Grain growth from homogeneous initial conditions : anomalous grain growth and special scaling states - Jiang, Yi; Mombach, Jose Carlos Merino; Glazier, James Alexander
We used the large-Q Potts model on a two-dimensional lattice to study the evolution of the disordered cluster developed from a perfect hexagonal lattice with a single defect. The distribution functions were not stable, while the average area and the number of grains in the cluster grew linearly in time. However, the grains at the boundary of the cluster formed a well defined region which reached a special scaling state with time invariant distributions but no scale change, contrary to the result of Levitan [Boris Levitan, Phys. Rev. Lett. 72, 4057 (1994)]. The rate of propagation of disorder is the...
Resonant islands without separatrix chaos - Corso, Gilberto Luiz; Rizzato, Felipe Barbedo
An alternative type of Hamiltonian nonlinear resonant island is analyzed. In the usual case where the resonant island is pendulumlike, chains bifurcated out of the central elliptic point undergo infinite cascades of period-doubling bifurcations as they approach the island boundary. In the present case we find that those chains undergo either period doubling or inverse saddle-node bifurcations, depending on the strength of perturbing terms. In the saddle-node case we show that just after a reconnection process, external chains cross the island boundary to collapse against the bifurcated internal chains.
Neural networks with high-order connections - Arenzon, Jeferson Jacob; Almeida, Rita Maria Cunha de
We present results for two difFerent kinds of high-order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical simulations. An optimal learning algorithm for fourth-order connections is given that improves the storage capacity without increasing the weight of the higherorder term. While the behavior of one of the models qualitatively resembles the original Hopfield one, the other presents a new and very rich behavior: depending on the strength of the fourth-order connections and the temperature, the system presents two distinct retrieval regions separated by a gap,...
Mitosis and growth in biological tissues - Mombach, Jose Carlos Merino; Almeida, Rita Maria Cunha de; Iglesias, Jose Roberto
We present a simulation of the growth of a two-dimensional biological cellular system in which the cells experience mitosis whenever the (area)/(perimeter) ratio reaches a critical value. The model also includes the effect of interfacial energy and temperature. A stationary state with a constant average area is attained. We calculate the distribution of cells as a function of area, perimeter, and number of sides and also the two-cell correlation function. The results depend on temperature and are in agreement with experimental data, simulations, and theoretical models.