Related papers: Superconcentration in surface growth
We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
Simple random coverage models, well studied in Euclidean space, can also be defined on a general compact metric space. By analogy with the geometric models, and with the discrete coupon collector's problem and with cover times for finite…
Condensational growth of cloud droplets due to supersaturation fluctuations is investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations with droplets being modeled as Lagrangian particles. The…
The uniqueness of a surface density of sources localized inside a spatial region $R$ and producing a given electric potential distribution in its boundary $B_0$ is revisited. The situation in which $R$ is filled with various metallic…
We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal…
We study the local and global roughness scaling in growth models with grains at the film surfaces. The local roughness, measured as a function of window size r, shows a crossover at a characteristic length r_c, from a rapid increase with…
We study models of spatial growth processes where initially there are sources of growth (indicated by the colour green) and sources of a growth-stopping (paralyzing) substance (indicated by red). The green sources expand and may merge with…
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…
Grain boundary roughness can affect electronic and mechanical properties of two-dimensional materials. This roughness depends crucially on the growth process by which the two-dimensional material is formed. To investigate the key mechanisms…
Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the…
The ability to cope with out-of-distribution (OOD) corruptions and adversarial attacks is crucial in real-world safety-demanding applications. In this study, we develop a general mechanism to increase neural network robustness based on…
We study the convergence of the predictive surface of regression trees and forests. To support our analysis we introduce a notion of adaptive concentration for regression trees. This approach breaks tree training into a model selection…
A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…
We discuss the behavior of a crystalline surface with a disordered substrate. We focus on the possible existence of a {\em super-rough} glassy phase, with height-height correlation functions which vary as the square logarithm of the…
Using renormalized field theory, we examine the dynamics of a growing surface, driven by an obliquely incident particle beam. Its projection on the reference (substrate) plane selects a ``parallel'' direction, so that the evolution equation…
We study the interplay between surface roughening and phase separation during the growth of binary films. Renormalization group calculations are performed on a pair of equations coupling the interface height and order parameter…
In many growth processes particles are highly mobile in an active layer at the surface, but are relatively immobile once incorporated in the bulk. We study models in which atoms are allowed to interact, equilibrate, and order on the…
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic…
In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it…