The interaction of flexural-gravity waves with periodic geometries

A periodic structure of finite extent is embedded within an otherwise uniform two-dimensional system consisting of finite-depth fluid covered by a thin elastic plate. An incident harmonic flexural-gravity wave is scattered by the structure. By using an approximation to the corresponding linearised boundary value problem that is based on a slowly varying structure in conjunction with a transfer matrix formulation, a method is developed that generates the whole solution from that for just one cycle of the structure, providing both computational savings and insight into the scattering process. Numerical results show that variations in the plate produce strong resonances about the ‘Bragg frequencies’ for relatively few periods. We find that certain geometrical variations in the plate generate these resonances above the Bragg value, whereas other geometries produce the resonance below the Bragg value. The familiar resonances due to periodic bed undulations tend to be damped by the plate.

Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

Enrichment and stability: a phenomenological coupling of energy value and carrying capacity

Simple predator–prey models with a prey-dependent functional response predict that enrichment (increased carrying capacity) destabilizes community dynamics: this is the ‘paradox of enrichment’. However, the energy value of prey is very important in this context. The intraspecific chemical composition of prey species determines its energy value as a food for the potential predator. Theoretical and experimental studies establish that variable chemical composition of prey affects the predator–prey dynamics. Recently, experimental and theoretical approaches have been made to incorporate explicitly the stoichiometric heterogeneity of simple predator–prey systems. Following the results of the previous experimental and theoretical advances, in this article we propose a simple phenomenological formulation of the variation of energy value at increased level of carrying capacity. Results of our study demonstrate that coupling the parameters representing the phenomenological energy value and carrying capacity in a realistic way, may avoid destabilization of community dynamics following enrichment. Additionally, under such coupling the producer–grazer system persists for only an intermediate zone of production—a result consistent with recent studies. We suggest that, while addressing the issue of enrichment in a general predator–prey model, the phenomenological relationship that we propose here might be applicable to avoid Rosenzweig’s paradox.

On the quasi-periodic nature of magnetopause flux transfer events

The recurrence rate of flux transfer events (FTEs) observed near the dayside magnetopause is discussed. A survey of magnetopause observations by the ISEE satellites shows that the distribution of the intervals between FTE signatures has a mode value of 3 min, but is highly skewed, having upper and lower decile values of 1.5 min and 18.5 min, respectively. The mean value is found to be 8 min, consistent with previous surveys of magnetopause data. The recurrence of quasi-periodic events in the dayside auroral ionosphere is frequently used as evidence for an association with magnetopause FTEs, and the distribution of their repetition intervals should be matched to that presented here if such an association is to be confirmed. A survey of 1 year's 15-s data on the interplanetary magnetic field (IMF) suggests that the derived distribution could arise from fluctuations in the IMF Bz component, rather than from a natural oscillation frequency of the magnetosphere-ionosphere system.

Precession and nutation in the eta Carinae binary system: evidence from the X-ray light curve

It is believed that eta Carinae is actually a massive binary system, with the wind-wind interaction responsible for the strong X-ray emission. Although the overall shape of the X-ray light curve can be explained by the high eccentricity of the binary orbit, other features like the asymmetry near periastron passage and the short quasi-periodic oscillations seen at those epochs have not yet been accounted for. In this paper we explain these features assuming that the rotation axis of eta Carinae is not perpendicular to the orbital plane of the binary system. As a consequence, the companion star will face eta Carinae on the orbital plane at different latitudes for different orbital phases and, since both the mass-loss rate and the wind velocity are latitude dependent, they would produce the observed asymmetries in the X-ray flux. We were able to reproduce the main features of the X-ray light curve assuming that the rotation axis of eta Carinae forms an angle of 29 degrees +/- 4 degrees with the axis of the binary orbit. We also explained the short quasi-periodic oscillations by assuming nutation of the rotation axis, with an amplitude of about 5 degrees and a period of about 22 days. The nutation parameters, as well as the precession of the apsis, with a period of about 274 years, are consistent with what is expected from the torques induced by the companion star.

Acquisition of Pavlovian Fear Conditioning Using beta-Adrenoceptor Activation of the Dorsal Premammillary Nucleus as an Unconditioned Stimulus to Mimic Live Predator-Threat Exposure

In the present work, we sought to mimic the internal state changes in response to a predator threat by pharmacologically stimulating the brain circuit involved in mediating predator fear responses, and explored whether this stimulation would be a valuable unconditioned stimulus (US) in an olfactory fear conditioning paradigm (OFC). The dorsal premammillary nucleus (PMd) is a key brain structure in the neural processing of anti-predatory defensive behavior and has also been shown to mediate the acquisition and expression of anti-predatory contextual conditioning fear responses. Rats were conditioned by pairing the US, which was an intra-PMd microinjection of isoproterenol (ISO; beta-adrenoceptor agonist), with amyl acetate odor-the conditioned stimulus (CS). ISO (10 and 40 nmol) induced the acquisition of the OFC and the second-order association by activation of beta-1 receptors in the PMd. Furthermore, similar to what had been found for contextual conditioning to a predator threat, atenolol (beta-1 receptor antagonist) in the PMd also impaired the acquisition and expression of OFC promoted by ISO. Considering the strong glutamatergic projections from the PMd to the dorsal periaqueductal gray (dPAG), we tested how the glutamatergic blockade of the dPAG would interfere with the OFC induced by ISO. Accordingly, microinjections of NMDA receptor antagonist (AP5, 6 nmol) into the dPAG were able to block both the acquisition, and partially, the expression of the OFC. In conclusion, we have found that PMd beta-1 adrenergic stimulation is a good model to mimic predatory threat-induced internal state changes, and works as a US able to mobilize the same systems involved in the acquisition and expression of predator-related contextual conditioning. Neuropsychopharmacology (2011) 36, 926-939; doi:10.1038/npp.2010.231; published online 5 January 2011

New Perspectives on beta-Adrenergic Mediation of Innate and Learned Fear Responses to Predator Odor

In the present study, we investigated the role of noradrenergic transmission in unconditioned and conditioned responses to predatory threats. First, we examined the effects of systemically injected beta-blockers on unconditioned and contextual conditioned response to cat odor. The centrally acting beta-blocker (propranolol) was able to impair unconditioned responses, as well as the acquisition of the contextual fear to cat odor; however, the peripherally acting (nadolol) was not effective. Next, we examined the neural substrate underlying the noradrenergic modulation of the defensive response to cat odor and focused on the dorsal premammillary nucleus (PMd), because it represents the hypothalamic site most responsive to predatory threats and, at the same time, presents a dense plexus of noradrenergic fibers. We were able to see that propranolol significantly reduced PMd-Fos expression in response to cat odor and that beta-adrenoceptor blockade in the PMd, before cat odor exposure, reduced defensive responses to the cat odor and to the cat odor-related environment. We have also shown that beta-adrenoceptor blockade in the PMd, before the exposure to cat odor-related context, impaired the contextual conditioned responses. Overall, the present results provide convincing evidence suggesting that central noradrenergic mediation is critical for the expression of unconditioned and contextual conditioned antipredatory responses. We have further shown that the PMd appears to be an important locus to mediate these beta-adrenoceptor effects.

Sensing danger through the olfactory system: The role of the hypothalamic dorsal premammillary nucleus

The dorsal premammillary nucleus (PMd) has a critical role on the expression of defensive responses to predator odor. Anatomical evidence suggests that the PMd should also modulate memory processing through a projecting branch to the anterior thalamus. By using a pharmacological blockade of the PMd with the NMDA-receptor antagonist 2-amino-5-phosphonopentanoic acid (AP5), we were able to confirm its role in the expression of unconditioned defensive responses, and further revealed that the nucleus is also involved in influencing associative mechanisms linking predatory threats to the related context. We have also tested whether olfactory fear conditioning, using coffee odor as CS, would be useful to model predator odor. Similar to cat odor, shock-paired coffee odor produced robust defensive behavior during exposure to the odor and to the associated context. Shock-paired coffee odor also up-regulated Fos expression in the PMd, and, as with cat odor, we showed that this nucleus is involved in the conditioned defensive responses to the shock-paired coffee odor and the contextual responses to the associated environment. (C) 2008 Elsevier Ltd. All rights reserved.

Dissecting the brain`s fear system reveals the hypothalamus is critical for responding in subordinate conspecific intruders

Effective defense against natural threats in the environment is essential for the survival of individual animals. Thus, instinctive behavioral responses accompanied by fear have evolved to protect individuals from predators and from opponents of the same species (dominant conspecifics). While it has been suggested that all perceived environmental threats trigger the same set of innately determined defensive responses, we tested the alternate hypothesis that different stimuli may evoke differentiable behaviors supported by distinct neural circuitry. The results of behavioral, neuronal immediate early gene activation, lesion, and neuroanatomical experiments indicate that the hypothalamus is necessary for full expression of defensive behavioral responses in a subordinate conspecific, that lesions of the dorsal premammillary nucleus drastically reduce behavioral measures of fear in these animals, and that essentially separate hypothalamic circuitry supports defensive responses to a predator or a dominant conspecific. It is now clear that differentiable neural circuitry underlies defensive responses to fear conditioning associated with painful stimuli, predators, and dominant conspecifics and that the hypothalamus is an essential component of the circuitry for the latter two stimuli.

Role of glutamate NMDA receptors and nitric oxide located within the periaqueductal gray on defensive behaviors in mice confronted by predator

The midbrain periaqueductal gray (PAG) is part of the brain system involved in active defense reactions to threatening stimuli. Glutamate N-methyl-d-aspartate (NMDA) receptor activation within the dorsal column of the PAG (dPAG) leads to autonomic and behavioral responses characterized as the fear reaction. Nitric oxide (NO) has been proposed to be a mediator of the aversive action of glutamate, since the activation of NMDA receptors in the brain increases NO synthesis. We investigated the effects of intra-dPAG infusions of NMDA on defensive behaviors in mice pretreated with a neuronal nitric oxide synthase (nNOS) inhibitor [N omega-propyl-l-arginine (NPLA)], in the same midbrain site, during a confrontation with a predator in the rat exposure test (RET). Male Swiss mice received intra-dPAG injections of NPLA (0.1 or 0.4 nmol/0.1 mu l), and 10 min later, they were infused with NMDA (0.04 nmol/0.1 mu l) into the dPAG. After 10 min, each mouse was placed in the RET. NMDA treatment enhanced avoidance behavior from the predator and markedly increased freezing behavior. These proaversive effects of NMDA were prevented by prior injection of NPLA. Furthermore, defensive behaviors (e.g., avoidance, risk assessment, freezing) were consistently reduced by the highest dose of NPLA alone, suggesting an intrinsic effect of nitric oxide on defensive behavior in mice exposed to the RET. These findings suggest a potential role of glutamate NMDA receptors and NO in the dPAG in the regulation of defensive behaviors in mice during a confrontation with a predator in the RET.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Periodic window arising in the parameter space of an impact oscillator

In the bi-dimensional parameter space of an impact-pair system, shrimp-shaped periodic windows are embedded in chaotic regions. We show that a weak periodic forcing generates new periodic windows near the unperturbed one with its shape and periodicity. Thus, the new periodic windows are parameter range extensions for which the controlled periodic oscillations substitute the chaotic oscillations. We identify periodic and chaotic attractors by their largest Lyapunov exponents. (C) 2010 Elsevier B.V. All rights reserved.

Bubbling transition to spatial mode excitation in an extended dynamical system

We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable. (C) 2008 Elsevier B.V. All rights reserved.

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Reentrant quantum Hall effect in bilayer system at high filling factors

We report on the measurements of the quantum Hall effect states in double quantum well structures at the filling factors v = 4N + 1 and 4N + 3, where N is the Landau index number, in the presence of the in-plane magnetic field. The quantum Hall states at these filling factors vanish and reappear several times. Repeated reentrance of the transport gap occurs due to the periodic vanishing of the tunneling amplitude in the presence of the in-plane field. When the gap vanishes, the transport becomes anisotropic. The anisotropy persist at half-odd filling factors, when bilayer quantum Hall states are recovered with increase of the tilt angle. (C) 2007 Elsevier B.V. All rights reserved.