Spatial updating, spatial transients, and regularities of a complex automaton with nonperiodic architecture

We study the dynamics of patterns exhibited by rule 52, a totalistic cellular automaton displaying intricate behaviors and wide regions of active/inactive synchronization patches. Systematic computer simulations involving 230 initial configurations reveal that all complexity in this automaton originates from random juxtaposition of a very small number of interfaces delimiting active/inactive patches. Such interfaces are studied with a sidewise spatial updating algorithm. This novel tool allows us to prove that the interfaces found empirically are the only interfaces possible for these periods, independently of the size of the automata. The spatial updating algorithm provides an alternative way to determine the dynamics of automata of arbitrary size, a way of taking into account the complexity of the connections in the lattice

Multistability, phase diagrams, and intransitivity in the Lorenz-84 low-order atmospheric circulation model

We report phase diagrams detailing the intransitivity observed in the climate scenarios supported by a prototype atmospheric general circulation model, namely, the Lorenz-84 low-order model. So far, this model was known to have a pair of coexisting climates described originally by Lorenz. Bifurcation analysis allows the identification of a remarkably wide parameter region where up to four climates coexist simultaneously. In this region the dynamical behavior depends crucially on subtle and minute tuning of the model parameters. This strong parameter sensitivity makes the Lorenz-84 model a promising candidate of testing ground to validate techniques of assessing the sensitivity of low-order models to perturbations of parameters

Some matrix elements for morse oscillators

In this paper general working equations for the Morse (r-r,)' rnatrix elements are given. These equations can be used to calculate the diagonal (m = n ) matrix elements and, for the off-diagonal (m≠n) elements, are simpler to use than the ones currently available in the literature. Also, in this paper a new approach is given which allows one to obtain simple formulas, in closed forrn, for the off-diagonal matrix elements. Explicit expressions are given for 1 = 1, 2, and 3

Some matrix elements for morse oscillators

In this paper general working equations for the Morse (r-r,)' rnatrix elements are given. These equations can be used to calculate the diagonal (m = n ) matrix elements and, for the off-diagonal (m≠n) elements, are simpler to use than the ones currently available in the literature. Also, in this paper a new approach is given which allows one to obtain simple formulas, in closed forrn, for the off-diagonal matrix elements. Explicit expressions are given for 1 = 1, 2, and 3

Distribuição da intensidade no espectro vibracional de moléculas diatômicas : comparação teórica e experimental nos sistemas N2(2+) e N2(1-)

Este trabalho consiste num estudo de espectroscopia de moléculas diatômicas.Spectroscopic properties of diatomic molecules are investigated

Distribuição da intensidade no espectro vibracional de moléculas diatômicas : comparação teórica e experimental nos sistemas N2(2+) e N2(1-)

Este trabalho consiste num estudo de espectroscopia de moléculas diatômicas.Spectroscopic properties of diatomic molecules are investigated

Infinite hierarchies of nonlinearly dependent periodic orbits

Quadratic maps are used to show explicitly that the skeleton of unstable periodic orbits underlying classical and quantum dynamics is stratified into a doubly infinite hierarchy of orbits inherited from a set of basic ‘‘seeds’’ through certain nonlinear transformations Tα(x). The hierarchy contains nonunique substructurings which arise from the different possibilities of sequencing the transformations Tα(x). The structuring of the orbital skeleton is shown to be generic for Abelian equations, i.e., for all dynamical systems generated by iterating rational functions