55 research outputs found
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 a temperature dependent FitzHugh-Nagumo model for the Belousov-Zhabotinskii reaction
This paper describes the identification of a temperature dependent FitzHugh-Nagumo model directly from experimental observations with controlled inputs. By studying the steady states and the trajectory of the phase of the variables, the stability of the model is analysed and a rule to generate oscillation waves is proposed.
The dependence of the oscillation frequency and propagation speed on the model parameters is then investigated to seek the appropriate control variables, which then become functions of temperature in the identified model. The results show that the proposed approach can provide a good representation of the dynamics of the oscillatory behaviour of a BZ reaction
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
Effective damping in the Raman cooling of trapped ions
We present a method of treating the interaction of a single three-level ion
with two laser beams. The idea is to apply a unitary transformation such that
the exact transformed Hamiltonian has one of the three levels decoupled for all
values of the detunings. When one takes into account damping, the evolution of
the system is governed by a master equation usually obtained via adiabatic
approximation under the assumption of far-detuned lasers. To go around the
drawbacks of this technique, we use the same unitary transformation to get an
effective master equation.Comment: 15 pages, 5 figures. To appear in Optics Communication
Mimicking a Kerrlike medium in the dispersive regime of second-harmonic generation
We find an effective Hamiltonian describing the process of second-harmonic
generation in the far-off resonant limit. We show that the dynamics of the
fundamental mode is governed by a Kerrlike Hamiltonian. Some dynamical
consequences are examined.Comment: 12 pages, 4 figures Submitted to Optics Communication
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