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Particles floating on the surface of a turbulent incompressible fluid accumulate along string-like structures, while leaving large regions of the flow domain empty. This is reflected experimentally by a very peaked probability distribution…
We present results of the numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy tailed probability distribution functions. Assuming that the distribution function of the random fluctuations…
Power-law type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constrains that limit the power-law range for the distributions…
In the mid-90's, it was shown that the statistics of aggregated time series from Internet traffic departed from those of traditional short range dependent models, and were instead characterized by asymptotic self-similarity. Following this…
In the present paper, we address the important point of the proportionality between the longitudinal integral lengthscale ($L$) and the characteristic mean flow width ($\delta$) using experimental data of an axisymmetric wake and a…
Intermittency is one of central obstacles for understanding small-scale dynamics in the fully developed hydrodynamic turbulence. The modern approach is largely based on the multifractal theory of Parisi and Frisch which is, however,…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…
Analytical solutions are derived for the steady-state size distributions of precipitating rain and snow particles assuming growth via collection of suspended cloud particles. Application of the Liouville equation to the transfer of…
Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…
Modern LLM pre-training consumes vast amounts of compute and training data, making the scaling behavior, or scaling laws, of different models a key distinguishing factor. Discrete diffusion language models (DLMs) have been proposed as an…
We have analyzed the spatial distribution of galaxies from the release of the Sloan Digital Sky Survey of galactic redshifts (SDSS DR7), applying the complete correlation function (conditional density), two-point conditional density…
We report moment distribution results from a laboratory earthquake fault experiment consisting of sheared elastic plates separated by a narrow gap filled with a two dimensional granular medium. Local measurement of strain displacements of…
This article proposes inference procedures for distribution regression models in duration analysis using randomly right-censored data. This generalizes classical duration models by allowing situations where explanatory variables' marginal…
Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences -- no…
We apply the scale-length method to several three dimensional samples of the Two degree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies…
Maxima of the scalar dissipation rate in turbulence appear in form of sheets and correspond to the potentially most intensive scalar mixing events. Their cross-section extension determines a locally varying diffusion scale of the mixing…
In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common…
Remote sensing of rainfall events is critical for both operational and scientific needs, including for example weather forecasting, extreme flood mitigation, water cycle monitoring, etc. Ground-based weather radars, such as NOAA's…
Precipitation exceedance probabilities are widely used in engineering design, risk assessment, and floodplain management. While common approaches like NOAA Atlas 14 assume that extreme precipitation characteristics are stationary over time,…
The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fundamental drivers of forecast accuracy. Here, we demonstrate…