Perturbed Three Vortex Dynamics

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated to completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half-plane, three coaxial slender vortex rings in three-space, and `restricted' four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff type arguments; and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic

Gender and educational leadership in England: a comparison of secondary headteachers' views over time

In the context of gender being a barrier to accessing leadership, this paper presents a comparison of the views of men and women head teacher (principals) of secondary schools in England in the 1990s and in 2004. The same survey instrument was used on both occasions. The perceptions of the head teachers show change in some areas and no change in others. Overall, women are more likely to become head teachers and are now less likely to be categorised into pastoral roles, but in some cases women still meet prejudice from governors and others in the wider community. Women head teachers are more likely to have partners and children than in the 1990s, sharing equally or carrying most of the domestic responsibilities, whereas male colleagues are most likely to have partners who take the majority of responsibility in the home. Essentialist stereotypes about women and men as leaders still prevail, although both the women and men head teachers see themselves as adopting a traditionally ‘feminine’ style of leadership. Women head teachers are likely to see some benefits in being a woman in a role stereotypically associated with men. However, there has been an increase in the proportion of women who feel that they have to prove their worth as a leader, and this may be linked with increased levels of accountability in schools

Stimulation of Capacitative Calcium Entry in HL-60 Cells By Nanosecond Pulsed Electric Fields

Nanosecond pulsed electric fields (nsPEFs) are hypothesized to affect intracellular structures in living cells providing a new means to modulate cell signal transduction mechanisms. The effects of nsPEFs on the release of internal calcium and activation of calcium influx in HL-60 cells were investigated by using real time fluorescent microscopy with Fluo-3 and fluorometry with Fura-2. nsPEFs induced an increase in intracellular calcium levels that was seen in all cells. With pulses of 60 ns duration and electric fields between 4 and 15 kV/cm, intracellular calcium increased 200-700 nM, respectively, above basal levels (similar to100 nM), while the uptake of propidium iodide was absent. This suggests that increases in intracellular calcium were not because of plasma membrane electroporation. nsPEF and the purinergic agonist UTP induced calcium mobilization in the presence and absence of extracellular calcium with similar kinetics and appeared to target the same inositol 1,4,5-trisphosphate- and thapsigargin-sensitive calcium pools in the endoplasmic reticulum. For cells exposed to either nsPEF or UTP in the absence of extracellular calcium, there was an electric field-dependent or UTP dose-dependent increase in capacitative calcium entry when calcium was added to the extracellular media. These findings suggest that nsPEFs, like ligand-mediated responses, release calcium from similar internal calcium pools and thus activate plasma membrane calcium influx channels or capacitative calcium entry

Ground states in low-dimensional quantum magnets

The ability to control the magnetic properties of low-dimensional magnetic systems is a major aim of research in condensed matter physics. Bespoke magnetic systems have potential uses in many practical applications and experimental investigations of theoretical predictions. To achieve this goal necessitates being able to determine the magnetic properties of these systems, which can require much expense in time, money and effort. In this thesis I present a methodology that can be used for characterising the properties of powdered, low-dimensional spin-1 antiferromagnets using commercially available measurement systems. The techniques involved are able to determine the magnetic properties of powdered systems containing isolated and exchange-coupled Ni2+ ions accurately enough such that a decision on growing single-crystals or measurements requiring more complicated measurements at specialist facilities can be made. Using this method, I then characterise the magnetic properties of a family of similar Ni2+-halide-halide-Ni2+ chains which show differing magnetic behaviour linked to the different bridging ligands. It is found that single-ion anisotropy in Ni2+ octahedral environments is not just dependent on the placement but also the electronic properties of the coordinated non-magnetic ligands. Also, magnetic interactions along the Ni2+ chains are strongly influenced by the size of the bridging halide ions. The distance between adjacent ions is less important. This property was exploited to explore bond disorder in the spin-1/2 quasi two-dimensional antiferromagnet (QuinH)2Cu(ClxBr

Imposed faster and slower walking speeds influence gait stability differently in Parkinson fallers

Objective To evaluate the effect of imposed faster and slower walking speeds on postural stability in people with Parkinson disease (PD). Design Cross-sectional cohort study. Setting General community. Participants Patients with PD (n=84; 51 with a falls history; 33 without) and age-matched controls (n=82) were invited to participate via neurology clinics and preexisting databases. Of those contacted, 99 did not respond (PD=36; controls=63) and 27 were not interested (PD=18; controls=9). After screening, a further 10 patients were excluded; 5 had deep brain stimulation surgery and 5 could not accommodate to the treadmill. The remaining patients (N=30) completed all assessments and were subdivided into PD fallers (n=10), PD nonfallers (n=10), and age-matched controls (n=10) based on falls history. Interventions Not applicable. Main Outcome Measures Three-dimensional accelerometers assessed head and trunk accelerations and allowed calculation of harmonic ratios and root mean square (RMS) accelerations to assess segment control and movement amplitude. Results Symptom severity, balance confidence, and medical history were established before participants walked on a treadmill at 70%, 100%, and 130% of their preferred speed. Head and trunk control was lower for PD fallers than PD nonfallers and older adults. Significant interactions indicated head and trunk control increased with speed for PD nonfallers and older adults, but did not improve at faster speeds for PD fallers. Vertical head and trunk accelerations increased with walking speed for PD nonfallers and older adults, while the PD fallers demonstrated greater anteroposterior RMS accelerations compared with both other groups. Conclusions The results suggest that improved gait dynamics do not necessarily represent improved walking stability, and this must be respected when rehabilitating gait in patients with PD

The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra

We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant geometric objects studied before by E. Cartan. Especially, the E. Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be treated in the frame work of the Wahlquist Estabrook prolongation structures on jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra is studied in great detail. An effective Maurer-Cartan one-forms construction is suggested that is very useful for applications. As an example of application the developed Lie-invariant geometric object theory for the Burgers nonlinear dynamical system is considered having given rise to finding an explicit form of the associated Lax type representation

A Memetic Analysis of a Phrase by Beethoven: Calvinian Perspectives on Similarity and Lexicon-Abstraction

This article discusses some general issues arising from the study of similarity in music, both human-conducted and computer-aided, and then progresses to a consideration of similarity relationships between patterns in a phrase by Beethoven, from the first movement of the Piano Sonata in A flat major op. 110 (1821), and various potential memetic precursors. This analysis is followed by a consideration of how the kinds of similarity identified in the Beethoven phrase might be understood in psychological/conceptual and then neurobiological terms, the latter by means of William Calvin’s Hexagonal Cloning Theory. This theory offers a mechanism for the operation of David Cope’s concept of the lexicon, conceived here as a museme allele-class. I conclude by attempting to correlate and map the various spaces within which memetic replication occurs

Mode mixing and losses in misaligned microcavities

We present a study on the optical losses of Fabry-P\'erot cavities subject to realistic transverse mirror misalignment. We consider mirrors of the two most prevalent surface forms: idealised spherical depressions, and Gaussian profiles generated by laser ablation. We first describe the mode mixing phenomena seen in the spherical mirror case and compare to the frequently-used clipping model, observing close agreement in the predicted diffraction loss, but with the addition of protective mode mixing at transverse degeneracies. We then discuss the Gaussian mirror case, detailing how the varying surface curvature across the mirror leads to complex variations in round trip loss and mode profile. In light of the severe mode distortion and strongly elevated loss predicted for many cavity lengths and transverse alignments when using Gaussian mirrors, we suggest that the consequences of mirror surface profile are carefully considered when designing cavity experiments.Comment: 16 pages, 12 figure

Efficient operator method for modelling mode mixing in misaligned optical cavities

The transverse field structure and diffraction loss of the resonant modes of Fabry-P\'erot optical cavities are acutely sensitive to the alignment and shape of the mirror substrates. We develop extensions to the `mode mixing' method applicable to arbitrary mirror shapes, which both facilitate fast calculation of the modes of cavities with transversely misaligned mirrors and enable the determination and transformation of the geometric properties of these modes. We show how these methods extend previous capabilities by including the practically-motivated case of transverse mirror misalignment, unveiling rich and complex structure of the resonant modes.Comment: 17 pages, 7 figure