Lipschitz stability in an inverse problem for the wave equation

We are interested in the inverse problem of the determination of the potential $p(x), x\in\Omega\subset\mathbb{R}^n$ from the measurement of the normal derivative $\partial_\nu u$ on a suitable part $\Gamma_0$ of the boundary of $\Omega$, where $u$ is the solution of the wave equation $\partial_{tt}u(x,t)-\Delta u(x,t)+p(x)u(x,t)=0$ set in $\Omega\times(0,T)$ and given Dirichlet boundary data. More precisely, we will prove local uniqueness and stability for this inverse problem and the main tool will be a global Carleman estimate, result also interesting by itself

Bulk elastic fingering instability in Hele-Shaw cells

We demonstrate experimentally the existence of a purely elastic fingering instability which arises when air penetrates into an elastomer confined in a Hele-Shaw cell. Fingers appear sequentially and propagate within the bulk of the material as soon as a critical strain, independent of the elastic modulus, is exceeded. Their width depends non-linearly on the distance between the confining glass plates. A key element in the driving force of the instability is the adhesion of layers of gels to the plates, which results in a considerable expense of elastic energy during the growth of the air bubble.Comment: Submitted to Physical Review letters; 5 pages; 6 figure

Structural Change and long memory in the GARCH(1,1)-model

It has long been known that the estimated persistence parameter in the GARCH(1,1) - model is biased upwards when the parameters of the model are not constant throughout the sample. The present paper explains the mechanics of this behavior for a particular class of estimates of the model parameters. It gives sufficient conditions for the estimated persistence to tend to one when the mean of the process changes, both for a given sample size (as the size of the structural change increases), and as sample size increases, extending previous results that were concerned with changes in the volatility parameters. --structural change,long memory,GARCH

Paving the Way to Simpler: Experiencing from Maximizing Enrollment States in Streamlining Eligibility and Enrollment

Since 2009, the eight states (Alabama, Illinois, Louisiana, Massachusetts, New York, Utah, Virginia, and Wisconsin) participating in the Robert Wood Johnson Foundation's Maximizing Enrollment program have worked to streamline and simplify enrollment systems, policies, and processes for children and those eligible for health coverage in 2014. The participating states aimed to reduce enrollment barriers for consumers and administrative burdens in processing applications and renewals for staff by making improvements and simplifications at every step of the enrollment process. Although the states began their work before the enactment of the Affordable Care Act (ACA), their efforts positioned them well for implementation in 2014, and offer experiences and lessons that other states may find useful in their efforts to improve efficiency, lower costs, and promote responsible stewardship of limited public resources

Consideration of residual stress and geometry during heat treatment to decrease shaft bending

In automotive industry, heat treatment of components is implicitly related to distortion. This phenomenon is particularly obvious in the case of gearbox parts because of their typical geometry and precise requirements. Even if distortion can be anticipated to an extent by experience, it remains complex to comprehend. Scientific literature and industrial experience show that the whole manufacturing process chain has an influence on final heat treatment distortions. This paper presents an approach to estimate the influence of some factors on the distortion, based on the idea of a distortion potential taking into account not only geometry but also the manufacturing process history. Then the idea is developed through experiments on an industrial manufacturing process to understand the impact of residual stress due to machining on shaft bending and teeth distortion during heat treatment. Instead of being measured, residual stress is being neutralized. By comparing lots between each other, connections between gear teeth geometry and manufacturing steps before heat treatment are obtained. As a consequence, geometrical nonconformities roots can be determined more easily thanks to this diagnosis tool, and corrective actions can be applied. Secondly, the influence of product geometry on bending is experimentally considered. Moreover, metallurgical observations enable to explain the influence of workpieces geometry on shaft bending. Thanks to the obtained results, process and product recommendations to decrease shafts bending are proposed