This paper deals with the evolution of fronts or interfaces propagating with normal velocity v n = f − cκ, where f is a spatially periodic function, c a constant and κ the mean curvature. This study is motivated by the propagation of phase boundaries and dislocation loops through heterogeneous media. We establish a homogenization result when the scale of oscillation of f is small compared to the macroscopic dimensions, and show that the overall front is governed by a geometric law v n =f (n). We illustrate the results using examples. We also provide an explicit characterization of f in the limit c → ∞.

Complex alterations of the coagulation system in end stage liver disease lead to an increased risk of bleeding and mortality. In the present study, we investigated; 1. the association of pre-liver transplant rotational thrombelastometry (ROTEM™) variables with bleeding as well as 30-day-mortality and 2. the underlying pathophysiology. After approval from the local ethics committee, rotational thrombelastometry variables, conventional laboratory coagulation values, MELD score (model of end-stage liver disease), red blood cell loss, blood product use, coagulation factors, underlying disease, and demographic data were retrospectively analysed. Pre-transplant thrombelastometry clot lysis index (CLI) and MELD were the only variables associated with mortality, bleeding and blood product use, respectively. Mortality was 4.2%, when CLI was <85%, and increased to 25.7% when the CLI was >95%. Multivariate analysis including CLI and MELD score identified the CLI as an independent and the best predictor of 30-day-mortality. Interestingly, the inhibition of fibrinolysis did neither affect CLI nor the association of the variable with mortality. Thus, fibrinolysis can be excluded as the reason for low CLI values. In conclusion, low CLI values measured before the beginning of liver transplantation are associated with reduced bleeding and mortality, but do not indicate fibrinolysis.

This paper studies the overall evolution of fronts propagating with a normal velocity that depends on position, vn = f (x), where f is rapidly oscillating and periodic. A level-set formulation is used to rewrite this problem as the periodic homogenization of a Hamilton{Jacobi equation. The paper presents a series of variational characterization (formulae) of the e® ective Hamiltonian or e® ective normal velocity. It also examines the situation when f changes sign.

Abstract.This paper reviews sorne recent advances in understanding the mobility of twin and phase boundaries in martensites, and discusses the design of systematic experiments.