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Browsing by Author "Butler, Samuel"

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    Equilibrium shapes of two and three dimensional two-phase rotating fluid drops with surface tension: effects of inner drop displacement
    (American Institute of Physics, 2022-11-01) Butler, Samuel
    The shapes of rotating fluid drops held together by surface tension is an important field of study in fluid mechanics. Recently, experiments with micron-scale droplets of liquid helium have been undertaken and it has proven useful to compare the shapes of the resultant superfluid droplets with classical analogs. If the helium is a mixture of He3 and He4, two phases are present. In a recent paper, the shapes of rotating two phase fluid droplets were calculated where the inner drop was constrained to stay at the drop center. The outer shapes and dimensionless rotation rate-angular momentum relationships were shown to be similar to single phase drops provided that the density and surface tension scales were chosen appropriately. In the current paper, I investigate models in which the inner drop can displace from the centre. In order to simplify the analyses, two dimensional drops are first investigated. I show that the inner drop is unstable in the centre position if its density is greater than the outer density and that the inner drop will move towards the outer boundary of the drop in these cases. When the inner drop has a higher density than the outer drop, the moment of inertia of displaced inner drops is increased relative to centered drops and hence the kinetic energy is decreased. Shapes of two and three dimensional drops, rotation rate-angular momentum and kinetic and surface energy relationships are investigated for off-axis inner drops with parameters relevant to recent liquid He experiments.
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    Simple formulas for pseudoposition for electrical resistivity and IP in vertical boreholes based on mean positions of the sensitivity
    (Wiley, 2021-12) Butler, Samuel
    The electrical conductivity method in boreholes has been applied for exploration as well as engineering and environmental investigations. The simplest deployment involves placing electrodes at varying heights within a single borehole. Borehole surveys differ from surface surveys using colinear arrays in that the ground surface is in the line of the electrodes and so it influences the measured potential in the ground differently. Multiple electrodes can be deployed on a single multichannel cable resulting in measurements from nonstandard array configurations. The choice of the plot point for pseudosections can be difficult for these nonstandard arrays. The mean of the sensitivity function of a constant resistivity half space has been shown to yield simple and useful formulas for pseudopositions for four electrode surface arrays. In this contribution, I first derive the sensitivity function for electrodes in a vertical borehole and then calculate the vertical and horizontal sensitivity functions. I then derive simple formulas for the vertical and horizontal positions of the mean of the sensitivity function for electrodes in a vertical borehole. Pseudosections for synthetic data are shown to be more easily interpretable than pseudosections plotted using averages of the electrode positions. The simple formulas will be useful for plotting pseudosections for initial data visualization and for survey planning.