Propagation of fluid-filled fractures by fluid buoyancy is important in a variety of settings, from magmatic dykes and veins to water-filled crevasses in glaciers. Industrial hydro-fracturing utilises fluid-driven fractures to increase the permeability of rock formations, but few studies have quantified the effect of buoyancy on fracture pathways in this context. Analytical approximations for the buoyant ascent rate facilitate observation-based inference of buoyant effects in natural and engineered systems. Such analysis exists for two-dimensional fractures, but real fractures are three-dimensional (3-D). Here we present novel analysis to predict the buoyant ascent speed of 3-D fractures containing a fixed-volume batch of fluid. We provide two estimates of the ascent rate: an upper limit applicable at early time, and an asymptotic estimate (proportional to $t^{-2/3}$) describing how the speed decays at late time. We infer and verify these predictions by comparison with numerical experiments across a range of scales and analogue experiments on liquid oil in solid gelatine. We find the ascent speed is a function of the fluid volume, density, viscosity and the elastic parameters of the host medium. Our approximate solutions predict the ascent rate of fluid-driven fractures across a broad parameter space, including cases of water injection in shale and magmatic dykes. Our results demonstrate that in the absence of barriers or fluid loss, both dykes and industrial hydro-fractures can ascend by buoyancy over a kilometre within a day. We infer that barriers and fluid loss must cause the arrest of ascending fractures in industrial settings.

Basal crevasses are macroscopic structural discontinuities at the base of ice sheets and glaciers that arise by fracture. Motivated by observations and by the mechanics of elastic fracture, we hypothesise that spatial variations in basal stress (in the presence of basal water pressure) can promote and localise basal crevassing. We quantify this process in the theoretical context of linear elastic fracture mechanics. We develop a model evaluating the effect of shear-stress variation on the growth of basal crevasses. Our results indicate that sticky patches promote the propagation of basal crevasses, increase their length of propagation into the ice and, under some conditions, give them curved trajectories that incline upstream. A detailed exploration of the parameter space is conducted to gain a better understanding of the conditions under which sticky-patch-induced basal crevassing is expected beneath ice sheets and glaciers.

Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonov et al. (J. Geophys. Res., vol. 100 (B10), 1995, pp. 20433–20450) developed a simple model of reactive porous flow and numerically analysed its instability to channels. The instability relies on magma advection against a chemical solubility gradient and the porosity-dependent permeability of the porous host rock. We extend the previous analysis by systematically mapping out the parameter space. Crucially, we augment numerical solutions with asymptotic analysis to better understand the physical controls on the instability. We derive scalings for the critical conditions of the instability and analyse the associated bifurcation structure. We also determine scalings for the wavelengths and growth rates of the channel structures that emerge. We obtain quantitative theories for and a physical understanding of, first, how advection or diffusion over the reactive time scale sets the horizontal length scale of channels and, second, the role of viscous compaction of the host rock, which also affects the vertical extent of channelized flow. These scalings allow us to derive estimates of the dimensions of emergent channels that are consistent with the geologic record.

Objectives: The aim of this study was to identify natural subgroups of older adults based on cognitive performance, and to establish each subgroup’s characteristics based on demographic factors, physical function, psychosocial well-being, and comorbidity. Methods: We applied latent class (LC) modeling to identify subgroups in baseline assessments of 1345 Einstein Aging Study (EAS) participants free of dementia. The EAS is a community-dwelling cohort study of 70+ year-old adults living in the Bronx, NY. We used 10 neurocognitive tests and 3 covariates (age, sex, education) to identify latent subgroups. We used goodness-of-fit statistics to identify the optimal class solution and assess model adequacy. We also validated our model using two-fold split-half cross-validation. Results: The sample had a mean age of 78.0 (SD=5.4) and a mean of 13.6 years of education (SD=3.5). A 9-class solution based on cognitive performance at baseline was the best-fitting model. We characterized the 9 identified classes as (i) disadvantaged, (ii) poor language, (iii) poor episodic memory and fluency, (iv) poor processing speed and executive function, (v) low average, (vi) high average, (vii) average, (viii) poor executive and poor working memory, (ix) elite. The cross validation indicated stable class assignment with the exception of the average and high average classes. Conclusions: LC modeling in a community sample of older adults revealed 9 cognitive subgroups. Assignment of subgroups was reliable and associated with external validators. Future work will test the predictive validity of these groups for outcomes such as Alzheimer’s disease, vascular dementia and death, as well as markers of biological pathways that contribute to cognitive decline. (JINS, 2018, 24, 511–523)

In laboratory experiments that impose shear deformation on partially molten aggregates of initially uniform porosity, melt segregates into high-porosity sheets (bands in cross-section). The bands emerge at $15^{\circ }$–$20^{\circ }$ to the shear plane. A model of viscous anisotropy can explain these low angles whereas previous simpler models have failed to do so. The anisotropic model is complex, however, and the reason that it produces low-angle bands has not been understood. Here we show that there are two mechanisms: (i) suppression of the well-known tensile instability, and (ii) creation of a new shear-driven instability. We elucidate these mechanisms using linearised stability analysis in a coordinate system that is aligned with the perturbations. We consider the general case of anisotropy that varies dynamically with deviatoric stress, but approach it by first considering uniform anisotropy that is imposed a priori and showing the difference between static and dynamic cases. We extend the model of viscous anisotropy to include a strengthening in the direction of maximum compressive stress. Our results support the hypothesis that viscous anisotropy is the cause of low band angles in experiments.

Longitudinal administration of neuropsychological instruments are often used to assess age-related changes in cognition. Informative loss to follow-up may bias the results of these studies. Herein, we use auxiliary data to adjust for informative loss to follow-up. In the Einstein Aging Study, memory was assessed annually in a community sample of adults age 70+, free of dementia at baseline, using the free recall from the Free and Cued Selective Reminding Test, and via telephone using the Memory Impairment Screen for Telephone (the auxiliary data). Joint linear mixed models were used to assess how the effect of the APOE ε4 genotype may be affected by informative missingness in the in-person data. A total of 620 EAS participants contributed 2085 person years of follow-up to the analyses. Memory decline rates estimated in joint models were 19% greater in ε4 negative participants and 27% greater in ε4 positive participants compared to traditional approaches; the effect of APOE ε4 on memory decline was 37% greater. Joint modeling methods can help address bias caused by informative missing data in the estimation of the effect of risk factors on cognitive change, and may be applicable to a broader range of outcomes in longitudinal aging studies. (JINS, 2014, 20, 1–6)