Related papers: Discrete Growth Models
Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown off-lattice and clusters grown with antenna method with $N_{fp}=3,4,5,6,7$ and 8 allowed growth directions. With the help of…
A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…
We reconsider the four dimensional extremal black hole constructed in type IIB string theory as the bound state of D1-branes, D5-branes, momentum, and Kaluza-Klein monopoles. Specifically, we examine the case of an arbitrary number of…
Dark matter haloes in Lambda CDM simulations grow by mergers with other haloes as well as accretion of "diffuse" non-halo material. We quantify the mass growth rates via these two processes, dM_mer/dt and dM_dif/dt, and their dependence on…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
The inability of standard non-interacting cold dark matter (CDM) to account for the small scale structure of individual galaxies has led to the suggestion that the dark matter may undergo elastic and/or inelastic scattering. We simulate the…
The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation…
We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and…
Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth $R_N^{-\gamma}$ (where $R_N$ is the radius of the $N-$ particle cluster). For $\gamma > 1$ the…
For any integer $d\geq 1$ we construct examples of finitely presented algebras with intermediate growth of type $[e^{n^{d/(d+1)}}]$. We produce these examples by computing the growth types of some finitely presented metabelian Lie algebras.
We study the properties of a completely integrable deformation of the CGHS dilaton gravity model in two dimensions. The solution is shown to represent a singularity free black hole that at large distances asymptoticaly joins to the CGHS…
We propose to modify the saturation model of Golec-Biernat and Wusthoff by including DGLAP evolution. We find considerable improvement for the total deep inelastic cross section, in particular in the large Q^2 region. The successful…
This is a continuation of Part I.
Using stochastic conformal mappings we study the effects of anisotropic perturbations on diffusion limited aggregation (DLA) in two dimensions. The harmonic measure of the growth probability for DLA can be conformally mapped onto a constant…
This is my Ph.D. thesis defended earlier this year. It contains mostly information already presented in previous Bielefeld/Saclay papers on this subject, though in more detailed form. It also includes actual calculations and some…
There is hope to discover dark matter subhalos free of stars (predicted by the current theory of structure formation) by observing gaps they produce in tidal streams. In fact, this is the most promising technique for dark substructure…
This PhD thesis has the following structure: Chapter 1 - General introduction; Chapter 2 - Preliminaries; Chapter 3 - The Replicated Transfer Matrix; Chapter 4 - Finite Size Corrections On Random Graphs; Chapter 5 - The Random Field Ising…
Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process…
Models postulating the existence of additional spacelike dimensions of macroscopic or even infinite size, while viewing our observable universe as merely a 3-brane living in a higher-dimensional bulk were a major breakthrough when proposed…
The Internal Diffusion Limited Aggregation has been introduced by Diaconis and Fulton in 1991. It is a growth model defined on an infinite set and associated to a Markov chain on this set. We focus here on sets which are finitely generated…