Related papers: Off-lattice Noise Reduced Diffusion-limited Aggreg…
A new algorithm for the derivation of low-density expansions has been used to greatly extend the series for moments of the pair-connectedness on the directed square lattice near an impenetrable wall. Analysis of the series yields very…
The reduced density matrix is variationally optimized for the two-dimensional Hubbard model. Exploiting all symmetries present in the system, we have been able to study $6\times6$ lattices at various fillings and different values for the…
The E/SO sequence of a cluster defines a boundary redward of which a reliable weak lensing signal can be obtained from background galaxies, uncontaminated by cluster members. For bluer colors, both background and cluster members are…
Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based. Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of…
I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys.…
Clustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from "noise-looking" variables. We cast this problem as finding a low-dimensional projection of the data which is…
A finite size effect in the probing of the harmonic measure in simulation of diffusion-limited aggregation (DLA) growth is investigated. We introduce a variable size of probe particles, to estimate harmonic measure and extract the fractal…
Diffusion-limited aggregation (DLA) assumes that particles perform pure random walk at a finite temperature and aggregate when they come close enough and stick together. Although it is well known that DLA in two dimensions results in a…
The recent integration of deep learning and pairwise similarity annotation-based constrained clustering -- i.e., $\textit{deep constrained clustering}$ (DCC) -- has proven effective for incorporating weak supervision into massive data…
Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of…
Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven…
Limited-Angle Computed Tomography (LACT) is a challenging inverse problem where missing angular projections lead to incomplete sinograms and severe artifacts in the reconstructed images. While recent learning-based methods have demonstrated…
Cluster abundance measurements are among the most sensitive probes of the amplitude of matter fluctuations in the universe, which in turn can help constrain other cosmological parameters, like the dark energy equation of state or neutrino…
The fractal dimension is a central quantity in nonlinear dynamics and can be estimated via several different numerical techniques. In this review paper we present a self-contained and comprehensive introduction to the fractal dimension. We…
We have studied the properties of clusters of colloidal magnetic particles generated from a 2D aggregation model with dipolar interparticle interactions. Particles diffuse off-lattice, experiencing dipolar interactions with the already…
We simulated irreversible aggregation of non-interacting particles and of particles interacting via repulsive and attractive potentials explicitly implementing the rotational diffusion of aggregating clusters. Our study confirms that the…
A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…
We present high signal-to-noise measurements of the acoustic scale in the presence of nonlinear growth and redshift distortions using 320(Gpc/h)^3 of cosmological PM simulations. Using simple fitting methods, we obtain robust measurements…
We performed extensive numerical simulation of diffusion-limited aggregation in two dimensional channel geometry. Contrary to earlier claims, the measured fractal dimension D = 1.712 +- 0.002 and its leading correction to scaling are the…
We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s)…