Related papers: Bias-free simulation of diffusion-limited aggregat…
We review some computer algorithms for the simulation of off-lattice clusters grown from a seed, with emphasis on the diffusion-limited aggregation, ballistic aggregation and Eden models. Only those methods which can be immediately extended…
We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \mu. In addition, there is an aggregate, which…
In close analogy to diffusion limited aggregation (DLA) and inspired by a work of Roux, a random walker algorithm is constructed to solve the problem of crack growth in an elastic medium. In contrast to conventional lattice approaches, the…
The surface width scaling of Eden A clusters grown from a single aggregate site on the square lattice is investigated as a function of the noise reduction parameter. A two-exponent scaling ansatz is introduced and used to fit the results…
A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold $p_c\approx 0.655$ is found between…
Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the construction of a uniform probability distribution over a…
We investigate the scattering and absorption of light by random ballistic aggregates of spherical monomers. We present a general measure for the porosity of an irregular particle. Three different classes of ballistic aggregates are…
The dynamical cluster approximation (DCA) is a systematic extension beyond the single site approximation in dynamical mean field theory (DMFT), to include spatially non-local correlations in quantum many-body simulations of strongly…
We present algorithms for diffusion model sampling which obtain $\delta$-error in $\mathrm{polylog}(1/\delta)$ steps, given access to $\widetilde O(\delta)$-accurate score estimates in $L^2$. This is an exponential improvement over all…
Within the framework of hierarchical clustering we show that a simple Press-Schechter-like approximation, based on spherical dynamics, provides a good estimate of the evolution of the density field in the quasi-linear regime up to $\Sigma…
Clustering in high-dimensional spaces is nowadays a recurrent problem in many scientific domains but remains a difficult task from both the clustering accuracy and the result understanding points of view. This paper presents a…
Two-dimensional cluster-cluster aggregation is studied when clusters move both diffusively and sediment with a size dependent velocity. Sedimentation breaks the rotational symmetry and the ensuing clusters are not self-similar fractals: the…
The basic science responsible for the fascinating shapes of ice crystals and snowflakes is still not understood. Insufficient knowledge of the interaction potentials and the lack of relevant experimental access to the growth process are to…
Internal Diffusion Limited Aggregation is an interacting particle system that describes the growth of a random cluster governed by the boundary harmonic measure seen from an internal point. Our paper studies IDLA in $\mathbb{Z}^d$ driven by…
We investigate deterministic diffusion in periodic billiard models, in terms of the convergence of rescaled distributions to the limiting normal distribution required by the central limit theorem; this is stronger than the usual requirement…
Large-scale 3D generative models require substantial computational resources yet often fall short in capturing fine details and complex geometries at high resolutions. We attribute this limitation to the inefficiency of current…
We report coincident damped Lyman alpha (DLA) and sub-DLA absorption at z = 2.66 and z = 2.94 towards the z ~ 3 13.8 arcsecond separation binary quasar SDSS 1116+4118 AB. At the redshifts of the absorbers, this angular separation…
We performed a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear and quadratic term in the size of a dipole d, when the…
A new algorithm for the derivation of low-density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems. Numerical evidence shows that the computational complexity grows…
This study analyzes the sizes, shapes and correlations of $\lya$ clouds produced by a hydrodynamic simulation of a spatially flat CDM universe with a non-zero cosmological constant ($\Omega_0=0.4$, $\Lambda_0=0.6$, $\sigma_8 =0.79$), over…