Evolution PDEs and augmented eigenfunctions. I finite interval

The so-called unified method expresses the solution of an initial-boundary value problem for an evolution PDE in the finite interval in terms of an integral in the complex Fourier (spectral) plane. Simple initial-boundary value problems, which will be referred to as problems of type~I, can be solved via a classical transform pair. For example, the Dirichlet problem of the heat equation can be solved in terms of the transform pair associated with the Fourier sine series. Such transform pairs can be constructed via the spectral analysis of the associated spatial operator. For more complicated initial-boundary value problems, which will be referred to as problems of type~II, there does \emph{not} exist a classical transform pair and the solution \emph{cannot} be expressed in terms of an infinite series. Here we pose and answer two related questions: first, does there exist a (non-classical) transform pair capable of solving a type~II problem, and second, can this transform pair be constructed via spectral analysis? The answer to both of these questions is positive and this motivates the introduction of a novel class of spectral entities. We call these spectral entities augmented eigenfunctions, to distinguish them from the generalised eigenfunctions introduced in the sixties by Gel'fand and his co-authors

Analysis of Toxic Amyloid Fibril Interactions at Natively Derived Membranes by Ellipsometry

There is an ongoing debate regarding the culprits of cytotoxicity associated with amyloid disorders. Although small pre-fibrillar amyloid oligomers have been implicated as the primary toxic species, the fibrillar amyloid material itself can also induce cytotoxicity. To investigate membrane disruption and cytotoxic effects associated with intact and fragmented fibrils, the novel in situ spectroscopic technique of Total Internal Reflection Ellipsometry (TIRE) was used. Fibril lipid interactions were monitored using natively derived whole cell membranes as a model of the in vivo environment. We show that fragmented fibrils have an increased ability to disrupt these natively derived membranes by causing a loss of material from the deposited surface when compared with unfragmented fibrils. This effect was corroborated by observations of membrane disruption in live cells, and by dye release assay using synthetic liposomes. Through these studies we demonstrate the use of TIRE for the analysis of protein-lipid interactions on natively derived lipid surfaces, and provide an explanation on how amyloid fibrils can cause a toxic gain of function, while entangled amyloid plaques exert minimal biological activity

An Integrated Approach to Modeling Solar Electric Propulsion Vehicles During Long Duration, Near-Earth Orbit Transfers

Presentation of computer model simulations comparing and contrasting solar electric propulsion (SEP) vehicles simulated with an integrated model (SEPSIM) and without an integrated model

FUSE Measurements of Interstellar Fluorine

The source of fluorine is not well understood, although core-collapse supernovae, Wolf-Rayet stars, and asymptotic giant branch stars have been suggested. A search for evidence of the nu process during Type II supernovae is presented. Absorption from interstellar F I is seen in spectra of HD 208440 and HD 209339A acquired with the Far Ultraviolet Spectroscopic Explorer. In order to extract the column density for F I from the line at 954 A, absorption from H2 has to be modeled and then removed. Our analysis indicates that for H2 column densities less than about 3 x 10^20 cm^-2, the amount of F I can be determined from lambda 954. For these two sight lines, there is no clear indication for enhanced F abundances resulting from the nu process in a region shaped by past supernovae.Comment: 17 pages, 4 figures, accepted for publication in Ap

The Ratio of Ortho- to Para-H2 in Photodissociation Regions

We discuss the ratio of ortho- to para-H2 in photodissociation regions (PDRs). We draw attention to an apparent confusion in the literature between the ortho-to-para ratio of molecules in FUV-pumped vibrationally excited states, and the H2 ortho-to-para abundance ratio. These ratios are not the same because the process of FUV-pumping of fluorescent H2 emission in PDRs occurs via optically thick absorption lines. Thus, gas with an equilibrium ratio of ortho- to para-H2 equal to 3 will yield FUV-pumped vibrationally excited ortho-to-para ratios smaller than 3, because the ortho-H2 pumping rates are preferentially reduced by optical depth effects. Indeed, if the ortho and para pumping lines are on the ``square root'' part of the curve-of-growth, then the expected ratio of ortho and para vibrational line strengths is the square root of 3, ~ 1.7, close to the typically observed value. Thus, contrary to what has sometimes been stated in the literature, most previous measurements of the ratio of ortho- to para-H2 in vibrationally excited states are entirely consistent with a total ortho-to-para ratio of 3, the equilibrium value for temperatures greater than 200 K. We present an analysis and several detailed models which illustrate the relationship between the total ratios of ortho- to para-H2 and the vibrationally excited ortho-to-para ratios in PDRs. Recent Infrared Space Observatory (ISO) measurements of pure rotational and vibrational H2 emissions from the PDR in the star-forming region S140 provide strong observational support for our conclusions.Comment: 23 pages (including 5 figures), LaTeX, uses aaspp4.sty, accepted for publication in Ap

Cut-wire-pair structures as two-dimensional magnetic metamaterials

We study numerically and experimentally magnetic metamaterials based on cut-wire pairs instead of split-ring resonators. The cut-wire pair planar structure is extended in order to create a truly two-dimensional metamaterial suitable for scaling to optical frequencies. We fabricate the cut-wire metamaterial operating at microwave frequencies with lattice spacing around 10% of the free-space wavelength, and find good agreement with direct numerical simulations. Unlike the structures based on split-ring resonators, the nearest-neighbor coupling in cut-wire pairs can result in a magnetic stop-band with propagation in the transverse direction

Predicting polarization enhancement in multicomponent ferroelectric superlattices

Ab initio calculations are utilized as an input to develop a simple model of polarization in epitaxial short-period CaTiO3/SrTiO3/BaTiO3 superlattices grown on a SrTiO3 substrate. The model is then combined with a genetic algorithm technique to optimize the arrangement of individual CaTiO3, SrTiO3 and BaTiO3 layers in a superlattice, predicting structures with the highest possible polarization and a low in-plane lattice constant mismatch with the substrate. This modelling procedure can be applied to a wide range of layered perovskite-oxide nanostructures providing guidance for experimental development of nanoelectromechanical devices with substantially improved polar properties.Comment: 4 pages, submitted to PR