Magnetic shell enhancements during magnetic disturbances

Magnetic shell enhancements during magnetic field disturbances from Langmuir probe observations of electron density on Ariel I satellit

Force dipoles and stable local defects on fluid vesicles

An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal invariance of the two-dimensional bending energy is used to identify the distribution of energy as well as the stress established in the vesicle. While these states are local minima of the energy, this energy is degenerate; there is a zero mode in the energy fluctuation spectrum, associated with area and volume preserving conformal transformations, which breaks the symmetry between the two points. The volume constraint fixes the distance $S$, measured along the surface, between the two points; if it is relaxed, a second zero mode appears, reflecting the independence of the energy on $S$; in the absence of this constraint a pathway opens for the membrane to slip out of the defect. Logarithmic curvature singularities in the surface geometry at the points of contact signal the presence of external forces. The magnitude of these forces varies inversely with $S$ and so diverges as the points merge; the corresponding torques vanish in these defects. The geometry behaves near each of the singularities as a biharmonic monopole, in the region between them as a surface of constant mean curvature, and in distant regions as a biharmonic quadrupole. Comparison of the distribution of stress with the quadratic approximation in the height functions points to shortcomings of the latter representation. Radial tension is accompanied by lateral compression, both near the singularities and far away, with a crossover from tension to compression occurring in the region between them.Comment: 26 pages, 10 figure

Fedosov supermanifolds: II. Normal coordinates

The study of recently introduced Fedosov supermanifolds is continued. Using normal coordinates, properties of even and odd symplectic supermanifolds endowed with a symmetric connection respecting given sympletic structure are studied.Comment: 12 pages, Late

Broadening Responsibilities: Consideration Of The Potential To Broaden The Role Of Uniformed Fire Service Employees

What is this report about? This report, commissioned by the National Joint Council for Local Authority Fire and Rescue Services (NJC), aims to identify what impact, if any, firefighters can have on the delivery of emergency medical response and wider community health interventions in the UK. What are the overall conclusions? Appropriately trained and equipped firefighters co-responding1 to targeted, specific time critical medical events, such as cardiac arrest, can improve patient survival rates. The data also indicate that there is support from fire service staff – and a potential need from members of the public, particularly the elderly, isolated or vulnerable – to expand ‘wider work’. This includes winter warmth assessments, Safe and Well checks, community defibrillator training and client referrals when staff believe someone may have dementia, are vulnerable or even, for example, have substance dependencies such as an alcohol addiction. However, there is currently insufficient data to estimate the net benefit of this work

Yang-Mills theory a la string

A surface of codimension higher than one embedded in an ambient space possesses a connection associated with the rotational freedom of its normal vector fields. We examine the Yang-Mills functional associated with this connection. The theory it defines differs from Yang-Mills theory in that it is a theory of surfaces. We focus, in particular, on the Euler-Lagrange equations describing this surface, introducing a framework which throws light on their relationship to the Yang-Mills equations.Comment: 7 page

Spinor representation of surfaces and complex stresses on membranes and interfaces

Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the nineties, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature. As an application, the mesoscopic model for a fluid membrane as a surface described by the Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit construction is provided of the conserved complex-valued stress tensor characterizing this surface.Comment: 17 page

Variability of the Vela Pulsar-wind Nebula Observed with Chandra

The observations of the pulsar-wind nebula (PWN) around the Vela pulsar with the Advanced CCD Imaging Spectrometer aboard the Chandra X-ray Observatory, taken on 2000 April 30 and November 30, reveal its complex morphology reminiscent of that of the Crab PWN. Comparison of the two observations shows changes up to 30% in the surface brightness of the PWN features. Some of the PWN elements show appreciable shifts, up to a few arcseconds (about 10^{16} cm), and/or spectral changes. To elucidate the nature of the observed variations, further monitoring of the Vela PWN is needed.Comment: 7 pages (incl. 3 embedded PS figures), AASTEX, uses emulateapj5.sty. Submitted to ApJ Lett. For a high-resolution color PS image of Figure 3 (6.3 Mby), see http://www.astro.psu.edu/users/divas/velaneb_fig3.p

Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/maskae/CV_Warwick/Chemotaxis.html

Bogomol'nyi Decomposition for Vesicles of Arbitrary Genus

We apply the Bogomol'nyi technique, which is usually invoked in the study of solitons or models with topological invariants, to the case of elastic energy of vesicles. We show that spontaneous bending contribution caused by any deformation from metastable bending shapes falls in two distinct topological sets: shapes of spherical topology and shapes of non-spherical topology experience respectively a deviatoric bending contribution a la Fischer and a mean curvature bending contribution a la Helfrich. In other words, topology may be considered to describe bending phenomena. Besides, we calculate the bending energy per genus and the bending closure energy regardless of the shape of the vesicle. As an illustration we briefly consider geometrical frustration phenomena experienced by magnetically coated vesicles.Comment: 8 pages, 1 figure; LaTeX2e + IOPar