Level density and level-spacing distributions of random, self-adjoint, non-Hermitian matrices

We investigate the level-density $\sigma(x)$ and level-spacing distribution $p(s)$ of random matrices $M=AF\neq M^{\dagger}$ where $F$ is a (diagonal) inner-product and $A$ is a random, real symmetric or complex Hermitian matrix with independent entries drawn from a probability distribution $q(x)$ with zero mean and finite higher moments. Although not Hermitian, the matrix $M$ is self-adjoint with respect to $F$ and thus has purely real eigenvalues. We find that the level density $\sigma_F(x)$ is independent of the underlying distribution $q(x)$, is solely characterized by $F$, and therefore generalizes Wigner's semicircle distribution $\sigma_W(x)$. We find that the level-spacing distributions $p(s)$ are independent of $q(x)$, are dependent upon the inner-product $F$ and whether $A$ is real or complex, and therefore generalize the Wigner's surmise for level spacing. Our results suggest $F$-dependent generalizations of the well-known Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary Ensemble (GUE) classes.Comment: 5 pages, 5 figures, revised tex

Numerical approach to the Schrodinger equation in momentum space

The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily amenable to an analytical solution and is rarely taught. We present a numerical approach to the Schrodinger equation in momentum space. After a suitable discretization process, we obtain the Hamiltonian matrix and diagonalize it numerically. By considering a few examples, we show that this approach is ideal for exploring bound-states in a localized potential and complements the traditional (analytical or numerical) treatment of the Schrodinger equation in real-space.Comment: 14 pages, 4 figures, several changes and one figure correctio

Metals and Oxygen Mining from Meteorites, Asteroids and Planets using Reusable Ionic Liquids

In order for humans to explore beyond Low Earth Orbit both safely and economically, it will be essential to learn how to make use of in situ materials and energy in an environment much different than on earth. Precursor robotic missions will be necessary to determine what resources will be available and to demonstrate the capabilities for their use. To that end, we have recently been studying acidic Ionic Liquid (IL) systems for use in a low temperature (< 200 C) process to solubilize regolith, and to extract, as water, the oxygen available in metal oxides. Using this method, we have solubilized lunar regolith simulant (JSC-1A), as well as extraterrestrial materials in the form of meteorites, and have extracted up to 80% of the available oxygen. Moreover, by using a hydrogen gas electrode, we have shown that the IL can be regenerated at the anode and metals (e.g. iron) can be plated onto the cathode. These results indicate that IL processing is an excellent candidate for extracting oxygen in situ, for life support and propulsion, and for extracting metals to be used as feedstock in fabrication processes. We have obtained small amounts of meteorite materials believed by meteoriticists to have originated from our moon, Mars, and the asteroid Vesta, and were able to solubilize those using acidic IL systems. From the Vesta meteorite, we were able to extract about 60% of the available oxygen as water. As far as is known, this is the first time that extraterrestrial/earth hybrid water has been obtained. NMR analysis provided proof that the liquid retrieved is indeed water. We have also been able to electro-plate nickel and iron contained in meteorite material. By varying voltage they can be plated separately (electro-winning), and we plan to soon have sufficient quantities to form usable parts utilizing the additive manufacturing process

Development of extinction imagers for the determination of atmospheric optical extinction: final report

The primary goals of this project for JTO and ONR (Grant N00014-07-1-1060) were to further develop Extinction Imagers for use in the ocean environment, and to extend the capabilities into the Short Wave IR (SWIR). Extinction Imaging is a method for determining the effective extinction coefficient over an extended path using a sensor at one end of the path. It uses calibrated imagers to acquire the relative radiance of a dark target near the other the end of the path and the horizon sky in the direction of the dark target. It is completely passive and thus covert, and the hardware is robust and relatively inexpensive. It uses rigorous equations, which determine the extinction coefficient from the measured apparent contrast of the radiance of the dark target with respect to the horizon sky. The project was very successful. We found that the ocean surface could readily be used as a dark target in red and SWIR wavelengths. Both the red and the SWIR measurement results were excellent for daytime. Comparisons with standard instruments, as well as uncertainty analysis, indicated that extinction imagers provide better measurements of the atmospheric extinction losses over extended paths than other methods of which we are aware. Our secondary goals were to address the night regime, and to address slanted paths above the horizontal. Regarding night, we found that the visible sensor acquired excellent data, but the ocean surface was not a good dark target in our wavelengths. Recommendations on the handling of night are given in the report. Regarding the lines of sight above the horizon, we developed a slant path algorithm that determines beam transmittance. It performed very well. Recommendations are made regarding integration of these techniques for military applications.Joint Technology Office via Office of Naval ResearchGrant N00014-07-1-106

Metals and Oxygen Mining from Meteorites, Asteroids and Planets using Reusable Ionic Liquids

No abstract availabl

Structure and Colors of Diffuse Emission in the Spitzer Galactic First Look Survey

We investigate the density structure of the interstellar medium using new high-resolution maps of the 8 micron, 24 micron, and 70 micron surface brightness towards a molecular cloud in the Gum Nebula, made as part of the Spitzer Space Telescope Galactic First Look Survey. The maps are correlated with 100 micron images measured with IRAS. At 24 and 70 micron, the spatial power spectrum of surface brightness follows a power law with spectral index -3.5. At 24 micron, the power law behavior is remarkably consistent from the 0.2 degree size of our maps down to the 5 arcsecond spatial resolution. Thus, the structure of the 24 micron emission is self-similar even at milliparsec scales. The combined power spectrum produced from Spitzer 24 micron and IRAS 25 micron images is consistent with a change in the power law exponent from -2.6 to -3.5. The decrease may be due to the transition from a two-dimensional to three-dimensional structure. Under this hypothesis, we estimate the thickness of the emitting medium to be 0.3 pc.Comment: 13 Pages, 3 Figures, to be published in Astrophysical Journal Supplement Series (Spitzer Special Issue), volume 154. Uses aastex v5.

Making subaltern shikaris: histories of the hunted in colonial central India

Academic histories of hunting or shikar in India have almost entirely focused on the sports hunting of British colonists and Indian royalty. This article attempts to balance this elite bias by focusing on the meaning of shikar in the construction of the Gond ‘tribal’ identity in late nineteenth and early twentieth-century colonial central India. Coining the term ‘subaltern shikaris’ to refer to the class of poor, rural hunters, typically ignored in this historiography, the article explores how the British managed to use hunting as a means of state penetration into central India’s forest interior, where they came to regard their Gond forest-dwelling subjects as essentially and eternally primitive hunting tribes. Subaltern shikaris were employed by elite sportsmen and were also paid to hunt in the colonial regime’s vermin eradication programme, which targeted tigers, wolves, bears and other species identified by the state as ‘dangerous beasts’. When offered economic incentives, forest dwellers usually willingly participated in new modes of hunting, even as impact on wildlife rapidly accelerated and became unsustainable. Yet as non-indigenous approaches to nature became normative, there was sometimes also resistance from Gond communities. As overkill accelerated, this led to exclusion of local peoples from natural resources, to their increasing incorporation into dominant political and economic systems, and to the eventual collapse of hunting as a livelihood. All of this raises the question: To what extent were subaltern subjects, like wildlife, ‘the hunted’ in colonial India