Internal energy dissipation in Enceladus's ocean from tides and libration and the role of inertial waves

Enceladus is characterised by a south polar hot spot associated with a large outflow of heat, the source of which remains unclear. We compute the viscous dissipation resulting from tidal and libration forcing in the moon's subsurface ocean using the linearised Navier-Stokes equation in a 3-dimensional spherical model. We conclude that libration is the dominant cause of dissipation at the linear order, providing up to about 0.001 GW of heat to the ocean, which remains insufficient to explain the (about) 10 GW observed by Cassini. We also illustrate how resonances with inertial modes can significantly augment the dissipation. Our work is an extension to Rovira-Navarro et al. [2019] to include the effects of libration. The model developed here is readily applicable to the study of other moons and planets

Gibbs free energy difference between the undercooled liquid and the beta-phase of a Ti-Cr alloy

The heat of fusion and the specific heats of the solid and liquid have been experimentally determined for a Ti60Cr40 alloy. The data are used to evaluate the Gibbs free energy difference, DELTA-G, between the liquid and the beta-phase as a function of temperature to verify a reported spontaneous vitrification (SV) of the beta-phase in Ti-Cr alloys. The results show that SV of an undistorted beta-phase in the Ti60Cr40 alloy at 873 K is not feasible because DELTA-G is positive at the temperature. However, DELTA-G may become negative with additional excess free energy to the beta-phase in the form of defects

Gibbs free-energy difference between the glass and crystalline phases of a Ni-Zr alloy

The heats of eutectic melting and devitrification, and the specific heats of the crystalline, glass, and liquid phases have been measured for a Ni24Zr76 alloy. The data are used to calculate the Gibbs free-energy difference, DeltaGAC, between the real glass and the crystal on an assumption that the liquid-glass transition is second order. The result shows that DeltaGAC continuously increases as the temperature decreases in contrast to the ideal glass case where DeltaGAC is assumed to be independent of temperature

The Long-Term Erosion of Repeat-Purchase Loyalty

The study investigates the long-term erosion of repeat-purchase loyalty among consumers who purchase brands in a one-year base period. The study utilises a five-year consumer panel of continuous reporters. We identify brand buyers in a base year, then calculate the proportion that fail to buy the brand in later years. We analyse the top 20 brands in 10 consumer goods categories We find pronounced erosion in repeat-buying over the long-term. The proportion of buyers from a base year that fail to buy the brand in a later year increases steadily over time, from 57% in year 2 to 71.5% by year 5. Moreover, we identify brand and marketing mix factors linked to this over-time customer loss, or erosion. The study provides evidence that consumers’ propensity to buy particular brands changes over a period of years, even though those brands continue to exhibit stable market share. This evidence provides a different interpretation than the literature to date, which has viewed purchase propensities as fixed. The study finds that store brands and niche brands exhibit lower levels of erosion in their buyer base; that a broad range is associated with lower erosion, and that high price promotion incidence is associated with lower erosion for manufacturer brands. Loyalty erosion has been reported before (Ehrenberg, 1988; East & Hammond 1996) but only over short periods. This study examines the phenomenon over five years, confirms that the rate of erosion does diminish over time, and that it is related to category and brand characteristics, as well as marketing mix decisions