Statistical analysis of bubble and crystal size distributions: Formulations and procedures

Bubble and crystal size distributions have previously been described only by either exponential or power law functions. Within this limited framework, it has not been possible to characterize size distributions in a fully quantitative manner. We have developed an analytical and computational formulation with which to characterize and study crystal and bubble size distributions (BSD). This formulation demonstrates that all distributions known to date belong to the logarithmic family of statistical distributions. Four functions within the logarithmic family are best suited to natural bubbles and crystals (log normal, logistic, Weibull, and exponential). This characterization is supported by the fact that the power law function widely used for crystal and bubble size analysis is not a statistical distribution function, but rather represents an approximation of the upper regions (larger bubbles/crystals) of the logistic distribution, whose sizes are much larger than the mode. The coefficients for each of the four logarithmic functions can be derived by 1) best fit exceedance function of the logarithmic distribution, and 2) best fit of the linear transformation of the distribution probability density. A close match of the coefficients derived by the above two methods can be used as an indicator of correct function fitting (choice of initial values). Function fitting by exceedance curves leads to the most accurate statistical results, but has certain strict limitations, including 1) a requirement to rescale the base distribution function; 2) a higher failure rate for function fitting than that for distribution density; 3) uncertainty in observational data error estimates; and 4) unsuitability for visual interpretation. The most productive approach to visualization and interpretation of size distributions is through linear transformation of logarithmic distributions on the basis of probability densities. This also makes it possible to 1) clearly discern bimodal distributions; 2) assess the range of observed objects relative to the full range of the indicated distribution; 3) determine number densities for each mode directly; and 4) integrate to obtain total volume fraction for comparison with available observations. The latter could, in some cases, provide more accurate results than many measurement methods. Unambiguous definition of Bubble Number Density (BND) must be based on the number of bubbles per melt volume (not number of bubbles per bulk volume), so that like is done with crystals, it can be directly used as an indicator of basic vesiculation processes such that: a) nucleation leads to increase of BND, b) diffusive or decompressive bubble growth keeps BND constant, and c) coalescence decreases BND

High intensity polarized electron source

A proposed new high-luminosity electron–ion collider requires a polarized electron source of extremely high intensity. The MIT-Bates Laboratory, in collaboration with Brookhaven National Laboratory (BNL), has developed a new polarized electron gun that can be operated at currents in the mA range. This paper describes the design of the gun and beam line and also presents the results of the beam tests.DOE (Grants DE-­FG02-­94ER40818, DE-­SC0005807 and DE-­SC0008741

A new cryogenic apparatus to search for the neutron electric dipole moment

© 2019 IOP Publishing Ltd and Sissa Medialab. A cryogenic apparatus is described that enables a new experiment, nEDM@SNS, with a major improvement in sensitivity compared to the existing limit in the search for a neutron Electric Dipole Moment (EDM). This apparatus uses superfluid 4He to produce a high density of Ultra-Cold Neutrons (UCN) which are contained in a suitably coated pair of measurement cells. The experiment, to be operated at the Spallation Neutron Source at Oak Ridge National Laboratory, uses polarized 3He from an Atomic Beam Source injected into the superfluid 4He and transported to the measurement cells where it serves as a co-magnetometer. The superfluid 4He is also used as an insulating medium allowing significantly higher electric fields, compared to previous experiments, to be maintained across the measurement cells. These features provide an ultimate statistical uncertainty for the EDM of 2-3× 10-28 e-cm, with anticipated systematic uncertainties below this level

Measurement of the Vector and Tensor Asymmetries at Large Missing Momentum in Quasielastic ([→ over e],e′p) Electron Scattering from Deuterium

We report the measurement of the beam-vector and tensor asymmetries A[subscript ed][superscript V] and A[subscript d][superscript T] in quasielastic ([→ over e],e′p) electrodisintegration of the deuteron at the MIT-Bates Linear Accelerator Center up to missing momentum of 500  MeV/c. Data were collected simultaneously over a momentum transfer range 0.1<Q[superscript 2]<0.5  (GeV/c)[superscript 2] with the Bates Large Acceptance Spectrometer Toroid using an internal deuterium gas target polarized sequentially in both vector and tensor states. The data are compared with calculations. The beam-vector asymmetry A[subscript ed][superscript V] is found to be directly sensitive to the D-wave component of the deuteron and has a zero crossing at a missing momentum of about 320  MeV/c, as predicted. The tensor asymmetry A[subscript d][superscript T] at large missing momentum is found to be dominated by the influence of the tensor force in the neutron-proton final-state interaction. The new data provide a strong constraint on theoretical models