Frozen reaction fronts in steady flows: a burning-invariant-manifold perspective

The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the reacted domain is static, and the front appears "frozen". Our central result is that these frozen fronts in the two-dimensional fluid are composed of segments of burning invariant manifolds---invariant manifolds of front-element dynamics in $xy\theta$-space, where $\theta$ is the front orientation. Burning invariant manifolds (BIMs) have been identified previously as important local barriers to front propagation in fluid flows. The relevance of BIMs for frozen fronts rests in their ability, under appropriate conditions, to form global barriers, separating reacted domains from nonreacted domains for all time. The second main result of this paper is an understanding of bifurcations that lead from a nonfrozen state to a frozen state, as well as bifurcations that change the topological structure of the frozen front. Though the primary results of this study apply to general fluid flows, our analysis focuses on a chain of vortices in a channel flow with an imposed wind. For this system, we present both experimental and numerical studies that support the theoretical analysis developed here.Comment: 21 pages, 30 figure

Retirement Responses to Early Social Security Benefit Reductions

This paper evaluates potential responses to reductions in early Social Security retirement benefits. Using the Health and Retirement Study (HRS) linked to administrative records, we find that Social Security coverage is quite uneven in the older population: one-quarter of respondents in their late 50’s lacks coverage under the Disability Insurance program, and one-fifth lacks coverage for old-age benefits. Among those eligible for benefits, respondents who subsequently retired early appear quite similar initially to those who later filed for normal retirement benefits, but both groups were healthier and better educated than those who later filed for disability benefits. Next we investigate the potential impact of curtailing, and then eliminating, early Social Security benefits. A life-cycle model of retirement behavior provides estimated parameters used to simulate the effects of cutting early Social Security benefits on retirement pathways. We find that cutting early Social Security benefits would boost the probability of normal retirement by twice as much as it would the probability of disability retirement.

Mode-locking in advection-reaction-diffusion systems: an invariant manifold perspective

Fronts propagating in two-dimensional advection-reaction-diffusion (ARD) systems exhibit rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We explain this mode-locking phenomenon using so-called burning invariant manifolds (BIMs). In fact, the mode-locked profile is delineated by a BIM attached to a relative periodic orbit (RPO) of the front element dynamics. Changes in the type (and loss) of mode-locking can be understood in terms of local and global bifurcations of the RPOs and their BIMs. We illustrate these concepts numerically using a chain of alternating vortices in a channel geometry.Comment: 9 pages, 13 figure

The ‘EDHF’ Antagonist 14, 15 Epoxyeicosa-5(Z)-Enoic Acid has Vasodilator Properties in Mesenteric Vessels

There is now overwhelming evidence for Epoxyeicosatrienoic acids (EETs) as endothelial derived hyperpolarising factor (EDHF). Most recently, a number of pharmacological tools have been developed for the study of EETs in relation to EDHF responses. EETs have been shown to cause relaxation by activating smooth muscle large conductance Ca2+ sensitive K+ (BKCa) (Archer et al, 2003). This dilatory response has been shown to be specifically inhibited by its analogue 14, 15-epoxyeicosa-5 (Z) enoic acid (14, 15 EEZE) in both human internal mammary artery and bovine coronary artery (Archer et al, 2003). Here we have investigated the antagonist effects of 14, 15 EEZE in murine arteries. Male Black 6 mice (12-18 weeks) were killed by lethal exposure to CO2. First order arteries were isolated and mounted in wire myographs immersed in physiological salt solution (PSS). Arteries were equilibrated (30 mins) and tensions normalised as described previously (Mulvany and Halpern, 1977). Arteries incubated for 30 minutes with or without 3µg/ml 14, 15 EEZE. A concentration response curve to 11, 12 EET was performed cumulatively on arteries pre-contracted with EC80 U46619. In some experiments, arteries were pre-contracted with EC80 U46619, and concentration response to 14, 15 EEZE performed cumulatively.Non peer reviewe

Modeling Lifetime Earnings Paths: Hypothetical versus Actual Workers

To assess the distributional effects of social security reform proposals, it is essential to have good information on real-world workers’ lifetime earnings trajectories. Until recently, however, policymakers have relied on hypothetical earnings profiles for policy analysis. We use actual lifetime earnings data from the Health and Retirement Study (HRS) to compare actual workers’ covered earnings profiles to these hypothetical profiles. We show that the hypothetical profiles do not track earnings patterns of current retirees; thus lifetime pay levels are much higher than for most HRS workers. Therefore, using hypothetical profiles could misrepresent benefits paid and taxes collected under such reforms.

Weighted feature selection criteria for visual servoing of a telerobot

Because of the continually changing environment of a space station, visual feedback is a vital element of a telerobotic system. A real time visual servoing system would allow a telerobot to track and manipulate randomly moving objects. Methodologies for the automatic selection of image features to be used to visually control the relative position between an eye-in-hand telerobot and a known object are devised. A weighted criteria function with both image recognition and control components is used to select the combination of image features which provides the best control. Simulation and experimental results of a PUMA robot arm visually tracking a randomly moving carburetor gasket with a visual update time of 70 milliseconds are discussed