Two-cluster States Research Articles

Three-Cluster Equation Using the Two-Cluster RGM Kernel

We propose a new type of three-cluster equation which uses two-cluster resonating-group-method (RGM) kernels. In this equation, the orthogonality of the total wave-function to two-cluster Pauli-forbidden states is essential to eliminate redundant components admixed in the three-cluster systems. The explicit energy-dependence inherent in the exchange RGM kernel is self-consistently determined. For bound-state problems, this equation is straightforwardly transformed to the Faddeev equation which uses a modified singularity-free T-matrix constructed from the two-cluster RGM kernel. The approximation of the present three-cluster formalism can be examined with more complete calculation using the three-cluster RGM. As a simple example, we discuss three di-neutron (3d') and 3 alpha systems in the harmonic-oscillator variational calculation. The result of the Faddeev calculation is also presented for the 3' system.

Synchronization and Clustering of Arrays of Electrochemical Oscillators with Global Feedback

Experiments on chaotically oscillating arrays of nickel electrodes in sulfuric acid were carried out. A global feedback is added in which a signal proportional to the difference between the sum of the currents of all elements and a mean current is fed back to the applied potential. The addition of global feedback transforms a system of weakly coupled elements to one of complete synchronization. At intermediate feedback strengths, intermittent, unstable chaotic clusters are observed in which clusters of elements form and break up. Stable clusters or condensates form at somewhat higher feedback strengths. The stable clusters become periodic at higher gain; both two-cluster and three-cluster states are observed. With a further increase in the feedback gain, one of the clusters dominates the collective dynamics; its size increases until at some feedback strength the entire system is synchronized. Delay in the feedback signal also influences the interaction of the oscillators.

Transcritical loss of synchronization in coupled chaotic systems

The synchronization transition is described for a system of two asymmetrically coupled chaotic oscillators. Such a system can represent the two-cluster state in a large ensemble of globally coupled oscillators. It is shown that the transition can be typically mediated by a transcritical transversal bifurcation. The latter has a hard brunch that dominates the global dynamics, so that the synchronization transition is normally hard. For a particular example of coupled logistic maps a diversity of transition scenaria includes both local and global riddling. In the case of small non-identity of the interacting systems the riddling is shown to turn into an exterior or interior crisis.

Reentrant transitions in globally coupled active rotators with multiplicative and additive noises

We study the nonequilibrium phenomena in globally coupled active rotators with multiplicative and additive noises. It is shown that at a critical value of the multiplicative noise intensity the system undergoes noise-induced transition from a one-cluster state to a two-cluster state. Additive noise suppresses the effect of the multiplicative noise on the system, increasing the critical value of the multiplicative noise intensity. The system shows a reentrant transition at intermediate additive noise intensity.

Synchronization properties of spindle oscillations in a thalamic reticular nucleus model

1. We address the hypothesis of Steriade and colleagues that the thalamic reticular nucleus (RE) is a pacemaker for thalamocortical spindle oscillations by developing and analyzing a model of a large population of all-to-all coupled inhibitory RE neurons. 2. Each RE neuron has three ionic currents: a low-threshold T-type Ca2+ current (ICa-T), a calcium-activated potassium current (IAHP) and a leakage current (IL). ICa-T underlies a cell's postinhibitory rebound properties, whereas IAHP hyperpolarizes the neuron after a burst. Each neuron, which is a conditional oscillator, is coupled to all other RE neurons via fast gamma-aminobutyric acid-A (GABAA) and slow GABAB synapses. 3. For generating network oscillations IAHP may not be necessary. Synaptic inhibition can provide the hyperpolarization for deinactivating ICa-T that causes bursting if the reversal potentials for GABAA and GABAB synapses are sufficiently negative. 4. If model neurons display sufficiently powerful rebound excitability, an isolated RE network of such neurons oscillates with partial but typically not full synchrony. The neurons spontaneously segregate themselves into several macroscopic clusters. The neurons within a cluster follow the same time course, but the clusters oscillate differently from one another. In addition to activity patterns in which clusters burst sequentially (e.g., 2 or 3 clusters bursting alternately), a two-cluster state may occur with one cluster active and one quiescent. Because the neurons are all-to-all coupled, the cluster states do not have any spatial structure. 5. We have explored the sensitivity of such partially synchronized patterns to heterogeneity in cells' intrinsic properties and to simulated neuroelectric noise. Although either precludes precise clustering, modest levels of heterogeneity or noise lead to approximate clustering of active cells. The population-averaged voltage may oscillate almost regularly but individual cells burst at nearly every second cycle or less frequently. The active-quiescent state is not robust at all to heterogeneity or noise. Total asynchrony is observed when heterogeneity or noise is too large, e.g., even at 25% heterogeneity for our reference set of parameter values. 6. The fast GABAA inhibition (with a reversal potential more negative than, say, -65 mV) favors the cluster states and prevents full synchrony. Our simulation results suggest two mechanisms that can fully synchronize the isolated RE network model. With GABAA removed or almost totally blocked, GABAB inhibition (because it is slow) can lead to full synchrony, which is partially robust to heterogeneity and noise.(ABSTRACT TRUNCATED AT 400 WORDS)

Dynamics of a globally coupled laser model

We study analytically and numerically a model of N identical globally coupled lasers. We extend the discussion of the linear stability, presented in a recent paper [Silber et al., J. Opt. Soc. Am. B 10, 1121 (1993)] for general splay states. For semiconductor lasers, we find that the splay state is neutrally stable only for a narrow range \ensuremath{\Delta}, a parameter characterizing the splay state. We draw the phase diagram for semiconductor lasers using characteristic parameter values. We then analyze the model numerically, both for semiconductor lasers and for solid-state lasers. We also investigate the diffusion of the splay state on the solution branch in the presence of a noise term. Finally, we discuss the linear stability of the periodic two-cluster state found for semiconductor lasers.

Clustering and slow switching in globally coupled phase oscillators.

We consider a network of globally coupled phase oscillators. The interaction between any two of them is derived from a simple model of weakly coupled biological neurons and is a periodic function of the phase difference with two Fourier components. The collective dynamics of this network is studied with emphasis on the existence and the stability of clustering states. Depending on a control parameter, three typical types of dynamics can be observed at large time: a fully synchronized state of the network (one-cluster state), a totally incoherent state, and a pair of two-cluster states connected by heteroclinic orbits. This last regime is particularly sensitive to noise. Indeed, adding a small noise gives rise, in large networks, to a slow periodic oscillation between the two two-cluster states. The frequency of this oscillation is proportional to the logarithm of the noise intensity. These switching states should occur frequently in networks of globally coupled oscillators.

Non-spurious two-cluster harmonic oscillator wavefunctions

The authors consider a system of identical particles distributed in two clusters and described by harmonic oscillator wavefunctions. A set of non-spurious two-cluster states, whose centre-of-mass is at rest, is constructed. It is characterized by the cluster Yamanouchi symbols as well as by its overall permutational symmetry, angular momentum and total energy. Applications to nuclear cluster models, to the evaluation of nuclear spectroscopic factors, to the description of nuclei as quark-clusters, and to the study of interacting rare-gas clusters are pointed out.

Transition amplitudes in theN-body Faddeev-type theory

Within the framework of the Faddeev-type $N$ -body scattering formalism, we find the transition operators for all $N$ -body processes that start from two-cluster initial states, and construct the $N$ -body Faddeev-type equations they satisfy. In particular, we show that our previous $N$ -body generalizations of the three-body operator ${K}_{\ensuremath{\beta}\ensuremath{\alpha}}$ correspond to the $N$ -body scattering amplitudes for complete breakup, and that the Alt-Grassberger-Sandhas $N$ -body generalizations of the three-body transition operator ${U}_{\ensuremath{\beta}\ensuremath{\alpha}}$ correspond to $N$ -body elastic and rearrangement amplitudes. As an introduction, we give a simple derivation of the $N$ -body Faddeev-type equations for the wave-function components.