Quasi-Static Fractures in Disordered Media and Iterated Conformal Maps

We study the geometrical characteristic of quasi-static fractures in disordered media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lam\'e equations without resorting to lattice models. Typical fracture patterns exhibit increased ramification due to the increase of the stress at the tips. We find the roughness exponent of the experimentally relevant backbone of the fracture pattern; it crosses over from about 0.5 for small scales to about 0.75 for large scales, in excellent agreement with experiments. We propose that this cross-over reflects the increased ramification of the fracture pattern.Comment: submitted to Physical Review Letter

von Willebrand factor antigen compared with other factors in vasculitic syndromes.

In order to analyse their role as a specific marker of vascular damage and their value in monitoring disease activity the plasma concentrations of von Willebrand factor antigen (vWFAg) and the ristocetin cofactor (RiCoF) activities were determined in 43 children with vasculitis and 20 controls. These patients were sub-divided into three groups according to diagnosis: Henoch-Schönlein purpura (n = 18), polyarteritis nodosa (n = 16), and systemic lupus erythematosus (n = 9). High concentrations of vWFAg and activities of RiCoF were found in all the patient groups. vWFAg and RiCoF returned to normal as the patients became symptom free and remained above normal in those with continuing symptoms. The amount of vWFAg did not correlate with the acute phase reactants. vWFAg acted as a specific marker of vascular damage and was useful for the monitoring of disease activity both in small vessel vasculitis and systemic necrotising arteritis