Mathematical efficiency calibration methods for high quality laboratory based gamma spectrometry systems

The efficiency calibration of laboratory based gamma spectrometry systems typically involves the purchase or construction of calibration samples that are supposed to represent the geometries of the unknown samples to be measured. For complete and correct calibrations, these sample containers must span the operational range of the system, which at times can include difficult configurations of size, density, matrix, and source distribution. The efficiency calibration of a system is dependent not only on the detector, but on the radiation attenuation factors in the detector–source configuration, and therefore is invalid unless all parameters of the sample assay condition are identical to the calibration condition. An alternative to source-based calibrations is to mathematically model the efficiency response of a given detector–sample configuration. In this approach, the measurement system is calibrated using physically accurate models whose parameters can generally be easily measured. Using modeled efficiencies, systems can be quickly adapted to changing sample containers and detector configurations. This paper explores the advantages of using mathematically computed efficiencies in place of traditional source-based measured efficiencies for laboratory samples, focusing specifically on the possibility of sample optimization for a given detector, uncertainty estimation, and cascade summing corrections.     

Density gradient stabilization of electron temperature gradient driven turbulence in a spherical tokamak

In this Letter we report the first clear experimental observation of density gradient stabilization of electron temperature gradient driven turbulence in a fusion plasma. It is observed that longer wavelength modes, k(⊥)ρ(s) ? 10, are most stabilized by density gradient, and the stabilization is accompanied by about a factor of 2 decrease in the plasma effective thermal diffusivity.     

Acoustic trapping as a generic non-contact incubation site for multiplex bead-based assays

In this study, we show a significantly reduced assay time and a greatly increased bead recovery for a commercial Luminex-based multiplex diagnostic immunoassay by performing all liquid handling steps of the assay protocol in a non-contact acoustic trapping platform.     

Classification and unfoldings of 1:2 resonant Hopf Bifurcation

In this paper, we study the bifurcations of periodic solutions from an equilibrium point of a differential equation whose linearization has two pairs of simple pure imaginary complex conjugate eigenvalues which are in 1:2 ratio. This corresponds to a Hopf-Hopf mode interaction with 1:2 resonance, as occurs in the context of dissipative mechanical systems. Using an approach based on Liapunov-Schmidt reduction and singularity theory, we give a framework in which to study these problems and their perturbations in two cases: no distinguished parameter, and one distinguished (bifurcation) parameter. We give a complete classification of the generic cases and their unfoldings. (Accepted May 26, 1995) – Communicated by M. Golubitsky     

The solubility of magnetite and the hydrolysis and oxidation of Fe2+ in water to 300°C

The solubility of carefully characterized magnetite, Fe₃O₄, in dilute aqueous solutions saturated with H₂ has been measured at temperatures from 100 to 300°C in a flow apparatus. Solution compositions included either HCl or NaOH molalities of up to 1 and 40 mmole-kg^?1, respectively, and H₂ molalities of 0.0779, 0.779, and 8.57 mmole-kg^?1. The dependence of the equilibrium solubility on the pH and reduction potential were fitted to a scheme of soluble ferrous and ferric species consisting of Fe²⁺, FeOH⁺, Fe(OH)₂, Fe(OH) ₃ ^? , Fe(OH)₃, and Fe(OH) ₄ ^? . Solubility products from the fit, corresponding to the reactions $$\tfrac{1}{3}Fe_3 O_4 + (2 - b)H^ + + \tfrac{1}{3}H_2 \rightleftharpoons Fe(OH)_b^{2 - b} + (4/3 - b)H_2 O$$ and $$\tfrac{1}{3}Fe_3 O_4 + (3 - b)H^ + \rightleftharpoons Fe(OH)_b^{3 - b} + \tfrac{1}{6}H_2 + (4/3 - b)H_2 O$$ were used to derive thermodynamic constants for each species. The extrapolared value for the Gibbs energy of formation of Fe²⁺ at 25°C is ?88.92±2.0 kJ-mole^?1, consistent with standard reduction potentials in the range E^o(Fe²⁺)=?0.47±0.01 V. The temperature coefficient of the equilibrium Fe molality, (?m(Fe, sat.)/?T)_{m(H2).m(NaOH)}, changes from negative to positive as the NaOH molality is increased to the point where Fe(OH) ₃ ^? and Fe(OH) ₄ ^? predominate.     

Flux expulsion and trapping in rotating discs of type II superconductors

The magnetic flux rotating in step with a type II superconducting disc is measured with orthogonal pick up coils for various previous magnetic histories vs H₀ applied ⊥ to the axis of rotation. For some initial magnetic states, flux expulsion, independent of the rate of rotation, occurs during the initial rotation. A simple model where flux lines leave the specimen against the magnetic pressure in the active region accounts for the observations.