Related papers: Internal DLA in Higher Dimensions
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…
The adsorption of particles diffusing in a half-space bounded by the substrate and irreversibly sticking to the substrate upon contacts is investigated. We show that when absorbing particles are planar disks diffusing in the…
Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation…
What is the scaling limit of diffusion limited aggregation (DLA) in the plane? This is an old and famously difficult question. One can generalize the question in two ways: first, one may consider the {\em dielectric breakdown model}…
We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that…
Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated…
Extensive numerical simulation are reported for the structure and dynamics of large clusters on metal(100) surfaces. Different types of perimeter hopping processes makes center-of-mass of the cluster to follow a a random walk trajectory.…
Diffusional interactions within the Ostwald Ripening process are analyzed in the present paper. An {\it off-centre diffusion approach \/} is performed to point out the direct correlation between the size of clusters. Herein the diffusion…
We show that Internal Diffusion Limited Aggregation (IDLA) on $\mathbb{Z}^d$ has near optimal Cheeger constant when the growing cluster is large enough. This implies, through a heat kernel lower bound derived previously in [H], that simple…
This work provides an extension of parts of the classical finite dimensional sub-elliptic theory in the context of infinite dimensional compact connected metrizable groups. Given a well understood and well behaved bi-invariant Laplacian,…
We prove that the diffusion coefficient for the asymmetric exclusion process diverges at least as fast as $t^{1/4}$ in dimension $d=1$ and $(\log t)^{1/2}$ in $d=2$. The method applies to nearest and non-nearest neighbor asymmetric…
Interplanetary dust particles (IDPs) are an important constituent of the earth's stratosphere, interstellar and interplanetary medium, cometary comae and tails, etc. Their physical and optical characteristics are significantly influenced by…
The dynamics of classical hard particles in a quasi one-dimensional channel were studied since the 1960s and used for explaining processes in chemistry, physics and biology and in applications. Here we show that in a previously un-described…
We compute the O(1/N_f) correction to the predominantly gluonic flavour singlet twist-2 anomalous dimension used in polarized deep inelastic scattering. It is consistent with known two loop perturbation theory and we determine the three…
We discuss recent theoretical results on diffractive deeply inelastic scattering, focusing on the partonic picture of diffraction in configuration space and the predictions for the beta behavior and the scaling violation.
We present results of simulations which show unambiguously that DLA clusters are not self-affine, in contrast to frequent claims. The measured observable is the asymmetry of the last step of a walker before he sticks to the growing cluster.…
In this article, we consider the space-time Fractional (nonlocal) diffusion equation $$\partial_t^\beta u(t,x)={\mathtt{L}_D^{\alpha_1,\alpha_2}} u(t,x), \ \ t\geq 0, \ x\in D, $$ where $\partial_t^\beta$ is the Caputo fractional derivative…
If $A_q(\beta, \alpha, k)$ is the scattering amplitude, corresponding to a potential $q\in L^2(D)$, where $D\subset\R^3$ is a bounded domain, and $e^{ik\alpha \cdot x}$ is the incident plane wave, then we call the radiation pattern the…
We generalize the small scale dynamics of the universe by taking into account models with an equation of state which evolves with time, and provide a complete formulation of the cluster virialization attempting to address the nonlinear…
In this manuscript we investigate the capabilities of the Discrete Dipole Approximation (DDA) to simulate scattering from particles that are much larger than the wavelength of the incident light, and describe an optimized publicly available…