The Sort on Radioactive Waste Type model: A method to sort single-shell tanks into characteristic groups. Revision 2

The SORWT model presents a methodology to group SSTs that is both simple to understand and logical in its assumptions and construction. The SORWT model has predicted the existence of 24 groups of SSTs ranging from 22 tanks per group to two tanks per group. These 24 groups encompass 133 tanks and 93% of the total waste contained in SSTs. The first 14 groups (i.e., those that contain four tanks per group or more) represent 109 tanks and 83% of the total waste volume. This demonstrates the potential for using the SORWT model to efficiently allocate resources and to maximize characterization information gained by a minimum number of sampling events. The verification study has shown that the SST groups predicted by the SORWT model are statistically significant and reduce the variability in the concentrations for all analytes examined. The SORWT model organizes a vast amount of information and presents clear options on which SSTs are more desirable to sample. The model is also simple and flexible in its ability to incorporate new parameters such as new SST analytical data, shifting programmatic needs, and/or risk assessment-oriented criteria. This report presents the nominal composition, inventory, and uncertainty for five of the 24 SORWT groups, representing 28 tanks, 10% of the total waste volume, and 29% of the total sludge volume in SSTs. Consequently, this document provides a logical beginning framework for tank waste characterization until further information becomes available or different programmatic needs are identified

Bogoliubov Coefficients of 2D Charged Black Holes

We exactly calculate the thermal distribution and temperature of Hawking radiation for a two-dimensional charged dilatonic black hole after it has settled down to an "equilibrium" state. The calculation is carried out using the Bogoliubov coefficients. The background of the process is furnished by a preexisting black hole and not by collapsing matter as considered by Giddings and Nelson for the case of a Schwarzschild black hole. Furthermore, the vanishing of the temperature and/or the Hawking radiation in the extremal case is obtained as a regular limit of the general case.Comment: 9 pages, 1 eps figur

Modular Equations and Distortion Functions

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.Comment: 23 page

Quadruple Yukawa Unification in the Minimal Supersymmetric Model

Predictions for m_t, tan beta, m_nu_tau are calculated for quadruple third family t-b-tau-nu_tau Yukawa unified models in the MSSM. The renormalisation group equations for the 3 families of the MSSM, including the right handed neutrino, are presented. For right handed tau neutrino Majorana masses that are bigger than 10^11 GeV, the tau neutrino mass is consistent with present cosmological bounds. The m_t, tan beta predictions are approximately equivalent to those in triple third family Yukawa unified models.Comment: 10 pages plain LaTex, uuencoded .epsf files in part 2. Revised version has NO changes to content, merely changed format to .tex fil

The Sort on Radioactive Waste Type model: A method to sort single-shell tanks into characteristic groups. Revision 2

The SORWT model presents a methodology to group SSTs that is both simple to understand and logical in its assumptions and construction. The SORWT model has predicted the existence of 24 groups of SSTs ranging from 22 tanks per group to two tanks per group. These 24 groups encompass 133 tanks and 93% of the total waste contained in SSTs. The first 14 groups (i.e., those that contain four tanks per group or more) represent 109 tanks and 83% of the total waste volume. This demonstrates the potential for using the SORWT model to efficiently allocate resources and to maximize characterization information gained by a minimum number of sampling events. The verification study has shown that the SST groups predicted by the SORWT model are statistically significant and reduce the variability in the concentrations for all analytes examined. The SORWT model organizes a vast amount of information and presents clear options on which SSTs are more desirable to sample. The model is also simple and flexible in its ability to incorporate new parameters such as new SST analytical data, shifting programmatic needs, and/or risk assessment-oriented criteria. This report presents the nominal composition, inventory, and uncertainty for five of the 24 SORWT groups, representing 28 tanks, 10% of the total waste volume, and 29% of the total sludge volume in SSTs. Consequently, this document provides a logical beginning framework for tank waste characterization until further information becomes available or different programmatic needs are identified

Bose-Einstein condensation and superfluidity of dilute Bose gas in a random potential

We develop the dilute Bose gas model with random potential in order to understand the Bose system in random media such as 4He in porous glass. Using the random potential taking account of the pore size dependence, we can compare quantitatively the calculated specific heat with the experimental results, without free parameters. The agreement is excellent at low temperatures, which justifies our model. The relation between Bose condensation and superfluidity is discussed. Our model can predict some unobserved phenomena in this system.Comment: 9 pages, 11 figures, accepted for publication in Phys. Rev.

Exclusion statistics: A resolution of the problem of negative weights

We give a formulation of the single particle occupation probabilities for a system of identical particles obeying fractional exclusion statistics of Haldane. We first derive a set of constraints using an exactly solvable model which describes an ideal exclusion statistics system and deduce the general counting rules for occupancy of states obeyed by these particles. We show that the problem of negative probabilities may be avoided with these new counting rules.Comment: REVTEX 3.0, 14 page

Application of Time Transfer Function to McVittie Spacetime: Gravitational Time Delay and Secular Increase in Astronomical Unit

We attempt to calculate the gravitational time delay in a time-dependent gravitational field, especially in McVittie spacetime, which can be considered as the spacetime around a gravitating body such as the Sun, embedded in the FLRW (Friedmann-Lema\^itre-Robertson-Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte {\it et al.} (Class. Quant. Grav. 21:4463, 2004) and Teyssandier and Le Poncin-Lafitte (Class. Quant. Grav. 25:145020, 2008), which is originally related to Synge's world function $\Omega(x_A, x_B)$ and enables to circumvent the integration of the null geodesic equation. We re-examine the global cosmological effect on light propagation in the solar system. The round-trip time of a light ray/signal is given by the functions of not only the spacial coordinates but also the emission time or reception time of light ray/signal, which characterize the time-dependency of solutions. We also apply the obtained results to the secular increase in the astronomical unit, reported by Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267, 2004), and we show that the leading order terms of the time-dependent component due to cosmological expansion is 9 orders of magnitude smaller than the observed value of $d{\rm AU}/dt$, i.e., $15 \pm 4$ ~[m/century]. Therefore, it is not possible to explain the secular increase in the astronomical unit in terms of cosmological expansion.Comment: 13 pages, 2 figures, accepted for publication in General Relativity and Gravitatio

Study of Dipole Resonance Strength in 12-C via the Reactions 12-C(pol.p,p'c)

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Anisotropic Release of the Residual Zero-point Entropy in the Spin Ice Compound Dy2Ti2O7: Kagome-ice Behavior

We report the specific heat and entropy of single crystals of the spin ice compound Dy2Ti2O7 at temperatures down to 0.35 K. We apply magnetic fields along the four characteristic directions: [100], [110], [111] and [112]. Because of Ising anisotropy, we observe anisotropic release of the residual zero-point entropy, attributable to the difference in frustration dimensionality. In the high magnetic field along these four directions, the residual entropy is almost fully released and the activation entropy reaches Rln2. However, in the intermediate field region, the entropy in fields along the [111] direction is different from those for the other three field directions. For the [111] direction the frustration structure changes from that of three-dimensional(3D) pyrochlore to that of two-dimensional(2D) Kagome-like lattice with constraint due to the ice rule, leading to different values of zero-point entropy.Comment: 4 pages, 4 figures, to appear in Phys. Rev.