498 research outputs found
A cellular automata modelling of dendritic crystal growth based on Moore and von Neumann neighbourhood
An important step in understanding crystal growth patterns involves simulation of the growth processes using mathematical models. In this paper some commonly used models in this area are reviewed, and a new simulation model of dendritic crystal growth based on the Moore and von Neumann neighbourhoods in cellular automata models are introduced. Simulation examples are employed to find ap-
propriate parameter configurations to generate dendritic crystal growth patterns. Based on these new modelling results the relationship between tip growth speed
and the parameters of the model are investigated
Identification of the transition rule in a modified cellular automata model: the case of dendritic NH4Br crystal growth
A method of identifying the transition rule, encapsulated in a modified cellular automata (CA) model, is demonstrated using experimentally observed evolution of dendritic crystal growth patterns in NH4Br crystals. The influence of the factors, such as experimental set-up and image pre-processing, colour and size calibrations, on the method of identification are discussed in detail. A noise reduction parameter and the diffusion velocity of the crystal boundary are also considered. The results show that the proposed method can in principle provide a good representation of the dendritic growth anisotropy of any system
The Kinetic Basis of Morphogenesis
It has been shown recently (Shalygo, 2014) that stationary and dynamic
patterns can arise in the proposed one-component model of the analog
(continuous state) kinetic automaton, or kinon for short, defined as a
reflexive dynamical system with active transport. This paper presents
extensions of the model, which increase further its complexity and tunability,
and shows that the extended kinon model can produce spatio-temporal patterns
pertaining not only to pattern formation but also to morphogenesis in real
physical and biological systems. The possible applicability of the model to
morphogenetic engineering and swarm robotics is also discussed.Comment: 8 pages. Submitted to the 13th European Conference on Artificial Life
(ECAL-2015) on March 10, 2015. Accepted on April 28, 201
Identification of geometrical models of interface evolution for dendritic crystal growth
This paper introduces a method for identifying geometrical models of interface evolution, directly from experimental imaging data. These local growth models relate
normal growth velocity to curvature and its derivatives estimated along the growing interface. Such models can reproduce many qualitative features of dendritic crystal
growth as well as predict quantitatively its early stages of evolution. Numerical simulations and experimental crystal growth data are used to demonstrate the applicability of this approach
Numerical computations of facetted pattern formation in snow crystal growth
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 anisotropic attachment kinetics. It is by now well understood that the
morphological stability of ice crystals strongly depends on supersaturation,
crystal size and temperature. Until very recently it was very difficult to
perform numerical simulations of this highly anisotropic crystal growth. In
particular, obtaining facet growth in combination with dendritic branching is a
challenging task. We present numerical simulations of snow crystal growth in
two and three space dimensions using a new computational method recently
introduced by the authors. We present both qualitative and quantitative
computations. In particular, a linear relationship between tip velocity and
supersaturation is observed. The computations also suggest that surface energy
effects, although small, have a larger effect on crystal growth than previously
expected. We compute solid plates, solid prisms, hollow columns, needles,
dendrites, capped columns and scrolls on plates. Although all these forms
appear in nature, most of these forms are computed here for the first time in
numerical simulations for a continuum model.Comment: 12 pages, 28 figure
Solution of dendritic growth in a binary alloy by a novel point automata method
The aim of this paper is simulation of thermally induced liquid-solid dendritic
growth in a binary alloy (Fe-0.6%C) steel in two dimensions by a coupled deterministic
continuum mechanics heat and species transfer model and a stochastic localized phase change
kinetics model that takes into account the undercooling, curvature, kinetic, and
thermodynamic anisotropy. The stochastic model receives temperature and concentration
information from the deterministic model and the deterministic heat and species diffusion
equations receive the solid fraction information from the stochastic model. The heat and
species transfer models are solved on a regular grid by the standard explicit Finite Difference
Method (FDM). The phase-change kinetics model is solved by the novel Point Automata (PA)
approach. The PA method was developed and introduced [1,2] in order to circumvent the
mesh anisotropy problem, associated with the classical Cellular Automata (CA) method.
Dendritic structures are in the CA approach sensitive on the relative angle between the cell
structure and the preferential crystal growth direction which is not physical. The CA approach
used in the paper for reference comparison is established on quadratic cells and Neumann
neighborhood. The PA approach is established on randomly distributed points and
neighborhood configuration, similar as appears in meshless methods. Both methods provide
same results in case of regular PA node arrangements and neighborhood configuration with
five points. A comparison between both stochastic approaches has been made with respect to
dendritic growth with different orientations of crystallographic angles. It is demonstrated that
the new PA method can cope with dendritic growth of a binary alloy in any direction which is
not the case with the CA method
Toward a Comprehensive Model of Snow Crystal Growth: 4. Measurements of Diffusion-limited Growth at -15 C
We present measurements of the diffusion-limited growth of ice crystals from
water vapor at different supersaturation levels in air at a temperature of -15
C. Starting with thin, c-axis ice needle crystals, the subsequent growth
morphologies ranged from blocky structures on the needle tips (at low
supersaturation) to thin faceted plates on the needle tips (at high
supersaturation). We successfully modeled the experimental data, reproducing
both growth rates and growth morphologies, using a cellular-automata method
that yields faceted crystalline structures in diffusion-limited growth. From
this quantitative analysis of well-controlled experimental measurements, we
were able to extract information about the attachment coefficients governing
ice growth under different circumstances. The results strongly support previous
work indicating that the attachment coefficient on the prism surface is a
function of the width of the prism facet. Including this behavior, we created a
comprehensive model at -15 C that explains all the experimental data. To our
knowledge, this is the first demonstration of a kinetic model that reproduces a
range of diffusion-limited ice growth behaviors as a function of
supersaturation
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