Reducing the Effects of Unequal Number of Games on Rankings

Ranking is an important mathematical process in a variety of contexts such as information retrieval, sports and business. Sports ranking methods can be applied both in and beyond the context of athletics. In both settings, once the concept of a game has been defined, teams (or individuals) accumulate wins, losses, and ties, which are then factored into the ranking computation. Many settings involve an unequal number of games between competitors. This paper demonstrates how to adapt two sports rankings methods, the Colley and Massey ranking methods, to settings where an unequal number of games are played between the teams. In such settings, the standard derivations of the methods can produce nonsensical rankings. This paper introduces the idea of including a super-user into the rankings and considers the effect of this fictitious player on the ratings. We apply such techniques to rank batters and pitchers in Major League baseball, professional tennis players, and participants in a free online social game. The ideas introduced in this paper can further the scope that such methods are applied and the depth of insight they offer

An evaluation of mercury removal in the IDMS using the nitric acid flowsheet

The present DWPF flowsheet calls for the chemical treatment of waste sludge with 90 wt % formic acid prior to the addition of the Precipitate Hydrolysis Aqueous (PHA) product. An alternative processing methodology, denoted the Nitric Acid Flowsheet'', has been proposed. in the application of this flowsheet, nitric acid would be used to neutralize sludge base components (hydroxides and carbonates) prior to the addition of late wash PHA. The late wash PHA will contain sufficient quantities of formic acid to adequately complete necessary reduction-oxidation (REDOX) reactions

Cold collisions of OH and Rb. I: the free collision

We have calculated elastic and state-resolved inelastic cross sections for cold and ultracold collisions in the Rb($^1 S$) + OH($^2 \Pi_{3/2}$) system, including fine-structure and hyperfine effects. We have developed a new set of five potential energy surfaces for Rb-OH($^2 \Pi$) from high-level {\em ab initio} electronic structure calculations, which exhibit conical intersections between covalent and ion-pair states. The surfaces are transformed to a quasidiabatic representation. The collision problem is expanded in a set of channels suitable for handling the system in the presence of electric and/or magnetic fields, although we consider the zero-field limit in this work. Because of the large number of scattering channels involved, we propose and make use of suitable approximations. To account for the hyperfine structure of both collision partners in the short-range region we develop a frame-transformation procedure which includes most of the hyperfine Hamiltonian. Scattering cross sections on the order of $10^{-13}$ cm$^2$ are predicted for temperatures typical of Stark decelerators. We also conclude that spin orientation of the partners is completely disrupted during the collision. Implications for both sympathetic cooling of OH molecules in an environment of ultracold Rb atoms and experimental observability of the collisions are discussed.Comment: 20 pages, 16 figure

Long beating wavelength in the Schwarz-Hora effect

Thirty years ago, H.Schwarz has attempted to modulate an electron beam with optical frequency. When a 50-keV electron beam crossed a thin crystalline dielectric film illuminated with laser light, electrons produced the electron-diffraction pattern not only at a fluorescent target but also at a nonfluorescent target. In the latter case the pattern was of the same color as the laser light (the Schwarz-Hora effect). This effect was discussed extensively in the early 1970s. However, since 1972 no reports on the results of further attempts to repeat those experiments in other groups have appeared, while the failures of the initial such attempts have been explained by Schwarz. The analysis of the literature shows there are several unresolved up to now contradictions between the theory and the Schwarz experiments. In this work we consider the interpretation of the long-wavelength spatial beating of the Schwarz-Hora radiation. A more accurate expression for the spatial period has been obtained, taking into account the mode structure of the laser field within the dielectric film. It is shown that the discrepancy of more than 10% between the experimental and theoretical results for the spatial period cannot be reduced by using the existing quantum models that consider a collimated electron beam.Comment: 3 pages, RevTe

Immobilization of simulated high-level radioactive waste in borosilicate glass: Pilot scale demonstrations

The Integrated DWPF Melter System (IDMS), operated by the Savannah River Laboratory, is a pilot scale facility used in support of the start-up and operation of the Department of Energy's Defense Waste Processing Facility. The IDMS has successfully demonstrated, on an engineering scale (one-fifth), that simulated high level radioactive waste (HLW) sludge can be chemically treated with formic acid to adjust both its chemical and physical properties, and then blended with simulated precipitate hydrolysis aqueous (PHA) product and borosilicate glass frit to produce a melter feed which can be processed into a durable glass product. The simulated sludge, PHA and frit were blended, based on a product composition program, to optimize the loading of the waste glass as well as to minimize those components which can cause melter processing and/or glass durability problems. During all the IDMS demonstrations completed thus far, the melter feed and the resulting glass that has been produced met all the required specifications, which is very encouraging to future DWPF operations. The IDMS operations also demonstrated that the volatile components of the melter feed (e.g., mercury, nitrogen and carbon, and, to a lesser extent, chlorine, fluorine and sulfur) did not adversely affect the melter performance or the glass product

Phonon-Coupled Electron Tunneling in Two and Three-Dimensional Tunneling Configurations

We treat a tunneling electron coupled to acoustical phonons through a realistic electron phonon interaction: deformation potential and piezoelectric, in two or three-dimensional tunneling configurations. Making use of slowness of the phonon system compared to electron tunneling, and using a Green function method for imaginary time, we are able to calculate the change in the transition probability due to the coupling to phonons. It is shown using standard renormalization procedure that, contrary to the one-dimensional case, second order perturbation theory is sufficient in order to treat the deformation potential coupling, which leads to a small correction to the transmission coefficient prefactor. In the case of piezoelectric coupling, which is found to be closely related to the piezoelectric polaron problem, vertex corrections need to be considered. Summing leading logarithmic terms, we show that the piezoelectric coupling leads to a significant change of the transmission coefficient.Comment: 17 pages, 4 figure

Physical Electronics

Contains reports on three research projects

Quantum Phase and Quantum Phase Operators: Some Physics and Some History

After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions of the field: Are there (unique) quantum phase operators and are there quantum systems which can determine their nature? I conclude with a critique of recent proposals which have shed new light on the problem.Comment: 19 pages, 2 Figs. taken from published articles, LaTeX, to be published in Physica Scripta, Los Alamos preprint LA-UR-92-352

Application of airborne photogrammetry for the visualisation and assessment of contamination migration arising from a Fukushima waste storage facility

Airborne systems such as lightweight and highly portable unmanned aerial vehicles (UAVs) are becoming increasingly widespread in both academia and industry - with an ever-increasing range of applications, including (but not limited to), air quality sampling, wildlife monitoring and land-use mapping.In this work, high-resolution airborne photogrammetry obtained using a multi-rotor system operating at low survey altitudes, is combined with ground-based radiation mapping data acquired at an interim storage facility for wastes removed as part of the large-scale Fukushima clean-up program. The investigation aimed to assess the extent to which the remediation program at a specific site has contained the stored contaminants, as well as present a new methodology for rapidly surveying radiological sites globally. From the three-dimensional rendering of the site of interest, it was possible to not only generate a powerful graphic confirming the elevated radiological intensity existing at the location of the waste bags, but also to also illustrate the downslope movement of contamination due to species leakage from the large 1m3 storage bags. The entire survey took less than 1 h to perform, and was subsequently post-processed using graphical information software to obtain the renderings. The conclusions within this study not only highlight the usefulness of incorporating three-dimensional renderings within radiation mapping protocols, but also conclude that current methods of monitoring these storage facilities in the long term could be improved through the integration of UAVs within the standard protocol

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page