Multifacet holographic optical elements

New types of holographic optical elements, combining the flexibility of computer generated holograms with the large space bandwidth product and high diffraction efficiency of interferometrically recorded volume phase holograms, are demonstrated. The optical elements are recorded by subdividing a volume hologram film surface into numerous small areas (facets), each of which is individually exposed under computer control. Each facet is used to produce a portion of the desired final wavefront. Three different optical elements are demonstrated

Electromagnetic interference aspects of integrating a UHF/VHF receiver onboard Mariner 5

Electromagnetic interference assessment in integration of Mariner 5 UHF/VHF receive

Global Real Estate Markets - Cycles and Fundamentals

The correlations among international real estate markets are surprisingly high, given the degree to which they are segmented. While industrial, office and retail properties exist all around the world, they are not economic substitutes because of locational specificity. In addition, the broad securitization of real estate property companies has, until recently, lagged that of other types of companies. Never-the-less, international property returns move together in dramatic fashion. In this paper, we use eleven years of global property returns to explore the factors influencing this co-movement. We attribute a substantial amount of the correlation across world property markets to the effects of changes in GNP, suggesting that real estate is a bet on fundamental economic variables which are correlated across countries. A decomposition shows that a local production factor is more important in some countries than in others.

Singular Integral Equations

The integral equationP∫cK(ζ′,ζ)ζ′−ζφ(ζ′)dζ′=h(ζ)φ(ζ)+f(ζ)is shown to have simple solutions obtained by standard and elementary methods if h and K have appropriate analytic properties.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70799/2/JMAPAQ-7-12-2121-1.pd

An Inverse Scattering Transform for the Lattice Potential KdV Equation

The lattice potential Korteweg-de Vries equation (LKdV) is a partial difference equation in two independent variables, which possesses many properties that are analogous to those of the celebrated Korteweg-de Vries equation. These include discrete soliton solutions, Backlund transformations and an associated linear problem, called a Lax pair, for which it provides the compatibility condition. In this paper, we solve the initial value problem for the LKdV equation through a discrete implementation of the inverse scattering transform method applied to the Lax pair. The initial value used for the LKdV equation is assumed to be real and decaying to zero as the absolute value of the discrete spatial variable approaches large values. An interesting feature of our approach is the solution of a discrete Gel'fand-Levitan equation. Moreover, we provide a complete characterization of reflectionless potentials and show that this leads to the Cauchy matrix form of N-soliton solutions

Accuracy of the QUAD4 thick shell element

The accuracy of the relatively new QUAD4 thick shell element is assessed via comparison with a theoretical solution for thick homogeneous and honeycomb flat simply supported plates under the action of a uniform pressure load. The theoretical thick plate solution is based on the theory developed by Reissner and includes the effects of transverse shear flexibility which are not included in the thin plate solutions based on Kirchoff plate theory. In addition, the QUAD4 is assessed using a set of finite element test problems developed by the MacNeal-Schwendler Corp. (MSC). Comparison of the COSMIC QUAD4 element as well as those from MSC and Universal Analytics, Inc. (UAI) for these test problems is presented. The current COSMIC QUAD4 element is shown to have excellent comparison with both the theoretical solutions and also those from the two commercial versions of NASTRAN that it was compared to

Stochastic evolution of four species in cyclic competition

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios, from single species domination to coexistence between non-interacting species. Using exact results and numerical simulations we discuss the temporal evolution of the system for different values of $N$, for different values of the reaction rates, as well as for different initial conditions. As expected, the stochastic evolution is found to closely follow the mean-field result for large $N$, with notable deviations appearing in proximity of extinction events. Different ways of characterizing and predicting extinction events are discussed.Comment: 19 pages, 6 figures, submitted to J. Stat. Mec

Existence and Uniqueness Theorems for the Neutron Transport Equation

In an attempt to understand the conditions under which the neutron transport equation has solutions, and the properties of those solutions, a number of existence and uniqueness theorems are proved. One finds that the properties of the solution are closely related to the boundedness of the source as well as to certain velocity‐space integrals of the scattering kernel. Both time‐dependent and time‐independent equations are considered as are also the time‐dependent and time‐independent adjoint equations. Although only a very few of all possible existence and uniqueness theorems for these equations are considered here, the work may serve as a guide to the treatment of similar problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70329/2/JMAPAQ-4-11-1376-1.pd

Low Energy Gamma-Ray Emission from Galactic Black Holes

X-ray observations of Galactic black holes (GBHs) such as Cygnus X-1 have greatly advanced the understanding of these objects. However, the vast majority of the observations have been restricted to energies below ~200 keV. The Compton Gamma-Ray Observatory (CGRO) allowed for the first time simultaneous observations at energies from ~25 keV up to >1 GeV. In particular, the BATSE experiment aboard CGRO was able to monitor low-energy gamma-ray emission from Cygnus X-1, as well as other GBHs, nearly continuously over a nine year period. Using the Enhanced BATSE Occultation Package (EBOP), light curves and spectra in the energy range 25–2000 keV have been obtained for six GBHs. Based on the spectra when the GBHs were in a high gamma-ray flux state, it is suggested that at least two different classes of GBHs exist. The first is characterized by a Comptonization spectrum below ~200 keV followed by a soft power law excess as exhibited by Cygnus X-1, GRO J0422+32, GRO J1719−24, and GX 339-4. The second class is characterized by simple power law spectrum in the full 25–2000 keV range, with no evidence for a Comptonization component, as exhibited by GRO J1655−40 and GRS 1915+105.Gamma-ray observations can serve as an important diagnostic in studying the physical processes around GBHs. More sensitive observations in the future at energies >250 keV will help answer questions regarding issues such as the nonthermal electron distribution, state transitions, and the connection to jets