Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory

Copyright © 2004 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D, Vol 194, Issues 1-2, 2004, DOI:10.1016/j.physd.2004.02.002We consider a model of a Hopf bifurcation interacting as a codimension 2 bifurcation with a saddle-node on a limit cycle, motivated by a low-order model for magnetic activity in a stellar dynamo. This model consists of coupled interactions between a saddle-node and two Hopf bifurcations, where the saddle-node bifurcation is assumed to have global reinjection of trajectories. The model can produce chaotic behaviour within each of a pair of invariant subspaces, and also it can show attractors that are stuck-on to both of the invariant subspaces. We investigate the detailed intermittent dynamics for such an attractor, investigating the effect of breaking the symmetry between the two Hopf bifurcations, and observing that it can appear via blowout bifurcations from the invariant subspaces. We give a simple Markov chain model for the two-state intermittent dynamics that reproduces the time spent close to the invariant subspaces and the switching between the different possible invariant subspaces; this clarifes the observation that the proportion of time spent near the different subspaces depends on the average residence time and also on the probabilities of switching between the possible subspaces

Asymmetry in shape causing absolute negative mobility

We propose a simple classical concept of nanodevices working in an absolute negative mobility (ANM) regime: The minimal spatial asymmetry required for ANM to occur is embedded in the geometry of the transported particle, rather than in the channel design. This allows for a tremendous simplification of device engineering, thus paving the way towards practical implementations of ANM. Operating conditions and performance of our model device are investigated, both numerically and analytically.Comment: 6 pages; accepted for publication in PR

Circulation changes and teleconnections between glacial advances on the west coast of New Zealand and extended spells of drought years in South Africa

Twentieth century changes in the terminal position of the Franz Josef Glacier on the west coast of New Zealand are compared with an area‐averaged mean annual rainfall series for the summer rainfall region of South Africa. Distinctive teleconnections are evident in an out‐of‐phase relationship between the two series, each of which exhibits an oscillation of 18–20 years. Periods of glacial advance are shown to coincide with extended dry spells in South Africa, when drought years are prevalent. Reconstructed pressure anomaly fields are presented for periods of advance and recession of the glacier and for the inter‐decadal wet and dry spells in South Africa. In both cases major regional atmospheric circulation adjustments take place in a quasi‐regular fashion over time to produce an enhancement in westerly airflow during the periods of drought in Africa and glacial advance on the west coast of New Zealand. Extended wet periods and glacial recession are likewise shown to be associated with an enhancement of easterly components of the circulation. Changes in precipitation, temperature and moisture transport are examined and associations with the Southern Oscillation Index are investigated. Franz Josef glacial advances are shown to occur 4–5 years after the onset of enhanced south‐westerly airflow on to the west coast of New Zealand. Advances occur on average 4 years after the onset of extended dry spells in South Africa. Similar atmospheric circulation anomalies in the respective sectors of the Southern Hemisphere and adjustments in the locations of the positions of the ridges in standing wave three are responsible for this correspondence

Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory

We consider a model of a Hopf bifurcation interacting as a codimension 2 bifurcation with a saddle-node on a limit cycle, motivated by a low-order model for magnetic activity in a stellar dynamo. This model consists of coupled interactions between a saddle-node and two Hopf bifurcations, where the saddle-node bifurcation is assumed to have global reinjection of trajectories. The model can produce chaotic behaviour within each of a pair of invariant subspaces, and also it can show attractors that are stuck-on to both of the invariant subspaces. We investigate the detailed intermittent dynamics for such an attractor, investigating the effect of breaking the symmetry between the two Hopf bifurcations, and observing that it can appear via blowout bifurcations from the invariant subspaces. We give a simple Markov chain model for the two-state intermittent dynamics that reproduces the time spent close to the invariant subspaces and the switching between the different possible invariant subspaces; this clarifies the observation that the proportion of time spent near the different subspaces depends on the average residence time and also on the probabilities of switching between the possible subspaces

Infinities of stable periodic orbits in systems of coupled oscillators

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor

Students as partners: the development of an extensive reading program at the Ningbo Campus of the University of Nottingham

"Changing Reading Circles brought more than we expected: we also changed ourselves". A reading interest group at the University of Nottingham Ningbo China was changed to an employability award by a team of five students and two staff partners by the use of a Students as Change Agents student/staff partnership project. Responsibility and authority was devolved to students and the final product has resulted in more engagement in, and enthusiasm for, extensive reading. It also gave the student partners greater levels of self-belief, autonomy and understanding of their potential within an academic community

Chronic adolescent stress increases exploratory behavior but does not appear to change the acute stress response in adult male C57BL/6 mice

Chronic stress exposure in adolescence can lead to a lasting change in stress responsiveness later in life and is associated with increased mental health issues in adulthood. Here we investigate whether the Chronic Social Instability (CSI) paradigm influences the behavioral and molecular responses to novel acute stressors in mice, and whether it alters physiological responses influenced by the noradrenergic system. Using large cohorts of mice, we show that CSI mice display a persistent increase in exploratory behaviors in the open field test alongside small but widespread transcriptional changes in the ventral hippocampus. However, both the transcriptomic and behavioral responses to novel acute stressors are indistinguishable between groups. In addition, the pupillometric response to a tail shock, known to be mediated by the noradrenergic system, remains unaltered in CSI mice. Ultra-high performance liquid chromatography analysis of monoaminergic neurotransmitter levels in the ventral hippocampus also shows no differences between control or CSI mice at baseline or in response to acute stress. We conclude that CSI exposure during adolescence leads to persistent changes in exploratory behavior and gene expression in the hippocampus, but it does not alter the response to acute stress in adulthood and is unlikely to alter the function of the noradrenergic system

The Community Foehn Classification Experiment

Strong winds crossing elevated terrain and descending to its lee occur over mountainous areas worldwide. Winds fulfilling these two criteria are called “foehn” in this paper although different names exist depending on region, sign of temperature change at onset, and depth of overflowing layer. They affect local weather and climate and impact society. Classification is difficult because other wind systems might be superimposed on them or share some characteristics. Additionally, no unanimously agreed-upon name, definition nor indications for such winds exist. The most trusted classifications have been performed by human experts. A classification experiment for different foehn locations in the Alps and different classifier groups addressed hitherto unanswered questions about the uncertainty of these classifications, their reproducibility and dependence on the level of expertise. One group consisted of mountain meteorology experts, the other two of Masters degree students who had taken mountain meteorology courses, and a further two of objective algorithms. Sixty periods of 48 hours were classified for foehn/no foehn at five Alpine foehn locations. The intra-human-classifier detection varies by about 10 percentage points (interquartile range). Experts and students are nearly indistinguishable. The algorithms are in the range of human classifications. One difficult case appeared twice in order to examine reproducibility of classified foehn duration, which turned out to be 50% or less. The classification dataset can now serve as a testbed for automatic classification algorithms, which - if successful - eliminate the drawbacks of manual classifications: lack of scalability and reproducibility

A complete pupillometry toolbox for real-time monitoring of locus coeruleus activity in rodents

The locus coeruleus (LC) is a region in the brainstem that produces noradrenaline and is involved in both normal and pathological brain function. Pupillometry, the measurement of pupil diameter, provides a powerful readout of LC activity in rodents, primates and humans. The protocol detailed here describes a miniaturized setup that can screen LC activity in rodents in real-time and can be established within 1–2 d. Using low-cost Raspberry Pi computers and cameras, the complete custom-built system costs only ~300 euros, is compatible with stereotaxic surgery frames and seamlessly integrates into complex experimental setups. Tools for pupil tracking and a user-friendly Pupillometry App allow quantification, analysis and visualization of pupil size. Pupillometry can discriminate between different, physiologically relevant firing patterns of the LC and can accurately report LC activation as measured by noradrenaline turnover. Pupillometry provides a rapid, non-invasive readout that can be used to verify accurate placement of electrodes/fibers in vivo, thus allowing decisions about the inclusion/exclusion of individual animals before experiments begin

Directed Energy Interstellar Propulsion of WaferSats

In the nearly 60 years of spaceflight we have accomplished wonderful feats of exploration and shown the incredible spirit of the human drive to explore and understand our universe. Yet in those 60 years we have barely left our solar system with the Voyager 1 spacecraft launched in 1977 finally leaving the solar system after 37 years of flight at a speed of 17 km/s or less than 0.006% the speed of light. As remarkable as this is, we will never reach even the nearest stars with our current propulsion technology in even 10 millennium. We have to radically rethink our strategy or give up our dreams of reaching the stars, or wait for technology that does not exist. While we all dream of human spaceflight to the stars in a way romanticized in books and movies, it is not within our power to do so, nor it is clear that this is the path we should choose. We posit a technological path forward, that while not simple; it is within our technological reach. We propose a roadmap to a program that will lead to sending relativistic probes to the nearest stars and will open up a vast array of possibilities of flight both within our solar system and far beyond. Spacecraft from gram level complete spacecraft on a wafer (“wafer sats”) that reach more than ¼ c and reach the nearest star in 15 years to spacecraft with masses more than 105 kg (100 tons) that can reach speeds of near 1000 km/s such systems can be propelled to speeds currently unimaginable with our existing propulsion technologies. To do so requires a fundamental change in our thinking of both propulsion and in many cases what a spacecraft is. In addition to larger spacecraft, some capable of transporting humans, we consider functional spacecraft on a wafer, including integrated optical communications, optical systems and sensors combined with directed energy propulsion. Since “at home” the costs can be amortized over a very large number of missions. The human factor of exploring the nearest stars and exo-planets would be a profound voyage for humanity, one whose non-scientific implications would be enormous. It is time to begin this inevitable journey beyond our home