Related papers: Scaling limits for planar aggregation with subcrit…
In a series of three papers, we introduced a novel cluster formation model that describes the formation, growth, and disruption of star clusters in high-resolution cosmological simulations. We tested this model on a Milky Way-sized galaxy…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
We study an iterated temporal and contemporaneous aggregation of $N$ independent copies of a strongly stationary subcritical Galton-Watson branching process with regularly varying immigration having index $\alpha \in (0, 2)$. Limits of…
The scaling properties of the cluster size distribution of a system of diffusing clusters is studied in terms of a simple kinetic mean field model. It is shown that a one parameter family of mathematically valid scaling solutions exists.…
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…
We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when…
We consider a large class of random geometric graphs constructed from samples $\mathcal{X}_n = \{X_1,X_2,\ldots,X_n\}$ of independent, identically distributed observations of an underlying probability measure $\nu$ on a bounded domain…
We apply fractal analysis methods to investigate the scaling properties in the Abell and ACO catalogs of rich galaxy clusters. We also discuss different technical aspects of the method when applied to data sets with small number of points…
We investigate the transfer of power between different scales and coupling of modes during non-linear evolution of gravitational clustering in an expanding universe. We start with a power spectrum of density fluctuations that is…
We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size L_n at any fixed time prior to the critical time. The asymptotic…
Like early-type galaxies, also nearby galaxy clusters define a Fundamental Plane, a luminosity-radius, and a luminosity-velocity dispersion relations, whose physical origin is still unclear. By means of high resolution N--body simulations…
In the volume fraction range (0.005,0.08), we have obtained the temporal evolution of the structure factor $S(q)$, in extensive numerical simulations of both diffusion-limited and reaction-limited colloid aggregation in three dimensions. We…
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…
In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the…
The scaling ansatz of Hamilton et al. effectively extends the idea of self-similar scaling to initial power spectra of any generic shape. Applications of this ansatz have provided a semi-empirical analytical description of gravitational…
We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a…
We analyse with simple real-space statistics the Virgo consortium's cosmological N-body simulations. Significant clustering rapidly develops well below the initial mean interparticle separation \Lambda_i, where the gravitational force on a…
The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a…
We prove $\sqrt{\log n}$ lower bounds on the order of growth fluctuations in three planar growth models (first-passage percolation, last-passage percolation, and directed polymers) under no assumptions on the distribution of vertex or edge…
Conformal mapping models are used to study competition of noise and anisotropy in Laplacian growth. For that, a new family of models is introduced with the noise level and directional anisotropy controlled independently. Fractalization is…