Wrinkles in supported graphenes can be formed either by uniaxial compression or uniaxial tension beyond a certain critical load depending on the mode of loading.

Experimental and theoretical investigation of true axial stress transfer on regular-exfoliated-graphene micro-ribbons which are aligned to the loading direction.

The sedimentation of a red blood cell (RBC) through the blood plasma is described as the translation of a rigid inverted prolate spheroid through a quiescent unbounded viscous fluid. The inverted spheroid is moving with constant velocity along its axis of symmetry. The physical characteristics of the RBC and the blood plasma allow us to consider this problem as a Stokes flow problem. The Kelvin inversion method and the concept of semiseparation of variables for the Stokes operators, which we used for solving the Stokes flow past an RBC, are also employed here. The stream function is then expressed as a series expansion in terms of Gegenbauer functions of even order. Through this, important hydrodynamic quantities such as the drag force, the drag coefficient and the terminal settling velocity of the RBC are calculated. The celebrated Stokes formula for the drag force exerted on a sphere is now expanded in order to account for the shape deformation of an RBC. Sample streamlines are depicted showing the dependence of these quantities on the geometrical characteristics of the RBC and also of any inverted prolate spheroid. The obtained results seem to be directly applicable in medical tests such as the Erythrocyte Sedimentation Rate (ESR).

An exterior Dirichlet problem in a non-convex domain is solved analytically by combining two powerful methods: the well-known Kelvin transformation and the newly established method of generalized integral transforms introduced by Fokas (2001, Proc. R. Soc. A., 457, 371–393). In fact, our approach leads to an integral representation for the solution of Laplace's equation in the unbounded domain formed by the exterior of the Kelvin image of an equilateral triangle. First, we apply the Kelvin transformation of the given boundary with arbitrary data. Second, we use the Dirichlet-to-Neumann map (Dassios & Fokas, 2005, Proc. R. Soc. A., 461, 2721–2748). to obtain the unknown Neumann boundary values on the image boundary. Third, by inverting the Kelvin transformation, we derive the Neumann data on the original boundary. We demonstrate the 2D version of Kelvin transformation and we apply it to the equilateral triangle, which, through the Dirichlet-to-Neumann map, leads us in a natural way to a known integral representation of the solution.