Semiclassical collision theory. Multidimensional Bessel uniform approximation

A multidimensional Bessel uniform approximation for the semiclassical S matrix is derived for the case of four real stationary phase points. A formula is also developed for the particular case when four stationary phase points may be considered to be well separated in pairs. The latter equation is then used in the treatment of two real and two complex stationary phase points

Semiclassical collision theory. Application of multidimensional uniform approximations to the atom-rigid-rotor system

The multidimensional Bessel and Airy uniform approximations developed earlier in this series for the semiclassical S matrix are applied to the atom rigid−rotor system. The need is shown for (a) using a geoemetrical criterion for determining whether a stationary phase point (s.p.pt) is a maximum, minimum, or saddle point; (b) choosing a proper quadrilateral configuration of the s.p.pts. with the phases as nearly equal as possible; and (c) choosing a unit cell to favor near−separation of variables. (a) and (b) apply both to the Airy and to the Bessel uniform approximations, and (c) to the Bessel. The use of a contour plot both to understand and to facilitate the search in new cases is noted. The case of real and complex−valued stationary phase points is also considered, and the Bessel uniform−in−pairs approximation is applied. Comparison is made with exact quantum results. As in the one−dimensional case, the Bessel is an improvement over the Airy for ’’k = 0’’ transitions, while for other transitions they give similar results. Comparison in accuracy with the results of the integral method is also given. As a whole, the agreement can be considered to be reasonable. The improvement of the present over various more approximate results is shown

Advanced materials for space nuclear power systems

The overall philosophy of the research was to develop and characterize new high temperature power conversion and radiator materials and to provide spacecraft designers with material selection options and design information. Research on three candidate materials (carbide strengthened niobium alloy PWC-11 for fuel cladding, graphite fiber reinforced copper matrix composites for heat rejection fins, and tungsten fiber reinforced niobium matrix composites for fuel containment and structural supports considered for space power system applications is discussed. Each of these types of materials offers unique advantages for space power applications

Neutrino Oscillations Induced by Gravitational Recoil Effects

Quantum gravitational fluctuations of the space-time background, described by virtual D branes, may induce neutrino oscillations if a tiny violation of the Lorentz invariance (or a violation of the equivalence principle) is imposed. In this framework, the oscillation length of massless neutrinos turns out to be proportional to M/E^2, where E is the neutrino energy and M is the mass scale characterizing the topological fluctuations in the vacuum. Such a functional dependence on the energy is the same obtained in the framework of loop quantum gravity.Comment: 5 pages, LaTex fil

Astrophysical Probes of the Constancy of the Velocity of Light

We discuss possible tests of the constancy of the velocity of light using distant astrophysical sources such as gamma-ray bursters (GRBs), Active Galactic Nuclei (AGNs) and pulsars. This speculative quest may be motivated by some models of quantum fluctuations in the space-time background, and we discuss explicitly how an energy-dependent variation in photon velocity \delta c/ c \sim - E / M arises in one particular quantum-gravitational model. We then discuss how data on GRBs may be used to set limits on variations in the velocity of light, which we illustrate using BATSE and OSSE observations of the GRBs that have recently been identified optically and for which precise redshifts are available. We show how a regression analysis can be performed to look for an energy-dependent effect that should correlate with redshift. The present data yield a limit M \gsim 10^{15} GeV for the quantum gravity scale. We discuss the prospects for improving this analysis using future data, and how one might hope to distinguish any positive signal from astrophysical effects associated with the sources.Comment: 37 pages LaTeX, 9 eps figures included, uses aasms4.st

The colour-magnitude relations of ClJ1226.9+3332, a massive cluster of galaxies at z=0.89

(Abridged) The colour-magnitude relations of one of the most massive, high redshift clusters of galaxies known have been studied. Photometry has been measured in the V, R, I, z, F606W, F814W, J and K bands to a depth of K*+2.5 and spectroscopy confirms 27 K band selected cluster members. The V-K colours are equivalent to a rest-frame colour of ~2700A-J, and provide a very sensitive measure of star-formation activity. HST ACS imaging has been used to morphologically classify the galaxies. The cluster has a low early-type fraction compared to nearby clusters, with only 33% of the cluster members having types E or S0. The early-type member galaxies form a clear red-sequence in all colours. The scatter and slope of the relations show no evolution compared to the equivalent Coma cluster relations, suggesting the stellar populations are already very old. The normalisation of the relations has been compared to models based on synthetic stellar populations, and are most consistent with stellar populations forming at z>3. Some late-type galaxies were found to lie on the red-sequence, suggesting that they have very similar stellar populations to the early-types. These results present a picture of a cluster in which the early-type galaxies are all old, but in which there must be future morphological transformation of galaxies to match the early-type fraction of nearby clusters. In order to preserve the tight colour-magnitude relation of early-types seen in nearby clusters, the late-type galaxies must transform their colours, through the cessation of star-formation, before the morphological transformation occurs. Such evolution is observed in the late-types lying on the colour-magnitude relation.Comment: Accepted for publication in MNRAS. 14 pages, 5 figure

A workbook of exercises for following directions to be used with high achieving children in grades one, three and five

Thesis (Ed.M.)--Boston Universit

Developmental changes in the germinability, desiccation tolerance, hardseededness, and longevity of individual seeds of Trifolium ambiguum

Background and Aims: Using two parental clones of outcrossing Trifolium ambiguum as a potential model system, we examined how during seed development the maternal parent, number of seeds per pod, seed position within the pod, and pod position within the inflorescence influenced individual seed fresh weight, dry weight, water content, germinability, desiccation tolerance, hardseededness, and subsequent longevity of individual seeds. Methods: Near simultaneous, manual reciprocal crosses were carried out between clonal lines for two experiments. Infructescences were harvested at intervals during seed development. Each individual seed was weighed and then used to determine dry weight or one of the physiological behaviour traits. Key Results: Whilst population mass maturity was reached at 33–36 days after pollination (DAP), seed-to-seed variation in maximum seed dry weight, when it was achieved, and when maturation drying commenced, was considerable. Individual seeds acquired germinability between 14 and 44 DAP, desiccation tolerance between 30 and 40 DAP, and the capability to become hardseeded between 30 and 47 DAP. The time for viability to fall to 50 % (p50) at 60 % relative humidity and 45 °C increased between 36 and 56 DAP, when the seed coats of most individuals had become dark orange, but declined thereafter. Individual seed f. wt at harvest did not correlate with air-dry storage survival period. Analysing survival data for cohorts of seeds reduced the standard deviation of the normal distribution of seed deaths in time, but no sub-population showed complete uniformity of survival period. Conclusions: Variation in individual seed behaviours within a developing population is inherent and inevitable. In this outbreeder, there is significant variation in seed longevity which appears dependent on embryo genotype with little effect of maternal genotype or architectural factors

Dark Matter in SuperGUT Unification Models

After a brief update on the prospects for dark matter in the constrained version of the MSSM (CMSSM) and its differences with models based on minimal supergravity (mSUGRA), I will consider the effects of unifying the supersymmetry-breaking parameters at a scale above M_{GUT}. One of the consequences of superGUT unification, is the ability to take vanishing scalar masses at the unification scale with a neutralino LSP dark matter candidate. This allows one to resurrect no-scale supergravity as a viable phenomenological model.Comment: 12 pages, 16 figures, To be published in the Proceedings of the 6th DSU Conference, Leon, Mexico, ed. D. Delepin

What if Supersymmetry Breaking Unifies beyond the GUT Scale?

We study models in which soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, $M_{in}$, above the GUT scale, \mgut. We assume that the scalar masses and gaugino masses have common values, $m_0$ and $m_{1/2}$ respectively, at $M_{in}$. We use the renormalization-group equations of the minimal supersymmetric SU(5) GUT to evaluate their evolutions down to \mgut, studying their dependences on the unknown parameters of the SU(5) superpotential. After displaying some generic examples of the evolutions of the soft supersymmetry-breaking parameters, we discuss the effects on physical sparticle masses in some specific examples. We note, for example, that near-degeneracy between the lightest neutralino and the lighter stau is progressively disfavoured as $M_{in}$ increases. This has the consequence, as we show in $(m_{1/2}, m_0)$ planes for several different values of $\tan \beta$, that the stau coannihilation region shrinks as $M_{in}$ increases, and we delineate the regions of the $(M_{in}, \tan \beta)$ plane where it is absent altogether. Moreover, as $M_{in}$ increases, the focus-point region recedes to larger values of $m_0$ for any fixed $\tan \beta$ and $m_{1/2}$. We conclude that the regions of the $(m_{1/2}, m_0)$ plane that are commonly favoured in phenomenological analyses tend to disappear at large $M_{in}$.Comment: 24 pages with 11 eps figures; references added, some figures corrected, discussion extended and figure added; version to appear in EPJ