957 resultados para Reversible Hopf-zero bifurcation
Resumo:
The loss of dopamine in idiopathic or animal models of Parkinson's disease induces synchronized low-frequency oscillatory burst-firing in subthalamic nucleus neurones. We sought to establish whether these firing patterns observed in vivo were preserved in slices taken from dopamine-depleted animals, thus establishing a role for the isolated subthalamic-globus pallidus complex in generating the pathological activity. Mice treated with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) showed significant reductions of over 90% in levels of dopamine as measured in striatum by high pressure liquid chromatography. Likewise, significant reductions in tyrosine hydroxylase immunostaining within the striatum (>90%) and tyrosine hydroxylase positive cell numbers (65%) in substantia nigra were observed. Compared with slices from intact mice, neurones in slices from MPTP-lesioned mice fired significantly more slowly (mean rate of 4.2 Hz, cf. 7.2 Hz in control) and more irregularly (mean coefficient of variation of inter-spike interval of 94.4%, cf. 37.9% in control). Application of ionotropic glutamate receptor antagonists 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) and 2-amino-5-phosphonopentanoic acid (AP5) and the GABAA receptor antagonist picrotoxin caused no change in firing pattern. Bath application of dopamine significantly increased cell firing rate and regularized the pattern of activity in cells from slices from both MPTP-treated and control animals. Although the absolute change was more modest in control slices, the maximum dopamine effect in the two groups was comparable. Indeed, when taking into account the basal firing rate, no differences in the sensitivity to dopamine were observed between these two cohorts. Furthermore, pairs of subthalamic nucleus cells showed no correlated activity in slices from either control (21 pairs) or MPTP-treated animals (20 pairs). These results indicate that the isolated but interconnected subthalamic-globus pallidus network is not itself sufficient to generate the aberrant firing patterns in dopamine-depleted animals. More likely, inputs from other regions, such as the cortex, are needed to generate pathological oscillatory activity. © 2006 IBRO.
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We consider return-to-zero (RZ) pulses with random phase modulation propagating in a nonlinear channel (modelled by the integrable nonlinear Schrödinger equation, NLSE). We suggest two different models for the phase fluctuations of the optical field: (i) Gaussian short-correlated fluctuations and (ii) generalized telegraph process. Using the rectangular-shaped pulse form we demonstrate that the presence of phase fluctuations of both types strongly influences the number of solitons generated in the channel. It is also shown that increasing the correlation time for the random phase fluctuations affects the coherent content of a pulse in a non-trivial way. The result obtained has potential consequences for all-optical processing and design of optical decision elements.
Resumo:
The transition of internally heated inclined plane parallel shear flows is examined numerically for the case of finite values of the Prandtl number Pr. We show that as the strength of the homogeneously distributed heat source is increased the basic flow loses stability to two-dimensional perturbations of the transverse roll type in a Hopf bifurcation for the vertical orientation of the fluid layer, whereas perturbations of the longitudinal roll type are most dangerous for a wide range of the value of the angle of inclination. In the case of the horizontal inclination transverse roll and longitudinal roll perturbations share the responsibility for the prime instability. Following the linear stability analysis for the general inclination of the fluid layer our attention is focused on a numerical study of the finite amplitude secondary travelling-wave solutions (TW) that develop from the perturbations of the transverse roll type for the vertical inclination of the fluid layer. The stability of the secondary TW against three-dimensional perturbations is also examined and our study shows that for Pr=0.71 the secondary instability sets in as a quasi-periodic mode, while for Pr=7 it is phase-locked to the secondary TW. The present study complements and extends the recent study by Nagata and Generalis (2002) in the case of vertical inclination for Pr=0.
Resumo:
The authors study experimentally ~10 ps return-to-zero pulse propagation near the net dispersion zero of an optical fibre transmission line. Stable near-jitter-free propagation was observed over 70 Mm. Pulse stabilisation and ASE suppression were achieved through the saturable aborber mechanism of nonlinear polarisation rotation.
Resumo:
Non-linear solutions and studies of their stability are presented for flows in a homogeneously heated fluid layer under the influence of a constant pressure gradient or when the mass flux across any lateral cross-section of the channel is required to vanish. The critical Grashof number is determined by a linear stability analysis of the basic state which depends only on the z-coordinate perpendicular to the boundary. Bifurcating longitudinal rolls as well as secondary solutions depending on the streamwise x-coordinate are investigated and their amplitudes are determined as functions of the supercritical Grashof number for various Prandtl numbers and angles of inclination of the layer. Solutions that emerge from a Hopf bifurcation assume the form of propagating waves and can thus be considered as steady flows relative to an appropriately moving frame of reference. The stability of these solutions with respect to three-dimensional disturbances is also analyzed in order to identify possible bifurcation points for evolving tertiary flows.
Resumo:
The stability of internally heated convective flows in a vertical channel under the influence of a pressure gradient and in the limit of small Prandtl number is examined numerically. In each of the cases studied the basic flow, which can have two inflection points, loses stability at the critical point identified by the corresponding linear analysis to two-dimensional states in a Hopf bifurcation. These marginal points determine the linear stability curve that identifies the minimum Grashof number (based on the strength of the homogeneous heat source), at which the two-dimensional periodic flow can bifurcate. The range of stability of the finite amplitude secondary flow is determined by its (linear) stability against three-dimensional infinitesimal disturbances. By first examining the behavior of the eigenvalues as functions of the Floquet parameters in the streamwise and spanwise directions we show that the secondary flow loses stability also in a Hopf bifurcation as the Grashof number increases, indicating that the tertiary flow is quasi-periodic. Secondly the Eckhaus marginal stability curve, that bounds the domain of stable transverse vortices towards smaller and larger wavenumbers, but does not cause a transition as the Grashof number increases, is also given for the cases studied in this work.
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The transmission of weak signals through the visual system is limited by internal noise. Its level can be estimated by adding external noise, which increases the variance within the detecting mechanism, causing masking. But experiments with white noise fail to meet three predictions: (a) noise has too small an influence on the slope of the psychometric function, (b) masking occurs even when the noise sample is identical in each two-alternative forced-choice (2AFC) interval, and (c) double-pass consistency is too low. We show that much of the energy of 2D white noise masks extends well beyond the pass-band of plausible detecting mechanisms and that this suppresses signal activity. These problems are avoided by restricting the external noise energy to the target mechanisms by introducing a pedestal with a mean contrast of 0% and independent contrast jitter in each 2AFC interval (termed zero-dimensional [0D] noise). We compared the jitter condition to masking from 2D white noise in double-pass masking and (novel) contrast matching experiments. Zero-dimensional noise produced the strongest masking, greatest double-pass consistency, and no suppression of perceived contrast, consistent with a noisy ideal observer. Deviations from this behavior for 2D white noise were explained by cross-channel suppression with no need to appeal to induced internal noise or uncertainty. We conclude that (a) results from previous experiments using white pixel noise should be re-evaluated and (b) 0D noise provides a cleaner method for investigating internal variability than pixel noise. Ironically then, the best external noise stimulus does not look noisy.
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A method of all-optical passive quasi-regeneration in transoceanic 40 Gbit/s return-to-zero transmission systems with strong dispersion management was described. The use of in-line nonlinear optical loop mirrors (NOLM) by the method was demonstrated. The quasi-regeneration of signals performed by NOLMs was found to improve the systems's performance.
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Controlled polymerization of 2-chloro-1,3-butadiene using reversible addition–fragmentation chain transfer (RAFT) polymerization has been demonstrated for the first time. 2-Chloro-1,3-butadiene, more commonly known as chloroprene, has significant industrial relevance as a crosslinked rubber, with uses ranging from adhesives to integral automotive components. However, problems surrounding the inherent toxicity of the lifecycle of the thiourea-vulcanized rubber have led to the need for control over the synthesis of poly(2-chloro-1,3-butadiene). To this end, four chain transfer agents in two different solvents have been trialed and the kinetics are discussed. 2-Cyano-2-propylbenzodithioate (CPD) is shown to polymerize 2-chloro-1,3-butadiene in THF, using AIBN as an initiator, with complete control over the target molecular weight, producing polymers with low polydispersities (Mw/Mn < 1.25 in all cases).
Resumo:
The authors study experimentally ~10 ps return-to-zero pulse propagation near the net dispersion zero of an optical fibre transmission line. Stable near-jitter-free propagation was observed over 70 Mm. Pulse stabilisation and ASE suppression were achieved through the saturable aborber mechanism of nonlinear polarisation rotation.
Resumo:
This paper compares the experience of forecasting the UK government bond yield curve before and after the dramatic lowering of short-term interest rates from October 2008. Out-of-sample forecasts for 1, 6 and 12 months are generated from each of a dynamic Nelson-Siegel model, autoregressive models for both yields and the principal components extracted from those yields, a slope regression and a random walk model. At short forecasting horizons, there is little difference in the performance of the models both prior to and after 2008. However, for medium- to longer-term horizons, the slope regression provided the best forecasts prior to 2008, while the recent experience of near-zero short interest rates coincides with a period of forecasting superiority for the autoregressive and dynamic Nelson-Siegel models. © 2014 John Wiley & Sons, Ltd.