Related papers: Phase-space consistency of stellar dynamical model…
This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed.…
Both numerical simulations and observational evidence indicate that the outer regions of galaxies and dark matter haloes are typically mildly to significantly radially anisotropic. The inner regions can be significantly non-isotropic,…
The main purpose of this paper is to obtain physically stable stellar models coupled with anisotropic matter distribution in the context of $f(\mathcal{R},\mathrm{T}^{2})$ theory. For this, we consider a static spherical geometry and…
Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for $d$-dimensional spaces, and the resulting set of unitary matrices $S(d) $ is a basis for $d\times d$ matrices. If $N=d_{1}\times…
The dynamics of a general structured population is modelled using a general stochastic differential equation (SDE) with an infinite decomposability property. This property allows the population to be divided into an arbitrary number of…
A continuum model for growth of solids is developed, considering adatom deposition, surface diffusion, and configuration dependent incorporation rate. For amorphous solids it is related to surface energy densities. The high adatom density…
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…
Physical systems with non-reciprocal or dissipative forces evolve according to a generalization of Liouville's equation that accounts for the expansion and contraction of phase space volume. Here, we connect geometric descriptions of these…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
We obtain the non-linear relation between cosmological density and velocity perturbations by examining their joint dynamics in a two dimensional density-velocity divergence phase space. We restrict to spatially flat cosmologies consisting…
We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
We model a compact relativistic body with anisotropic pressures in the presence of an electric field. The equation of state is barotropic with a linear relationship between the radial pressure and the energy density. Simple exact models of…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
We discuss recent developments in the formulation of a Statistical Mechanics approach to non thermal systems, such as granular media. We review a few important numerical results on the assessment of Edwards' theory and, in particular, we…
We aim at estimating in a non-parametric way the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$, for $d \ge 2$, from the discrete observations of a finite sample…
Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial…
We continue the study of collisionless systems governed by additive $r^{-\alpha}$ interparticle forces by focusing on the influence of the force exponent $\alpha$ on radial orbital anisotropy. In this preparatory work we construct the…