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The evolution of a planar perturbation in a Einstein-de Sitter Universe is studied using a previously introduced Lagrangian scheme. An approximate discrete dynamical system is derived, which describes the mass agglomeration process…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
In order to attain a statistical description of the evolution of cosmic density fluctuations in agreement with results from the numerical simulations, we introduce a probability conditional formalism (CF) based on an inventory of isolated…
For many of the physical phenomena around us, we have developed sophisticated models explaining their behavior. Nevertheless, inferring specifics from visual observations is challenging due to the high number of causally underlying physical…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
The ConflUent System of Peak trajectories (CUSP) is a rigorous formalism in the framework of the peak theory that allows one to derive from first principles andno free parameters the typical halo properties from the statistics of peaks in…
We present a proof-of-principle implementation of the first fully covariant filtering scheme applied to relativistic fluid turbulence. The filtering is performed with respect to special observers, identified dynamically as moving with the…
In this paper we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We are specifically concerned with a new agent-based, continuous-in-space,…
Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These…
In this work, standard methods of the mixed thin-shell foramlism are refined using the framework of Colombeau's theory of generalized functions. To this end, systematic use is made of smooth generalized functions, in particular…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
Dense granular clusters often behave like macro-particles. We address this interesting phenomenon in a model system of inelastically colliding hard disks inside a circular box, driven by a thermal wall at zero gravity. Molecular dynamics…
We calculate the multiplicity function of matter condensations by directly considering the actual, deeply non-linear density field, which we compare to the popular Press-Schechter approximation. We show the mass function is a function of a…
The morphological nature of structures that form under gravitational instability has been of central interest to cosmology for over two decades. A remarkable feature of large scale structures in the Universe is that they occupy a relatively…
The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle…
We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation-fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the…
Understanding the dynamics of material objects advected by turbulent flows is a long standing question in fluid dynamics. In this perspective article we focus on the characterization of the statistical properties of non-interacting…
We develop a path-integral formalism to study the formation of large-scale structures in the universe. Starting from the equations of motion of hydrodynamics (single-stream approximation) we derive the action which describes the statistical…
Surface growth, i.e., the addition or removal of mass from the boundary of a solid body, occurs in a wide range of processes, including the growth of biological tissues, solidification and melting, and additive manufacturing. To understand…
Information Retrieval systems can be improved by exploiting context information such as user and document features. This article presents a model based on overlapping probabilistic or fuzzy clusters for such features. The model is applied…