Operator Transformations Between Exactly Solvable Potentials and Their Lie Group Generators

One may obtain, using operator transformations, algebraic relations between the Fourier transforms of the causal propagators of different exactly solvable potentials. These relations are derived for the shape invariant potentials. Also, potentials related by real transformation functions are shown to have the same spectrum generating algebra with Hermitian generators related by this operator transformation.Comment: 13 pages with one Postscript figure, uses LaTeX2e with revte

The use of Fe-30% Ni and Fe-30% Ni-Nb alloys as model systems for studying the microstructural evolution during the hot deformation of austenite

The development of physically-based models of microstructural evolution during thermomechanical processing of metallic materials requires knowledge of the internal state variable data, such as microstructure, texture, and dislocation substructure characteristics, over a range of processing conditions. This is a particular problem for steels, where transformation of the austenite to a variety of transformation products eradicates the hot deformed microstructure. This article reports on a model Fe-30wt% Ni-based alloy, which retains a stable austenitic structure at room temperature, and has, therefore, been used to model the development of austenite microstructure during hot deformation of conventional low carbon-manganese steels. It also provides an excellent model alloy system for microalloy additions. Evolution of the microstructure and crystallographic texture was characterized in detail using optical microscopy, X-ray diffraction (XRD), SEM, EBSD, and TEM. The dislocation substructure has been quantified as a function of crystallographic texture component for a variety of deformation conditions for the Fe-30% Ni-based alloy. An extension to this study, as the use of a microalloyed Fe-30% Ni-Nb alloy in which the strain induced precipitation mechanism was studied directly. The work has shown that precipitation can occur at a much finer scale and higher number density than hitherto considered, but that pipe diffusion leads to rapid coarsening. The implications of this for model development are discussed

Influence of severe plastic deformation on the precipitation hardening of a FeSiTi steel

The combined strengthening effects of grain refinement and high precipitated volume fraction (~6at.%) on the mechanical properties of FeSiTi alloy subjected to SPD processing prior to aging treatment were investigated by atom probe tomography and scanning transmission electron microscopy. It was shown that the refinement of the microstructure affects the precipitation kinetics and the spatial distribution of the secondary hardening intermetallic phase, which was observed to nucleate heterogeneously on dislocations and sub-grain boundaries. It was revealed that alloys successively subjected to these two strengthening mechanisms exhibit a lower increase in mechanical strength than a simple estimation based on the summation of the two individual strengthening mechanisms

Time evolution of the Rabi Hamiltonian from the unexcited vacuum

The Rabi Hamiltonian describes a single mode of electromagnetic radiation interacting with a two-level atom. Using the coupled cluster method, we investigate the time evolution of this system from an initially empty field mode and an unexcited atom. We give results for the atomic inversion and field occupation, and find that the virtual processes cause the field to be squeezed. No anti-bunching occurs.Comment: 25 pages, 8 figures, RevTe

Summing Divergent Perturbative Series in a Strong Coupling Limit. The Gell-Mann - Low Function of the \phi^4 Theory

An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Operation of the algorithm is illustrated by test examples, method for estimating errors is developed, and an optimization procedure is described. Application of the algorithm to the $\phi^4$ theory gives a behavior $\beta(g)\approx 7.4 g^{0.96}$ at large $g$ for its Gell-Mann -- Low function. The fact that the exponent is close to unity can be interpreted as a manifestation of the logarithmic branching of the type $\beta(g)\sim g (\ln g)^{-\gamma}$ (with $\gamma\approx 0.14$), which is confirmed by independent evidence. In any case, the $\phi^4$ theory is internally consistent. The procedure of summing perturbartive series with arbitrary values of expansion parameter is discussed.Comment: 23 pages, PD

Increased L‐[1– 11 C] Leucine Uptake in the Leptomeningeal Angioma of Sturge‐Weber Syndrome: A PET Study

BACKGROUND AND PURPOSE We used L‐[1– 11 C]leucine (LEU) positron emission tomography (PET) to measure amino acid uptake in children with Sturge‐Weber syndrome (SWS), and to relate amino acid uptake measures with glucose metabolism. METHODS LEU and 2‐deoxy‐2[ 18 F]fluoro‐D‐glucose (FDG) PET were performed in 7 children (age: 5 months‐13 years) with unilateral SWS. Asymmetries of LEU uptake in the posterior brain region, underlying the angioma and in frontal cortex, were measured and correlated with glucose hypometabolism. Kinetic analysis of LEU uptake was performed in 4 patients. RESULTS Increased LEU standard uptake value (SUV, mean: 15.1%) was found in the angioma region in 6 patients, and smaller increases in LEU SUV (11.5%) were seen in frontal cortex in 4 of the 6 patients, despite normal glucose metabolism in frontal regions. High LEU SUV was due to both increased tracer transport (3/4 patients) and high protein synthesis rates (2/4). FDG SUV asymmetries in the angioma region were inversely related to LEU SUV asymmetries ( r =–.83, P = .042). CONCLUSIONS Increased amino acid uptake in the angioma region and also in less affected frontal regions may provide a marker of pathological mechanisms contributing to chronic brain damage in children with SWS. J Neuroimaging 2012;22:177‐183.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91095/1/j.1552-6569.2010.00565.x.pd

Quantitative molecular thermochemistry based on path integrals

The calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normal mode analysis to calculate the vibrational and rotational contributions. We utilize path integral Monte Carlo (PIMC) for going beyond the harmonic analysis, to calculate the vibrational and rotational contributions to ab initio energies. This is an application and extension of a method previously developed in our group

What's in a grade? The multidimensional nature of what teacher-assigned grades assess in high school

Historically, teacher-assigned grades have been seen as unreliable subjective measures of academic knowledge, since grades and standardized tests have traditionally correlated at about the 0.5 to 0.6 level, and thus explain about 25–35% of each other. However, emerging literature indicates that grades may be a multidimensional assessment of both student academic knowledge and a student's ability to negotiate the social processes of schooling, such as behavior, participation, and effort. This study analyzed the high school transcript component of the Education Longitudinal Study of 2002 (ELS:2002) using multidimensional scaling (MDS) to describe the relationships between core subject grades, non-core subject grades, and standardized test scores in mathematics and reading. The results indicate that when accounting for the academic knowledge component assessed through standardized tests, teacher-assigned grades may be a useful assessment of a student's ability at the non-cognitive aspects of school. Implications for practice, research, and policy are discussed

Anisotropy in mechanical properties and fracture behavior of an oxide dispersion Fe20Cr5Al alloy

Anisotropy of fracture toughness and fracture behavior of Fe20Cr5Al oxide dispersion-strengthened alloy has been investigated by means of compression tests, hardness tests, and wedge splitting test. The results show a small effect of the compression direction on yield strength (YS) and strain hardening. The YS is minimum for longitudinal direction and maximum for the tangential direction. The transverse plastic strain ratio is similar for tangential and longitudinal directions but very different from that in normal direction. Hardness depends on the indentation plane; it is lower for any plane parallel to the L-T plane and of similar magnitude for the other orthogonal planes, i.e., the L-S and T-S planes. Macroscopically, two failure modes have been observed after wedge-splitting tests, those of LS and TS specimens in which fracture deviates along one or two branches normal to the notch plane, and those of LT, TL, SL, and ST specimens in which fracture propagates along the notch plane. Besides LT and TL specimens present delaminations parallel to L-T plane. Both, the fracture surface of branching cracks and that of the delaminations, show an intergranular brittle fracture appearance. It is proposed that the main cause of the delamination and crack branching is the alignment in the mesoscopic scale of the ultrafine grains structure which is enhanced by the 〈110〉- texture of the material and by the presence in the grain boundaries of both yttria dispersoids and impurity contaminations. An elastoplastic finite element analysis was performed to study what stress state is the cause of the branches and delaminations. It is concluded that the normal to the crack branches and/or the shear stress components could determine the crack bifurcation mechanism, whereas the delamination it seems that it is controlled by the magnitude of the stress component normal to the delamination plane. © The Minerals, Metals & Materials Society and ASM International 2014.Peer Reviewe

Variation within and between Closely Related Species Uncovers High Intra-Specific Variability in Dispersal

Mounting evidence shows that contrasting selection pressures generate variability in dispersal patterns among individuals or populations of the same species, with potential impacts on both species dynamics and evolution. However, this variability is hardly considered in empirical works, where a single dispersal function is considered to adequately reflect the species-specific dispersal ability, suggesting thereby that within-species variation is negligible as regard to inter-specific differences in dispersal abilities. We propose here an original method to make the comparison of intra- and inter-specific variability in dispersal, by decomposing the diversity of that trait along a phylogeny of closely related species. We used as test group European butterflies that are classic study organisms in spatial ecology. We apply the analysis separately to eight metrics that reflect the dispersal propensity, the dispersal ability or the dispersal efficiency of populations and species. At the inter-specific level, only the dispersal ability showed the signature of a phylogenetic signal while neither the dispersal propensity nor the dispersal efficiency did. At the within-species level, the partitioning of dispersal diversity showed that dispersal was variable or highly variable among populations: intra-specific variability represented from 11% to 133% of inter-specific variability in dispersal metrics. This finding shows that dispersal variation is far from negligible in the wild. Understanding the processes behind this high within-species variation should allow us to properly account for dispersal in demographic models. Accordingly, to encompass the within species variability in life histories the use of more than one value per trait per species should be encouraged in the construction of databases aiming at being sources for modelling purposes