Turbulence in Globally Coupled Maps

The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map lattices. New features arise in the globally coupled system; for instance, the transition to turbulence takes place discontinuously at some critical values of the parameters of the system. The critical boundaries between different regimes (laminar, turbulent and fully turbulent) of the system are calculated on the parameter space. Windows of turbulence are present on some ranges of the coupling parameter. The system also exhibits nontrivial collective behavior. A map for the instantaneous fraction of turbulent elements is proposed. This map describes many of the observed properties of the system.Comment: 6 pages LaTeX; 6 figures available upon request from authors. To appear in Phys. Rev. E (1996

Information transfer and nontrivial collective behavior in chaotic coupled map networks

The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local unit possesses about the collective dynamics. Applications to locally and globally coupled map systems are considered. The prediction error exhibits phase transitions at critical values of the coupling for the onset of ordered collective behavior in these networks. This information measure may be used as an order parameter for the characterization of complex behavior in extended chaotic systems.Comment: 4 pp.,4 figs., Accepted in Phys. Rev. E, Rapid Communications (2002

Hierarchical Model for the Evolution of Cloud Complexes

The structure of cloud complexes appears to be well described by a "tree structure" representation when the image is partitioned into "clouds". In this representation, the parent-child relationships are assigned according to containment. Based on this picture, a hierarchical model for the evolution of Cloud Complexes, including star formation, is constructed, that follows the mass evolution of each sub-structure by computing its mass exchange (evaporation or condensation) with its parent and children, which depends on the radiation density at the interphase. For the set of parameters used as a reference model, the system produces IMFs with a maximum at too high mass (~2 M_sun) and the characteristic times for evolution seem too long. We show that these properties can be improved by adjusting model parameters. However, the emphasis here is to illustrate some general properties of this nonlinear model for the star formation process. Notwithstanding the simplifications involved, the model reveals an essential feature that will likely remain if additional physical processes are included. That is: the detailed behavior of the system is very sensitive to variations on the initial and external conditions, suggesting that a "universal" IMF is very unlikely. When an ensemble of IMFs corresponding to a variety of initial or external conditions is examined, the slope of the IMF at high masses shows variations comparable to the range derived from observational data. (Abridged)Comment: Latex, 29 pages, 13 figures, accepted for publication in Ap

On the Thermal Instability in a Contracting Gas Cloud and Formation of a Bound Cluster

We perform linear analysis of thermal instability in a contracting large cloud filled with warm HI gas and investigate the effect of metallicity and radiation flux. When the cloud reaches critical density n_f, the cloud fragments into cool, dense condensations because of thermal instability. For a lower metallicity gas cloud, the value of n_f is high. Collision between condensations will produce self-gravitating clumps and stars thereafter. From the result of calculation, we suggest that high star formation efficiency and bound cluster formation are realized in low-metallicity and/or strong-radiation environments.Comment: 7 pages, including 7 figures, LaTeX2e(emulateapj5.sty) To appear in ApJ, Jun 10, 200

Dynamics of Coupling Functions in Globally Coupled Maps: Size, Periodicity and Stability of Clusters

It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the formation of clusters in a globally coupled map system and the resulting periodicity of the global interaction. The allowed distributions of elements among periodic clusters is also found to depend on the functional form of the coupling. Through the analogy between globally coupled maps and a single driven map, the clustering behavior of the former systems can be characterized. By using this analogy, the dynamics of periodic clusters in systems displaying a constant global coupling are predicted; and for a particular family of coupling functions, it is shown that the stability condition of these clustered states can straightforwardly be derived.Comment: 12 pp, 5 figs, to appear in PR

Interleukin-1beta tear concentration in glaucomatous and ocular hypertensive patients treated with preservative-free nonselective beta-blockers

PURPOSE: To evaluate the ocular surface inflammatory response to the presence of preservatives in nonselective beta-blocker eyedrops. DESIGN: Prospective, crossover, single-masked, randomized clinical study. METHODS: STUDY POPULATION: Twenty primary open angle glaucoma or ocular hypertensive patients were divided in two groups, one treated with preservative-free timolol 0.5% (group 1) and the other with preserved timolol 0.5% (group 2) eyedrops. After 60 days of therapy and 3 more weeks of washout, the two groups switched to the other therapy. PROCEDURE: At each visit,basal tear samples were collected from the inferior conjunctival fornix for the determination of interleukin (IL)-1 tear concentrations by an enzyme-linked immunosorbent assay. Intraocular pressure measurement, conjunctival hyperemia, superficial punctate keratitis, and tear film breakup time were evaluated. MAIN OUTCOME MEASURE: IL-1 concentration in tears following the use of preserved eyedrops. RESULTS: IL-1 tear concentrations increased significantly in both groups, compared with baseline values,during preserved timolol therapy. There were no statistically significant changes in hyperemia and superficial punctate keratitis throughout the study in either group.A statistically significant breakup time reduction was observed in both groups after 30 days and after 60 days of preserved therapy. CONCLUSION: The use of preservatives in timolol 0.5% eyedrops leads to tear film instability and ocular surface inflammatory changes documented by a reduction of breakup time and an increase of IL-1 tear concentrations.Preservative-free beta-blockers are preferable for long-term hypotensive therapy to prevent ocular surface inflammation

Emergence of patterns in driven and in autonomous spatiotemporal systems

The relationship between a driven extended system and an autonomous spatiotemporal system is investigated in the context of coupled map lattice models. Specifically, a locally coupled map lattice subjected to an external drive is compared to a coupled map system with similar local couplings plus a global interaction. It is shown that, under some conditions, the emergent patterns in both systems are analogous. Based on the knowledge of the dynamical responses of the driven lattice, we present a method that allows the prediction of parameter values for the emergence of ordered spatiotemporal patterns in a class of coupled map systems having local coupling and general forms of global interactions.Comment: 7 pages, 3 figs, submitted to PRE (2002

Simple Models for Turbulent Self-Regulation in Galaxy Disks

We propose that turbulent heating, wave pressure and gas exchanges between different regions of disks play a dominant role in determining the preferred, quasi-equilibrium, self-similar states of gas disks on large-scales. We present simple families of analytic, thermohydrodynamic models for these global states, which include terms for turbulent pressure and Reynolds stresses. Star formation rates, phase balances, and hydrodynamic forces are all tightly coupled and balanced. The models have stratified radial flows, with the cold gas slowly flowing inward in the midplane of the disk, and with the warm/hot phases that surround the midplane flowing outward. The models suggest a number of results that are in accord with observation, as well as some novel predictions, including the following. 1) The large-scale gas density and thermal phase distributions in galaxy disks can be explained as the result of turbulent heating and spatial couplings. 2) The turbulent pressures and stresses that drive radial outflows in the warm gas also allow a reduced circular velocity there. This effect was observed by Swaters, Sancisi and van der Hulst in NGC 891, a particularly turbulent edge-on disk. The models predict that the effect should be universal in such disks. 3) They suggest that a star formation rate like the phenomenological Schmidt Law is the natural result of global thermohydrodynamical balance, and may not obtain in disks far from equilibrium. (Abridged)Comment: 37 pages, 1 gif figure, accepted for publication in the Astrophysical Journa

Periodicity Manifestations in the Turbulent Regime of Globally Coupled Map Lattice

We revisit the globally coupled map lattice (GCML). We show that in the so called turbulent regime various periodic cluster attractor states are formed even though the coupling between the maps are very small relative to the non-linearity in the element maps. Most outstanding is a maximally symmetric three cluster attractor in period three motion (MSCA) due to the foliation of the period three window of the element logistic maps. An analytic approach is proposed which explains successfully the systematics of various periodicity manifestations in the turbulent regime. The linear stability of the period three cluster attractors is investigated.Comment: 34 pages, 8 Postscript figures, all in GCML-MSCA.Zi