Multi-Phase Patterns in Periodically Forced Oscillatory Systems

Periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency. We study extended oscillatory systems that respond to uniform periodic forcing at one quarter of the forcing frequency (the 4:1 resonance). These systems possess four coexisting stable states, corresponding to uniform oscillations with successive phase shifts of $\pi/2$. Using an amplitude equation approach near a Hopf bifurcation to uniform oscillations, we study front solutions connecting different phase states. These solutions divide into two groups: $\pi$-fronts separating states with a phase shift of $\pi$ and $\pi/2$-fronts separating states with a phase shift of $\pi/2$. We find a new type of front instability where a stationary $\pi$-front ``decomposes'' into a pair of traveling $\pi/2$-fronts as the forcing strength is decreased. The instability is degenerate for an amplitude equation with cubic nonlinearities. At the instability point a continuous family of pair solutions exists, consisting of $\pi/2$-fronts separated by distances ranging from zero to infinity. Quintic nonlinearities lift the degeneracy at the instability point but do not change the basic nature of the instability. We conjecture the existence of similar instabilities in higher 2n:1 resonances (n=3,4,..) where stationary $\pi$-fronts decompose into n traveling $\pi/n$-fronts. The instabilities designate transitions from stationary two-phase patterns to traveling 2n-phase patterns. As an example, we demonstrate with a numerical solution the collapse of a four-phase spiral wave into a stationary two-phase pattern as the forcing strength within the 4:1 resonance is increased

A Phase Front Instability in Periodically Forced Oscillatory Systems

Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where $\omega_{forcing}/\omega_{system}=2n$ ($n>1$). Stationary fronts shifting the oscillation phase by $\pi$ lose stability below a critical forcing strength and decompose into $n$ traveling fronts each shifting the phase by $\pi/n$. The instability designates a transition from stationary two-phase patterns to traveling $n$-phase patterns

Narcolepsy and Cataplexy – a practical approach to diagnosis and managing the impact of this chronic condition on children and their families

Narcolepsy is a relatively common neurological condition affecting the regulation of normal sleep/wake cycles leading to excessive daytime sleepiness (EDS). It is almost certainly under-recognised as it has a prevalence of 20–50 per 100,000 population and most cases have an onset in adolescence. Cataplexy (attacks of muscle weakness often precipitated by strong emotions) is a hallmark of this condition and represents the intrusion of REM sleep into wakefulness. Narcolepsy is caused by destruction of hypocretin producing cells due to an autoimmune process often by an infective trigger. Hypocretin is found in the hypothalamus and plays a role in stabilisation of the transition between wake and sleep states. In establishing a diagnosis a comprehensive history to exclude other causes of EDS, including poor sleep habits, is essential. Primary sleep related conditions such as sleep apnoea should be excluded. Investigations for confirmation of the diagnosis include Actigraphy, Polysomnography (PSG), Multiple Sleep Latency Testing (MSLT) and CSF analysis. The symptoms of this debilitating condition can have a huge impact on a child's life and are often vastly underestimated. The impact of EDS on cognitive function is an important factor in difficulties at school, mood, quality of life and future career opportunities. Advances in understanding the pathophysiology have led to trials of novel treatment approaches. The aim of this article is to briefly summarise the recent advances in understanding and give an overview of this important condition for those who are involved in the care of a child with this disease

Unlocking the secrets of mutable collagenous tissue

© Biochemical Society. The mutable collagenous tissue (MCT) of echinoderms (e.g. sea cucumbers, starfish and sea urchins) is unique because of its ability to 'switch' mechanical states rapidly and reversibly - from stiff to soft and vice versa. This kind of tissue in humans, for example, in skin, tendons and ligaments, does not have this property. So what are the molecular-level secrets by which MCT achieves this transformative ability? New real-time ultrastructural investigations are beginning to shed light on this question. Synchrotron X-ray measurements of dynamic molecular conformational changes point to the key factor being the gel-like matrix between the collagen fibrils. These findings could have applications for developing treatments for collagen-based disorders

RAPID: Ecological Resistance of Multiply Stressed Populations: The Response of Tidal Marsh Birds and Plants to Hurricane Sandy

All animal and plant populations can weather change. However, the amount of environmental change a population can absorb is likely to depend upon other, past and ongoing stresses that the population experiences. This project will test whether the ability of populations of native plants and animals in coastal marshes to withstand the recent, extreme storm Hurricane Sandy was greater or less in marshes more subject to past stresses. Researchers will compare the abundances of marsh plants and animals before and after the storm and test whether vulnerability was greater in more specialized species or in marshes surrounded by development, invaded by introduced plants, or challenged by high rates of sea-level rise, and whether previous protection of areas from different kinds of development or use helped reduce vulnerability. By addressing these questions using current theories of ecosystem disturbance, the research will provide general insights on the effects of disturbance and stress on native species and habitats. This research also will provide a specific assessment of Hurricane Sandy\u27s impact on tidal marshes, a vital buffer against storm damage. This will help managers target specific marshes for conservation and restoration and improve the efficiency of planned federal restoration efforts. The work will also inform future coastal management planning by identifying which types of marshes are most vulnerable to future disturbances. Findings will be disseminated to local, state, and federal partners through the Saltmarsh Habitat and Avian Research Program, a cooperative consortium of universities, non-governmental organizations, and state and Federal agency partners working together to conserve tidal marsh habitats and the species they support (www.tidalmarshbirds.org). The project will also help train 20 field technicians

Can the thermal instability drive turbulence?

The thermal instability with a piecewise power law cooling function is investigated using one- and three-dimensional simulations with periodic and shearing-periodic boundary conditions in the presence of constant thermal diffusion and kinematic viscosity coefficients. Consistent with earlier findings, the flow behavior depends on the average density, . When $\bra{\rho}$ is in the range 1-5 x 10^{-24} g cm^{-3} the system is unstable and segregates into cool and warm phases with temperatures of roughly 100 and 10^4 K, respectively. However, in all cases the resulting average pressure is independent of and just a little above the minimum value. For a constant heating rate of 0.015 erg g^{-1} s^{-1}, the mean pressure is around 24 x 10^{-14} dyn (corresponding to p/k_B ~ K cm^{-3}). Cool patches tend to coalesce into bigger ones. In all cases investigated there is no sustained turbulence, which is in agreement with earlier results. Simulations in which turbulence is driven by a body force show that when rms velocities of between 10 and 30 km/s are obtained, the resulting dissipation rates rates are comparable to the thermal energy input rate. The resulting mean pressures are then about 30 x 10^{-14} dyn, corresponding to p/k_B ~ 2170 K cm^{-3}. This is comparable to the value expected for the Galaxy. Differential rotation tends to make the flow two-dimensional, that is, uniform in the streamwise direction, but this does not lead to instability.Comment: 10 pages, 13 figure

Poincare' normal forms and simple compact Lie groups

We classify the possible behaviour of Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and thus the corresponding simple compact Lie groups. The ``renormalized forms'' (in the sense of previous work by the author) of these systems is also discussed; in this way we are able to simplify the classification and moreover to analyze systems with zero linear part. We also briefly discuss the convergence of the normalizing transformations.Comment: 17 pages; minor corrections in revised versio

Monitoring intelligent distribution power systems: a power quality plan

Power system monitoring capabilities and requirements are evolving rapidly. The traditional monitoring framework in Australian distribution networks involves biannual readings of maximum demand at each distribution substation. As utilities respond to developments in metering and communications technology, automated collection and retrieval of quasi-real-time system data between substations and central repositories is now feasible. This gives network managers a significantly increased understanding of distribution network dynamic activity such as daily and seasonal load profiles. This leads to the increased ability of utilities to exploit metering data for power quality analysis purposes. This paper examines the scope for, and challenges associated with, integration of power quality monitoring with advanced metering. Emphasis is directed towards technical and regulatory conditions applying to Australian distribution utilities. Particular consideration is given to the different characteristics of the various types of sites where monitoring is required

Preventing and lessening exacerbations of asthma in school-age children associated with a new term (PLEASANT) : Study protocol for a cluster randomised control trial

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedBackground: Within the UK, during September, there is a pronounced increase in the number of unscheduled medical contacts by school-aged children (4-16 years) with asthma. It is thought that that this might be caused by the return back to school after the summer holidays, suddenly mixing with other children again and picking up viruses which could affect their asthma. There is also a drop in the number of prescriptions administered in August. It is possible therefore that children might not be taking their medication as they should during the summer contributing to them becoming ill when they return to school. It is hoped that a simple intervention from the GP to parents of children with asthma at the start of the summer holiday period, highlighting the importance of maintaining asthma medication can help prevent increased asthma exacerbation, and unscheduled NHS appointments, following return to school in September.Methods/design: PLEASANT is a cluster randomised trial. A total of 140 General Practices (GPs) will be recruited into the trial; 70 GPs randomised to the intervention and 70 control practices of "usual care" An average practice is expected to have approximately 100 children (aged 4-16 with a diagnosis of asthma) hence observational data will be collected on around 14000 children over a 24-month period. The Clinical Practice Research Datalink will collect all data required for the study which includes diagnostic, prescription and referral data.Discussion: The trial will assess whether the intervention can reduce exacerbation of asthma and unscheduled medical contacts in school-aged children associated with the return to school after the summer holidays. It has the potential to benefit the health and quality of life of children with asthma while also improving the effectiveness of NHS services by reducing NHS use in one of the busiest months of the year. An exploratory health economic analysis will gauge any cost saving associated with the intervention and subsequent impacts on quality of life. If results for the intervention are positive it is hoped that this could be adopted as part of routine care management of childhood asthma in general practice. Trial registration: Current controlled trials: ISRCTN03000938 (assigned 19/10/12) http://www.controlled-trials.com/ISRCTN03000938/.UKCRN ID: 13572.Peer reviewe

Normalizations with exponentially small remainders for nonautonomous analytic periodic vector fields

In this paper we deal with analytic nonautonomous vector fields with a periodic time-dependancy, that we study near an equilibrium point. In a first part, we assume that the linearized system is split in two invariant subspaces E0 and E1. Under light diophantine conditions on the eigenvalues of the linear part, we prove that there is a polynomial change of coordinates in E1 allowing to eliminate up to a finite polynomial order all terms depending only on the coordinate u0 of E0 in the E1 component of the vector field. We moreover show that, optimizing the choice of the degree of the polynomial change of coordinates, we get an exponentially small remainder. In the second part, we prove a normal form theorem with exponentially small remainder. Similar theorems have been proved before in the autonomous case : this paper generalizes those results to the nonautonomous periodic case