Modelling the entrainment and motion of particles in a gap: Application to abrasive wear

The microscale abrasion or ball-cratering test is being increasingly applied to a wide range of bulk materials and coatings. The response of materials to this test depends critically on the nature of the motion of the abrasive particles in the contact zone: whether they roll and produce multiple indentations in the coating, or slide causing grooving abrasion. Similar phenomena also occur when hard contaminant particles enter a lubricated contact. This paper presents simple quantitative two-dimensional models which describe two aspects of the interaction between a hard abrasive particle and two sliding surfaces. The first model treats the conditions under which a spherical abrasive particle of size d can be entrained into the gap between a rotating sphere of radius R and a plane surface. These conditions are determined by the coefficients of friction between the particle and the sphere, and the particle and the plane, denoted by μs and μp respectively. This model predicts that the values of (μs + μp) and 2μs should both exceed √2d/R for the particles to be entrained into the contact. If either is less than this value, the particle will slide against the sphere and never enter the contact. The second model describes the mechanisms of abrasive wear in a contact when an idealized rhombus-sectioned prismatic particle is located between two parallel plane surfaces separated by a certain distance, which can represent either the thickness of a fluid film or the spacing due to the presence of other particles. It is shown that both the ratio of particle size to the separation of the surfaces and the ratio of the hardnesses of the two surfaces have important influences on the particle motion and hence on the mechanism of the resulting abrasive wear. Results from this model are compared with experimental observations, and the model is shown to lead to realistic predictions. © IMechE 2003.

Spatial models of bistability in biological collectives

We explore collective behavior in biological systems using a cooperative control framework. In particular, we study a hysteresis phenomenon in which a collective switches from circular to parallel motion under slow variation of the neighborhood size in which individuals tend to align with one another. In the case that the neighborhood radius is less than the circular motion radius, both circular and parallel motion can occur. We provide Lyapunov-based analysis of bistability of circular and parallel motion in a closed-loop system of self-propelled particles with coupled-oscillator dynamics. ©2007 IEEE.

The role of androgens in fetal growth: observational study in two genetic models of disordered androgen signalling.

OBJECTIVE: To examine the role of androgens on birth weight in genetic models of altered androgen signalling. SETTING: Cambridge Disorders of Sex Development (DSD) database and the Swedish national screening programme for congenital adrenal hyperplasia (CAH). PATIENTS: (1) 29 girls with XY karyotype and mutation positive complete androgen insensitivity syndrome (CAIS); (2) 43 girls and 30 boys with genotype confirmed CAH. MAIN OUTCOME MEASURES: Birth weight, birth weight-for-gestational-age (birth weight standard deviation score (SDS)) calculated by comparison with national references. RESULTS: Mean birth weight SDS in CAIS XY infants was higher than the reference for girls (mean, 95% CI: 0.4, 0.1 to 0.7; p=0.02) and was similar to the national reference for boys (0.1, -0.2 to 0.4). Birth weight SDS in CAH girls was similar to the national reference for girls (0.0, -0.2 to 0.2) and did not vary by severity of gene mutation. Birth weight SDS in CAH boys was also similar to the national reference for boys (0.2, -0.2 to 0.6). CONCLUSION: CAIS XY infants have a birth weight distribution similar to normal male infants and birth weight is not increased in infants with CAH. Alterations in androgen signalling have little impact on birth weight. Sex dimorphism in birth size is unrelated to prenatal androgen exposure.