Stochastic study of a non-linear self-excited system with friction

ThispaperproposestwomethodsbasedonthePolynomialChaostocarryout the stochastic study of a self-excited non-linear system with friction which is commonly used to represent brake-squeal phenomenon. These methods are illustrated using three uncertain configurations and validated using comparison with Monte Carlo simulation results. First, the stability of the static equilibrium point is examined by computing stochastic eigenvalues. Then, for unstable ranges of the equilibrium point, a constrained harmonic balance method is developed to determine subsequent limit cycles in the deterministic case; it is then adapted to the stochastic case. This demonstrates the effectiveness of the methods to fit complex eigenmodes as well as limit cycles dispersion with a good accuracy

Relationships between pathology and crystal structure in breast calcifications: an in situ X-ray diffraction study in histological sections

Calcifications are not only one of the most important early diagnostic markers of breast cancer, but are also increasingly believed to aggravate the proliferation of cancer cells and invasion of surrounding tissue. Moreover, this influence appears to vary with calcification composition. Despite this, remarkably little is known about the composition and crystal structure of the most common type of breast calcifications, and how this differs between benign and malignant lesions. We sought to determine how the phase composition and crystallographic parameters within calcifications varies with pathology, using synchrotron X-ray diffraction. This is the first time crystallite size and lattice parameters have been measured in breast calcifications, and we found that these both parallel closely the changes in these parameters with age observed in fetal bone. We also discovered that these calcifications contain a small proportion of magnesium whitlockite, and that this proportion increases from benign to in situ to invasive cancer. When combined with other recent evidence on the effect of magnesium on hydroxyapatite precipitation, this suggests a mechanism explaining observations that carbonate levels within breast calcifications are lower in malignant specimens