688 research outputs found
Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations
In this article, we study the self-similar solutions of the 2-component
Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}%
\rho_{t}+u\rho_{x}+\rho u_{x}=0
m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation}
with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation
method, we can obtain a class of blowup or global solutions for or
. In particular, for the integrable system with , we have the
global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}%
\rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right)
}{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi}
0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right.
,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x
\overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}%
>0,\text{ }\overset{\cdot}{a}(0)=a_{1}
f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right)
^{2}}% \end{array} \right. \end{equation}
where with and are
arbitrary constants.\newline Our analytical solutions could provide concrete
examples for testing the validation and stabilities of numerical methods for
the systems.Comment: 5 more figures can be found in the corresponding journal paper (J.
Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm
Equations, Shallow Water System, Analytical Solutions, Blowup, Global,
Self-Similar, Separation Method, Construction of Solutions, Moving Boundar
Method of making a piezoelectric shear wave resonator
An acoustic shear wave resonator comprising a piezoelectric film having its C-axis substantially inclined from the film normal such that the shear wave coupling coefficient significantly exceeds the longitudinal wave coupling coefficient, whereby the film is capable of shear wave resonance, and means for exciting said film to resonate. The film is prepared by deposition in a dc planar magnetron sputtering system to which a supplemental electric field is applied. The resonator structure may also include a semiconductor material having a positive temperature coefficient of resonance such that the resonator has a temperature coefficient of resonance approaching 0 ppm
High resolution optothermal spectroscopy of pyridine in the S-1 state
The optothermal technique has been utilized to obtain the first high resolution spectrum of pyridine in the region of the S1←S0 electronic transition. Rotational profiles for several vibronic bands (000,6a10,16b206a10,6a20,1210) were measured and found to be severely homogeneously broadened with linewidths of the order of 3–5 GHz, in agreement with previous lifetime measurements. Rotational constants of pyridine in the excited S1 vibronic levels were extracted by a band contour analysis. The values obtained are in good agreement with results from ab initio calculations, also presented here
Mexico's Health System: More Comprehensive Reform Needed
Jason Lakin discusses and critiques a Policy Forum that reviews 25 years of reform to the Mexican health system and argues that more comprehensive reform is needed
Design and analysis of DNA strand displacement devices using probabilistic model checking
Designing correct, robust DNA devices is difficult because of the many possibilities for unwanted interference between molecules in the system. DNA strand displacement has been proposed as a design paradigm for DNA devices, and the DNA strand displacement (DSD) programming language has been developed as a means of formally programming and analysing these devices to check for unwanted interference. We demonstrate, for the first time, the use of probabilistic verification techniques to analyse the correctness, reliability and performance of DNA devices during the design phase. We use the probabilistic model checker prism, in combination with the DSD language, to design and debug DNA strand displacement components and to investigate their kinetics. We show how our techniques can be used to identify design flaws and to evaluate the merits of contrasting design decisions, even on devices comprising relatively few inputs. We then demonstrate the use of these components to construct a DNA strand displacement device for approximate majority voting. Finally, we discuss some of the challenges and possible directions for applying these methods to more complex designs
Facilitating adjustments : evaluating a series of reasonable adjustments workshops for mainstream healthcare professionals
Introduction: Having experienced several nationally reported clinical
incidents East Kent Hospitals (EKH) developed data that indicated that
people with Intellectual Disability (ID) were at greater risk of being
admitted via A&E, and repeatedly admitting, compared to the general
population.
Health Education England supported EKH to undertake workshops
for doctors and other local non -ID specialist professionals on making
adjustments for people with ID.
Methods: A team of three experts by experience – including people
with ID and family carers- and three ID Nurses were employed to
develop and co-facilitate a series of workshops.
Practice Development methods such as Fourth Generation Evaluation
were employed and included in the learning outcomes and educational
methods.
Results: Nine workshops were held over a two years; 120 participants
attended, only 10% had a medical background.
A thematic analysis of participant’s data indicated an emerging
concept, preparedness. Participants wished to be better prepared to make
adjustments before the patient’s arrival.
Implications: This evaluation is prescient as UK parliament is due to
consult on education for all healthcare professionals on ID in light of
#Oliverscampaign.
It is recommended that responsibility for ID education resides with
service providers, employing local experts, reflecting local data, and be
experiential with a work-based project component.
Local informatics systems ought to flag and alert staff of people with
learning disabilities using services
Amplified biochemical oscillations in cellular systems
We describe a mechanism for pronounced biochemical oscillations, relevant to
microscopic systems, such as the intracellular environment. This mechanism
operates for reaction schemes which, when modeled using deterministic rate
equations, fail to exhibit oscillations for any values of rate constants. The
mechanism relies on amplification of the underlying stochasticity of reaction
kinetics within a narrow window of frequencies. This amplification allows
fluctuations to beat the central limit theorem, having a dominant effect even
though the number of molecules in the system is relatively large. The mechanism
is quantitatively studied within simple models of self-regulatory gene
expression, and glycolytic oscillations.Comment: 35 pages, 6 figure
Detection of C in Diffuse Interstellar Clouds
The smallest polyatomic carbon chain, C, has been identified in
interstellar clouds (A1 mag) towards Ophiuchi, 20 Aquilae,
and Persei by detection of the origin band in its
electronic transition, near 4052\AA.
Individual rotational lines were resolved up to =30 enabling the rotational
level column densities and temperature distributions to be determined. The
inferred limits for the total column densities (1 to 2
cm) offer a strong incentive to laboratory and astrophysical searches
for the longer carbon chains. Concurrent searches for C, C and
C were negative but provide sensitive estimates for their maximum
column densities.Comment: 14 pages, 5 figures, 3 tables. To appear in the Astrophysical Journa
Electromagnetically Induced Transparency and Slow Light with Optomechanics
Controlling the interaction between localized optical and mechanical
excitations has recently become possible following advances in micro- and
nano-fabrication techniques. To date, most experimental studies of
optomechanics have focused on measurement and control of the mechanical
subsystem through its interaction with optics, and have led to the experimental
demonstration of dynamical back-action cooling and optical rigidity of the
mechanical system. Conversely, the optical response of these systems is also
modified in the presence of mechanical interactions, leading to strong
nonlinear effects such as Electromagnetically Induced Transparency (EIT) and
parametric normal-mode splitting. In atomic systems, seminal experiments and
proposals to slow and stop the propagation of light, and their applicability to
modern optical networks, and future quantum networks, have thrust EIT to the
forefront of experimental study during the last two decades. In a similar
fashion, here we use the optomechanical nonlinearity to control the velocity of
light via engineered photon-phonon interactions. Our results demonstrate EIT
and tunable optical delays in a nanoscale optomechanical crystal device,
fabricated by simply etching holes into a thin film of silicon (Si). At low
temperature (8.7 K), we show an optically-tunable delay of 50 ns with
near-unity optical transparency, and superluminal light with a 1.4 microseconds
signal advance. These results, while indicating significant progress towards an
integrated quantum optomechanical memory, are also relevant to classical signal
processing applications. Measurements at room temperature and in the analogous
regime of Electromagnetically Induced Absorption (EIA) show the utility of
these chip-scale optomechanical systems for optical buffering, amplification,
and filtering of microwave-over-optical signals.Comment: 15 pages, 9 figure
Third party consultation: a method for the study and resolution of conflict
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66597/2/10.1177_002200277201600105.pd
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