Integral behaviour for localized synchronization in nonidentical extended systems

We report the synchronization of two nonidentical spatially extended fields, ruled by one-dimensional complex Ginzburg-Landau equations. The two fields are prepared in different dynamical regimes, and interact via an imperfect coupling consisting of a given number of local controllers Nc . The strength of the coupling is ruled by the parameter «. We show that, in the limit of three controllers per correlation length, the synchronization behavior is not affected if the product «Nc /N is kept constant, providing a sort of integral behavior for localized synchronization

Extended bidomain modeling of defibrillation: quantifying virtual electrode strengths in fibrotic myocardium

Defibrillation is a well-established therapy for atrial and ventricular arrhythmia. Here, we shed light on defibrillation in the fibrotic heart. Using the extended bidomain model of electrical conduction in cardiac tissue, we assessed the influence of fibrosis on the strength of virtual electrodes caused by extracellular electrical current. We created one-dimensional models of rabbit ventricular tissue with a central patch of fibrosis. The fibrosis was incorporated by altering volume fractions for extracellular, myocyte and fibroblast domains. In our prior work, we calculated these volume fractions from microscopic images at the infarct border zone of rabbit hearts. An average and a large degree of fibrosis were modeled. We simulated defibrillation by application of an extracellular current for a short duration (5 ms). We explored the effects of myocyte-fibroblast coupling, intra-fibroblast conductivity and patch length on the strength of the virtual electrodes present at the borders of the normal and fibrotic tissue. We discriminated between effects on myocyte and fibroblast membranes at both borders of the patch. Similarly, we studied defibrillation in two-dimensional models of fibrotic tissue. Square and disk-like patches of fibrotic tissue were embedded in control tissue. We quantified the influence of the geometry and fibrosis composition on virtual electrode strength. We compared the results obtained with a square and disk shape of the fibrotic patch with results from the one-dimensional simulations. Both, one- and two-dimensional simulations indicate that extracellular current application causes virtual electrodes at boundaries of fibrotic patches. A higher degree of fibrosis and larger patch size were associated with an increased strength of the virtual electrodes. Also, patch geometry affected the strength of the virtual electrodes. Our simulations suggest that increased fibroblast-myocyte coupling and intra-fibroblast conductivity reduce virtual electrode strength. However, experimental data to constrain these modeling parameters are limited and thus pinpointing the magnitude of the reduction will require further understanding of electrical coupling of fibroblasts in native cardiac tissues. We propose that the findings from our computational studies are important for development of patient-specific protocols for internal defibrillators

Thermal convection in a rotating binary viscoelastic liquid mixture

In this work we report theoretical and numerical results on convection in a viscoelastic binary mixture under rotation. In particular, we focus in the Maxwelian case of viscoelastic fluid. We obtain explicit expressions for the convective thresholds in terms of the mixture parameters of the system in the case of idealized boundary conditions. We also calculate numerically the convective thresholds for the case of realistic rigid-rigid boundary conditions

Anomalous synchronization of spatially extended chaotic systems in the presence of asymmetric coupling

Communicated by Werner Ebeling and Bernardo Spagnolo This paper describes the e ects of an asymmetric coupling in the synchronization of two spatially extended systems. Namely, we report the consequences induced by the presence of asymmetries in the coupling con guration of a pair of one-dimensional elds obeying Complex Ginzburg Landau equations. While synchronization always occurs for large enough coupling strengths, asymmetries have the e ect of enhancing synchronization and play a crucial role in setting the threshold for the appearance of the synchronized dynamics, as well as in selecting the statistical and dynamical properties of the synchronized motion. We discuss the process of synchronization in the presence of asymmetries by using some analytic expansions valid for a regime of soft spatial temporal chaos (i.e. phase turbulence regime). The in uence of phase singularities that break the validity of the analysis is also discussed

Controlling and synchronizating space time chaos

Control and synchronization of continuous space-extended systems is realized by means of a finite number of local tiny perturbations. The perturbations are selected by an adaptive technique, and they are able to restore each of the independent unstable patterns present within a space time chaotic regime, as well as to synchronize two space time chaotic states. The effectiveness of the method and the robustness against external noise is demonstrated for the amplitude and phase turbulent regimes of the one-dimensional complex Ginzburg-Landau equation. The problem of the minimum number of local perturbations necessary to achieve control is discussed as compared with the number of independent spatial correlation lengths

Dissipative dynamics of an open Bose Einstein condensate

As an atomic Bose Einstein condensate BEC.is coupled to a source of uncondensed atoms at the same temperature and to a sink extraction towards an atom laser.the idealized description in terms of a Gross–Pitaevsky equation GP. no longer holds. Under suitable physical assumptions we show that the dissipative BEC obeys a Complex Ginzburg Landau equation CGL.and for some parameter range it undergoes a space time patterning. As a consequence, the density of BEC atoms within the trap displays non trivial space time correlations, which can be detected by monitoring the density profile of the outgoing atom laser. The patterning condition requires a negative scattering length, as e.g. in 7Li. In such a case we expect a many domain collapsed regime, rather than a single one as reported for a closed BEC. q2000 Elsevier Science B.V. All rights reserved

Synchronization of spatially extended chaotic systems with asymmetric coupling

In this paper, we report the consequences induced by the presence of asymmetries in the coupling scheme on the synchronization process of a pair of one-dimensional complex fields obeying Complex Ginzburg Landau equations. While synchronization always occurs for large enough coupling strengths, asymmetries have the effect of modifying synchronization thresholds and play a crucial role in selecting the statistical and dynamical properties of the highly coupled synchronized motion. Possible consequences of such symmetry induced effects in biological and natural systems are discussed

Characterization of synchronization spatiotemporal states in coupled non identical complex Ginzburg-Landau equations.

We characterize the synchronization of two nonidentical spatially extended elds ruled by onedimensional Complex Ginzburg{Landau equations, in the two regimes of phase and amplitude turbulence. If two elds display the same dynamical regime, the coupling induces a transition to a completely synchronized state. When, instead, the two elds are in di erent dynamical regimes, the transition to complete synchronization is mediated by defect synchronization. In the former case, the synchronized manifold is dynamically equivalent to that of the unsynchronized systems, while in the latter case the synchronized state substantially di ers from the unsynchronized one, and it is mainly dictated by the synchronization process of the space-time defects

On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems

In a previous paper, Elorza and Burillo explored the coherence property in fuzzy consequence operators. In this paper we show that fuzzy closing operators of mathematical morphology are always coherent operators. We also show that the coherence property is the key to link the four following families: fuzzy closing morphological operators, fuzzy consequence operators, fuzzy preorders and fuzzy closure and co-closure systems. This will allow to translate important well-known properties from the field of approximate reasoning to the field of image processing

Asymmetric coupling effects in the synchronization of spatially extended chaotic systems

We analyze the effects of asymmetric couplings in setting different synchronization states for a pair of unidimensional fields obeying complex Ginzburg-Landau equations. Novel features such as asymmetry enhanced complete synchronization, limits for the appearance of phase synchronized states, and selection of the final synchronized dynamics are reported and characterized