An intrinsic state generating the ground state rotational band of a deformed nucleus and its approximate equivalence to an algebraic-variational treatment: Illustration by an exactly soluble model

We construct a class of intrinsic or trial states to generate the ground state band of a rotating nucleus in a highly schematized shell model possessing R(5) symmetry. This model is described in the preceding paper. The exponential form of the state links this work to a line of recent developments tracing back ultimately to the work of Jancovici and Schiff on the generator coordinate method. For the present case the state is a product of BCS states and is seen to contain more general (four-particle) correlations than a single deformed BCS state. A technique for the construction of the states is described. The major result of this paper is the proof that the cranking variational principle associated with the trial state is essentially equivalent (exactly equivalent in the thermodynamic or large system limit) to the algebraic-variational method described in the preceding paper, when the latter is restricted to the oneband approximation. The existence of sharp phase transitions in the model is then investigated analytically. A spherical to deformed transition is thus confirmed, as well as an anti-pairing transition. As explained, this is unrelated to the Coriolis anti-pairing phenomena.     

Asymptotic behavior of nonexpansive mappings in normed linear spaces

LetT be a nonexpansive mapping on a normed linear spaceX. We show that there exists a linear functional.f, ‖f‖=1, such that, for allx∈X, lim_n→x f(T ⁿ x/n)=lim_n→x‖T ⁿ x/n ‖=α, where α≡inf _y∈c ‖Ty-y‖. This means, ifX is reflexive, that there is a faceF of the ball of radius α to whichT ⁿ x/n converges weakly for allx (inf_z∈f g(T ⁿ x/n-z)→0, for every linear functionalg); ifX is strictly conves as well as reflexive, the convergence is to a point; and ifX satisfies the stronger condition that its dual has Fréchet differentiable norm then the convergence is strong. Furthermore, we show that each of the foregoing conditions on X is satisfied if and only if the associated convergence property holds for all nonexpansiveT. Supported by National Science Foundation Grant MCS-79-066.     

Equations-of-motion approach to a quantum theory of large-amplitude collective motion

The equations-of-motion approach to large-amplitude collective motion is implemented both for systems of coupled bosons, also studied in a previous paper, and for systems of coupled fermions. For the fermion case, the underlying formulation is that provided by the generalized Hartree-Fock approximation (or generalized density matrix method). To obtain results valid in the semi-classical limit, as in most previous work, we compute the Wigner transform of quantum matrices in the representation in which collective coordinates are diagonal and keep only the leading contributions. Higher-order contributions can be retained, however, and, in any case, there is no ambiguity of requantization. The semi-classical limit is seen to comprise the dynamics of time-dependent Hartree-Fock theory (TDHF) and a classical canonicity condition. By utilizing a well-known parametrization of the manifold of Slater determinants in terms of classical canonical variables, we are able to derive and understand the equations of the adiabatic limit in full parallelism with the boson case. As in the previous paper, we can thus show: (i) to zero and first order in the adiabatic limit the physics is contained in Villars' equations; (ii) to second order there is consistency and no new conditions. The structure of the solution space (discussed thoroughly in the previous paper) is summarized. A discussion of associated variational principles is given. A form of the theory equivalent to self-consistent cranking is described. A method of solution is illustrated by working out several elementary examples. The relationship to previous work, especially that of Zeievinsky and Marumori and coworkers is discussed briefly. Three appendices deal respectively with the equations-of-motion method, with useful properties of Slater determinants, and with some technical details associated with the fermion equations of motion.     

Gas-chromatographic quantitation of lindane in household insecticide spray cans

Summary A method was developed for the determination of the lindane content of commercial household insecticide spray aerosols. After the propellant is removed from the chilled contents of the spray packages the hydrocarbon solution is analysed for its lindane content by electron-capture gas chromatography. Pure -isomer of hexachlorocyclohexane serves as the internal standard. Experimental error is ± 5%.

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Gas-chromatographische Bestimmung von Lindan in Haushalts-Spraydosen

Zusammenfassung Das Treibmittel wird durch Ausfrieren abgetrennt und die Insecticidlösung gas-chromatographisch mit Electron-capture Detektor analysiert. Das reine -Isomere dient als innerer Standard. Der Fehler beträgt ± 5%.

     

Dynamics of a Local Perturbation in the X-Y Model II—Excitations

Excitations of a single spin embedded in the X Y chain are studied. We find that the magnetization does not approach equilibrium, even if the external magnetic field approaches a non-zero limit, and that oscillatory excitation resonates with the edge of the one-particle spectrum band.     

Large-scale carbohydrate analysis by capillary array electrophoresis: part 1. Separation and scale-up

A 96-capillary array electrophoresis (CAE) instrument has been adapted for large-scale mono- and oligosaccharide analysis and characterization. Operational protocols and data processing tools have been developed to optimize the CAE system for this application. Effects of different additives to the running buffer on efficiency and capillary-to-capillary performance reproducibility have been studied.     

Large-scale carbohydrate analysis by capillary array electrophoresis: part 2. Data normalization and quantification

Automated 96-capillary array electrophoresis (CAE) methodology described in the first part of the present work offered large-scale high-performance profiling of oligo- and monosaccharides to fulfill the needs of bioindustrial laboratories. Sensitivity at low nanomolar concentration, good resolving power and reliability achieved in the experiments is invaluable for monitoring reaction products from enzymatic polysaccharide digestion with numerous applications in agricultural, chemical and food industries. In addition to optimization of mono- and oligosaccharide separations in CAE system and necessary operational protocol modifications, capillary-to-capillary and run-to-run variation in migration time and signal intensity necessitated development of data normalization tools. Internal fluorescent standards have been incorporated into the analysis aiding migration time normalization and CAE trace alignment. Data processing, visualization, and programming tools have been developed along with quantification approaches.     

Detection and localization of inclusions in plates using inversion of point actuated surface displacements

A numerical simulation is carried out demonstrating the use of plate surface vibration measurements for detecting and locating inclusions within the structure. A finite element code is used to calculate normal surface displacement for both steel and mortar plates subjected to a monochromatic point force. The data is generated for the homogeneous plate and the identical plate within which exists a small rectangular inclusion. It is observed that when the elastic modulus of the inclusion is orders of magnitude lower than the base material, resonances of the inclusion produce large local displacements that are readily observed in the raw displacement data. For more modest moduli differences, there are no such directly observable effects. In this case, three inverse algorithms are used to process the displacement data. The first two are local inversion techniques that each yield a spatial map of the elastic modulus normalized by density. These algorithms successfully detect and localize the inclusion based on its modulus difference from that of the base plate. The third technique uses a form of the inhomogeneous equation of motion to obtain the induced force distribution connected with the inclusion. The spatial mapping of this force also successfully detects and localizes the inclusion.