Stick-slip and force chain evolution in a granular bed in response to a grain intruder.

The mechanical response of granular beds under applied stresses is often characterized by repeated cycles of stick-slip. Using the discrete element method, we examine stick-slip from a concentrated force loading-imposed by a single grain that is drawn through a densely packed, periodic granular bed via a stiff virtual spring. Force chains continually form and collapse ahead of the intruder grain. A comprehensive characterization of the birth-death evolution of these load-bearing structures, along with their surrounding contact cycles, reveals a well-defined shear zone of around eight particle diameters from the intruder, encapsulating: (i) long force chains that form buttresses with the fixed bottom wall for support, (ii) a region where the collapse of the most stable, persistent three-cycles preferentially occur to the point where they are essentially depleted by the end of the first cycle of stick-slip, and (iii) an inner core where force chain buckling events concentrate. Dilatancy is greatest in this inner core, and in the region next to the free surface. During slip, secondary force chains briefly form behind the intruder: these transient force chains, most of which comprise only 3 particles, form in the direction that is roughly perpendicular to the intruder motion.

Carotid artery anatomy and geometry as risk factors for carotid atherosclerotic disease.

BACKGROUND AND PURPOSE: Traditional vascular risk factors do not completely explain the asymmetry, racial, and sex differences in carotid artery disease. Carotid anatomy and geometry may play a role in the pathogenesis of internal carotid artery (ICA) stenosis, but their effects are unknown. We hypothesized that carotid artery anatomy and geometry would be independently associated with ICA stenosis. METHOD: This is a retrospective study of patients with CT angiography at Monash Medical Centre, 2006 to 2007. Carotid arteries were segmented using semiautomated methods to estimate measures of carotid anatomy and geometry. Measurements of carotid artery geometry were performed according to the recent article by Thomas and colleagues. ICA stenosis was dichotomized as <30% or ≥ 30% stenosis. Cluster logistic regression was used to examine the associations of anatomy and geometry with stenosis accounting for the paired arteries within subjects, adjusting for age, sex, and vascular risk factors. RESULTS: Mean age of the sample (n=178) was 68.4 years (SD, 14 years). The following were independently associated with ICA stenosis: ICA radius at the bifurcation (OR, 0.20; 95% CI, 0.14-0.29), ICA angle (OR, 1.05 per degree increment; 95% CI, 1.04-1.07), age (OR, 1.05 per year increment; 95% CI, 1.03-1.07), male sex (OR, 1.72; 95% CI, 1.08-2.8), and ever-smoker (OR, 1.85; 95% CI, 1.15-2.96). CONCLUSIONS: Carotid anatomy and geometry may enhance the risk of stenosis independent of traditional vascular risk factors and may be of help in very early identification of patients at high risk of developing carotid artery atherosclerosis for aggressive intervention.

Does the principle of minimum work apply at the carotid bifurcation: a retrospective cohort study.

BACKGROUND: There is recent interest in the role of carotid bifurcation anatomy, geometry and hemodynamic factors in the pathogenesis of carotid artery atherosclerosis. Certain anatomical and geometric configurations at the carotid bifurcation have been linked to disturbed flow. It has been proposed that vascular dimensions are selected to minimize energy required to maintain blood flow, and that this occurs when an exponent of 3 relates the radii of parent and daughter arteries. We evaluate whether the dimensions of bifurcation of the extracranial carotid artery follow this principle of minimum work. METHODS: This study involved subjects who had computed tomographic angiography (CTA) at our institution between 2006 and 2007. Radii of the common, internal and external carotid arteries were determined. The exponent was determined for individual bifurcations using numerical methods and for the sample using nonlinear regression. RESULTS: Mean age for 45 participants was 56.9 ± 16.5 years with 26 males. Prevalence of vascular risk factors was: hypertension--48%, smoking--23%, diabetes--16.7%, hyperlipidemia--51%, ischemic heart disease--18.7%.The value of the exponent ranged from 1.3 to 1.6, depending on estimation methodology. CONCLUSIONS: The principle of minimum work (defined by an exponent of 3) may not apply at the carotid bifurcation. Additional factors may play a role in the relationship between the radii of the parent and daughter vessels.

Defining random loose packing for nonspherical grains.

The concept of "random loose packing" (RLP) has evolved through extensive study of loose packings of spheres, which has resulted in an accepted definition as the loosest packing that can be obtained by pouring grains. We extend this consideration to packings of nonspherical grains (ellipsoids) formed by slow settling in a viscous liquid, and perform a detailed analysis of the structural properties of the resulting packings. We find that as in the case of spheres the loosest ellipsoid packings are generated for grains with high interparticle friction. However, unlike spheres, these packings cannot be considered random as they have a significant degree of orientational ordering that increases with the grain's aspect ratio. This demonstrates that applying sedimentation or pouring techniques that have become part of the commonly held definition of RLP, will not generate random packings of ellipsoids. The consequences for the accepted definition of RLP and its applicability to nonspherical grains is discussed.