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 $\sigma=1$ or $-1$. In particular, for the integrable system with $\sigma=1$, 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 $\eta=\frac{x}{a(s)^{1/3}}$ with $s=3t;$ $\xi>0$ and $\alpha\geq0$ 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 C3_{3} in Diffuse Interstellar Clouds

The smallest polyatomic carbon chain, C$_{3}$, has been identified in interstellar clouds (A$_{v}\sim$1 mag) towards $\zeta$ Ophiuchi, 20 Aquilae, and $\zeta$ Persei by detection of the origin band in its $A^{1}\Pi_{u}-X^{1}\Sigma^{+}_{g}$ electronic transition, near 4052\AA. Individual rotational lines were resolved up to $J$=30 enabling the rotational level column densities and temperature distributions to be determined. The inferred limits for the total column densities ($\sim$1 to 2$\times10^{12}$ cm$^{-2}$) offer a strong incentive to laboratory and astrophysical searches for the longer carbon chains. Concurrent searches for C$_2^{+}$, C$_2^{-}$ and C$_3^{-}$ 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