Related papers: Internal DLA in Higher Dimensions
Aiming at comparing different morphological models of galaxy clusters, we use two new methods to make a cosmological model-independent test of the distance-duality (DD) relation. The luminosity distances come from Union2 compilation of…
The pair-correlation function $g(r,t)$ and its Fourier transform, the structure factor $S(q,t)$, are computed during the gelation process of identical spherical particles using the diffusion-limited cluster-cluster aggregation model in a…
Self-assembly of particles with short-range attraction and long-range repulsion (SALR) interactions on a flat and on a spherical surface is compared. Molecular dynamics (MD) simulations are performed for the two systems having the same area…
We model the 10 micron absorption spectra of nonspherical particles composed of amorphous silicate. We consider two classes of particles, compact ones and fractal aggregates composed of homogeneous spheres. For the compact particles we…
The asymptotics of sizes of clusters for the Arratia flow is considered, the Arratia flow being a system of coalescing Wiener processes starting from the real axis and independent before they meet. A cluster at time t is defined as a set of…
The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for any aperture, the…
This paper discusses the topic of dimensionality reduction for $k$-means clustering. We prove that any set of $n$ points in $d$ dimensions (rows in a matrix $A \in \RR^{n \times d}$) can be projected into $t = \Omega(k / \eps^2)$…
We consider the problem of clustering in the learning-augmented setting, where we are given a data set in $d$-dimensional Euclidean space, and a label for each data point given by an oracle indicating what subsets of points should be…
There is a result related to the average number of the $(\delta, \eta)$-LLL bases in dimension $n$ in theoretical sense but the formula seems to be complicated and computing in high dimension takes a long time. In practical sense, we…
Two exponents, $\delta$, for size distribution of $n$-atom clusters, $Y(n)\sim n^{-\delta}$, have been found in Au clusters sputtered from embedded Au nanoparticles under swift heavy ion irradiation. For small clusters, below 12.5 nm in…
Suspensions of hard core spherical particles of diameter $D$ with inter-core connectivity range $\delta$ can be described in terms of random geometric graphs, where nodes represent the sphere centers and edges are assigned to any two…
Motivated by the problem of filtering candidate pairs in inner product similarity joins we study the following inner product estimation problem: Given parameters $d\in {\bf N}$, $\alpha>\beta\geq 0$ and unit vectors $x,y\in {\bf R}^{d}$…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
We analyze subsamples of Abell and ACO cluster catalogs, in order to study the spatial properties of the large scale matter distribution. The subsamples analyzed are estimated to be nearly complete and are the standard ones used in the…
We study the nature of the phase transition in the multifractal formalism of the harmonic measure of Diffusion Limited Aggregates (DLA). Contrary to previous work that relied on random walk simulations or ad-hoc models to estimate the low…
High-energy factorization in QCD is investigated beyond leading order and its relationship to the factorization theorem of mass singularities is established to any collinear accuracy. Flavour non-singlet observables are shown to be regular…
We demonstrate that diffusiophoretic, thermophoretic and chemotactic phenomena in turbulence lead to clustering of particles on multi-fractal sets that can be described using one single framework, valid when the particle size is much…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
Random sequential adsorption with diffusional relaxation, of two by two square objects on the two-dimensional square lattice is studied by Monte Carlo computer simulation. Asymptotically for large lattice sizes, diffusional relaxation…
We prove that the harmonic measure is stationary, unique and invariant on the interface of DLA growing on a cylinder surface. We provide a detailed theoretical analysis puzzling together multiscaling, multifractality and conformal…