479 research outputs found
Oscillatory dynamics in a heterogeneous surface reaction: Breakdown of the mean-field approximation
Hierarchical mean-field rate equations and lattice-gas simulations were developed to elucidate the effects of the breakdown of the mean-field approximation for a model heterogeneous chemical oscillator that represents a simple extension of the well-known monomer-dimer surface reaction model. The bifurcation structure of the reaction kinetics depends sensitively on the details of surface transport processes, and the oscillatory behavior exhibited by the site approximation rate equations is not generally robust with respect to spatial correlations
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 , measured
along the surface, between the two points; if it is relaxed, a second zero mode
appears, reflecting the independence of the energy on ; 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 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
Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds
We study curvature functionals for immersed 2-spheres in a compact,
three-dimensional Riemannian manifold M. Under the assumption that the
sectional curvature of M is strictly positive, we prove the existence of a
smoothly immersed sphere minimizing the L^{2} integral of the second
fundamental form. Assuming instead that the sectional curvature is less than or
equal to 2, and that there exists a point in M with scalar curvature bigger
than 6, we obtain a smooth 2-sphere minimizing the integral of 1/4|H|^{2} +1,
where H is the mean curvature vector
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
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
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