A Hybrid Observer for a Distributed Linear System with a Changing Neighbor Graph

A hybrid observer is described for estimating the state of an $m>0$ channel, $n$-dimensional, continuous-time, distributed linear system of the form $\dot{x} = Ax,\;y_i = C_ix,\;i\in\{1,2,\ldots, m\}$. The system's state $x$ is simultaneously estimated by $m$ agents assuming each agent $i$ senses $y_i$ and receives appropriately defined data from each of its current neighbors. Neighbor relations are characterized by a time-varying directed graph $\mathbb{N}(t)$ whose vertices correspond to agents and whose arcs depict neighbor relations. Agent $i$ updates its estimate $x_i$ of $x$ at "event times" $t_1,t_2,\ldots$ using a local observer and a local parameter estimator. The local observer is a continuous time linear system whose input is $y_i$ and whose output $w_i$ is an asymptotically correct estimate of $L_ix$ where $L_i$ a matrix with kernel equaling the unobservable space of $(C_i,A)$. The local parameter estimator is a recursive algorithm designed to estimate, prior to each event time $t_j$, a constant parameter $p_j$ which satisfies the linear equations $w_k(t_j-\tau) = L_kp_j+\mu_k(t_j-\tau),\;k\in\{1,2,\ldots,m\}$, where $\tau$ is a small positive constant and $\mu_k$ is the state estimation error of local observer $k$. Agent $i$ accomplishes this by iterating its parameter estimator state $z_i$, $q$ times within the interval $[t_j-\tau, t_j)$, and by making use of the state of each of its neighbors' parameter estimators at each iteration. The updated value of $x_i$ at event time $t_j$ is then $x_i(t_j) = e^{A\tau}z_i(q)$. Subject to the assumptions that (i) the neighbor graph $\mathbb{N}(t)$ is strongly connected for all time, (ii) the system whose state is to be estimated is jointly observable, (iii) $q$ is sufficiently large, it is shown that each estimate $x_i$ converges to $x$ exponentially fast as $t\rightarrow \infty$ at a rate which can be controlled.Comment: 7 pages, the 56th IEEE Conference on Decision and Contro

Chaos in wavy-stratified fluid-fluid flow

We perform a nonlinear analysis of a fluid-fluid wavy-stratified flow using a simplified two-fluid model (TFM), i.e., the fixed-flux model (FFM), which is an adaptation of the shallow water theory for the two-layer problem. Linear analysis using the perturbation method illustrates the short-wave physics leading to the Kelvin-Helmholtz instability (KHI). The interface dynamics are chaotic, and analysis beyond the onset of instability is required to understand the nonlinear evolution of waves. The two-equation FFM solver based on a higher-order spatiotemporal finite difference scheme is used in the current simulations. The solution methodology is verified, and the results are compared with the measurements from a laboratory-scale experiment. The finite-time Lyapunov exponent (FTLE) based on simulations is comparable and slightly higher than the autocorrelation function decay rate, consistent with previous findings. Furthermore, the FTLE is observed to be a strong function of the angle of inclination, while the root mean square of the interface height exhibits a square-root dependence. It is demonstrated that this simple 1-D FFM captures the essential chaotic features of the interface dynamics. This study also adds to a growing body of work indicating that a TFM with appropriate short wavelength physics is well-behaved and chaotic beyond the KHI.Fil: Vaidheeswaran, Avinash. National Energy Technology Laboratory; Estados Unidos. West Virginia University Research Corporation; Estados UnidosFil: Clausse, Alejandro. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados. Provincia de Buenos Aires. Gobernación. Comision de Investigaciones Científicas. Grupo de Plasmas Densos Magnetizados; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; ArgentinaFil: Fullmer, William D.. National Energy Technology Laboratory; Estados Unidos. Leidos; Estados UnidosFil: Marino, Raúl. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: López de Bertodano, Martín. Purdue University. School Of Nuclear Engineering; Estados Unido

Elevated Blood Lead Concentrations and Vitamin D Deficiency in Winter and Summer in Young Urban Children

BACKGROUND: It is widely recognized that blood lead concentrations are higher in the summer than in winter. Although the effects of some environmental factors such as lead in dust on this phenomenon have been studied, relationships to sunlight-induced vitamin D synthesis have not been adequately investigated. Vitamin D status is influenced by the diet, sunlight exposure, age, skin pigmentation, and other factors, and may modify gastrointestinal lead absorption or release of lead stored in bones into the bloodstream. OBJECTIVE AND METHODS: We collected paired blood samples from 142 young, urban African-American and Hispanic children in the winter and summer to study the seasonal increase in blood lead and its relationships to vitamin D nutrition, age, and race. RESULTS: A winter/summer (W/S) increase in blood lead concentrations of 32.4% was found for children 1–3 years of age. There was a smaller W/S increase of 13.0% in children 4–8 years of age. None of the 51 Hispanic children had an elevated blood lead concentration (≥ 10 μg/dL) during the winter, and only one had an elevated summertime concentration. In contrast, elevated blood lead concentrations were frequent in the 91 African-American children, especially those 1–3 years of age. For the latter, the percentage with elevated blood lead levels increased from 12.2% in winter to 22.5% in summer. A 1.2% W/S increase in serum 25-hydroxy-vitamin D (serum 25-OH-D) concentrations was found for children 1–3 years of age. However, in children 4–8 years of age the W/S increase in serum 25-OH-D was much larger—33.6%. The percentages of children with low (< 16 μg/L) serum 25-OH-D concentrations were 12.0% in winter and 0.7% in summer and were consistently greater in African-American than in Hispanic children. The seasonal increases in blood lead and serum 25-OH-D in children 4–8 years of age were significantly associated. CONCLUSION: The higher summertime serum 25-OH-D concentrations for the 4- to 8-year-old children are likely caused by increased sunlight-induced vitamin D synthesis and may contribute to the seasonal increase in blood lead. Age and race are key factors that affect blood lead and vitamin D nutrition, as well as their interactions, in young urban children

The Type Ia Supernova Rate in Radio and Infrared Galaxies from the CFHT Supernova Legacy Survey

We have combined the large SN Ia database of the Canada-France-Hawaii Telescope Supernova Legacy Survey and catalogs of galaxies with photometric redshifts, VLA 1.4 GHz radio sources, and Spitzer infrared sources. We present eight SNe Ia in early-type host galaxies which have counterparts in the radio and infrared source catalogs. We find the SN Ia rate in subsets of radio and infrared early-type galaxies is ~1-5 times the rate in all early-type galaxies, and that any enhancement is always <~ 2 sigma. Rates in these subsets are consistent with predictions of the two component "A+B" SN Ia rate model. Since infrared properties of radio SN Ia hosts indicate dust obscured star formation, we incorporate infrared star formation rates into the "A+B" model. We also show the properties of SNe Ia in radio and infrared galaxies suggest the hosts contain dust and support a continuum of delay time distributions for SNe Ia, although other delay time distributions cannot be ruled out based on our data.Comment: 14 pages, 6 figures, 7 tables, accepted for publication in A