770 research outputs found
Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator
Originally motivated by a stability problem in Fluid Mechanics, we study the
spectral and pseudospectral properties of the differential operator on , where is a
real-valued function and a small parameter. We define
as the infimum of the real part of the spectrum of
, and as the supremum of the norm of the
resolvent of along the imaginary axis. Under appropriate
conditions on , we show that both quantities ,
go to infinity as , and we give precise
estimates of the growth rate of . We also provide an example
where is much larger than if is
small. Our main results are established using variational "hypocoercive"
methods, localization techniques and semiclassical subelliptic estimates.Comment: 38 pages, 4 figure
Three-dimensional stability of Burgers vortices
Burgers vortices are explicit stationary solutions of the Navier-Stokes
equations which are often used to describe the vortex tubes observed in
numerical simulations of three-dimensional turbulence. In this model, the
velocity field is a two-dimensional perturbation of a linear straining flow
with axial symmetry. The only free parameter is the Reynolds number , where is the total circulation of the vortex and is
the kinematic viscosity. The purpose of this paper is to show that Burgers
vortex is asymptotically stable with respect to general three-dimensional
perturbations, for all values of the Reynolds number. This definitive result
subsumes earlier studies by various authors, which were either restricted to
small Reynolds numbers or to two-dimensional perturbations. Our proof relies on
the crucial observation that the linearized operator at Burgers vortex has a
simple and very specific dependence upon the axial variable. This allows to
reduce the full linearized equations to a vectorial two-dimensional problem,
which can be treated using an extension of the techniques developped in earlier
works. Although Burgers vortices are found to be stable for all Reynolds
numbers, the proof indicates that perturbations may undergo an important
transient amplification if is large, a phenomenon that was indeed observed
in numerical simulations.Comment: 31 pages, no figur
Clinicians' perspectives on the duty of candour: Implications for medical ethics education
© The Author(s) 2017. Content: Truth-telling is an integral part of medical practice in many parts of the world. However, recent public inquiries, including the Francis Inquiry reveal that a duty of candour in practise, are at times compromised. Consequently, the duty of candour became a statutory requirement in England. This study aimed to explore clinicians’ perspectives of the implications of the legislation for medical ethics education, as raising standards to improve patient safety remains an international concern. Methods: One-to-one interviews with clinical educators from various specialties who contribute to the MBChB programme at the authors’ university. Once data saturation had been assessed, transcripts were analysed using a thematic approach by the following concurrent activities: data reduction and coding into themes. Example quotations are used to illustrate that key themes are grounded in the data. Results: Eleven clinical educators were interviewed; three general practitioners, six physicians and two surgeons. Thematic analysis identified three key themes; reaction to legislation, barriers to implementation and areas of the medical curriculum that can be further developed to better prepare future doctors. Conclusions: Currently, the legislation is not reaching all frontline staff; there remains a lack of appropriate training and teaching on the legislation that responds to the perceived challenges to implementing candour. These challenges include tensions in the clinical workplace and concerns about the patient’s best interests conflicting with requirements of the legislation. Both undergraduate and postgraduate curricula need to integrate teaching on the implications of the legislation and take a practice based approach in doing so
The intention to disclose medical errors among doctors in a referral hospital in North Malaysia
Asymptotic diophantine approximation:the multiplicative case
Let and be irrational real numbers and 0<\F<1/30. We prove
a precise estimate for the number of positive integers that satisfy
\|q\alpha\|\cdot\|q\beta\|<\F. If we choose \F as a function of we get
asymptotics as gets large, provided \F Q grows quickly enough in terms of
the (multiplicative) Diophantine type of , e.g., if
is a counterexample to Littlewood's conjecture then we only
need that \F Q tends to infinity. Our result yields a new upper bound on sums
of reciprocals of products of fractional parts, and sheds some light on a
recent question of L\^{e} and Vaaler.Comment: To appear in Ramanujan Journa
Absolute frequency measurements of 85Rb nF7/2 Rydberg states using purely optical detection
A three-step laser excitation scheme is used to make absolute frequency
measurements of highly excited nF7/2 Rydberg states in 85Rb for principal
quantum numbers n=33-100. This work demonstrates the first absolute frequency
measurements of rubidium Rydberg levels using a purely optical detection
scheme. The Rydberg states are excited in a heated Rb vapour cell and Doppler
free signals are detected via purely optical means. All of the frequency
measurements are made using a wavemeter which is calibrated against a GPS
disciplined self-referenced optical frequency comb. We find that the measured
levels have a very high frequency stability, and are especially robust to
electric fields. The apparatus has allowed measurements of the states to an
accuracy of 8.0MHz. The new measurements are analysed by extracting the
modified Rydberg-Ritz series parameters.Comment: 12 pages, 5 figures, submitted to New. J. Phy
Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles
We describe a technique for manipulating quantum information stored in
collective states of mesoscopic ensembles. Quantum processing is accomplished
by optical excitation into states with strong dipole-dipole interactions. The
resulting ``dipole blockade'' can be used to inhibit transitions into all but
singly excited collective states. This can be employed for a controlled
generation of collective atomic spin states as well as non-classical photonic
states and for scalable quantum logic gates. An example involving a cold
Rydberg gas is analyzed
Superconducting proximity effect in clean ferromagnetic layers
We investigate superconducting proximity effect in clean ferromagnetic layers
with rough boundaries. The subgap density of states is formed by Andreev bound
states at energies which depend on trajectory length and the ferromagnetic
exchange field. At energies above the gap, the spectrum is governed by resonant
scattering states. The resulting density of states, measurable by tunneling
spectroscopy, exhibits a rich structure, which allows to connect the
theoretical parameters from experiments.Comment: 11 pages, 5 figures (included
Absolute spin-valve effect with superconducting proximity structures
We investigate spin dependent transport in hybrid
superconductor(S)--normal-metal(N)--ferromagnet(F) structures under conditions
of proximity effect. We demonstrate the feasibility of the absolute spin-valve
effect for a certain interval of voltages in a system consisting of two coupled
tri-layer structures. Our results are also valid for non-collinear magnetic
configurations of the ferromagnets.Comment: 1 TEX file, 2 Postscript files. Accepted for publication in Physical
Review Letter
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