m⟩ ∼ [g(τ)]ζ (m). We find that g(τ) is independent of spacecraft position and . The f−1 scaling fluctuates with radial spacecraft position. This confirms that, whereas the f−1 fluctuations are directly influenced by the corona, the inertial range fluctuations are consistent with locally evolving turbulence, but with an envelope g(τ) , which captures the formation of the quiet fast solar wind.

Scaling and a Fokker‐Planck model for fluctuations in geomagnetic indices and comparison with solar wind ε as seen by Wind and ACE

The evolution of magnetospheric indices on temporal scales shorter than that of substorms is characterized by bursty, intermittent events that may arise from turbulence intrinsic to the magnetosphere or that may reflect solar wind‐magnetosphere coupling. This leads to a generic problem of distinguishing between the features of the system and those of the driver. We quantify scaling properties of short‐term (up to few hours) fluctuations in the geomagnetic indices AL and AU during solar minimum and maximum, along with the parameter ε that is a measure of the solar wind driver. We find that self‐similar statistics provide a good approximation for the observed scaling properties of fluctuations in the geomagnetic indices, regardless of the solar activity level, and in the ε parameter at solar maximum. This self‐similarity persists for fluctuations on timescales at least up to about 1–2 hours. The scaling exponent of AU index fluctuations show dependence on the solar cycle, and the trend follows that found in the scaling of fluctuations in ε. The values of their corresponding scaling exponents, however, are always distinct. Fluctuations in the AL index are insensitive to the solar cycle, as well as being distinct from those in the ε parameter. This approximate self‐similar scaling leads to a Fokker‐Planck model which, we show, captures the probability density function of fluctuations and provides a stochastic dynamical equation (Langevin equation) for time series of the geomagnetic indices.

Particle shape determination from polarization fluctuations of scattered radiation

When the number of scattering centers is small and/or varying, non-Gaussian fluctuations of coherently scattered radiation can yield vestigial information about the character of the individuals. The probability density functions of fluctuations in polarized light scattered from ensembles of small spheroidal particles are calculated. The particle dynamics are governed by Brownian motion, so their orientation is random relative to the incident polarized radiation, and the number of illuminated scattering centers can fluctuate according to Poisson statistics. It is demonstrated that the probability density functions of the scattered radiation may be used to discriminate the particle shape unambiguously, provided that the mean number of them is sufficiently small.