8,647 research outputs found
Parking to achieve conscious competence: A reflection about practice development in the context of people with learning disabilities using hospital services
In qualifying as a learning disability nurse during the Project 2000 era, I was influenced by the Health of the Nation for people with learning disabilities (Department of Health, 1995). This document inspired my curiosity as to how to ensure individuals with learning disabilities received similar care to those of the general population. Combining this with experiences of services which practised within more rigid boundaries, prompted me to develop my skills in advocating for people with learning disabilities, enabling individuals to have their say, and more recently to work in partnership co-producing and facilitating training.
This reflection draws upon several influential processes; the trustâs specialist nurse review; attending the International Practice Development School; the service reorganisation; along with exploring the role with other specialist nurses, leading me to consider areas for development both for myself and the organisation. These influences have led me to focus on clinical leadership; developing a framework for clinical staff to provide care that is person centred and adapted to their needs and that of their family; and the possibility of developing a system of clinical links
Momentum Maps and Measure-valued Solutions (Peakons, Filaments and Sheets) for the EPDiff Equation
We study the dynamics of measure-valued solutions of what we call the EPDiff
equations, standing for the {\it Euler-Poincar\'e equations associated with the
diffeomorphism group (of or an -dimensional manifold )}.
Our main focus will be on the case of quadratic Lagrangians; that is, on
geodesic motion on the diffeomorphism group with respect to the right invariant
Sobolev metric. The corresponding Euler-Poincar\'e (EP) equations are the
EPDiff equations, which coincide with the averaged template matching equations
(ATME) from computer vision and agree with the Camassa-Holm (CH) equations in
one dimension. The corresponding equations for the volume preserving
diffeomorphism group are the well-known LAE (Lagrangian averaged Euler)
equations for incompressible fluids. We first show that the EPDiff equations
are generated by a smooth vector field on the diffeomorphism group for
sufficiently smooth solutions. This is analogous to known results for
incompressible fluids--both the Euler equations and the LAE equations--and it
shows that for sufficiently smooth solutions, the equations are well-posed for
short time. In fact, numerical evidence suggests that, as time progresses,
these smooth solutions break up into singular solutions which, at least in one
dimension, exhibit soliton behavior. With regard to these non-smooth solutions,
we study measure-valued solutions that generalize to higher dimensions the
peakon solutions of the (CH) equation in one dimension. One of the main
purposes of this paper is to show that many of the properties of these
measure-valued solutions may be understood through the fact that their solution
ansatz is a momentum map. Some additional geometry is also pointed out, for
example, that this momentum map is one leg of a natural dual pair.Comment: 27 pages, 2 figures, To Alan Weinstein on the occasion of his 60th
Birthda
Variational Principles for Lagrangian Averaged Fluid Dynamics
The Lagrangian average (LA) of the ideal fluid equations preserves their
transport structure. This transport structure is responsible for the Kelvin
circulation theorem of the LA flow and, hence, for its convection of potential
vorticity and its conservation of helicity.
Lagrangian averaging also preserves the Euler-Poincar\'e (EP) variational
framework that implies the LA fluid equations. This is expressed in the
Lagrangian-averaged Euler-Poincar\'e (LAEP) theorem proven here and illustrated
for the Lagrangian average Euler (LAE) equations.Comment: 23 pages, 3 figure
Singular solutions of a modified two-component Camassa-Holm equation
The Camassa-Holm equation (CH) is a well known integrable equation describing
the velocity dynamics of shallow water waves. This equation exhibits
spontaneous emergence of singular solutions (peakons) from smooth initial
conditions. The CH equation has been recently extended to a two-component
integrable system (CH2), which includes both velocity and density variables in
the dynamics. Although possessing peakon solutions in the velocity, the CH2
equation does not admit singular solutions in the density profile. We modify
the CH2 system to allow dependence on average density as well as pointwise
density. The modified CH2 system (MCH2) does admit peakon solutions in velocity
and average density. We analytically identify the steepening mechanism that
allows the singular solutions to emerge from smooth spatially-confined initial
data. Numerical results for MCH2 are given and compared with the pure CH2 case.
These numerics show that the modification in MCH2 to introduce average density
has little short-time effect on the emergent dynamical properties. However, an
analytical and numerical study of pairwise peakon interactions for MCH2 shows a
new asymptotic feature. Namely, besides the expected soliton scattering
behavior seen in overtaking and head-on peakon collisions, MCH2 also allows the
phase shift of the peakon collision to diverge in certain parameter regimes.Comment: 25 pages, 11 figure
A Discrete Theory of Connections on Principal Bundles
Connections on principal bundles play a fundamental role in expressing the
equations of motion for mechanical systems with symmetry in an intrinsic
fashion. A discrete theory of connections on principal bundles is constructed
by introducing the discrete analogue of the Atiyah sequence, with a connection
corresponding to the choice of a splitting of the short exact sequence.
Equivalent representations of a discrete connection are considered, and an
extension of the pair groupoid composition, that takes into account the
principal bundle structure, is introduced. Computational issues, such as the
order of approximation, are also addressed. Discrete connections provide an
intrinsic method for introducing coordinates on the reduced space for discrete
mechanics, and provide the necessary discrete geometry to introduce more
general discrete symmetry reduction. In addition, discrete analogues of the
Levi-Civita connection, and its curvature, are introduced by using the
machinery of discrete exterior calculus, and discrete connections.Comment: 38 pages, 11 figures. Fixed labels in figure
Magnetic Field Limits on SGRs
We measure the period and spin-down rate for SGR 1900+14 during the
quiescient period two years before the recent interval of renewed burst
activity. We find that the spin-down rate doubled during the burst activity
which is inconsistent with both mangetic dipole driven spin down and a magnetic
field energy source for the bursts. We also show that SGRs 1900+14 and 1806-20
have braking indices of 1 which indicate that the spin-down is due to
wind torques and not magnetic dipole radiation. We further show that a
combination of dipole radiation, and wind luminosity, coupled with estimated
ages and present spin parameters, imply that the magnetic fields of SGRs
1900+14 and 1806-20 are less than the critical field of 4 G and
that the efficiency for conversion of wind luminosity to x-ray luminosity is
<2%.Comment: 5 pages, 2 figures submitted to 5th Huntsville GRB Symposium
proceeding
Discrete Mechanics and Optimal Control Applied to the Compass Gait Biped
This paper presents a methodology for generating locally optimal control policies for simple hybrid mechanical systems, and illustrates the method on the compass gait biped. Principles from discrete mechanics are utilized to generate optimal control policies as solutions of constrained nonlinear optimization problems. In the context of bipedal walking, this procedure provides a comparative measure of the suboptimality of existing control policies. Furthermore, our methodology can be used as a control design tool; to demonstrate this, we minimize the specific cost of transport of periodic orbits for the compass gait biped, both in the fully actuated and underactuated case
- âŚ