Related papers: Physical improvements to a mesoscopic cellular aut…
We introduce a three-dimensional, computationally feasible, mesoscopic model for snow crystal growth, based on diffusion of vapor, anisotropic attachment, and a semi-liquid boundary layer. Several case studies are presented that faithfully…
We describe a numerical model of faceted crystal growth using a cellular automata method that incorporates admolecule diffusion on faceted surfaces in addition to bulk diffusion in the medium surrounding the crystal. The model was developed…
We derive a set of algorithms for simulating the diffusion-limited growth of faceted crystals using local cellular automata. This technique has been shown to work well in reproducing realistic crystal morphologies, and the present work…
A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…
I describe a new approach to the classification of snow crystal morphologies that focuses on the most common growth behaviors that appear in normal air under conditions of constant applied temperature and water-vapor supersaturation. The…
We describe a comprehensive model for the formation and morphological development of atmospheric ice crystals growing from water vapor, also known as snow crystals. Our model derives in part from empirical measurements of the intrinsic ice…
Facetted growth of snow crystals leads to a rich diversity of forms, and exhibits a remarkable sixfold symmetry. Snow crystal structures result from diffusion limited crystal growth in the presence of anisotropic surface energy and…
We review several aspects of aerodynamics that affect the growth, morphology, and symmetry of snow crystals. We derive quantitative estimates for aerodynamical forces that orient falling snow crystals, estimate how air flow around snow…
This monograph reviews our current understanding of the physical dynamics of ice crystal growth, focusing on the spontaneous formation of complex structures from water vapor (called snow crystals) as a function of temperature,…
We describe laboratory-grown snow crystals that exhibit a triangular, plate-like morphology, and we show that the occurrence of these crystals is much more frequent than one would expect from random growth perturbations of the more-typical…
This paper presents a matrix of 206 snow crystal growth observations as a function of temperature and water vapor supersaturation in air, each illustrating the morphology and size of a crystal forming on the tip of an isolated c-axis ice…
The work introduces a 3D cellular automaton model for the spatial and crystallographic prediction of spherulite growth phenomena in polymers at the mesoscopic scale. The automaton is discrete in time, real space, and orientation space. The…
The dendrite growth in casting and additive manufacturing is rather important and related to the formation of some defects. However, quantitatively simulating the growth of dendrites with arbitrary crystallographic orientations in…
Inspired by the approach of kinetic theory of gases, a three-level description (microscopic, mesoscopic and macroscopic) of cellular automaton is presented. To provide an analytical treatment a simple domino cellular automaton with…
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…
Snowflake growth provides us with a fascinating example of spontaneous pattern formation in nature. Attempts to understand this phenomenon have led to important insights in non-equilibrium dynamics observed in various active scientific…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
We examine the molecular dynamics of crystal growth in the presence of surface melting and surface impurities, and from this propose a detailed microscopic model for the growth of ice from the vapor phase. Our model naturally accounts for…
The results of modeling of radiation defects formation and evolution on the surface and in the volume of a crystal are presented in this article. Statistical properties are calculated for the investigated system. It is revealed that defects…
Snow crystals growing from water vapor occasionally exhibit morphologies with three-fold (trigonal) symmetry, even though the ice crystal lattice has a molecular structure with six-fold symmetry. In extreme cases, thin platelike snow…