Identification of a spatio-temporal model of crystal growth based on boundary curvature

A new method of identifying the spatio-temporal transition rule of crystal growth is introduced based on the connection between growth kinetics and dentritic morphology. Using a modified three-point-method, curvatures of the considered crystal branch are calculated and curvature direction is used to measure growth velocity. A polynomial model is then produced based on a curvature-velocity relationship to represent the spatio-temporal growth process. A very simple simulation example is used initially to clearly explain the methodology. The results of identifying a model from a real crystal growth experiment show that the proposed method can produce a good representation of crystal growth

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

Identification of excitable media using a scalar coupled map lattice model

The identification problem for excitable media is investigated in this paper. A new scalar coupled map lattice (SCML) model is introduced and the orthogonal least squares algorithm is employed to determinate the structure of the SCML model and to estimate the associated parameters. A simulated pattern and a pattern observed directly from a real Belousov-Zhabotinsky reaction are identified. The identified SCML models are shown to possess almost the same local dynamics as the original systems and are able to provide good long term predictions

Spatio-temporal modelling of wave formation in an excitable chemical medium based on a revised FitzHugh-Nagumo model

The wavefront profile and the propagation velocity of waves in an experimentally observed Belousov-Zhabotinskii reaction are analyzed and a revised FitzHumgh-Nagumo(FHN) model of these systems is identified. The ratio between the excitation period and the recovery period, for a solitary wave are studied, and included within the model. Averaged travelling velocities at different spatial positions are shown to be consistent under the same experimental conditions. The relationship between the propagation velocity and the curvature of the wavefront are also studied to deduce the diffusion coefficient in the model, which is a function of the curvature of the wavefront and not a constant. The application of the identified model is demonstrated on real experimental data and validated using multi-step ahead predictions

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

Identification of radius-vector functions of interface evolution for star-shaped crystal growth

This paper introduces a new method based on a radius-vector function for identifying the spatio-temporal transition rule of star-shaped crystal growth directly from experimental crystal growth imaging data. From the morphology point of view, the growth is decomposed as initial conditions, uniform growth and directional growth, which is represented by a static polynomial model based on the Fourier expansion. A recursive model is also introduced to help understand the dynamic characteristics of the observed systems. The applicability of the proposed approach is demonstrated using data from a simulation and from a real crystal growth experiment