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Smoothing operation to make continuous density field from observed point-like distribution of galaxies is crucially important for topological or morphological analysis of the large-scale structure, such as, the genus statistics or the area…
Under ideal conditions, the probability density function (PDF) of a random variable, such as a sensor measurement, would be well known and amenable to computation and communication tasks. However, this is often not the case, so the user…
Theoretical investigations into the deflection angle caused by microlenses offer a direct path to uncovering principles of the cosmological microlensing effect. This work specifically concentrates on the the probability density function…
At any given scale, 3$\times$2-point statistics extract only three numbers from the joint distribution of the cosmic matter density and galaxy density fluctuations: their variances and their covariance. It is well known that the full shape…
In this work we derive the evolution equation for the density contrast considering open system cosmology, where the influence of adiabatic particle production process on the dynamic of a homogeneous and isotropic is investigated within a…
We investigate the skewness of galaxy number density fluctuations as a possible probe to test gravity theories. We find that the specific linear combination of the skewness parameters corresponds to the coefficients of the second-order…
A general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time. The scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of…
Using third-order perturbation theory, we derive a relation between the mean divergence of the peculiar velocity given density and the density itself. Our calculations assume Gaussian initial conditions and are valid for Gaussian filtering…
Random advection of Lagrangian tracer scalar field $\theta (t,x)$ by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations are maintained by a source concentrated at the integral…
An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable…
An attractive and simple hypothesis for the formation of large-scale structure is that it developed by gravitational instability from primordial fluctuations with an initially Gaussian probability distribution. Non-linear gravitational…
We derive a recursion relation in the framework of Lagrangian perturbation theory, appropriate for studying the inhomogeneities of the large scale structure of the universe. We use the fact that the perturbative expansion of the matter…
In assumed probability density function (pdf) methods of turbulent combustion, the shape of the scalar pdf is assumed a priori and the pdf is parametrized by its moments for which model equations are solved. In non-premixed flows the beta…
To understand the nature of the accelerated expansion of the Universe, we need to combine constraints on the expansion rate and growth of structure. The growth rate is usually extracted from three dimensional galaxy maps by exploiting the…
The 1-point matter density probability distribution function (PDF) captures some of the non-Gaussian information lost in standard 2-point statistics. The matter PDF can be well predicted at mildly non-linear scales using large deviations…
The purpose of the present paper is to derive a partial differential equation (PDE) for the single-time single-point probability density function (PDF) of the velocity field of a turbulent flow. The PDF PDE is a highly non-linear…
We investigate velocity probability distribution functions (PDF) of sheared hard-sphere suspensions. As observed in our Stokes flow simulations and explained by our single-particle theory, these PDFs can show pronounced deviations from a…
Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The…
Turbulence structure resulting from multi-fluid or multi-species, variable-density isotropic turbulence interaction with a Mach 2 shock is studied using turbulence-resolving shock-capturing simulations and Eulerian (grid) and Lagrangian…
The group of Conservative transformations is an enlargement of the group of diffeomorphisms which leads to a richer geometry than that of general relativity. The field variables of the theory are the usual orthonormal tetrads and also…