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Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed…
The notions of self-organised criticality (SOC) and turbulence are traditionally considered to be applicable to disjoint classes of phenomena. Nevertheless, scale-free burst statistics is a feature shared by turbulent as well as…
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we…
We present experimental results on simultaneous space-time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as…
We calculate the one-point probability distribution function (PDF) for cosmic density in non-linear regime of the gravitational evolution. Under the local approximation that the evolution of cosmic fluid fields can be characterized by the…
The Fluctuating Force Fluctuating Torque (F3T) model is developed and evaluated for the dynamics of a turbulent particle-gas suspension of rough spherical particles in a turbulent Couette flow in the limit where the viscous relaxation time…
The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same functional form. Here, we identify the analytical form of the PDF of one such measure, the order…
The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
The two-point statistics of the cosmic velocity field, measured from galaxy peculiar velocity (PV) surveys, can be used as a dynamical probe to constrain the growth rate of large-scale structures in the universe. Most works use the…
We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for…
One of the key advantages of 3D rendering is its ability to simulate intricate scenes accurately. One of the most widely used methods for this purpose is Gaussian Splatting, a novel approach that is known for its rapid training and…
The one-point probability distribution function (PDF) is a powerful summary statistic for non-Gaussian cosmological fields, such as the weak lensing (WL) convergence reconstructed from galaxy shapes or cosmic microwave background (CMB)…
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 use a suite of 3D simulations of star-forming molecular clouds, with and without stellar feedback and magnetic fields, to investigate the effectiveness of different fitting methods for volume and column density probability distribution…
We develop a Lagrangian Perturbation Theory (LPT) framework to study the clustering of cold dark matter (CDM) in cosmologies with massive neutrinos. We follow the trajectories of CDM particles with Lagrangian displacements fields up to…
According to modern developments in turbulence theory, the "dissipation" scales (u.v. cut-offs) $\eta$ form a random field related to velocity increments $\delta_{\eta}u$. In this work we, using Mellin's transform combined with the Gaussain…
We derive a multifractal model for the velocity probability density distribution function (PDF), which is valid from the inertial range to the viscous range. The model gives a continuous evolution of velocity PDFs from large to small…
Collisionless suspensions of inertial particles (finite-size impurities) are studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of random dynamical systems are used to identify and to characterise in full generality…
We propose a new method to linearise cosmological mass density fields using higher order Lagrangian perturbation theory (LPT). We demonstrate that a given density field can be expressed as the sum of a linear and a nonlinear component which…