The propagation of a crack at a weak disordered interface between two elastic plates is investigated numerically. The fracture front evolution is described as the depinning of an elastic line in a random field of toughness. The relevance of this approach is critically tested by comparing the roughness front properties, the statistics of the local avalanches and the crack velocity distribution with recent experimental results. Our simulations capture the main features of the fracture front evolution, even though a few experimental findings are not consistent with the behavior of an elastic line close to the depinning transition. Possible improvements of the model are discussed. Finally, the average avalanche shape and the time asymmetry of the fracture front dynamics is investigated numerically so that the comparison with experiments can be pushed further in future studies.

Mastitis is an infection of the mammary glands in dairy cows. It is characterized by the presence in the milk of inflammatory cells (leukocytes) and possibly bacteria. This inflammation can have clinical consequences with changes in the appearance of the milk and visible inflammation of the udder. However, most often, the disease remains subclinical with no symptoms, the infected cows simply show a rise in somatic cell count (CCS), however, and these consequences are as severe as clinical mastitis, alteration of the composition of the milk and decrease in production. Treatment is mainly based on the use of antibiotics, which is not always effective.

The objective of our study was to see the impact of subclinical mastitis on the structure of the mammary gland. We have performed histological sections of fragments belonging to the mammary gland of dairy cows brought to the slaughterhouse after the drop in milk yield due to subclinical mastitis. Of the 101 samples, 36 showed no change in tissue structure, while 65 of the samples showed significant inflammation. Our second objective was to test the effect of honey directly on the isolated bacterium (Staphylococcus aureus). The effect of honey was more active than the antibiotic gentamicin.

This work examines the two-dimensional motion of non-Newtonain Williamson nano fluid with heat and mass transfer through porous medium over an exponentially stretching sheet. The system is stressed by an external uniform magnetic field and the thermal diffusion with chemical reaction and heat generation are considered. The system of partial differential equations which describe the momentum, energy and concentration equations of the fluid is transformed to an ordinary differential equations by using the suitable transformations. Then these equations have been solved numerically by using Runge-Kutta method based on shooting technique. The numerical formulas of the velocity, temperature and concentration are obtained.  The effects of the physical parameters of the problem on these formulas are discussed and illustrated graphically. It is found that the physical parameters of the problem play an important rule to control the fluid flow.