Related papers: Discrete Growth Models
I review the main steps made so far towards the construction of a (semi) analytical model for describing the growth history of bound virialized objects or haloes in the gravitational instability scenario. I mainly focus on those models…
These notes review theoretical models of massive black hole formation, growth and observables. They start with a brief summary of basic properties of massive black hole properties. The current view on massive black holes and active galactic…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
We study the following growth model on a regular d-ary tree. Points at distance n adjacent to the existing subtree are added with probabilities proportional to alpha^{-n}, where alpha<1 is a positive real parameter. The heights of these…
We study the structural regularities and irregularities of the reals in inner models of set theory. Starting with $L$, G\"{o}del's constructible universe, our study of the reals is thus two-fold. On the one hand, we study how their…
The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site…
We study techniques for deciding the computational complexity of infinite-domain constraint satisfaction problems. For certain fundamental algebraic structures Delta, we prove definability dichotomy theorems of the following form: for every…
This paper is a short review of the connection between certain types of growth processes and the integrable systems theory, written from the viewpoint of the latter. Starting from the dispersionless Lax equations for the 2D Toda hierarchy,…
Image completion techniques have made significant progress in filling missing regions (i.e., holes) in images. However, large-hole completion remains challenging due to limited structural information. In this paper, we address this problem…
A recently proposed theory for diffusion-limited aggregation (DLA), which models this system as a random branched growth process, is reviewed. Like DLA, this process is stochastic, and ensemble averaging is needed in order to define…
We give an algorithm that computes the final state of certain growth models without computing all intermediate states. Our technique is based on a "least action principle" which characterizes the odometer function of the growth process.…
We present a new class of 3D black hole initial data sets for numerical relativity. These data sets go beyond the axisymmetric, ``gravity wave plus rotating black hole'' single black hole data sets by creating a dynamic, distorted hole with…
In this paper, we analyze the scaling behavior of \emph{Diffusion Limited Aggregation} (DLA) simulated by Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns in a good…
We develop a model of globular cluster (GC) formation within the cosmological hierarchy of structure formation. The model is rooted in the `two-phase' scenario of galaxy formation developed in Paper-I, where the fast accretion of dark…
We show that a subdominant component of dissipative dark matter resembling the Standard Model can form many intermediate-mass black hole seeds during the first structure formation epoch. We also observe that, in the presence of this matter…
Magnetically charged dilatonic black holes have a perturbatively infinite ground state degeneracy associated with an infinite volume throat region of the geometry. A simple argument based on causality is given that these states do not have…
Understanding the role of solute diffusivities in equilibrium tie-line selection during growth of a second phase in ternary and higher multicomponent two phase alloys is an important problem due to the strong dependence of mechanical…
To observe the dynamic formation of black holes in general relativity, one essentially needs to prove that closed trapped surfaces form during evolution from initial data that do not already contain trapped surfaces. We discuss the recent…
Given an orientation-preserving diffeomorphism of the interval [0;1], consider the uniform norm of the differential of its n-th iteration. We get a function of n called the growth sequence. Its asymptotic behaviour is an interesting…
The method of iterated conformal maps for the study of Diffusion Limited Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and related processes. We emphasize the fundamental difference between these processes: DLA…