Capillary buckling of a thin film adhering to a sphere

We present a combined theoretical and experimental study of the buckling of a thin film wrapped around a sphere under the action of capillary forces. A rigid sphere is coated with a wetting liquid, and then wrapped by a thin film into an initially cylindrical shape. The equilibrium of this cylindrical shape is governed by the antagonistic effects of elasticity and capillarity: elasticity tends to keep the film developable while capillarity tends to curve it in both directions so as to maximize the area of contact with the sphere. In the experiments, the contact area between the film and the sphere has cylindrical symmetry when the sphere radius is small, but destabilises to a non-symmetric, wrinkled configuration when the radius is larger than a critical value. We combine the Donnell equations for near-cylindrical shells to include a unilateral constraint with the impenetrable sphere, and the capillary forces acting along a moving edge. A non-linear solution describing the axisymmetric configuration of the film is derived. A linear stability analysis is then presented, which successfully captures the wrinkling instability, the symmetry of the unstable mode, the instability threshold and the critical wavelength. The motion of the free boundary at the edge of the region of contact, which has an effect on the instability, is treated without any approximation

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Limiting distributions for explosive PAR(1) time series with strongly mixing innovation

This work deals with the limiting distribution of the least squares estimators of the coefficients a r of an explosive periodic autoregressive of order 1 (PAR(1)) time series X r = a r X r--1 +u r when the innovation {u k } is strongly mixing. More precisely {a r } is a periodic sequence of real numbers with period P \textgreater{} 0 and such that P r=1 |a r | \textgreater{} 1. The time series {u r } is periodically distributed with the same period P and satisfies the strong mixing property, so the random variables u r can be correlated

Circumstellar discs: What will be next?

This prospective chapter gives our view on the evolution of the study of circumstellar discs within the next 20 years from both observational and theoretical sides. We first present the expected improvements in our knowledge of protoplanetary discs as for their masses, sizes, chemistry, the presence of planets as well as the evolutionary processes shaping these discs. We then explore the older debris disc stage and explain what will be learnt concerning their birth, the intrinsic links between these discs and planets, the hot dust and the gas detected around main sequence stars as well as discs around white dwarfs.Comment: invited review; comments welcome (32 pages

Biochemical evidence for an alternate pathway in N-linked glycoprotein biosynthesis

Asparagine-linked glycosylation is a complex protein modification conserved among all three domains of life. Herein we report the in vitro analysis of N-linked glycosylation from the methanogenic archaeon Methanococcus voltae. Using a suite of synthetic and semisynthetic substrates, we show that AglK initiates N-linked glycosylation in M. voltae through the formation of α-linked dolichyl monophosphate N-acetylglucosamine, which contrasts with the polyprenyl diphosphate intermediates that feature in both eukaryotes and bacteria. Notably, AglK has high sequence homology to dolichyl phosphate β-glucosyltransferases, including Alg5 in eukaryotes, suggesting a common evolutionary origin. The combined action of the first two enzymes, AglK and AglC, afforded an α-linked dolichyl monophosphate glycan that serves as a competent substrate for the archaeal oligosaccharyl transferase AglB. These studies provide what is to our knowledge the first biochemical evidence revealing that, despite the apparent similarity of the overall pathways, there are actually two general strategies to achieve N-linked glycoproteins across the domains of life.National Institutes of Health (U.S.) (Grant GM039334

Scaling of peak flows with constant flow velocity in random self-similar networks

A methodology is presented to understand the role of the statistical self-similar topology of real river networks on scaling, or power law, in peak flows for rainfall-runoff events. We created Monte Carlo generated sets of ensembles of 1000 random self-similar networks (RSNs) with geometrically distributed interior and exterior generators having parameters <i>p</i><sub>i</sub> and <i>p</i><sub>e</sub>, respectively. The parameter values were chosen to replicate the observed topology of real river networks. We calculated flow hydrographs in each of these networks by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling exponents β and φ characterizing power laws with respect to drainage area, and corresponding to the width functions and flow hydrographs respectively, were estimated. We found that, in general, φ > β, which supports a similar finding first reported for simulations in the river network of the Walnut Gulch basin, Arizona. Theoretical estimation of β and φ in RSNs is a complex open problem. Therefore, using results for a simpler problem associated with the expected width function and expected hydrograph for an ensemble of RSNs, we give heuristic arguments for theoretical derivations of the scaling exponents β<sup><i>(E)</i></sup> and φ<sup><i>(E)</i></sup> that depend on the Horton ratios for stream lengths and areas. These ratios in turn have a known dependence on the parameters of the geometric distributions of RSN generators. Good agreement was found between the analytically conjectured values of β<sup><i>(E)</i></sup> and φ<sup><i>(E)</i></sup> and the values estimated by the simulated ensembles of RSNs and hydrographs. The independence of the scaling exponents φ<sup><i>(E)</i></sup> and φ with respect to the value of flow velocity and runoff intensity implies an interesting connection between unit hydrograph theory and flow dynamics. Our results provide a reference framework to study scaling exponents under more complex scenarios of flow dynamics and runoff generation processes using ensembles of RSNs

Alternate space station freedom configuration considerations to accommodate solar dynamic power

The results of a technical audit of the Space Station Freedom Program conducted by the Program Director was announced in early 1989 and included a proposal to use solar dynamic power generation systems to provide primary electrical energy for orbital flight operations rather than photovoltaic solar array systems. To generate the current program baseline power of 75 kW, two or more solar concentrators approximately 50 feet in diameter would be required to replace four pairs of solar arrays whose rectangular blanket size is approximately 200 feet by 30 feet. The photovoltaic power system concept uses solar arrays to generate electricity that is stored in nickel-hydrogen batteries. The proposed concept uses the solar concentrator dishes to reflect and focus the Sun's energy to heat helium-xenon gas to drive electricity generating turbines. The purpose here is to consider the station configuration issues for incorporation of solar dynamic power system components. Key flight dynamic configuration geometry issues are addressed and an assembly sequence scenario is developed

Blending Geospatial Technology and Traditional Ecological Knowledge to Enhance Restoration Decision-Support Processes in Coastal Louisiana

More informed coastal restoration decisions have become increasingly important given limited resources available for restoration projects and the increasing magnitude of marsh degradation and loss across the Gulf Coast. This research investigated the feasibility and benefits of integrating geospatial technology with the traditional ecological knowledge (TEK) of an indigenous Louisiana coastal population to assess the impacts of current and historical ecosystem change on community viability. The primary goal was to provide coastal resource managers with a decision-support tool that allows for a more comprehensive method of assessing localized ecological change in the Gulf Coast region, which can also benefit human community sustainability. Using remote sensing (RS) and geographic information systems (GIS) mapping products, integrated with a coastal community’s TEK to achieve this goal, the research team determined a method for producing vulnerability/sustainability mapping products for an ecosystem-dependent livelihood base of a coastal population based on information derived from RS imagery prioritized with TEK. This study also demonstrates how such an approach can engage affected community residents who are interested in determining and addressing the causes and mitigating the decline of marsh habitat. Historical image data sets of the study area were acquired to understand evolution of land change to current conditions and project future vulnerability. Image-processing procedures were developed and applied to produce maps that detail land change in the study area at time intervals from 1968 to 2009. This information was combined in a GIS with acquired TEK and scientific data sets relating to marsh vegetation health and vulnerability characteristics to produce mapping products that provide new information for use in the coastal restoration decision-making process. This information includes: (1) marsh areas that are most vulnerable; and (2) the areas that are most significant to community sustainability