Convergence of eigenvalues for a highly non-self-adjoint differential operator

In this paper we study a family of operators dependent on a small parameter $\epsilon > 0$, which arise in a problem in fluid mechanics. We show that the spectra of these operators converge to N as $\epsilon \to 0$, even though, for fixed $\epsilon > 0$, the eigenvalue asymptotics are quadratic.Comment: 16 page

Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples

This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed sensing (CS) when the power spectrum is sparse, but applies to sparse and nonsparse power spectra alike. The estimates are consistent piecewise constant approximations whose resolutions (width of the piecewise constant segments) are controlled by the periodicity of the multi-coset sampling. We show that compressive estimates exhibit better tradeoffs among the estimator's resolution, system complexity, and average sampling rate compared to their noncompressive counterparts. For suitable sampling patterns, noncompressive estimates are obtained as least squares solutions. Because of the non-negativity of power spectra, compressive estimates can be computed by seeking non-negative least squares solutions (provided appropriate sampling patterns exist) instead of using standard CS recovery algorithms. This flexibility suggests a reduction in computational overhead for systems estimating both sparse and nonsparse power spectra because one algorithm can be used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure

Commensurability oscillations due to pinned and drifting orbits in a two-dimensional lateral surface superlattice

We have simulated conduction in a two-dimensional electron gas subject to a weak two-dimensional periodic potential, $V_x \cos(2\pi x/a) + V_y \cos(2\pi y/a)$. The usual commensurability oscillations in $\rho_{xx}(B)$ are seen with $V_x$ alone. An increase of $V_y$ suppresses these oscillations, rather than introducing the additional oscillations in $\rho_{yy}(B)$ expected from previous perturbation theories. We show that this behavior arises from drift of the guiding center of cyclotron motion along contours of an effective potential. Periodic modulation in the magnetic field can be treated in the same way.Comment: 3 pages text, 4 eps figures, revte

The Sellout by Paul Beatty: Unmitigated Blackness in Obama\u27s America

Visibility and invisibility are long-standing tropes in the African-American literary tradition. Frequently they are presented in satiric language. I argue that Paul Beatty\u27s Mann Booker Award-winning novel The Sellout now holds an important role in this tradition. Specifically, The Sellout hearkens specifically to Ralph Ellison\u27s Invisible Man and to Paul Beatty\u27s earlier novel The White Boy Shuffle. Further, The Sellout exposes the ongoing presence and function of racism in an America that has elected its first African-American president, Barack Obama, and that now claims to be post-racial, even as its spectral reproduction and commodification of blackness persist. By analyzing the four primary male characters, I show that the novel concludes that America is not yet ready for true multicultural heterogeneity because neither white America nor black America has truly reconciled itself with America\u27s historical and continuing racism, and I show that the novel\u27s solution is an anti-racist philosophy of Unmitigated Blackness

Sagnac effect in a chain of mesoscopic quantum rings

The ability to interferometrically detect inertial rotations via the Sagnac effect has been a strong stimulus for the development of atom interferometry because of the potential 10^{10} enhancement of the rotational phase shift in comparison to optical Sagnac gyroscopes. Here we analyze ballistic transport of matter waves in a one dimensional chain of N coherently coupled quantum rings in the presence of a rotation of angular frequency, \Omega. We show that the transmission probability, T, exhibits zero transmission stop gaps as a function of the rotation rate interspersed with regions of rapidly oscillating finite transmission. With increasing N, the transition from zero transmission to the oscillatory regime becomes an increasingly sharp function of \Omega with a slope \partialT/\partial \Omega N^2. The steepness of this slope dramatically enhances the response to rotations in comparison to conventional single ring interferometers such as the Mach-Zehnder and leads to a phase sensitivity well below the standard quantum limit

Evolution of secondary electron emission characteristics of spacecraft surfaces: Importance to spacecraft charging

Secondary electron emission (SEE) plays a key role in spacecraft charging [Garrett, 1981; Frooninckx and Sojka, 1992] . As a result, spacecraft charging codes require knowledge of the SEE characteristics of various materials in order to predict vehicle potentials in various orbital environments [Katz, et. al., 1986]. Because SEE is a surface phenomenon, occurring in the first few atomic layers of a material, the SEE characteristics of a given surface are extremely sensitive to changes in surface condition—e.g., the addition or removal of surface contaminants, or changes in surface morphology. That spacecraft surfaces can and generally do undergo significant evolution during their operational lifetimes is a fact well established by NASA\u27s Long Duration Exposure Facility (LDEF) [Crutcher, et al., 1991a]. Deposition and removal of contaminants can occur as a result of preferential adsorption of gases on cooler surfaces, the collection of ionized gases on negatively charged surfaces, atomic-oxygen-induced oxidation, photodissociation under vacuum uv bombardment, and ion-induced desorption. Since SEE is material-dependent phenomenon, it is reasonable to assume that as a spacecraft\u27s surfaces evolve, so too do it\u27s SEE characteristics. In order to determine whether or not charging models need incorporate the effects of changing surface conditions aboard operating spacecraft, data assessing the impact of these changes on the SEE characteristics of various surfaces are required. Measurements have therefore been made investigating the dynamic evolution of secondary electron (SE) yields resulting from energetic electron bombardment of typical spacecraft materials in a rarefied atmosphere representative of the microenvironment surrounding space vehicles. A detailed report of the experiment and results has been given elsewhere [Davies, 1996; Davies and Dennison, 1997]; what follows here is a brief summary

The instability of planetary systems in binaries: how the Kozai mechanism leads to strong planet-planet interactions

In this letter we consider the evolution of a planetary system around a star inside a wide binary. We simulate numerically the evolution of the planetary orbits for both co-planar and highly-inclined systems. We find that the Kozai mechanism operates in the latter case. This produces a highly eccentric outer planet whose orbit crosses those of some of the inner planets. Strong planet-planet interactions then follow resulting in the ejection of one or more planets. We note that planetary systems resembling our solar system, formed around single stars in stellar clusters may exchange into binaries and thus will be vulnerable to planet stripping. This process will reduce the number of solar-system like planetary systems, and may produce at least some of the observed extra-solar planets.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter

Applications of Secondary Electron Energy- and Angular-Distributions to Spacecraft Charging

Secondary electron (SE) emission from spacecraft surfaces as a result of energetic electron bombardment is a key process in the electrical charging of spacecraft. It has been suggested that incorporating more complete knowledge of the energy- and angular-distributions of secondary electrons is necessary to fully model how SE emission and spacecraft charging are affected by re-adsorption of low energy electrons in the presence of charge-induced electrostatic fields and ambient magnetic fields in the spacecraft environment. We present data for such energy- and angular-distributions from sputtered, polycrystalline gold surfaces. The data are compared to empirical SE emission models and found to agree well. We also discuss at what level inclusion of such energy- and angular-distributions will affect models of spacecraft charging for both positive and negative surface charging

Scientific Objectives, Measurement Needs, and Challenges Motivating the PARAGON Aerosol Initiative

Aerosols are involved in a complex set of processes that operate across many spatial and temporal scales. Understanding these processes, and ensuring their accurate representation in models of transport, radiation transfer, and climate, requires knowledge of aerosol physical, chemical, and optical properties and the distributions of these properties in space and time. To derive aerosol climate forcing, aerosol optical and microphysical properties and their spatial and temporal distributions, and aerosol interactions with clouds, need to be understood. Such data are also required in conjunction with size-resolved chemical composition in order to evaluate chemical transport models and to distinguish natural and anthropogenic forcing. Other basic parameters needed for modeling the radiative influences of aerosols are surface reflectivity and three-dimensional cloud fields. This large suite of parameters mandates an integrated observing and modeling system of commensurate scope. The Progressive Aerosol Retrieval and Assimilation Global Observing Network (PARAGON) concept, designed to meet this requirement, is motivated by the need to understand climate system sensitivity to changes in atmospheric constituents, to reduce climate model uncertainties, and to analyze diverse collections of data pertaining to aerosols. This paper highlights several challenges resulting from the complexity of the problem. Approaches for dealing with them are offered in the set of companion papers