62,228 research outputs found
ICF core sets for low back pain: do they include what matters to patients?
To investigate whether the International Classification of Functioning Disability and Health (ICF) Core Sets for low back pain encompass the key functional problems of patients
Understanding Teacher Leadership in Middle School Mathematics: A Collaborative Research Effort
We report findings from a collaborative research effort designed to examine how teachers act as leaders in their schools. We find that teachers educated by the Math in the Middle Institute act as key sources of advice for colleagues within their schools while drawing support from a network consisting of other teachers in the program and university-level advisors. In addition to reporting on our findings, we reflect on our research process, noting some of the practical challenges involved, as well as some of the benefits of collaboration
Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions
We describe how the semiclassical theory of radical pair recombination
reactions recently introduced by two of us [D. E. Manolopoulos and P. J. Hore,
J. Chem. Phys. 139, 124106 (2013)] can be generalised to allow for different
singlet and triplet recombination rates. This is a non-trivial generalisation
because when the recombination rates are different the recombination process is
dynamically coupled to the coherent electron spin dynamics of the radical pair.
Furthermore, because the recombination operator is a two-electron operator, it
is no longer sufficient simply to consider the two electrons as classical
vectors: one has to consider the complete set of 16 two-electron spin operators
as independent classical variables. The resulting semiclassical theory is first
validated by comparison with exact quantum mechanical results for a model
radical pair containing 12 nuclear spins. It is then used to shed light on the
spin dynamics of a carotenoid-porphyrin-fullerene (CPF) triad containing
considerably more nuclear spins which has recently been used to establish a
'proof of principle' for the operation of a chemical compass [K. Maeda et al.,
Nature 453, 387 (2008)]. We find in particular that the intriguing biphasic
behaviour that has been observed in the effect of an Earth-strength magnetic
field on the time-dependent survival probability of the photo-excited C+PF-
radical pair arises from a delicate balance between its asymmetric
recombination and the relaxation of the electron spin in the carotenoid
radical
A multiphase model describing vascular tumour growth
In this paper we present a new model framework for studying vascular tumour growth, in which the blood vessel density is explicitly considered. Our continuum model comprises conservation of mass and momentum equations for the volume fractions of tumour cells, extracellular material and blood vessels. We include the physical mechanisms that we believe to be dominant, namely birth and death of tumour cells, supply and removal of extracellular fluid via the blood and lymph drainage vessels, angiogenesis and blood vessel occlusion. We suppose that the tumour cells move in order to relieve the increase in mechanical stress caused by their proliferation. We show how to reduce the model to a system of coupled partial differential equations for the volume fraction of tumour cells and blood vessels and the phase averaged velocity of the mixture. We consider possible parameter regimes of the resulting model. We solve the equations numerically in these cases, and discuss the resulting behaviour. The model is able to reproduce tumour structure that is found `in vivo' in certain cases. Our framework can be easily modified to incorporate the effect of other phases, or to include the effect of drugs
Magnetothermodynamics: Measuring equations of state in a relaxed magnetohydrodynamic plasma
We report the first measurements of equations of state of a fully relaxed
magnetohydrodynamic (MHD) laboratory plasma. Parcels of magnetized plasma,
called Taylor states, are formed in a coaxial magnetized plasma gun, and are
allowed to relax and drift into a closed flux conserving volume. Density, ion
temperature, and magnetic field are measured as a function of time as the
Taylor states compress and heat. The theoretically predicted MHD and double
adiabatic equations of state are compared to experimental measurements. We find
that the MHD equation of state is inconsistent with our data.Comment: 4 pages, 4 figure
An affine generalization of evacuation
We establish the existence of an involution on tabloids that is analogous to
Schutzenberger's evacuation map on standard Young tableaux. We find that the
number of its fixed points is given by evaluating a certain Green's polynomial
at , and satisfies a "domino-like" recurrence relation.Comment: 32 pages, 7 figure
Stability of relative equilibria with singular momentum values in simple mechanical systems
A method for testing -stability of relative equilibria in Hamiltonian
systems of the form "kinetic + potential energy" is presented. This method
extends the Reduced Energy-Momentum Method of Simo et al. to the case of
non-free group actions and singular momentum values. A normal form for the
symplectic matrix at a relative equilibrium is also obtained.Comment: Partially rewritten. Some mistakes fixed. Exposition improve
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