Artificial boundary conditions for the Stokes and Navier-Stokes equations in domains that are layer-like at infinity

Artificial boundary conditions are presented to approximate solutions to Stokes- and Navier-Stokes problems in domains that are layer-like at infinity. Based on results about existence and asymptotics of the solutions v^infinity, p^infinity to the problems in the unbounded domain Omega the error v^infinity - v^R, p^infinity - p^R is estimated in H^1(Omega_R) and L^2(Omega_R), respectively. Here v^R, p^R are the approximating solutions on the truncated domain Omega_R, the parameter R controls the exhausting of Omega. The artificial boundary conditions involve the Steklov-Poincare operator on a circle together with its inverse and thus turn out to be a combination of local and nonlocal boundary operators. Depending on the asymptotic decay of the data of the problems, in the linear case the error vanishes of order O(R^{-N}), where N can be arbitrarily large.

Happy growers! Relationship quality in the German organic apple chain

Relational factors between supply chain actors have been acknowledged to contribute significantly to competitiveness. With the example of the German market for organic apples the suitability of the concept of the Relational View for explaining competitiveness was investigated. Structured interviews were conducted with selected actors of the supply chain. Actors at all levels of the supply chain proved to be highly committed and described their business relations as satisfying and trustful. Strong vertical and horizontal collaboration was found. Thus, the Relational View proved to be highly suitable to explain competitiveness in the market for organic apples.